[ { "id": "2018-higher-level-EV-q1a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Only one linear pattern begins with \"1, 7\". Fill in the three boxes below so that the numbers form this linear pattern.\nLinear pattern: 1, 7, ___, ___, ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Linear pattern (common first difference of 6): 13, 19, 25. So the pattern is 1, 7, 13, 19, 25.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q1ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Martin is saving to buy a bike. He has €100 saved to begin with. He saves another €20 each month. Work out how much in total Martin will have saved after 4 months.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "100 + (20 × 4) = €180.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q1aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "The bike costs €240. Work out how many months in total Martin must save for in order to have enough money to buy the bike.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "240 − 100 = 140; 140 ÷ 20 = 7 months. (OR 240 − 180 = 60; 60 ÷ 20 = 3; 3 + 4 = 7 months.)", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q1b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 15, "marks_confidence": "high", "question_text": "Many different quadratic patterns begin with \"1, 7\". Fill in the three boxes below so that the numbers form a quadratic pattern.\nQuadratic pattern: 1, 7, ___, ___, ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Any quadratic sequence continuing 1, 7 with a non-zero constant second difference, e.g. 1, 7, 14, 22, 31 (second difference of 1). No credit for the linear continuation 13, 19, 25.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q1b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Lisa is saving to buy a laptop. It costs €320. Each week she saves the same amount of money. She has €50 saved to begin with. After 18 weeks, Lisa will have exactly enough money to buy the laptop. Work out how much money Lisa saves each week.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(320 − 50)/18 = 270/18 = €15 each week.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q10a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 15, "marks_confidence": "high", "question_text": "The rates and bands for income tax are as follows:\n€35 000 @ 20%, balance @ 40%.\nLorna has a gross income of €50 000 for the year. Using the rates and bands above, work out her total income tax for the year.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Balance = 50 000 − 35 000 = 15 000. Tax = 0.20 × 35 000 + 0.40 × 15 000 = 7000 + 6000 = €13 000.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q10a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Write the following four numbers in order, from the smallest to the biggest: 2·34, −3, √5, 2.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "−3, 2, √5, 2·34 (since √5 ≈ 2·24).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q10b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Complete the graph on the next page to show the amount of income tax for every gross income up to €60 000 per year. Show all your working out. (The amount of income tax is shown for gross incomes up to €10 000.)", "has_images": true, "image_notes": "Coordinate grid. x-axis 'Gross income per year (in €)' from 0 to 60 000 (gridlines every 10 000). y-axis 'Amount of income tax (in €)' from 0 to 18 000 (gridlines every 2000). A solid line is already drawn from (0, 0) up to about (10 000, 2000); the student completes the graph beyond €10 000.", "topic": "Functions", "marking_scheme_answer": "Line continues at 20% slope to (35 000, 7000), then changes to a 40% slope up to (60 000, 17 000). Graph must show a change of slope at x = 35 000. (At x = 50 000, tax = 13 000; at x = 60 000, tax = 17 000.)", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q10b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Write each of these four numbers into the correct region in the Venn diagram below, where ℝ is the set of real numbers, ℤ is the set of integers, and ℕ is the set of natural numbers. One has been done already.", "has_images": true, "image_notes": "Three nested ovals: outer ℝ, inside it ℤ, inside that ℕ. The number 2·34 is already placed in the ℝ region (outside ℤ). The four numbers to place are 2·34, −3, √5, 2.", "topic": "Number", "marking_scheme_answer": "√5 goes in ℝ only (outside ℤ); −3 goes in ℤ (but outside ℕ); 2 goes in ℕ; 2·34 is already placed in ℝ only.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q10c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "This graph doesn't take tax credits into account. Assume that everyone gets a tax credit of €3000. On the diagram above, draw a graph to show the amount of income tax to be paid for every gross income from €15 000 to €60 000 per year, taking this tax credit into account.", "has_images": true, "image_notes": "Same income-tax coordinate grid as part (b): x-axis gross income 0-60 000, y-axis amount of income tax 0-18 000, with the existing tax line drawn. Student adds a new (dotted) line shifted down by €3000 to account for the tax credit, from €15 000 to €60 000.", "topic": "Functions", "marking_scheme_answer": "Draw the tax line from part (b) shifted down by €3000 (the tax credit) over the range €15 000 to €60 000 — shown as the dotted line on the model diagram.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q11", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Write down an inequality in x represented by each of the number lines shown below. Put a tick in the correct box in each case to show whether x ∈ ℕ, x ∈ ℤ, or x ∈ ℝ. The first one is done. (First row, done: −3 ≤ x < 2, domain ℝ. Three further number lines to interpret.)", "has_images": true, "image_notes": "Table 'Number line' | 'Inequality in x' | 'Domain (tick ℕ, ℤ or ℝ)'. Row 1 (worked): a solid bar from filled dot at −3 to open dot at 2, inequality −3 ≤ x < 2, ℝ ticked. Row 2: discrete filled dots at −3, −2, −1, 0, 1 (no connecting bar). Row 3: discrete filled dots at 1, 2, 3. Row 4: open dot at −2, solid bar to open dot at 4. Number lines span −4 to 4.", "topic": "Algebra", "marking_scheme_answer": "Row 2: −3 ≤ x ≤ 1, x ∈ ℤ. Row 3: 1 ≤ x ≤ 3, x ∈ ℕ (e.g. 0.5 < x < 4 with ℤ/ℕ also accepted). Row 4: −2 < x < 4, x ∈ ℝ. Various equivalent inequalities with matching domain are accepted.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q11a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Eoin is E years old. Complete the table below by writing the age of each of the other people in terms of E. Eoin: Eoin's age = E. Grace: 7 years younger than Eoin. Evan: twice as old as Eoin. Aoibhe: 3 years older than Eoin.", "has_images": true, "image_notes": "Table with columns 'Person', 'Description of their age', 'Age, in years (in terms of E)'. Rows: Eoin / Eoin's age / E (given); Grace / 7 years younger than Eoin / blank; Evan / Twice as old as Eoin / blank; Aoibhe / 3 years older than Eoin / blank.", "topic": "Algebra", "marking_scheme_answer": "Grace = E − 7; Evan = 2E; Aoibhe = E + 3.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q11b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Grace is half Eoin's age. Work out Eoin's age.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(1/2)E = E − 7; 7 = (1/2)E; E = 14 years.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q12a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Write the following as a single fraction in its simplest form.\n2/(n − 3) − 5/(2n + 5)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "[2(2n + 5) − 5(n − 3)] / [(n − 3)(2n + 5)] = (4n + 10 − 5n + 15) / [(n − 3)(2n + 5)] = (−n + 25) / [(n − 3)(2n + 5)]. (Marking scheme model solution combines the two fractions over the common denominator and simplifies the numerator.)", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q12a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 15, "marks_confidence": "high", "question_text": "A mapping diagram of the function g: x ↦ x^2 is shown below. Fill in the 4 missing entries in the diagram.", "has_images": true, "image_notes": "Mapping (arrow) diagram. Left oval 'x' inputs (top to bottom): 5, 3, −6, 0, and an empty box. Right oval 'g(x) = x^2' outputs: 25 (from 5), then three empty boxes (from 3, −6, 0), and 49 at the bottom (arrow from the empty input box). So the missing outputs are 9, 36, 0 and the missing input is 7 (or −7) mapping to 49.", "topic": "Functions", "marking_scheme_answer": "Missing outputs: 3 → 9, −6 → 36, 0 → 0; missing input: 7 or −7 → 49.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q12b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Show that (4x − 3)^2 + 24x is positive for all values of x ∈ ℝ.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(4x − 3)^2 + 24x = 16x^2 − 24x + 9 + 24x = 16x^2 + 9. Since x^2 ≥ 0 for all real x, 16x^2 + 9 ≥ 9 > 0, so the expression is positive for all x ∈ ℝ.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q12b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 3, "marks_confidence": "derived", "question_text": "Write down the range of the function g(x), as shown in the diagram. Range = { , , , , }.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Range = {25, 9, 36, 0, 49}.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q12c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "g(3^7) = 3^7 × 3^7. Write 3^7 × 3^7 in the form 3^n, where n ∈ ℕ. 3^7 × 3^7 = 3^( ).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3^7 × 3^7 = 3^14 (n = 14).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q13a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 10, "marks_confidence": "derived", "question_text": "Below are four statements about three non-empty sets P, Q, and R in a universal set U. Put a tick in the correct box in each case to show whether each statement is always true, sometimes true, or never true. (Note: P′ is the complement of the set P.) Statements: 1. #(P ∪ Q) = #(P) + #(Q); 2. P \\ Q = P ∩ Q; 3. (P ∩ Q)′ = P′ ∪ Q′; 4. P ∪ (Q ∩ R) = (P ∪ Q) ∩ (P ∪ R).", "has_images": true, "image_notes": "Table with columns 'Statement', 'Always true', 'Sometimes true', 'Never true', each row having three tick-boxes. Four statement rows: (1) #(P∪Q) = #(P) + #(Q); (2) P\\Q = P∩Q; (3) (P∩Q)′ = P′∪Q′; (4) P∪(Q∩R) = (P∪Q)∩(P∪R).", "topic": "Number", "marking_scheme_answer": "1: Sometimes true; 2: Never true; 3: Always true; 4: Always true. (Parts (a) and (b) share a single 15D mark scale, total 15 marks.)", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q13a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Find the value of 4p − 3m, when p = 5 and m = 2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4(5) − 3(2) = 20 − 6 = 14.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q13b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "In the case of Statement 1 in the table, justify your answer.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Statement 1 is only sometimes true: #(P ∪ Q) = #(P) + #(Q) holds when P and Q are disjoint (P ∩ Q = ∅), but not when they overlap, because then shared elements are counted twice. Give one example where it is true and one where it is false. (Parts (a) and (b) share a single 15D mark scale.)", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q13b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Solve the equation 3(x + 5) + 2(2x + 3) = 0.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(x+5) + 2(2x+3) = 0 → 3x + 15 + 4x + 6 = 0 → 7x + 21 = 0 → 7x = −21 → x = −3.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q14a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 15, "marks_confidence": "high", "question_text": "Use factors to simplify (2n^2 + n − 15) / (n^2 − 9).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(2n − 5)(n + 3) / [(n + 3)(n − 3)] = (2n − 5)/(n − 3).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q14a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 10, "marks_confidence": "derived", "question_text": "Draw the graph of the following function in the domain −2 ≤ x ≤ 2, for x ∈ ℝ: y = 2x + 3.", "has_images": true, "image_notes": "Coordinate grid provided, x-axis from −2 to 2, y-axis from −3 to 8. Student must draw the line y = 2x + 3.", "topic": "Functions", "marking_scheme_answer": "Straight line through points e.g. (−2, −1), (0, 3) and (2, 7) — a line of slope 2 and y-intercept 3 drawn over −2 ≤ x ≤ 2.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q14b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 10, "marks_confidence": "derived", "question_text": "Draw the graph of the following function in the domain −2 ≤ x ≤ 2, for x ∈ ℝ: y = x^2 − 1.", "has_images": true, "image_notes": "Coordinate grid provided, x-axis from −2 to 2, y-axis from −3 to 8. Student must draw the curve y = x^2 − 1.", "topic": "Functions", "marking_scheme_answer": "U-shaped parabola through points (−2, 3), (−1, 0), (0, −1), (1, 0), (2, 3), drawn as a smooth curve over −2 ≤ x ≤ 2.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q14bi", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)(i)", "parent_question": "14", "marks": 5, "marks_confidence": "derived", "question_text": "For all values of a, b, and x ∈ ℝ: (x + a)(x + b) = x^2 + (a + b)x + ab. Using this fact, or otherwise, solve the following equation in x, where a and b are constants. Give each answer in terms of a or b.\nx^2 + (a + b)x + ab = 0\nAnswer: x = ___ or x = ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x + a)(x + b) = 0, so x + a = 0 or x + b = 0, giving x = −a or x = −b.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q14bii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)(ii)", "parent_question": "14", "marks": 5, "marks_confidence": "derived", "question_text": "Simplify [x^2 + (a + b)x + ab] ÷ (x + a).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x + a)(x + b) ÷ (x + a) = x + b.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q15a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "15(a)", "parent_question": "15", "marks": 5, "marks_confidence": "high", "question_text": "Factorise 3x + 6y.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(x + 2y).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q15b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "15(b)", "parent_question": "15", "marks": 5, "marks_confidence": "high", "question_text": "Multiply out and simplify (2x + 7)(x − 4).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2x(x−4) + 7(x−4) = 2x^2 − 8x + 7x − 28 = 2x^2 − x − 28.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q15ci", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "15(c)(i)", "parent_question": "15", "marks": 5, "marks_confidence": "derived", "question_text": "Harry knows that (x − 2)(x + 8) = x^2 + 6x − 16. Hence, or otherwise: solve the equation x^2 + 6x − 16 = 0.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x − 2 = 0 or x + 8 = 0 → x = 2 or x = −8 (also obtainable via the quadratic formula).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q15cii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "15(c)(ii)", "parent_question": "15", "marks": 5, "marks_confidence": "derived", "question_text": "Hence, or otherwise: simplify (x^2 + 6x − 16) ÷ (x − 2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x^2 + 6x − 16) ÷ (x − 2) = (x − 2)(x + 8) ÷ (x − 2) = x + 8.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q2ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Phil is an athlete. The graph shows the number of calories (in kcal) she burns per hour, depending on her average heart rate. (Note: the axes do not start at (0, 0).) Use the graph to estimate how many calories Phil would burn in one hour if she had an average heart rate of 170 beats per minute.\nCalories burnt in one hour = ___ kcal", "has_images": true, "image_notes": "Line graph. x-axis 'Average heart rate (beats per minute)' from 100 to 180 (gridlines every 10). y-axis 'Calories burned per hour (kcal/hour)' from 200 to 900 (gridlines every 100). A single straight line rises from about (110, 200) up to about (180, 850). Axes do not start at origin.", "topic": "Functions", "marking_scheme_answer": "Reading from the graph at 170 beats/min gives approximately 750 kcal (tolerance ±10 on y-axis, ±1 on x-axis).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q2ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Jakub makes a 4-digit password, using the digits of his date of birth: 2, 5, 1, 0, 9, 8. He doesn't use any digit more than once. Write down a password Jakub could make that is: an odd number.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Any 4-digit password using the given digits without repetition, and ending in 1, 5, or 9 (an odd digit). For example: 2581.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q2aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Use the graph to work out Phil's average heart rate when she burns 300 kcal in 30 minutes.\nAverage heart rate = ___ beats per minute", "has_images": true, "image_notes": "Same line graph as 2(a)(i): x-axis average heart rate 100-180, y-axis calories burned per hour 200-900, straight rising line from ~(110,200) to ~(180,850). 300 kcal in 30 minutes = 600 kcal per hour, then read across to the line.", "topic": "Functions", "marking_scheme_answer": "300 kcal in 30 minutes = 600 kcal in 1 hour; reading 600 on the y-axis across to the line gives an average heart rate of approximately 155 beats per minute (tolerance ±1 on x-axis).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q2aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Write down a password Jakub could make that is: a multiple of 5.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Any 4-digit password using the given digits without repetition, and ending in 0 or 5. For example: 2980.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q2b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Phil runs a series of stages. In each stage she runs a slow run of 60 m, and then a sprint. In each stage after stage 1, she sprints 50 m more than she did in the previous stage. Complete the table below, showing the distance that she runs slowly and the distance that she sprints in each stage, as well as the total distance per stage. Give the values in the last row in terms of n, where appropriate. (Given: Stage 1: slow 60, sprint 50, total 110; Stage 2: slow 60, sprint 100, total 160; Stage 3: slow 60, sprint 150; complete stages 3, 4, 5 and n.)", "has_images": true, "image_notes": "Table with columns 'Stage', 'Slow run (metres)', 'Sprint (metres)', 'Total distance (metres)'. Filled rows: Stage 1 -> 60, 50, 110; Stage 2 -> 60, 100, 160; Stage 3 -> 60, 150, (blank). Rows for stages 4, 5 and n are blank to be completed.", "topic": "Algebra", "marking_scheme_answer": "Stage 3 total = 210; Stage 4: 60, 200, 260; Stage 5: 60, 250, 310. Row n: slow run = 60, sprint = 50n, total = 60 + 50n.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q2b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Write down the largest number that Jakub could use as a password.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "9852.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q2c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "In one of the stages, Phil runs slowly for 60 metres at 2 metres per second, and then sprints 150 metres at 7.5 metres per second. Work out Phil's average speed for this stage, in metres per second.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Total distance = 60 + 150 = 210 m. Slow time = 60/2 = 30 s; sprint time = 150/7.5 = 20 s; total time = 50 s. Average speed = 210/50 = 4.2 m/s.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q3a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Patrick worked for a weekend washing cars in a garage. In total, 35 cars were washed in the garage that weekend. Patrick washed 14 of them. Work out the percentage of the cars that Patrick washed.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(14/35) × 100 = 40%.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q3a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Fill in the boxes to make this a linear pattern: __ , 10 , 14 , __ , __ .", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "6, 10, 14, 18, 22 (constant first difference of 4).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q3b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Patrick was paid £200 Sterling for the weekend. He converted this money to US Dollars ($). The exchange rates are shown below.\n€1 = £0.88 Sterling\n€1 = $1.18 US Dollars\nWork out how many US Dollars ($) Patrick got for his £200 Sterling. Give your answer correct to the nearest cent.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "£200 ÷ 0.88 = €227.27..., then × 1.18 = $268.18 (to 2 decimal places).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q3b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Fill in the boxes to make this a quadratic pattern: 2 , 4 , 7 , __ , __ .", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2, 4, 7, 11, 16 (first differences 2, 3, 4, 5; constant second difference of 1).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q4a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "F is the set of factors of 12. List the six elements of the set F.\nF = { ___ , ___ , ___ , ___ , ___ , ___ }", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "F = {1, 2, 3, 4, 6, 12}.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q4a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "A sheet is folded in half a number of times. After 1 fold, there are 2 layers. After 2 folds, there are 4 layers. After 3 folds, there are 8 layers, and so on. Fill in the table to show the number of layers after each of the first 6 folds.", "has_images": true, "image_notes": "Two-row table. Row 'Number of folds': 1, 2, 3, 4, 5, 6. Row 'Number of layers': 2, 4, 8, then three empty cells to complete for folds 4, 5, 6.", "topic": "Number", "marking_scheme_answer": "Layers for folds 4, 5, 6 are 16, 32, 64 (full row: 2, 4, 8, 16, 32, 64).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q4b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "The sets P and S are as follows: P is the set of all prime numbers; S is the set of all square numbers (i.e. all numbers n^2, where n ∈ ℕ). The Venn diagram shows the sets F, P, and S. Write each of the factors of 12 from part (a) into the correct region in the set F in the Venn diagram.", "has_images": true, "image_notes": "Three-circle Venn diagram showing overlapping sets labelled F (top left), P (top right), and S (bottom). All three circles overlap in the centre.", "topic": "Number", "marking_scheme_answer": "Place factors of 12 into the correct regions of F: primes (in F∩P) = 2, 3; square numbers (in F∩S) = 1, 4; neither prime nor square (in F only) = 6, 12.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q4b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Work out the least number of folds that would be needed to have more than 500 layers.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "2, 4, 8, 16, 32, 64, 128, 256, 512 — i.e. 9 folds (512 > 500).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q4c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Put a tick in the correct box to show what kind of pattern is made by the number of layers. Tick one box only (linear / quadratic / exponential). Justify your answer.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Exponential. Justification: the number of layers doubles each time (it is a geometric/doubling sequence); the first differences are not constant and the first and second differences both keep changing.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q4d", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "After a certain number of folds, there are roughly 1 million layers. Roughly how many layers will there be after 3 more folds?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1 000 000 × 2 × 2 × 2 = 8 million layers.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q5a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Work out the value of 3p − 4t^2, when p = 6 and t = 5.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(6) − 4(5^2) = 18 − 100 = −82.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q5ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)(i)", "parent_question": "5", "marks": 8, "marks_confidence": "derived", "question_text": "The following is part of a bus timetable from Galway to Limerick. James lives in Oranmore. He needs to be in Limerick by 09:30. What is the latest time that James can get the bus from Oranmore?", "has_images": true, "image_notes": "Bus timetable table titled 'Time' with three service columns. Rows: Galway depart 06:40 / 07:20 / 07:50; Oranmore depart 06:48 / 07:28 / 07:57; Gort depart 07:36 / 08:16 / 08:45; Ennis depart 08:05 / 08:45 / 09:14; Limerick arrive 08:45 / 09:25 / 09:44.", "topic": "Number", "marking_scheme_answer": "07:28 (the bus arriving Limerick at 09:25, which is before 09:30; the 07:57 bus arrives 09:44 which is too late).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q5aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)(ii)", "parent_question": "5", "marks": 7, "marks_confidence": "derived", "question_text": "How long does his bus journey take, from Oranmore to Limerick?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "09:25 − 07:28 = 1 hour 57 minutes.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q5b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 10, "marks_confidence": "high", "question_text": "Multiply out and simplify (2x − 3)(4 − 5x + x^2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2x^3 − 13x^2 + 23x − 12.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q5bi", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)(i)", "parent_question": "5", "marks": 8, "marks_confidence": "derived", "question_text": "It takes Gina 1 hour and 15 minutes to drive from Oranmore to Limerick. What fraction of an hour is 15 minutes? Answer (tick one box only): 1/15, 1/12, 1/5, 1/4.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1/4.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q5bii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)(ii)", "parent_question": "5", "marks": 7, "marks_confidence": "derived", "question_text": "The distance from Oranmore to Limerick is 90 km. Work out Gina's average speed for the journey, in km/hour.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Speed = distance/time = 90/1.25 = 72 km/hr.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q5c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 10, "marks_confidence": "high", "question_text": "Factorise fully 10de − df − 5ef + 2d^2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(2d − f)(5e + d).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "A sheet is folded in half a number of times. h(x) = 2^x is the number of layers after x folds. Fill in the table to show the number of layers after each of the first 6 folds. (Given: x = 1 -> 2, x = 2 -> 4, x = 3 -> 8; complete x = 4, 5, 6.)", "has_images": true, "image_notes": "Two-row table. Top row 'Number of folds, x' with values 1, 2, 3, 4, 5, 6. Bottom row 'Number of layers, h(x)' with 2, 4, 8 filled and the cells for 4, 5, 6 blank.", "topic": "Functions", "marking_scheme_answer": "After 4, 5, 6 folds: 16, 32, 64.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q6ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)(i)", "parent_question": "6", "marks": 8, "marks_confidence": "derived", "question_text": "Oisín earns €30 000 per year. He pays tax at 20%. Work out Oisín's gross tax per year.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "30 000 × 20% = €6000.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q6aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)(ii)", "parent_question": "6", "marks": 7, "marks_confidence": "derived", "question_text": "Oisín's tax credits are €3300 per year. Work out his net pay per year.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "6000 − 3300 = 2700 (tax due); 30 000 − 2700 = €27 300 net pay.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "List the elements of the domain and the range of h(x) that are shown in the table above.\nDomain = { ___ }\nRange = { ___ }", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Domain = {1, 2, 3, 4, 5, 6}; Range = {2, 4, 8, 16, 32, 64}.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q6b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Aoife's weekly pay was €800. She got a pay rise of 5%. Work out Aoife's weekly pay after the pay rise.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "800 × 0.05 = 40; 800 + 40 = €840 (OR 800 × 1.05 = €840).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the least number of folds that would be needed to have more than 500 layers.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "2^9 = 512 > 500, so 9 folds.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6d", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the number of layers after 12 folds. Give your answer in the form a × 10^n, where a ∈ ℝ, 1 ≤ a < 10, and n ∈ ℕ.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "2^12 = 4096 = 4.096 × 10^3 layers.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6e", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(e)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Explain what the following statement means, in terms of folds and layers.\nh(14) > 10 000", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "It means that after 14 folds there are more than 10 000 layers (2^14 = 16 384 > 10 000).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6f", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(f)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Put a tick in the correct box to show what kind of pattern is made by the number of layers. Tick one box only (linear / quadratic / exponential / none of these). Justify your answer.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Exponential. Justification: the number of layers doubles (is multiplied by 2) with each extra fold, i.e. h(x) = 2^x.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6g", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(g)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "After a certain number of folds, there are k layers. How many layers will there be after 3 more folds? Give your answer in terms of k.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "k × 2 × 2 × 2 = 8k layers.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q6h", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(h)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "After a certain number of folds, there are 2^p layers. How many layers will there be after 3 more folds? Give your answer in the form 2^m, where m is in terms of p.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "2^p × 2^3 = 2^(p+3).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q7a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Joonas has an unlimited supply of €5 notes and €2 coins. Fill in the table to show three different ways in which he can use these to make exactly €27. One way is already done. (Given: Way 1 = 1 note, 11 coins, total €27; complete Way 2 and Way 3, each totalling €27.)", "has_images": true, "image_notes": "Table with columns 'Number of €5 notes', 'Number of €2 coins', 'Total amount of money'. Rows 'Way 1' (1 note, 11 coins, €27), 'Way 2' (blank, blank, €27), 'Way 3' (blank, blank, €27).", "topic": "Number", "marking_scheme_answer": "Three combinations of 5a + 2b = 27: (1 note, 11 coins), (3 notes, 6 coins), (5 notes, 1 coin).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q7a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 8, "marks_confidence": "derived", "question_text": "Amina wants to buy a pair of runners. She can buy them online for £51·24. The currency conversion rate is €1 = £0·90. Convert £51·24 to euro. Give your answer correct to the nearest cent.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "51.24 ÷ 0.90 = 56.933... = €56.93 (to 2 decimal places).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q7b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "Explain how he could use his supply of €5 notes and €2 coins to make every whole number value of money greater than €3 (i.e. to make €n for every n ∈ ℕ, where n > 3).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Every whole number greater than 3 can be made: even amounts are made using only €2 coins; odd amounts are made using one €5 note plus the appropriate number of €2 coins (5 + 2k gives every odd value from 5 upwards, and €4 is two coins). Any valid equivalent explanation accepted.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q7b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 7, "marks_confidence": "derived", "question_text": "The same runners are for sale in a local sports shop for €65. Amina has a voucher for 15% off anything she buys in this shop. Work out how much the runners will cost Amina if she uses this voucher.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "65 × 0.15 = 9.75; 65 − 9.75 = €55.25 (OR 65 × 0.85 = €55.25).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q7ci", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "The local sports shop buys t-shirts for €20 each and sells them for €28 each. Work out the profit on each t-shirt, in euro.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "28 − 20 = €8 profit.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q7cii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the percentage profit on each t-shirt (as a percentage of the cost price).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "8/20 × 100 = 40%.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q8a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 15, "marks_confidence": "high", "question_text": "Solve the following equation. Give each answer correct to two decimal places.\nx^2 − 4x − 7 = 0", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Using the quadratic formula: x = (4 ± √(16 + 28))/2 = (4 ± √44)/2, giving x = 5.32 or x = −1.32 (to 2 decimal places).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q8ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Emma is going to some exercise classes in a gym. The graphs show the cost per month for 2 different gyms, Gym A and Gym B, for up to 10 classes. Based on the graphs, complete the following sentence correctly: If Emma goes to 6 classes per month in Gym B, it will cost € ___ .", "has_images": true, "image_notes": "Line graph, x-axis 'Number of classes per month' 0 to 10, y-axis 'Cost per month (€)' 0 to 100 in steps of 10. Two straight lines from a common starting point at (0,20): Gym A rises steeply reaching about €100 at 10 classes (slope ~€8/class); Gym B rises more gently reaching about €70 at 10 classes (slope €5/class, so Gym B = 20 + 5×classes). The lines cross at 4 classes (cost €40).", "topic": "Functions", "marking_scheme_answer": "€50 (Gym B at 6 classes: 20 + 5×6 = 50).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q8aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Gym A and Gym B cost the same for ___ classes per month.", "has_images": true, "image_notes": "Same Gym A vs Gym B cost line graph as in part (i); the two lines intersect at 4 classes per month (cost €40).", "topic": "Functions", "marking_scheme_answer": "4 classes (where the two lines intersect).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q8aiii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(iii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "If Emma goes to 10 classes per month, then Gym ___ will be cheaper.", "has_images": true, "image_notes": "Same Gym A vs Gym B cost line graph; at 10 classes Gym A costs about €100 while Gym B costs €70, so Gym B is lower.", "topic": "Functions", "marking_scheme_answer": "Gym B (cheaper at 10 classes).", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q8b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "The solutions of the equation x^2 − x − 2 = 0 are x = −1 and x = 2. The table below shows three graphs, A, B, and C. One of these is the graph of the function f(x) = x^2 − x − 2. Put a tick in the correct box to show which of these is the graph of f(x) = x^2 − x − 2. Tick one box only. Justify your answer.", "has_images": true, "image_notes": "Three upward-opening parabolas labelled A, B, C, each on x-y axes. Graph A: roots near x = −1 and x = 2, vertex below the x-axis, y-intercept near −2 (x-axis shown −2 to 3, y to 6). Graph B: roots near x = 0 and x = 3, vertex around y = −2 (x from −2 to 3). Graph C: roots near x = −3 and x = 1, y-intercept near −3 (x from −3 to 2).", "topic": "Functions", "marking_scheme_answer": "Graph A. Justification: it has roots at x = −1 and x = 2 and a y-intercept of −2 (f(0) = −2), matching f(x) = x^2 − x − 2.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q8b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Fill in the two missing values to complete the following statement correctly: \"Gym B costs € ___ per month, plus € ___ for each class.\"", "has_images": true, "image_notes": "Refers to the Gym B line on the cost graph: starts at €20 when 0 classes and increases by €5 per class.", "topic": "Functions", "marking_scheme_answer": "Gym B costs €20 per month plus €5 for each class.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q9a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "A group of friends makes a video and posts it on YouTube. They know that they will be paid approximately €15 for each 10 000 views of the video. Work out how many views of the video they would need in order to be paid €45.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(45/15) × 10 000 = 3 × 10 000 = 30 000 views.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q9ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)(i)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "The Venn diagram below shows the sets A and B. List the elements of the following set: A = { }.", "has_images": true, "image_notes": "Two overlapping ovals labelled A (left) and B (right). Elements: only in A: t; in the overlap A∩B: s, a, e; only in B: x, m.", "topic": "Number", "marking_scheme_answer": "A = {t, a, s, e}.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q9aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)(ii)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "List the elements of the following set: A ∩ B = { }.", "has_images": true, "image_notes": "Same Venn diagram of sets A and B; the overlap region A∩B contains s, a, e.", "topic": "Number", "marking_scheme_answer": "A ∩ B = {a, e}.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q9aiii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)(iii)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "List the elements of the following set: B\\A = { }.", "has_images": true, "image_notes": "Same Venn diagram of sets A and B; the region only in B (not in A) contains x and m.", "topic": "Number", "marking_scheme_answer": "B\\A = {x, m}.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q9b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Work out how much (in euro) they will be paid for 80 000 views of the video.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(80 000/10 000) × 15 = 8 × 15 = €120.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-ordinary-level-EV-q9b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Tom says: \"P ∩ Q is a subset of P, for any two sets P and Q.\" State whether Tom's statement is always true, sometimes true, or never true. Tick one box only. Justify your answer.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Always true. Justification: if an element is in both P and Q (i.e. in P ∩ Q) then it must also be in P, so the part in the middle is contained in the whole set P.", "source_pdf": "2018 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q9c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Work out how much (in euro) they will be paid, on average, for 1 view of the video.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15/10 000 = €0.0015 (= 1.5 × 10^-3).", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q9d", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "The video costs them €70 to make. It does not cost them anything to post the video on YouTube. Write an expression in x for the profit (in euro) they will get for x views of the video.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Profit = revenue − cost = 0.0015x − 70.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q9ei", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(e)(i)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "There are 7 people in the group. They divide the profit from the video evenly between them. They each get €200 in profit. Write an equation in x to represent this information, where x is the total number of views of the video.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(0.0015x − 70)/7 = 200.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-EV-q9eii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(e)(ii)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the value of x, the total number of views of the video.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "0.0015x − 70 = 1400, so 0.0015x = 1470, giving x = 980 000.", "source_pdf": "2018 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q1a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Níl ach patrún líneach amháin a thosaíonn le \"1, 7\". Líon isteach na trí bhosca thíos sa chaoi is go mbeidh na huimhreacha sa phatrún líneach sin.\nPatrún líneach: 1, 7, __, __, __", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Common difference = 7 − 1 = 6. So the next three terms are 13, 19, 25. (Linear sequence T_n = a + (n−1)d, i.e. y = mx + c.)", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q1ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Tá Máirtín ag sábháil airgid le haghaidh rothar a cheannach. Tá €100 sábháilte cheana aige. Sábhálann sé €20 breise in aghaidh na míosa. Oibrigh amach an méid airgid san iomlán a bheidh sábháilte ag Máirtín tar éis 4 mhí.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "100 + (20 × 4) = €180. So after 4 months Máirtín has €180 saved.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q1aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Cosaíonn an rothar €240. Oibrigh amach an méid míonna san iomlán a chaithfidh Máirtín a bheith ag sábháil airgid le go mbeidh go leor airgid aige chun an rothar a cheannach.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "240 − 100 = 140; 140 ÷ 20 = 7 [months], i.e. 7 months further saving (total time, with €100 already saved). [Sample: 240 − 100 = 140, 140 ÷ 20 = 7.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q1b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 15, "marks_confidence": "high", "question_text": "Tosaíonn a lán patrúin cearnacha éagsúla le \"1, 7\". Líon isteach na trí bhosca thíos sa chaoi is go mbeidh na huimhreacha ina bpatrún cearnach.\nPatrún cearnach: 1, 7, __, __, __", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Any valid quadratic (second-difference constant) sequence starting 1, 7. Sample answer: 1, 7, 14, 22, 31 (using a quadratic rule an^2 + bn + c). Many correct answers possible.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q1b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Tá Lisa ag sábháil airgid le haghaidh ríomhaire glúine a cheannach. Cosaíonn sé €320. Gach seachtain, sábhálann sí an méid céanna airgid. Tá €50 sábháilte cheana aici. Tar éis 18 seachtain, beidh díreach go leor airgid sábháilte ag Lisa chun an ríomhaire glúine a cheannach. Oibrigh amach an méid airgid a shábhálann Lisa in aghaidh na seachtaine.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(320 − 50) / 18 = 270/18 = €15 per week.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q10a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 15, "marks_confidence": "high", "question_text": "Tá na rátaí agus na bandaí le haghaidh cáin ioncaim mar seo a leanas:\n€35 000 @ 20%, an t-iarmhéid @ 40%.\n(a) Tá ioncam comhlán de €50 000 ag Lorna don bhliain. Bain úsáid as na rátaí agus na bandaí thuas agus oibrigh amach a cáin ioncaim iomlán don bhliain.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Iarmhéid = 50 000 − 35 000 = 15 000. Tax = 0·2 × 35 000 + 0·4 × 15 000 = 7 000 + 6 000 = €13 000.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q10a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Scríobh na ceithre uimhir seo a leanas de réir oird, ón uimhir is lú go dtí an uimhir is mó: 2·34, −3, √5, 2. Freagra = __ , __ , __ , __ .", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Ascending order: −3, 2, √5, 2.34 (since √5 ≈ 2.236, which lies between 2 and 2.34).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q10b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Críochnaigh an graf ar an gcéad leathanach eile chun go dtaispeánfar an méid cáin ioncaim ar gach ioncam comhlán suas go dtí €60 000 in aghaidh na bliana. Taispeáin do chuid oibre go léir. Taispeántar an méid cáin ioncaim le haghaidh ioncaim chomhlána suas go dtí €10 000.", "has_images": true, "image_notes": "Coordinate grid: x-axis \"Ioncam comhlán in aghaidh na bliana (ina €)\" 0 to 60 000; y-axis \"An méid cáin ioncaim (ina €)\" 0 to 18 000. A line already drawn from origin to ~€10 000 income (gradient 0·2). Candidate extends it: straight to (35 000, 7000), then steeper (gradient 0·4) to (60 000, 17 000).", "topic": "Functions", "marking_scheme_answer": "At x = 35 000, y = 0·2 × 35 000 = 7000. At x = 60 000, y = 7000 + 0·4 × 25 000 = 7000 + 10 000 = €17 000. The graph is two straight segments: (0,0)→(35 000, 7000) then (35 000, 7000)→(60 000, 17 000).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q10b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Scríobh gach ceann de na ceithre uimhir sin san fhearann ceart sa léaráid Venn thíos, áit arb é R tacar na réaduimhreacha, Z tacar na slánuimhreacha, agus N tacar na n-uimhreacha aiceanta. Tá ceann amháin díobh déanta cheana féin. (2·34 atá lonnaithe sa réigiún R amháin.)", "has_images": true, "image_notes": "Nested Venn diagram of number sets: outermost ellipse R (réaduimhreacha / reals), inside it Z (slánuimhreacha / integers), inside that N (uimhreacha aiceanta / naturals). 2·34 already placed in R (outside Z). Student must place −3, √5 and 2.", "topic": "Number", "marking_scheme_answer": "2 goes in N (natural number); −3 goes in Z but not N (integer); √5 goes in R only (irrational real); 2·34 already in R only.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q10c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Ní chuireann an graf sin creidmheasanna cánach san áireamh. Glac leis go bhfaigheann gach duine creidmheas cánach de €3000. Ar an léaráid thuas, tarraing graf chun go dtaispeánfar an méid cáin ioncaim a bheadh le híoc ar gach ioncam comhlán ó €15 000 go dtí €60 000 in aghaidh na bliana, an creidmheas cánach sin curtha san áireamh agat.", "has_images": true, "image_notes": "Same tax grid as 10(b). A new (dashed) line drawn showing tax reduced by the €3000 credit, valid between income €15 000 and €60 000; it is the original tax line shifted down by €3000 (parallel/lower than the 10(b) line) over that range.", "topic": "Functions", "marking_scheme_answer": "Draw the tax line reduced by the €3000 credit between €15 000 and €60 000 — i.e. the 10(b) graph shifted down by €3000 over that income range (tax payable = gross tax − 3000).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q11", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Scríobh síos éagothromóid in x atá á léiriú ag gach ceann de na huimhir-línte a thaispeántar thíos. Cuir tic (✓) sa bhosca ceart i ngach cás chun go dtaispeánfar cé acu x ∈ N, x ∈ Z, nó x ∈ R. Tá an chéad cheann déanta. (Líne 1 sampla: −3 ≤ x < 2, R, ticeáilte.) Líne 2: ponc líonta ag −3, −2, −1, 0, 1. Líne 3: poncanna líonta ag 1, 2, 3. Líne 4: ciorcail oscailte ag −2 agus 4 le líne eatarthu.", "has_images": true, "image_notes": "Table of four number lines (axis −4 to 4). Row 1 (worked): closed dot at −3, open dot at 2, bold line between → −3 ≤ x < 2, ℝ ticked. Row 2: closed dots at −3, −2, −1, 0, 1 (discrete). Row 3: closed dots at 1, 2, 3 (discrete). Row 4: open circles at −2 and 4 with bold continuous line between. Tick boxes ℕ / ℤ / ℝ for each.", "topic": "Algebra", "marking_scheme_answer": "Line 2: −3 ≤ x ≤ 1, x ∈ ℤ. Line 3: 1 ≤ x ≤ 3, x ∈ ℕ (or 0·5 < x < 4, x ∈ ℤ). Line 4: −2 < x < 4, x ∈ ℝ.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q11a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Is é E an aois atá ag Eoin, i mblianta. (a) Críochnaigh an tábla thíos, agus aois gach duine eile á scríobh isteach i dtéarmaí E. (Duine / Cur síos ar a aois / Aois ina blianta i dtéarmaí E: Eoin = Aois Eoin = E; Grace = 7 mbliana níos óige ná Eoin; Evan = Dhá oiread níos sine ná Eoin; Aoibhe = 3 bliana níos sine ná Eoin.)", "has_images": true, "image_notes": "Table with columns 'Duine' (person), 'Cur síos ar a aois' (description of age), 'Aois, ina blianta (i dtéarmaí E)'. Rows: Eoin — Aois Eoin — E; Grace — 7 mbliana níos óige ná Eoin — (blank); Evan — Dhá oiread níos sine ná Eoin — (blank); Aoibhe — 3 bliana níos sine ná Eoin — (blank).", "topic": "Algebra", "marking_scheme_answer": "Grace = E − 7; Evan = 2E; Aoibhe = E + 3.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q11b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Is ionann aois Grace agus leath aois Eoin. Oibrigh amach an aois atá ag Eoin.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Grace's age = ½E and also = E − 7, so ½E = E − 7 → 7 = ½E → E = 14 [blianta]. Eoin is 14 years old.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q12a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Scríobh é seo mar chodán aonair san fhoirm is simplí.\n2/(n − 3) − 5/(2n + 5)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "[2(2n+5) − 5(n−3)] / [(n−3)(2n+5)] = (4n + 10 − 5n + 15)/[(n−3)(2n+5)] = (−n + 25)/[(n−3)(2n+5)] = (−n + 25)/(2n² − n − 15).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q12a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 15, "marks_confidence": "high", "question_text": "Taispeántar thíos léaráid mhapála den fheidhm g : x ↦ x². (a) Líon isteach sa léaráid an 4 iontráil atá ar iarraidh. (Mapálann 5↦25, 3↦?, −6↦?, 0↦?, ?↦49.)", "has_images": true, "image_notes": "Mapping (arrow) diagram for g(x) = x². Left oval 'x' contains 5, 3, −6, 0 and an empty box; right oval 'g(x) = x²' contains 25, three empty boxes, and 49. Arrows map 5→25, 3→box, −6→box, 0→box, box→49.", "topic": "Functions", "marking_scheme_answer": "3 ↦ 9; −6 ↦ 36; 0 ↦ 0; and the input mapping to 49 is 7 or −7 (so 7 ↦ 49).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q12b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Taispeáin go bhfuil (4x − 3)² + 24x dearfach le haghaidh gach luach ar x ∈ R.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(4x − 3)² + 24x = 16x² − 24x + 9 + 24x = 16x² + 9. Since x² ≥ 0, 16x² ≥ 0, so 16x² + 9 > 0 for all x ∈ ℝ (always positive).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q12b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 3, "marks_confidence": "derived", "question_text": "Scríobh síos raon na feidhme g(x), mar a thaispeántar sa léaráid. Raon = { , , , , }.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Raon (range) = {25, 9, 36, 0, 49}. [Q12(b) and (c) share one 5C scale; marks split as derived.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q12c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "g(3⁷) = 3⁷ × 3⁷. Scríobh 3⁷ × 3⁷ san fhoirm 3ⁿ, áit a mbeidh n ∈ ℕ. 3⁷ × 3⁷ = 3^__.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3⁷ × 3⁷ = 3^14 (add the indices: 7 + 7 = 14). [Q12(b) and (c) share one 5C scale; marks split as derived.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q13a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 10, "marks_confidence": "derived", "question_text": "Taispeántar thíos ceithre ráiteas faoi thrí thacar neamh-fholmha P, Q, agus R in uilethacar U. (a) Cuir tic (✓) sa bhosca ceart i ngach cás chun a thaispeáint cé acu fíor i gcónaí, fíor uaireanta, nó ní fíor riamh atá gach ceann de na ráitis. Nóta: is é P' comhlánú an tacair P.\n1: #(P ∪ Q) = #(P) + #(Q)\n2: P\\Q = P ∩ Q\n3: (P ∩ Q)' = P' ∪ Q'\n4: P ∪ (Q ∩ R) = (P ∪ Q) ∩ (P ∪ R)", "has_images": true, "image_notes": "Table: column \"Ráiteas\" lists four set statements; tick-box columns \"Fíor i gcónaí\", \"Fíor uaireanta\", \"Ní fíor riamh\" for each of statements 1–4.", "topic": "Number", "marking_scheme_answer": "1: Fíor uaireanta (sometimes true — only when P and Q are disjoint). 2: Ní fíor riamh (never true; the correct identity is P\\Q = P ∩ Q'). 3: Fíor i gcónaí (always — De Morgan's law). 4: Fíor i gcónaí (always — distributive law).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q13a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Faigh luach 4p − 3m, áit a bhfuil p = 5 agus m = 2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4(5) − 3(2) = 20 − 6 = 14.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q13b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "I gcás Ráiteas 1 sa tábla, cosain do fhreagra.\nCosaint:", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Give one example where it holds and one where it does not, e.g. for P = {1, 2}, Q = {3, 4} (disjoint) #(P∪Q) = #(P)+#(Q) = 4; but for P = {1, 2}, Q = {1, 3} it fails because the common element is counted twice. So #(P∪Q) = #(P) + #(Q) only when P ∩ Q = ∅ — hence \"fíor uaireanta\".", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q13b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Réitigh an chothromóid 3(x + 5) + 2(2x + 3) = 0.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(x+5) + 2(2x+3) = 0 → 3x + 15 + 4x + 6 = 0 → 7x + 21 = 0 → 7x = −21 → x = −3.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q14a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 15, "marks_confidence": "high", "question_text": "Bain úsáid as fachtóirí agus simpligh (2n² + n − 15)/(n² − 9).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(2n² + n − 15)/(n² − 9) = [(2n − 5)(n + 3)] / [(n + 3)(n − 3)] = (2n − 5)/(n − 3).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q14a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 10, "marks_confidence": "derived", "question_text": "Tarraing graf na feidhme seo a leanas san fhearann −2 ≤ x ≤ 2, le haghaidh x ∈ ℝ: y = 2x + 3.", "has_images": true, "image_notes": "Blank coordinate grid provided: x-axis from −2 to 2, y-axis from −3 to 8. Student must plot the straight line y = 2x + 3 over −2 ≤ x ≤ 2.", "topic": "Functions", "marking_scheme_answer": "Straight line y = 2x + 3 from x = −2 (point (−2, −1)) to x = 2 (point (2, 7)); passes through (0, 3). [Q14(a) and (b) share one 20D scale; marks split as derived.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q14b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 10, "marks_confidence": "derived", "question_text": "Tarraing graf na feidhme seo a leanas san fhearann −2 ≤ x ≤ 2, le haghaidh x ∈ ℝ: y = x² − 1.", "has_images": true, "image_notes": "Blank coordinate grid provided: x-axis from −2 to 2, y-axis from −3 to 8. Student must plot the curve (parabola) y = x² − 1 over −2 ≤ x ≤ 2.", "topic": "Functions", "marking_scheme_answer": "Parabola y = x² − 1 over −2 ≤ x ≤ 2; key points (−2, 3), (−1, 0), (0, −1), (1, 0), (2, 3); U-shaped curve with minimum at (0, −1). [Q14(a) and (b) share one 20D scale; marks split as derived.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q14bi", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)(i)", "parent_question": "14", "marks": 5, "marks_confidence": "derived", "question_text": "Le haghaidh gach luach de a, b, agus x ∈ R: (x + a)(x + b) = x² + (a + b)x + ab. Agus úsáid á bhaint agat as an bhfíric seo, nó ar shlí eile, freagair an dá cheist a leanas. (i) Réitigh an chothromóid seo a leanas in x, áit ar tairisigh iad a agus b. Bíodh gach freagra díobh i dtéarmaí a nó b.\nx² + (a + b)x + ab = 0\nFreagra: x = ____ nó x = ____", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x² + (a + b)x + ab = (x + a)(x + b) = 0 → x + a = 0 or x + b = 0 → x = −a or x = −b.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q14bii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)(ii)", "parent_question": "14", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Simpligh [x² + (a + b)x + ab] ÷ (x + a).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "[x² + (a + b)x + ab] ÷ (x + a) = (x + a)(x + b) ÷ (x + a) = x + b.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q15a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "15(a)", "parent_question": "15", "marks": 5, "marks_confidence": "high", "question_text": "Fachtóirigh 3x + 6y.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3x + 6y = 3(x + 2y).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q15b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "15(b)", "parent_question": "15", "marks": 5, "marks_confidence": "high", "question_text": "Iolraigh amach agus simpligh (2x + 7)(x − 4).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(2x + 7)(x − 4) = 2x(x − 4) + 7(x − 4) = 2x² − 8x + 7x − 28 = 2x² − x − 28.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q15ci", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "15(c)(i)", "parent_question": "15", "marks": 5, "marks_confidence": "derived", "question_text": "Tá a fhios ag Anraí go bhfuil (x − 2)(x + 8) = x² + 6x − 16. Uaidh sin, nó ar shlí eile: (i) réitigh an chothromóid x² + 6x − 16 = 0.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x² + 6x − 16 = 0 → (x − 2)(x + 8) = 0 → x = 2 or x = −8. [Q15(c)(i) and (ii) share one 10D scale; marks split as derived.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q15cii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "15(c)(ii)", "parent_question": "15", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) simpligh (x² + 6x − 16) ÷ (x − 2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x² + 6x − 16) ÷ (x − 2) = (x − 2)(x + 8) ÷ (x − 2) = x + 8 (also obtainable by long division). [Q15(c)(i) and (ii) share one 10D scale; marks split as derived.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q2ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Lúthchleasaí is ea Phil. Taispeántar sa ghraf thíos an líon calraí (ina kcal) a bhíonn á ndó aici san uair, ag brath ar a croíráta meánach. Nóta: ní thosaíonn na haiseanna ag (0, 0).\n(i) Bain úsáid as an ngraf agus meastachán á dhéanamh agat ar an líon calraí a bheadh á ndó ag Phil san uair dá mba é 170 buille sa nóiméad a croíráta meánach.\nCalraí á dhóitear san uair = ____ kcal", "has_images": true, "image_notes": "Line graph. x-axis \"Croíráta meánach (líon buillí san uair)\" from 100 to 180; y-axis \"Calraí á ndó san uair (kcal/uair)\" from 200 to 900. A straight rising line; at x = 170 the line reads approximately 750 kcal.", "topic": "Functions", "marking_scheme_answer": "Read from graph at 170 beats/min: approximately 750 kcal.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q2ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Déanann Jakub pasfhocal 4 dhigit, ag úsáid na ndigití atá ina dháta breithe: 2, 5, 1, 0, 9, 8. Ní úsáideann sé aon cheann de na digití níos mó ná uair amháin. Scríobh síos pasfhocal a d'fhéadfadh Jakub a dhéanamh a bheadh ina: (i) chorruimhir.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Any 4-digit number using four of the given digits (no digit repeated) that ends in an odd digit, e.g. 8521. (Sample accepts any password of 4 digits from {2,5,1,0,9,8}, no repeats, ending in 1, 5 or 9.)", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q2aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Bain úsáid as an ngraf agus tú ag oibriú amach croíráta meánach Phil nuair a bhíonn 300 kcal á ndó aici in 30 nóiméad.\nCroíráta meánach = ____ buille sa nóiméad", "has_images": true, "image_notes": "Same line graph as 2(a)(i): x = beats/min (100–180), y = kcal burned per hour (200–900). 300 kcal in 30 min equals 600 kcal in 1 hour; read across at y = 600 to find the corresponding x value.", "topic": "Functions", "marking_scheme_answer": "300 kcal in 30 min = 600 kcal per hour. Reading the graph at 600 kcal gives a heart rate of approximately 155 beats per minute.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q2aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Scríobh síos pasfhocal a d'fhéadfadh Jakub a dhéanamh a bheadh ina: (ii) iolraí de 5.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Any 4-digit number using four of the given digits (no digit repeated) that ends in 0 or 5, e.g. a multiple of 5.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q2b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Ritheann Phil i sraith de bhabhtaí éagsúla. I ngach babhta ritheann sí go mall ar feadh 60 m, agus ansin ritheann sí de ráib. I ngach babhta tar éis Babhta 1, ritheann sí de ráib 50 m níos faide ná mar a rith sí sa bhabhta roimhe sin. Críochnaigh an tábla thíos, chun go dtaispeánfar an fad a ritheann sí go mall agus an fad a ritheann sí de ráib i ngach babhta, mar aon leis an fad iomlán i ngach ceann de na babhtaí. Tabhair na luachanna sa líne dheireanach i dtéarmaí n, nuair is cuí.", "has_images": true, "image_notes": "Table with columns: Babhta (round), Rith mall (méadair), Ráib (méadair), Fad iomlán (méadair). Rows given: 1 → 60, 50, 110; 2 → 60, 100, 160; 3 → 60, 150 (iomlán blank). Rows 4, 5 and n to be completed.", "topic": "Algebra", "marking_scheme_answer": "Rith mall is always 60. Ráib: row3=150, row4=200, row5=250, row n=50n. Fad iomlán: row3=210, row4=260, row5=310, row n=60+50n.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q2b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Scríobh síos an uimhir is mó a d'fhéadfadh Jakub a úsáid mar phasfhocal. (Pasfhocal 4 dhigit, ag úsáid na ndigití 2, 5, 1, 0, 9, 8, gan aon digit a úsáid níos mó ná uair amháin.)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "9852 (the largest 4-digit number formable from the digits 2,5,1,0,9,8 without repeats).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q2c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "I gceann amháin de na babhtaí, ritheann Phil: go mall ar feadh 60 méadar ag 2 mhéadar sa tsoicind, agus ansin de ráib ar feadh 150 méadar ag 7·5 méadar sa tsoicind. Oibrigh amach meánluas Phil sa bhabhta sin, ina mhéadair sa tsoicind.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Total distance = 60 + 150 = 210 m. Time slow = 60/2 = 30 s; time sprint = 150/7·5 = 20 s; total time = 50 s. Average speed = 210/50 = 4·2 m/s.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q3a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "D'oibrigh Pádraig ag ní carranna i ngaráiste ar feadh deireadh seachtaine. Níodh 35 carr san iomlán sa gharáiste an deireadh seachtaine sin. Nigh Pádraig 14 de na cairr sin. Oibrigh amach an céatadán de na cairr a nigh Pádraig.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "14/35 × 100 = 2/5 × 100 = 40%.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q3a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Líon isteach na boscaí sa chaoi is go mbeidh patrún líneach ann: __ , 10 , 14 , __ , __ .", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Linear pattern with common difference 4: 6, 10, 14, 18, 22. (General term Tₙ = a + (n − 1)d, i.e. 4n + 2.)", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q3b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Íocadh £200 Steirling le Pádraig don deireadh seachtaine. D'iompaigh sé an t-airgead sin go Dollair SA ($). Taispeántar thíos na rátaí malairte.\n€1 = £0·88 Steirling\n€1 = $1·18 Dollar SA\nOibrigh amach cé mhéad Dollar SA ($) a fuair Pádraig dá £200 Steirling. Bíodh do fhreagra ceart go dtí an cent is gaire.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "£200 → € : 200/0·88 = €227·27...; then × 1·18 → $268·18 (correct to nearest cent). [$268·18 to 2 d.p.]", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q3b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Líon isteach na boscaí sa chaoi is go mbeidh patrún cearnach ann: 2 , 4 , 7 , __ , __ .", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Quadratic (square) pattern with first differences 2, 3, 4, 5: 2, 4, 7, 11, 16. (Second difference constant = 1; Tₙ = an² + bn + c.)", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q3c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Cuir tic sa bhosca ceart chun go dtaispeánfar an cineál patrúin a dhéantar le líon na sraitheanna. Cuir tic (✓) i mbosca amháin. Cosain do fhreagra. Roghanna: líneach / cearnach / easpónantúil.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Refers to the folding-paper pattern of Question 4 (1, 2, 4, 8, ...): easpónantúil (exponential). Justification: the number of strips doubles each time (×2). [Q3(c) and (d) share one 10C scale.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q3d", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(d)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Tar éis líon áirithe fillteacha a dhéanamh, tá 1 mhilliún sraith ann, a bheag nó a mhór. Cé mhéad sraith, a bheag nó a mhór, a bheidh ann tar éis 3 fhilleadh eile a dhéanamh?", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Each fold doubles the number, so after 3 more folds: 1,000,000 × 2 × 2 × 2 = 8,000,000 strips (approximately 8 million). [Q3(c) and (d) share one 10C scale.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q4a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Is é F tacar na bhfachtóirí atá ag 12. (a) Scríobh isteach sé bhall thacar F.\nF = { __, __, __, __, __, __ }", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "F = {1, 2, 3, 4, 6, 12}.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q4a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Déantar bileog a fhilleadh ina dhá leath roinnt uaireanta. Tar éis 1 fhilleadh a dhéanamh, tá 2 shraith ann. Tar éis 2 fhilleadh a dhéanamh, tá 4 shraith ann. Tar éis 3 fhilleadh a dhéanamh, tá 8 sraith ann, agus mar sin de. Líon isteach an tábla chun go dtaispeánfar an líon sraitheanna atá ann tar éis gach ceann de na chéad 6 fhilleadh. (Tábla: Líon fillteacha 1–6; Líon sraitheanna le 1=2, 2=4, 3=8 tugtha.)", "has_images": true, "image_notes": "Two-row table. Top row 'Líon fillteacha' (number of folds): 1, 2, 3, 4, 5, 6. Bottom row 'Líon sraitheanna' (number of layers): 2, 4, 8, then blanks to fill for 4, 5, 6.", "topic": "Algebra", "marking_scheme_answer": "Doubling each time: for folds 1–6 the layers are 2, 4, 8, 16, 32, 64.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q4b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Tá na tacair P agus C mar a leanas. Is é P tacar na bpríomhuimhreacha go léir. Is é C tacar na n-uimhreacha cearnacha go léir (i.e. na huimhreacha n² go léir, áit a bhfuil n ∈ N). Taispeántar na tacair F, P, agus C sa léaráid Venn thíos. (b) Scríobh gach ceann d'fhachtóirí 12 ó chuid (a) sa réigiún ceart i dtacar F sa léaráid Venn.", "has_images": true, "image_notes": "Venn diagram with a large set F containing two overlapping circles P (top right, prime numbers) and C (bottom right, square numbers). Each factor of 12 is placed: P∩F = {2, 3}; C∩F = {4, 12}; F only (neither prime nor square) = {6} and {1}? Scheme model places 1 and 6 in F only, 2 and 3 in P, 4 and 12 in C (1 is square so 1 sits in C; 4=2² and ... interpret per scheme regions).", "topic": "Number", "marking_scheme_answer": "Place each factor in F: primes 2, 3 go in P∩F; square numbers go in C∩F (1 = 1², 4 = 2²); remaining factors 6 and 12 (neither prime nor a perfect square) go in F only. Sample placement: P region {2, 3}; C region {1, 4}; F-only region {6, 12}.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q4b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 15, "marks_confidence": "high", "question_text": "Oibrigh amach an líon is lú filleadh ba ghá a dhéanamh chun níos mó ná 500 sraith a fháil.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Layers double: 2, 4, 8, 16, 32, 64, 128, 256, 512. 2⁹ = 512 > 500, so 9 folds are needed.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q5a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Oibrigh amach luach 3p − 4t², áit a bhfuil p = 6 agus t = 5.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(6) − 4(5²) = 18 − 4(25) = 18 − 100 = −82.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q5ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)(i)", "parent_question": "5", "marks": 8, "marks_confidence": "derived", "question_text": "Seo cuid d'amchlár bus ó Ghaillimh go Luimneach. (Amanna imeachta/teachta: Gaillimh 06:40, 07:20, 07:50; Órán Mór 06:48, 07:28, 07:57; Gort 07:36, 08:16, 08:45; Inis 08:05, 08:45, 09:14; Luimneach teacht 08:45, 09:25, 09:44.) Tá Séamas ina chónaí in Órán Mór. Caithfidh sé bheith i Luimneach faoi 09:30. (i) Cén t-am is déanaí ar féidir le Séamas an bus a fháil ó Órán Mór?", "has_images": true, "image_notes": "Bus timetable table with column header 'Am' (Time) and three time columns. Rows: Gaillimh (imeacht/departure) 06:40, 07:20, 07:50; Órán Mór (imeacht) 06:48, 07:28, 07:57; Gort (imeacht) 07:36, 08:16, 08:45; Inis (imeacht) 08:05, 08:45, 09:14; Luimneach (teacht/arrival) 08:45, 09:25, 09:44.", "topic": "Number", "marking_scheme_answer": "The 07:28 bus from Órán Mór arrives in Luimneach at 09:25 (before 09:30); the next (07:57) arrives 09:44 (too late). Answer: 07:28.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q5aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)(ii)", "parent_question": "5", "marks": 7, "marks_confidence": "derived", "question_text": "Cén fad ama a thógann a thuras ar an mbus, ó Órán Mór go Luimneach? (Don bhus a fhaightear ag 07:28.)", "has_images": true, "image_notes": "Uses the same bus timetable as part (i): Órán Mór 07:28 → Luimneach 09:25.", "topic": "Number", "marking_scheme_answer": "09:25 − 07:28 = 1 hour 57 minutes (1 uair 57 nóiméad).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q5b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 10, "marks_confidence": "high", "question_text": "Iolraigh amach agus simpligh (2x − 3)(4 − 5x + x²).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(2x − 3)(4 − 5x + x²) = 8x − 10x² + 2x³ − 12 + 15x − 3x² = 2x³ − 13x² + 23x − 12.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q5bi", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)(i)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Caitheann Gina 1 uair an chloig agus 15 nóiméad ag tiomáint ó Órán Mór go Luimneach. (i) Cén céatadán d'aon uair an chloig é 15 nóiméad? Freagra (cuir tic i mbosca amháin): 1/15, 1/12, 1/5, 1/4.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15 minutes = 15/60 of an hour = 1/4. Tick the 1/4 box.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q5bii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)(ii)", "parent_question": "5", "marks": 10, "marks_confidence": "derived", "question_text": "Is é an fad ó Órán Mór go Luimneach ná 90 km. Oibrigh amach meánluas Gina don turas sin, ina km/uair.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Luas = achar / am = 90 / 1.25 = 72 km/uair (average speed 72 km/h, since 1 hour 15 min = 1.25 hours).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q5c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 10, "marks_confidence": "high", "question_text": "Fachtóirigh go hiomlán 10de − df − 5ef + 2d².", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "10de − df − 5ef + 2d² = 5e(2d − f) + d(2d − f) = (2d − f)(5e + d).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Déantar bileog a fhilleadh ina dhá leath roinnt uaireanta. Is é h(x) = 2^x an líon sraitheanna tar éis x filleadh a dhéanamh. (a) Líon isteach an tábla chun go dtaispeánfar an líon sraitheanna a bheidh ann tar éis gach ceann de na chéad 6 fhilleadh a dhéanamh.\nLíon fillteacha, x: 1, 2, 3, 4, 5, 6\nLíon sraitheanna, h(x): 2, 4, 8, ...", "has_images": true, "image_notes": "Table with row \"Líon fillteacha, x\" = 1, 2, 3, 4, 5, 6 and row \"Líon sraitheanna, h(x)\" to complete; first three entries given as 2, 4, 8.", "topic": "Functions", "marking_scheme_answer": "h(x) = 2^x: 16, 32, 64. Full row: x = 1→2, 2→4, 3→8, 4→16, 5→32, 6→64.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q6ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)(i)", "parent_question": "6", "marks": 8, "marks_confidence": "derived", "question_text": "Tuilleann Oisín €30 000 in aghaidh na bliana. Íocann sé cáin ag 20%. (i) Oibrigh amach cáin chomhlán Oisín in aghaidh na bliana.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "30 000 × 20% = €6 000 (gross tax for the year).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q6aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)(ii)", "parent_question": "6", "marks": 7, "marks_confidence": "derived", "question_text": "Is iad creidmheasanna cánach Oisín ná €3300 in aghaidh na bliana. Oibrigh amach an pá glan atá aige in aghaidh na bliana.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Tax due = 6 000 − 3 300 (tax credits) = 2 700. Net pay = 30 000 − 2 700 = €27 300.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Liostaigh na baill atá in fhearann agus i raon h(x) a thaispeántar sa tábla thuas.\nFearann = { ... }\nRaon = { ... }", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Fearann (domain) = {1, 2, 3, 4, 5, 6}; Raon (range) = {2, 4, 8, 16, 32, 64}.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q6b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Ba é €800 pá seachtainiúil Aoife. Tugadh ardú pá 5% di. Oibrigh amach pá seachtainiúil Aoife tar éis an ardú pá.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "800 × 0.05 = 40, so 800 + 40 = €840 (or 800 × 1.05 = €840).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach an líon is lú filleadh ba ghá a dhéanamh chun níos mó ná 500 sraith a fháil.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Need 2^x > 500. 2^9 = 512 > 500, so 9 fillteacha (folds).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6d", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach an líon sraitheanna a bheidh ann tar éis 12 fhilleadh a dhéanamh. Bíodh do fhreagra sa fhoirm a × 10^n, áit a mbeidh a ∈ R, 1 ≤ a < 10, agus n ∈ N.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "2^12 = 4096 = 4·096 × 10³.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6e", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(e)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Mínigh cad a chiallaíonn an ráiteas seo a leanas, i dtéarmaí fillteacha agus sraitheanna.\nh(14) > 10 000", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "It means that after 14 folds there will be more than 10 000 layers (sraitheanna). [2^14 = 16384 > 10 000.]", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6f", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(f)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Cuir tic sa bhosca ceart chun go dtaispeánfar an cineál patrúin a dhéantar leis an líon sraitheanna atá ann. Cuir tic (✓) i mbosca amháin. Cosain do fhreagra.\nlíneach □ cearnach □ easpónantúil □ ní ceann ar bith díobh sin é □\nCosaint:", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Easpónantúil (exponential). Reason (fáth): the number of layers doubles each time (dúblaíonn sé gach uair) — constant ratio.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6g", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(g)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Tar éis líon áirithe fillteacha a dhéanamh, tá k sraith ann. Cé mhéad sraith a bheidh ann tar éis 3 fhilleadh eile a dhéanamh? Bíodh do fhreagra i dtéarmaí k.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "k × 2 × 2 × 2 = 8k.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q6h", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(h)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Tar éis líon áirithe fillteacha a dhéanamh, tá 2^p sraith ann. Cé mhéad sraith a bheidh ann tar éis 3 fhilleadh eile a dhéanamh? Bíodh do fhreagra san fhoirm 2^m, áit a mbeidh m i dtéarmaí p.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "2^p × 2 × 2 × 2 = 2^p × 2³ = 2^(p+3), so m = p + 3.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q7a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Tá líon gan teorainn de nótaí €5 agus de bhoinn €2 ag Joonas. (a) Líon isteach an tábla, agus taispeáin trí shlí éagsúla inar féidir leis úsáid a bhaint astu sin chun €27 a dhéanamh go díreach. Tá slí amháin déanta cheana féin.\n(An líon nótaí €5 / An líon bonn €2 / An méid iomlán airgid): Slí 1: 1, 11, €27; Slí 2: __, __, €27; Slí 3: __, __, €27.", "has_images": true, "image_notes": "Table with columns \"An líon nótaí €5\", \"An líon bonn €2\", \"An méid iomlán airgid\". Row Slí 1 pre-filled: 1, 11, €27. Rows Slí 2 and Slí 3 to be completed (each must total €27).", "topic": "Number", "marking_scheme_answer": "Any two further combinations totalling €27. Sample: Slí 2 = (3 notes of €5, 6 coins of €2) → 15 + 12 = 27; Slí 3 = (5 notes of €5, 1 coin of €2) → 25 + 2 = 27.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q7a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 8, "marks_confidence": "derived", "question_text": "Ba mhaith le hAmina péire bróg reatha a cheannach. (a) Is féidir léi iad a cheannach ar líne ar £51·24. Is é an ráta malairte ná €1 = £0·90. Athraigh £51·24 go euro. Bíodh do fhreagra ceart go dtí an cent is gaire.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "51.24 ÷ 0.90 = 56.933... = €56.93 (correct to the nearest cent). [Q7(a) and (b) share one 15D scale.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q7b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "Mínigh an chaoi ar féidir leis úsáid a bhaint as an soláthar nótaí €5 agus bonn €2 atá aige chun gach luach slánuimhreach airgid níos mó ná €3 a dhéanamh (i.e. chun €n a dhéanamh le haghaidh gach n ∈ N, áit a bhfuil n > 3).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Every whole number greater than €3 can be formed: even amounts are made from €2 coins; odd amounts are made by including one €5 note (an odd) together with €2 coins for the rest. So both even and odd whole-euro values above €3 are reachable. (Argument by parity / combinations of 5 and 2.)", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q7b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 7, "marks_confidence": "derived", "question_text": "Tá na bróga reatha céanna á díol i siopa spóirt áitiúil ar phraghas €65. Tá dearbhán ag Amina ar fiú laghdú de 15% é ar aon earra a cheannaíonn sí sa siopa sin. Oibrigh amach cé mhéad a chosnóidh na bróga reatha má úsáideann sí an dearbhán sin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15% of 65 = 9.75; 65 − 9.75 = €55.25. [Q7(a) and (b) share one 15D scale.]", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q7ci", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Ceannaíonn an siopa spóirt áitiúil t-léinte ar €20 an ceann, agus díolann sé iad ar €28 an ceann. (c)(i) Oibrigh amach brabús t-léine amháin, ina euro.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "28 − 20 = €8 (profit on one t-shirt).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q7cii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach brabús céatadánach t-léine amháin (mar chéatadán den chostphraghas).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(8 / 20) × 100 = 40% percentage profit.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q8a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 15, "marks_confidence": "high", "question_text": "Réitigh an chothromóid seo a leanas. Bíodh gach freagra ceart go dtí dhá ionad dheachúlacha.\nx² − 4x − 7 = 0", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x = (−(−4) ± √((−4)² − 4(1)(−7))) / (2(1)) = (4 ± √(16+28))/2 = (4 ± √44)/2 = 5·316... or −1·316..., i.e. x = 5·32 or x = −1·32 (2 d.p.).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q8ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Tá Emma ag dul go roinnt ranganna corpoiliúna i spórtlann. Taispeántar sna graif thíos an costas in aghaidh na míosa atá ar 2 spórtlann éagsúla, Spórtlann A agus Spórtlann B, le haghaidh suas le 10 rang. (a)(i) Má théann Emma go 6 rang gach mí i Spórtlann B, cosnóidh sé €__.", "has_images": true, "image_notes": "Line graph: x-axis 'An líon ranganna in aghaidh na míosa' (0 to 10), y-axis 'Costas in aghaidh na míosa (€)' (0 to 100 in steps of 10). Two straight lines: Spórtlann A (steeper, starting near €10 at 0 rang, rising to about €100 at 10) and Spórtlann B (less steep, starting at €20 at 0 rang, rising to about €70 at 10). At 6 ranganna, line B reads about €50.", "topic": "Functions", "marking_scheme_answer": "Reading Spórtlann B graph at 6 classes: €50.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q8aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Cosnaíonn Spórtlann A agus Spórtlann B an méid céanna do __ rang in aghaidh na míosa. (Líon isteach an líon ranganna ina mbíonn an dá spórtlann ar comhchostas.)", "has_images": true, "image_notes": "Same two-line graph; the lines A and B intersect at approximately 4 classes (the point where both cost the same).", "topic": "Functions", "marking_scheme_answer": "The two lines intersect at 4 classes (where both gyms cost the same).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q8aiii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(iii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Má théann Emma go 10 rang gach mí, beidh Spórtlann __ níos saoire. (Líon isteach A nó B.)", "has_images": true, "image_notes": "Same graph; at 10 classes Spórtlann B (about €70) is below Spórtlann A (about €100), so B is cheaper.", "topic": "Functions", "marking_scheme_answer": "Spórtlann B (B is cheaper at 10 classes).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q8b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Is iad x = −1 agus x = 2 réitigh na cothromóide x² − x − 2 = 0. Taispeántar sa tábla thíos trí ghraf, A, B, agus C. Is ceann díobh seo graf na feidhme f(x) = x² − x − 2. Cuir tic sa bhosca ceart chun go dtaispeánfar cé acu de na graif sin a léiríonn an fheidhm f(x) = x² − x − 2. Cuir tic (✓) i mbosca amháin. Cosain do fhreagra.\nA □ B □ C □\nCosaint:", "has_images": true, "image_notes": "Three parabola graphs labelled A, B, C, each on x/y axes. Graf A: upward parabola crossing x-axis at x = −1 and x = 2, y-intercept at −2 (minimum below axis). Graf B: upward parabola, vertex on/above the axis (different roots). Graf C: upward parabola on x-axis range about −3 to 2. Correct graph must have roots at x = −1 and x = 2 and pass through (0, −2).", "topic": "Functions", "marking_scheme_answer": "Graph A. Justification: f(x) = x² − x − 2 has roots x = −1 and x = 2 and y-intercept f(0) = −2; only graph A meets these (cuts x-axis at −1 and 2, cuts y-axis at −2).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q8b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Líon isteach an dá luach atá ar iarraidh chun an ráiteas seo a leanas a chríochnú i gceart: \"Cosaíonn Spórtlann B €__ in aghaidh na míosa, móide €__ ar gach rang.\"", "has_images": true, "image_notes": "Same line graph for Spórtlann B, used to read the fixed monthly cost (y-intercept) and the cost per class (slope).", "topic": "Functions", "marking_scheme_answer": "Spórtlann B costs €20 per month plus €5 for each class (fixed cost €20, rate €5 per class).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q9a", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Déanann grúpa cairde físeán amháin agus cuireann siad ar YouTube é. Tá a fhios acu go n-íocfar €15 leo, a bheag nó a mhór, le haghaidh gach 10 000 amharc den fhíseán. Bain úsáid as an eolas sin chun na ceisteanna seo a leanas a fhreagairt. (a) Oibrigh amach an méid amharcanna a bheadh ag teastáil chun go n-íocfar €45 leo.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "45/15 × 10 000 = 30 000 amharc (views).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q9ai", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)(i)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeántar na tacair A agus B sa léaráid Venn thíos. Liostaigh baill gach ceann de na tacair seo a leanas. (i) A = { }.", "has_images": true, "image_notes": "Venn diagram with two overlapping ellipses, A (left) and B (right). In A only: t. In the overlap (A ∩ B): s, a, e. In B only: x, m.", "topic": "Number", "marking_scheme_answer": "A = {t, s, a, e} (elements in A, i.e. A-only plus the intersection).", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q9aii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)(ii)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) A ∩ B = { }.", "has_images": true, "image_notes": "Same Venn diagram; intersection region contains s, a, e.", "topic": "Number", "marking_scheme_answer": "A ∩ B = {a, s, e}.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q9aiii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)(iii)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "(iii) B\\A = { }.", "has_images": true, "image_notes": "Same Venn diagram; elements in B but not in A are x, m.", "topic": "Number", "marking_scheme_answer": "B\\A = {x, m}.", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q9b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Oibrigh amach an méid airgid (ina euro) a íocfar leo le haghaidh 80 000 amharc den fhíseán.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "80 000/10 000 × 15 = €120.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-ordinary-level-IV-q9b", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Deir Tomás: \"Is fothacar de P é P ∩ Q, le haghaidh aon dá thacar P agus Q.\" Luaigh cé acu fíor i gcónaí, fíor uaireanta, nó ní fíor riamh é ráiteas Thomáis. Cuir tic (✓) i mbosca amháin. Cosain do fhreagra.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Fíor i gcónaí (always true): every element of P ∩ Q is in P, so P ∩ Q is a subset of P for any sets P and Q. (Sample/justification: P ∩ Q ⊆ P; example may be given.)", "source_pdf": "2018 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q9c", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Oibrigh amach an méid airgid (ina euro) a íocfar leo, ar an meán, le haghaidh 1 amharc amháin den fhíseán.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15/10 000 = €0·0015 (i.e. €1·5 × 10⁻³, or €3/2000).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q9d", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Cosnaíonn sé €70 orthu an físeán a dhéanamh. Ní chosnaíonn sé faic orthu an físeán a chur ar YouTube. Faigheann siad €70 don bhrabús (ina euro) a gheobhaidh siad le haghaidh x amharc den fhíseán. Scríobh slonn in x don bhrabús (ina euro) a gheobhaidh siad le haghaidh x amharc den fhíseán.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Brabús = Ioncam − Costas = 0·0015x − 70.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q9ei", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(e)(i)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Tá 7 nduine sa ghrúpa. Roinneann siad an brabús ón bhfíseán go cothrom eatarthu féin. Faigheann siad €200 an duine mar bhrabús. (i) Scríobh cothromóid in x ón t-eolas sin a léiriú, áit arb é x líon iomlán na n-amharcanna den fhíseán.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Total profit = 7 × 200 = €1400, so (0·0015x − 70)/7 = 200, i.e. 0·0015x − 70 = 1400.", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2018-higher-level-IV-q9eii", "subject_n": "Mathematics", "year": 2018, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(e)(ii)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Oibrigh amach luach x, líon iomlán na n-amharcanna den fhíseán.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "0·0015x − 70 = 1400 → 0·0015x = 1470 → x = 980 000 amharc (views).", "source_pdf": "2018 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q1a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "There are 85 students in third year in Liam's school. 2/5 of these students do Business Studies. Work out the number of these students who do not do Business Studies.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(3/5) × 85 = 51 (or (2/5) × 85 = 34, then 85 − 34 = 51). Answer: 51 students.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q1a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Tickets for a concert cost €70, €80, and €100. Rafael bought three tickets. The total cost was €240. What tickets could Rafael have bought? The tickets could have cost €___, €___, and €___.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "€80, €80 and €80 OR €70, €70 and €100 (any three tickets totalling €240).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q1b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 2, "marks_confidence": "derived", "question_text": "26 of the students in third year do Art. Work out the percentage of students in third year who do Art, correct to one decimal place.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(26/85) × 100 = 30·588 = 30·6 %.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q1b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "A booking fee of 8% is added to the €240. Find the total price after the booking fee is added.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "240 × 1·08 = €259·20 (8% of 240 = 19·20; 240 + 19·20 = €259·20).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q1c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "The ratio of students to teachers in Liam's school was 15:1. The school hired one extra teacher, while the number of students stayed the same. The new ratio of students to teachers was a:1, where a ∈ ℚ. Put a tick (✓) in the correct box to show which statement is true: a > 15, a = 15, a < 15. Tick one box only. Give an example to support your answer.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "a < 15. E.g. original ratio 15:1; with one extra teacher the ratio becomes 15:2 = 7·5:1, and 7·5 < 15.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q1c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "In total, 60 000 tickets were sold for the concert, as follows: 20 000 tickets at €70 each, 25 000 tickets at €80 each, 15 000 tickets at €100 each. Work out the total cost of all of the 60 000 tickets that were sold.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "20 000 × 70 = 1 400 000; 25 000 × 80 = 2 000 000; 15 000 × 100 = 1 500 000; total = €4 900 000.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q10a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 10, "marks_confidence": "derived", "question_text": "Draw each of the following two functions in the domain −2 ≤ x ≤ 2, for x ∈ ℝ. Show your working out. Function: y = 10x − 4x^2.", "has_images": true, "image_notes": "Coordinate grid for plotting y = 10x − 4x^2. x-axis from −2 to 2; y-axis from −40 to 40 (gridlines every 10). A blank working grid is provided alongside.", "topic": "Functions", "marking_scheme_answer": "Plot the points (−2, −36), (−1, −14), (0, 0), (1, 6), (2, 4) and draw the smooth curve (downward parabola).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q10ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "The weight of an elephant is 5400 kg. Write the weight of the elephant in grams. 5400 kg = ___ grams.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 400 000 grams.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q10aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "The weight of a mouse is 19 grams. Write the correct figure from the following list into the sentence below. Show your working out. Options: 300, 3000, 30 000, 300 000. 'The weight of the elephant is roughly ___ times the weight of the mouse.'", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 400 000 ÷ 19 = 284 210·... ≈ 300 000 times.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q10b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "derived", "question_text": "Draw each of the following two functions in the domain −2 ≤ x ≤ 2, for x ∈ ℝ. Show your working out. Function: y = 3^x.", "has_images": true, "image_notes": "Coordinate grid for plotting y = 3^x. x-axis from −2 to 2; y-axis from −6 to 10 (gridlines every 2). A blank working grid is provided alongside.", "topic": "Functions", "marking_scheme_answer": "Plot the points (−2, 1/9 ≈ 1/2 on this scale), (−1, 1/3), (0, 1), (1, 3), (2, 9) and draw the smooth exponential curve. (Scheme lists approximate plotted values (−2, 1/2), (−1, 1/2), (0,1), (1,3), (2,9).)", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q10b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Fill in the table below to show each number in the form 10^n, where n ∈ ℕ. Numbers given: 100 (= 10^2), 10 000, 10^3 × 10^9, 10.", "has_images": true, "image_notes": "Two-column table 'Number' and 'Number in the form 10^n'. Rows: 100 → 10^2 (given); 10 000 → blank; 10^3 × 10^9 → blank; 10 → blank.", "topic": "Number", "marking_scheme_answer": "10 000 = 10^4; 10^3 × 10^9 = 10^12; 10 = 10^1.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q10c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Write 5400 in the form a × 10^n, where 1 ≤ a < 10 and n ∈ ℕ.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5·4 × 10^3.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q11", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Solve the following equation. Give your answer in the form m/n where m, n ∈ ℕ. (3x + 5)/2 + (x − 4)/3 = 16.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "[3(3x + 5) + 2(x − 4)]/6 = 16 → 9x + 15 + 2x − 8 = 96 → 11x + 7 = 96 → 11x = 89 → x = 89/11.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q11a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Ruairí has a weekend job. His total pay per day is a fixed rate plus tips. The tips are a percentage of the customer spend. The graph below shows Ruairí's total pay per day, depending on the customer spend. R is his total pay per day (in euro) and S is the customer spend (in hundreds of euro). What is Ruairí's fixed rate per day (his pay when the customer spend is €0)? Answer: ___.", "has_images": true, "image_notes": "Line graph: x-axis 'Customer spend, S (€00)' from 0 to 5; y-axis 'Total pay per day, R (€)' from 0 to 140. A straight line starts at R = 80 when S = 0 and rises with slope 10, e.g. passing through about (5,130).", "topic": "Functions", "marking_scheme_answer": "€80 (the y-intercept, R when S = 0).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q11bi", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)(i)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "On one day, the customer spend was €500 (so S = 5). What was Ruairí's total pay on that day? Answer: ___.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "€130 (read from the graph at S = 5).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q11bii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)(ii)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "How much did Ruairí get paid in tips on that day? Answer: ___.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "€50 (total €130 − fixed rate €80 = €50).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q11c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "The point (2·5, 105) is on the graph. Explain what this means in the context of Ruairí's total pay and the customer spend.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Ruairí gets paid €105 (total pay) when the customer spend is €250 (S = 2·5 hundred euro).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q11d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(d)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Three equations are given below in terms of R and S. Tick (✓) the correct box to show which one corresponds to the graph of Ruairí's total pay. Tick one box only. Justify your answer. Options: R = 80 − 10S, R = 130 + 10S, R = 80 + 10S.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "R = 80 + 10S. Justification: y-intercept = €80 and slope = 10 (gives the integer point (0,80) and matches the rising line).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q11e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(e)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Cillian also has a weekend job. Cillian's total pay per day, C, is: C = 60 + 20S, where S is the customer spend (in hundreds of euro). Draw the graph of Cillian's pay, C, on the axes below, for 0 ≤ S ≤ 5 and S ∈ ℝ.", "has_images": true, "image_notes": "Blank coordinate grid: x-axis 'Customer spend, S (€00)' from 0 to 5; y-axis 'Total pay per day, C (€)' from 0 to 160 (marked every 20). Student draws the line C = 60 + 20S.", "topic": "Functions", "marking_scheme_answer": "Straight line C = 60 + 20S: y-intercept (0,60), slope 20; e.g. plot (0,60) and (5,160) and join. (Two points plotted correctly gives high partial credit.)", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q12a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Factorise a^2 − 16n^2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "a^2 − (4n)^2 = (a − 4n)(a + 4n).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q12a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "The table below shows the graph of each of the given inequalities. Fill in the missing graph and the missing inequality, labelled A and B. x ∈ ℕ in each case. Row 1 (Example): x < 4 with its number line shown. Row 2: x > 2, draw graph A. Row 3: inequality B, with its number line graph shown.", "has_images": true, "image_notes": "Table 'Inequality (x ∈ ℕ)' and 'Graph'. Row 1 (Example): x < 4, number line from -1 to 7 with dots on 0,1,2,3 (natural numbers less than 4). Row 2: inequality x > 2, graph A to be drawn (dots on 3,4,5,6,7...). Row 3: number line shown with given dots (B); the inequality to be written. Number lines run from -1 to 7.", "topic": "Algebra", "marking_scheme_answer": "For A (x > 2): plot the points 3, 4, 5, 6, 7 on the number line (x ∈ ℕ). For B: write a valid inequality matching the shown graph, e.g. x > 5·1 OR x ≥ 6 (any inequality whose natural-number solutions match the plotted points).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q12bi", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 8, "marks_confidence": "derived", "question_text": "One of the factors of 8x^2 + 45x − 18 is x + 6. Factorise 8x^2 + 45x − 18.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8x^2 + 45x − 18 = (8x − 3)(x + 6).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q12bi", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Ailbhe writes two inequalities in A, and graphs each one. One inequality and one graph are shown in the table below. Complete the table by filling in the missing inequality and graph, labelled G and H. A ∈ ℝ in each case. Row 1: A ≥ 13, draw graph G. Row 2: inequality H, with its number line graph shown.", "has_images": true, "image_notes": "Table 'Inequality (A ∈ ℝ)' and 'Graph', number lines from 12 to 20. Row 1: A ≥ 13, graph G to be drawn (filled dot at 13 with line going right). Row 2: graph shown (H) — line from the left up to an open dot at 18; the inequality to be written.", "topic": "Algebra", "marking_scheme_answer": "For G (A ≥ 13): number line with a filled (closed) dot at 13 and a ray going right (A ∈ ℝ). For H: A < 18 (open dot at 18, ray going left, matching the shown graph).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q12bii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 7, "marks_confidence": "derived", "question_text": "Write down one quadratic expression in x, other than 8x^2 + 45x − 18, that has x + 6 as a factor. Give your answer in the form ax^2 + bx + c, where a, b, c ∈ ℝ.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Any quadratic with (x + 6) as a factor, e.g. (x + 6)(x + 1) = x^2 + 7x + 6.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q12bii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "A teenage disco has the following rule about the age, A, of students: 'Students must be 13 years of age or older, but less than 18.' To represent this rule, should Ailbhe use the union, the intersection, or the complement of the two sets in part (b)(i)? Tick (✓) one box only: union, intersection, complement.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Intersection.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q12c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Show that 2y + 3 is a factor of 2y^3 − 9y^2 − 28y − 15.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Dividing: (2y^3 − 9y^2 − 28y − 15) ÷ (2y + 3) = y^2 − 6y − 5 with no remainder, so 2y + 3 is a factor (verify via long division / array method).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q13", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13", "parent_question": "13", "marks": 15, "marks_confidence": "high", "question_text": "Draw the graph of the function f(x) = x^2 − x − 2 on the axes below, for −2 ≤ x ≤ 3, x ∈ ℝ.", "has_images": true, "image_notes": "Coordinate grid with x-axis from -2 to 3 and y-axis from -3 to 8, labelled x and y. Student plots and joins the parabola f(x) = x^2 − x − 2.", "topic": "Functions", "marking_scheme_answer": "Plot points (−2,4), (−1,0), (0,−2), (1,−2), (2,0), (3,4) and join with a smooth curve (parabola). Roots at x = −1 and x = 2; minimum near (0·5, −2·25).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q13a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Freda is starting an exercise program. She wants to increase her power output (P). One formula for P is P = 36w + 62h + 1800, where w is Freda's weight (in kilograms) and h is the height (in metres) that she can jump. Work out the value of P when w = 70 kg and h = 0·65 m.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "P = 36(70) + 62(0·65) + 1800 = 2520 + 40·3 + 1800 = 4360·3.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q13b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "After one week, Freda's power output (P) has increased by 8. Her weight (w) has not changed. Work out the new value of h after this week, correct to two decimal places.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "New P = 4360·3 + 8 = 4368·3; 36(70) + 62h + 1800 = 4368·3 → 62h = 48·3 → h = 0·779 = 0·78 m.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q13c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "The graph shows the value of P for different heights (h) when w = 70 kg. This graph cuts the y-axis when P = 4320. Draw a graph to show the values of P for different heights (h) when w = 80 kg, using the same axes, scales, and domain. State on the diagram the value of P where your graph cuts the y-axis. (Note: the P-axis does not start at 0.)", "has_images": true, "image_notes": "Line graph in a bordered box. Vertical axis 'Power output, P' (does not start at 0, broken scale); horizontal axis 'Height, h'. A single straight line with positive slope is given, labelled w = 70 kg, cutting the y-axis at P = 4320. Student draws a second straight line for w = 80 kg, parallel to and above the given line, cutting the y-axis at 4680.", "topic": "Functions", "marking_scheme_answer": "For w = 80 kg: P = 36(80) + 62h + 1800 = 62h + 4680; draw a line parallel to the given w = 70 line, above it, with y-intercept 4680.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q13d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(d)", "parent_question": "13", "marks": 10, "marks_confidence": "high", "question_text": "Freda finds a second formula for power output. She sets the two formulas equal. This gives the following identity, where f is Freda's height (in metres): 60w + 80h − 15f − 1300 = 36w + 62h + 1800. Use this to write h in terms of w and f.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "60w + 80h − 15f − 1300 = 36w + 62h + 1800 → 18h = −24w + 15f + 3100 → h = (15f − 24w + 3100)/18.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q14a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 10, "marks_confidence": "high", "question_text": "The first three terms of a sequence are: Term 1 = 6x − 3, Term 2 = x^2 − 2x, Term 3 = 4x^2 + 3x. Fill in the table to write each of the first differences in its simplest form in terms of x. (First Difference 1: Term 2 − Term 1 = x^2 − 2x − (6x − 3) = ...; First Difference 2: Term 3 − Term 2 = ...)", "has_images": true, "image_notes": "A two-column table. Column 1 header 'First Difference 1: Term 2 − Term 1' is pre-filled with x^2 − 2x − (6x − 3) = and gridded space to complete. Column 2 header 'First Difference 2: Term 3 − Term 2' is blank gridded space to complete.", "topic": "Algebra", "marking_scheme_answer": "First Difference 1 = Term 2 − Term 1 = x^2 − 2x − (6x − 3) = x^2 − 8x + 3. First Difference 2 = Term 3 − Term 2 = (4x^2 + 3x) − (x^2 − 2x) = 3x^2 + 5x.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q14b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 5, "marks_confidence": "high", "question_text": "Show that, if the terms form a linear sequence, then 2x^2 + 13x − 3 = 0.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Linear sequence ⇒ equal first differences: x^2 − 8x + 3 = 3x^2 + 5x → 0 = 2x^2 + 13x − 3, i.e. 2x^2 + 13x − 3 = 0.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q14c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(c)", "parent_question": "14", "marks": 10, "marks_confidence": "high", "question_text": "Solve the equation 2x^2 + 13x − 3 = 0. Give each answer correct to three decimal places.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "a = 2, b = 13, c = −3; x = (−13 ± √(169 + 24))/4 = (−13 ± √193)/4; x = 0·223 or x = −6·723.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q2a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 3, "marks_confidence": "derived", "question_text": "Write down the four factors of 45, apart from 1 and 45.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3, 5, 9, 15.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q2ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "Michael runs a weekly lottery. The cost of running each lottery is €80, including the prizes. He gets roughly €400 from selling tickets for each lottery. Work out the profit that Michael makes from each lottery.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "400 − 80 = €320.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q2aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "Work out the least number of lotteries that Michael must run to make over €1000 in profit. Show your working out.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1000 / 320 = 3·125, so 4 lotteries (320 + 320 + 320 + 320 = 1280 > 1000).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q2b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 2, "marks_confidence": "derived", "question_text": "n is a whole number bigger than 1. It has just two factors: 1 and n. Put a tick (✓) in the correct box to show what name is given to this type of number. Tick one box only: composite, prime, square.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Prime.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q2b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Siobhán and Ava win a lotto jackpot. They divide it so that Siobhán gets €25 000 and Ava gets €45 000. Write the ratio 25 000 : 45 000 in its simplest form.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 : 9.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q2c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "p is a whole number. Apart from 1 and p, the only other factor that p has is 7. Work out the value of p.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "p = 49.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q2ci", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)(i)", "parent_question": "2", "marks": 6, "marks_confidence": "derived", "question_text": "The jackpots for an American and an Irish lotto were as follows: Irish jackpot €4·8 million, American jackpot $5·3 million. The exchange rate at the time was €1 = $1·15. Show that the Irish jackpot was worth more than the American one.", "has_images": true, "image_notes": "Small two-column table. Row 'Irish jackpot' = €4·8 million; row 'American jackpot' = $5·3 million.", "topic": "Number", "marking_scheme_answer": "€4·8 million × 1·15 = $5·52 million > $5·3 million; OR convert the American jackpot: $5·3 / 1·15 = €4·61 million < €4·8 million. Either way the Irish jackpot is worth more.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q2cii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)(ii)", "parent_question": "2", "marks": 4, "marks_confidence": "derived", "question_text": "Give an example of an exchange rate that would make the American jackpot worth more than the Irish one. €1 = $___.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Accept any positive value less than $1·10416, for example €1 = $1 (any rate where 5·3 / rate > 4·8).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q2d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Write down the four factors of 12k + 8, apart from 1 and 12k + 8. Two of the factors should be in terms of k.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2, 4, 3k + 2, 6k + 4.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q3a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "The distance between the Earth and Mars is at least 56 000 000 km. Write this distance in the form a × 10^n km, where 1 ≤ a < 10 and n ∈ ℕ.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "56 000 000 = 5·6 × 10^7 km.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q3ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Alex's gross pay is €29 000 per year. She pays income tax at a rate of 20%. Find 20% of €29 000.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "29 000 × 0·2 = €5800.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q3aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Alex has a tax credit of €3400. Work out Alex's net pay per year.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "29 000 − 5800 + 3400 = €26 600 (tax due = 5800 − 3400 = 2400; net = 29 000 − 2400).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q3b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "The diameter of a human hair is roughly 0·0075 cm. Write this diameter in the form b × 10^n cm, where 1 ≤ b < 10 and n ∈ ℤ.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "0·0075 = 7·5 × 10^−3 cm.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q3b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Alex bought a motorbike in 2017. Its value at that time was €14 000. After one year its value was €12 600. Write €12 600 as a percentage of €14 000.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(12 600 / 14 000) × 100 = 90%.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q3c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Lewis was driving at 90 km per hour when he sneezed. During the sneeze, his eyes were closed for half a second. Work out how many metres he travelled in this time.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "90 km/h × 1000 = 90 000 m/hr; ÷60 = 1500 m/min; ÷60 = 25 m/sec; × 0·5 = 12·5 m in half a second.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q4", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Damien is putting a mirror on a wall. The wall is 330 cm wide and the mirror is 100 cm wide. Damien wants to put the mirror in the middle of the wall, as shown. Work out the value of L, the distance from the mirror to each end of the wall.", "has_images": true, "image_notes": "Diagram of a wall (rectangle) labelled 'Wall', total width 330 cm. A smaller centred rectangle labelled 'Mirror' is 100 cm wide. On each side of the mirror a double arrow labelled L marks the equal gap from the mirror to each end of the wall.", "topic": "Number", "marking_scheme_answer": "L = (330 − 100) / 2 = 115 cm.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q4ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(i)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Katie has a gross annual income of €52 460. 8·5% of this is deducted in pension contributions. The amount that is left is Katie's taxable income. Work out Katie's taxable income, after the pension contributions have been deducted.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "0·085 × 52 460 = 4459·10; Taxable income = 52 460 − 4459·10 = €48 000·90 (or 0·915 × 52 460).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q4aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(ii)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Katie pays income tax on her taxable income at a rate of 20% on the first €34 000, and 40% on the balance. She has annual tax credits of €4200. Work out Katie's net income, after income tax has been deducted.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Standard: 0·2 × 34 000 = 6 800; Higher: 0·4 × (48 000·90 − 34 000) = 0·4 × 14 000·90 = 5 600·36; Gross tax = 12 400·36; less tax credit 4 200 = 8 200·36; Net income = 48 000·90 − 8 200·36 = €39 800·54.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q4b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Katie got a credit card bill 3 months ago for €420. The interest rate on her credit card is 2% per month, compounded monthly. She has not paid off any of her bill. Work out what her bill is now. Give your answer in euro, correct to the nearest cent.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "420 × 1·02^3 = €445·71 (interest €25·71).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q4c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Katie bought a motorbike last year. Since she bought it, the motorbike lost 10% of its value. The value of the motorbike is now €12 150. Work out the value of the motorbike when Katie bought it.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "12 150 = 90% of original value; 12 150 / 0·9 = €13 500.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q5", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Solve the equation: (2x + 3)/5 = 7.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2x + 3 = 35; 2x = 32; x = 16.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q5a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 2, "marks_confidence": "derived", "question_text": "The sets A, B, and C are as follows: A is the set of multiples of 2 = {2, 4, ...}; B is the set of multiples of 3 = {3, 6, ...}; C is the set of multiples of 4 = {4, 8, ...}. Write down a number that is in A ∩ B ∩ C.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Any multiple of 12 (e.g. 12).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q5b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 3, "marks_confidence": "derived", "question_text": "Explain why C is a subset of A.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "A is the set of even numbers and C is the set of multiples of 4; every multiple of 4 is even (a multiple of 2), so C ⊆ A.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q5c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "These sets A, B, and C are shown in the Venn diagram. There are 7 different regions in the Venn diagram. Because C is a subset of A, there are two regions in the Venn diagram that have no elements. Write an X in each of these two regions in the Venn diagram above.", "has_images": true, "image_notes": "A three-circle Venn diagram for sets A (multiples of 2), B (multiples of 3), and C (multiples of 4). The three overlapping circles create 7 regions. Since C ⊆ A, the regions of C that lie outside A are empty: namely the part of C alone (outside A and B) and the part of C ∩ B that is outside A. Students mark X in those two empty regions.", "topic": "Number", "marking_scheme_answer": "Mark X in the two regions where C lies outside A: the C-only region and the (B ∩ C) region that is outside A (both empty because C ⊆ A).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q5d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Each of the other five regions in the Venn diagram has some elements. In each of these five regions in the Venn diagram above, write one of the elements that is in that region.", "has_images": true, "image_notes": "Same three-circle Venn diagram of A (multiples of 2), B (multiples of 3), C (multiples of 4). Student writes one example element into each of the five non-empty regions, e.g. A-only (e.g. 2), B-only (e.g. 3), A∩B only (e.g. 6), A∩C only (e.g. 4 or 8), A∩B∩C (e.g. 12).", "topic": "Number", "marking_scheme_answer": "Place a valid element in each of the five non-empty regions; there are infinitely many valid solutions (e.g. A-only: 2; B-only: 3; A∩B not C: 6; A∩C not B: 4 or 8; A∩B∩C: 12).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q6a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 8, "marks_confidence": "derived", "question_text": "Poppy and Ella ran a 5 km race. The simplified graph shows the time it took Ella to run d km during the race. One of the points on the graph is marked A. Distance is on the horizontal axis, so for example it took Ella 26 minutes to run the whole 5 km. Using the figures in the table, draw a graph on the diagram above to show the time it took Poppy to run d km during the race, for 0 ≤ d ≤ 5 and d ∈ ℝ.", "has_images": true, "image_notes": "Line graph: x-axis 'Distance in race, d (km)' from 0 to 5; y-axis 'Total time (minutes)' from 0 to 30 (gridlines every 5). Ella's line is drawn rising from origin (0,0) up to (5,26), labelled 'Ella'; point A is marked on Ella's line at about d=2, time ≈ 8 min. A table gives total times (minutes): Poppy at d = 1,2,3,4,5 = 5, 10, 17, 24, 30; Ella at d = 1 = 4 and d = 5 = 26 (other Ella values blank to be filled in part (b)).", "topic": "Functions", "marking_scheme_answer": "Plot Poppy's 6 points including (0,0): (0,0), (1,5), (2,10), (3,17), (4,24), (5,30); join to show an increasing function.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q6a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "The first three patterns in a sequence are shown. Pattern 1 has 2 squares, Pattern 2 has 5 squares, Pattern 3 has 10 squares. Draw Pattern 4 in the sequence.", "has_images": true, "image_notes": "Three growing L-shaped square patterns. Pattern 1: 2 small squares (an upper square with one square below it). Pattern 2: 5 squares (a vertical column of 2 with a 2×2 block forming an L). Pattern 3: 10 squares (a column of 4 plus a 3×3 block, L-shape). Each pattern n has n^2 + 1 small squares.", "topic": "Algebra", "marking_scheme_answer": "Draw Pattern 4 with 17 small squares (4^2 + 1 = 17), continuing the L-shaped arrangement (e.g. a 4×4 block plus an extra column/row giving 17 squares).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q6b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 7, "marks_confidence": "derived", "question_text": "Using Ella's graph, fill in the three missing values in the table below. (Table: Total time taken for Ella, in minutes, for distances d = 1, 2, 3, 4, 5 km.)", "has_images": true, "image_notes": "Table with columns 'Distance in the race (km)', 'Total time taken for Poppy (minutes)', 'Total time taken for Ella (minutes)'. Rows: 1 -> Poppy 5, Ella 4; 2 -> Poppy 10, Ella blank; 3 -> Poppy 17, Ella blank; 4 -> Poppy 24, Ella blank; 5 -> Poppy 30, Ella 26. Ella values read from her line graph in part (a).", "topic": "Functions", "marking_scheme_answer": "Reading Ella's line: d=2 -> 8, d=3 -> 14, d=4 -> 20 (with d=1 -> 4 and d=5 -> 26 given).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q6b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Fill in the table to show the number of small squares in each of the first four patterns. Table columns: Pattern (1, 2, 3, 4) and Number of small squares (Pattern 2 is given as 5).", "has_images": true, "image_notes": "Two-column table. Column 'Pattern': 1, 2, 3, 4. Column 'Number of small squares': row for Pattern 2 pre-filled with 5; rows for Patterns 1, 3 and 4 left blank to be completed.", "topic": "Algebra", "marking_scheme_answer": "Pattern 1 = 2, Pattern 2 = 5, Pattern 3 = 10, Pattern 4 = 17.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q6c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Show that Poppy's times in the table do not make a quadratic sequence.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Poppy's terms 5, 10, 17, 24, 30; first differences 5, 7, 7, 6; second differences 2, 0, −1 are not constant, so the sequence is not quadratic.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q6c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "The number of small squares in Pattern n is: n^2 + 1. Use this to work out the number of small squares in Pattern 20.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(20)^2 + 1 = 401.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q6d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "It took Ella 26 minutes to run the 5 km. Work out Ella's average speed for the race. Give your answer in km per hour, correct to two decimal places.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Speed = (5/26) × 60 = 11·54 km/hr.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q6d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "What kind of sequence is made by the number of small squares in each pattern? Tick (✓) one box only: linear, quadratic, exponential. Give a reason for your answer.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Quadratic. Reason: the second difference is a constant, OR n^2 is in the formula.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q6e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(e)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Tick (✓) the correct box to show what happened Ella's speed after 2 km, which is marked A on the graph. Tick one box only: Ella's speed increased, Ella's speed decreased, Ella's speed stayed the same. Justify your answer.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Ella's speed decreased: the first 2 km took 8 minutes, but the next 2 km took 12 minutes, so she was slower after 2 km.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q6f", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(f)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Ciarán also ran the 5 km race. He drew the graph to show the time it took him to run d km during the race. The part of Ciarán's graph marked C is a vertical line. What does the part C tell us about Ciarán's running at this stage of the race? Give as much detail as possible.", "has_images": true, "image_notes": "Line graph of Ciarán's race: x-axis 'Distance in the race, d (km)' from 0 to 5; y-axis 'Total time (minutes)' from 0 to 30 (gridlines every 5). The graph rises overall, but the segment marked C is a vertical line at about d = 2 km, where total time increases (from about 12 to 17 minutes) while distance stays fixed.", "topic": "Functions", "marking_scheme_answer": "The vertical part C means Ciarán stopped: distance stayed the same (at about 2 km) while time continued to pass (about 5 minutes), so he was stationary for roughly 5 minutes.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q6g", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(g)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Brendan says: \"Ciarán's graph does not show total time as a function of distance (d).\" Give a reason why Brendan is correct.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "For a function each input (distance) can have only one output (time); the vertical line means one distance value maps to many times, so it is not a function of distance.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q7a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 8, "marks_confidence": "derived", "question_text": "Multiply out and simplify (x + 3)(x − 2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x^2 − 2x + 3x − 6 = x^2 + x − 6.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q7ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 3, "marks_confidence": "derived", "question_text": "Describe each of the following sets. Be as specific as possible. (i) The set of natural numbers, ℕ.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Positive whole numbers (e.g. {1, 2, 3, ...}).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q7aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 2, "marks_confidence": "derived", "question_text": "Describe each of the following sets. Be as specific as possible. (ii) The set of integers, ℤ.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Positive and negative whole numbers and zero (e.g. {..., −2, −1, 0, 1, 2, ...}).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q7b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Graph the following inequality on the number line given: −3 < x ≤ 2, where x ∈ ℝ.", "has_images": true, "image_notes": "A table with two columns. Left column 'Inequality' contains: −3 < x ≤ 2, where x ∈ ℝ. Right column 'Number line' shows a number line marked from −4 to 4. Student graphs the interval: open (hollow) circle at −3, closed (filled) circle at 2, with the segment between them shaded.", "topic": "Algebra", "marking_scheme_answer": "Number line with an open circle at −3 (excluded), a closed/filled circle at 2 (included), and the segment between them shaded.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q7b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 7, "marks_confidence": "derived", "question_text": "Factorise x^2 − 64.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x + 8)(x − 8).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q7c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "Use algebra to solve the following inequality: −7 < 8 − 3g ≤ 11.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "−7 < 8 − 3g ≤ 11 → −15 < −3g ≤ 3 → 5 > g ≥ −1 (i.e. −1 ≤ g < 5).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q8", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "The Venn diagram shows the number of people in a youth club (U) who play music (M) and sport (S), where n ∈ ℕ. (M only = 52; M ∩ S = 184 − n; S only = 2n; outside both, in U = 125.) Work out the maximum number of people who could be in the youth club.", "has_images": true, "image_notes": "Venn diagram inside a rectangle labelled U (universal set). Two overlapping ellipses: left ellipse M (music), right ellipse S (sport). M-only region = 52; the overlap M ∩ S = 184 − n; S-only region = 2n; the region inside the rectangle but outside both circles = 125. n ∈ ℕ.", "topic": "Algebra", "marking_scheme_answer": "Total = 52 + (184 − n) + 2n + 125 = 361 + n. To maximise, n is as large as possible; the overlap 184 − n ≥ 0 gives n ≤ 184, so maximum n = 184; maximum people = 361 + 184 = 545.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q8a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 8, "marks_confidence": "derived", "question_text": "Poppy and Ella ran a 5 km race. The table shows the total time it took Poppy and Ella to run each of the given distances during the race. It took Ella 26 minutes to run the whole 5 km. Using the graph, fill in the three missing values for Ella in the table above.", "has_images": true, "image_notes": "Table with columns 'Distance in the race (km)' (1, 2, 3, 4, 5), 'Total time taken for Ella (minutes)' and 'Total time taken for Poppy (minutes)'. Given Ella times: at 1 km = ?, 2 km = ?, 3 km = ?, 4 km = ?, 5 km = 26 (Ella column has three missing values to fill from the line graph). Poppy times given: 1 km = 5, 2 km = 10, 3 km = 17, 4 km = 24, 5 km = 30. A linear graph of Ella's time vs distance is provided, with one point marked A near (2,8).", "topic": "Functions", "marking_scheme_answer": "Ella's missing times read from the straight-line graph (line through origin to (5,26)): 1 km = 4 min (4·2 ≈ 4), 3 km = 14 min (15·6 ≈ 16 on a 26/5 line), 4 km = 20 min (model solution: Distance 1 → 4, 2 → 8, 3 → 14, 4 → 20, 5 → 26).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q8b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 7, "marks_confidence": "derived", "question_text": "Using the figures in the table, draw a graph on the diagram below to show the time it took Poppy to run d km during the race, for 0 ≤ d ≤ 5 and d ∈ ℝ.", "has_images": true, "image_notes": "Coordinate grid: x-axis 'Distance in the race, d (km)' from 0 to 5; y-axis 'Total time (minutes)' from 0 to 30. Ella's line is already drawn (straight line from origin up to about (5,26), labelled 'Ella'), with point A marked near (2,8). Student must plot Poppy's points (1,5), (2,10), (3,17), (4,24), (5,30) and join them.", "topic": "Functions", "marking_scheme_answer": "Plot Poppy's points (0,0), (1,5), (2,10), (3,17), (4,24), (5,30) and join. (6 points required including (0,0); allow tolerance ±0·5 on the y-axis.)", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q8c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 7, "marks_confidence": "derived", "question_text": "Who finished first, Ella or Poppy? Tick (✓) one box only. Give a reason for your answer.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Ella. Reason: Ella took 26 minutes (< 30 minutes for Poppy), so Ella finished first.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q8d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 8, "marks_confidence": "derived", "question_text": "Tick (✓) the correct box to show what happened to Ella's speed after 2 km, which is marked A on the graph. Tick one box only: Ella's speed increased / Ella's speed decreased / Ella's speed stayed the same. Justify your answer.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Ella's speed decreased. Justification: it took her longer to run the next kilometre — her pace (slope) changed from 4 minute/km to 6 minute/km (the graph gets steeper).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q8e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(e)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "It took Poppy 30 minutes to run the 5 km. Work out Poppy's average speed for the race, in km per hour.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 / 0·5 = 10 km/hr (30 minutes = 0·5 hour; OR 30 min → 5 km, so 60 min → 10 km).", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q9a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "A school team orders t-shirts and half zips. Jill, Mike, Ted, and Gary order t-shirts (T). Jill and Alice order half zips (Z). Ben and Zena don't order either. Use this information to complete the Venn diagram below to show this information, where: U is the whole team (the universal set), T is the set of people ordering t-shirts, Z is the set of people ordering half zips.", "has_images": true, "image_notes": "Venn diagram with universal set U (rectangle) and two overlapping ovals labelled T and Z. Mike is shown in T only; Ben is shown outside both sets in U. Students place: Ted and Gary in T only; Jill in the overlap T∩Z; Alice in Z only; Zena outside both sets.", "topic": "Probability", "marking_scheme_answer": "T only: Mike, Ted, Gary. T∩Z: Jill. Z only: Alice. Outside both (in U only): Ben, Zena.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q9ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)(i)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Gertie writes down the following sequence, which repeats every three terms: 3, 6, 4, 3, 6, 4, 3, ... The 1st term is 3. Write down the value of the 12th term.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "12th term = 4 (12 ÷ 3 = 4 remainder 0, so it equals the 3rd term, 4).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q9aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)(ii)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Work out the value of the 100th term in this sequence.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "100 ÷ 3 = 33 remainder 1, so the 100th term equals the 1st term = 3.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q9b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Describe how to find the value of the nth term in the sequence, where n ∈ ℕ, without listing all the terms from the 1st to the nth.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Divide n by 3 and use the remainder: remainder 0 → nth term = 3rd term (4); remainder 1 → nth term = 1st term (3); remainder 2 → nth term = 2nd term (6).", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q9b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "In total, how many students are on the team? Answer: ___.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "7 students.", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q9c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Gertie made her sequence 3, 6, 4, 3, 6, 4, 3, ... by picking 3 as the 1st term, and then using this rule: If a term is odd, multiply it by 2 to get the next term. If a term is even, add 2 to it and half your answer to get the next term. For example, 3 is odd, so the next term is 2 × 3, which is 6. 6 is even, so the next term is (1/2) × (6 + 2), which is 4. A different sequence follows the same rule, but has 8 as the 1st term. Work out the next four terms of this sequence. (Working out: 2nd term = (1/2) × (8 + 2) = ...)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Starting at 8: 8 (even) → (1/2)(8+2)=5; 5 (odd) → 5×2=10; 10 (even) → (1/2)(10+2)=6; 6 (even) → (1/2)(6+2)=4. Next four terms: 5, 10, 6, 4.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-ordinary-level-EV-q9c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 11, "marks_confidence": "derived", "question_text": "Write each term from the following list into the correct space in the table below, to match each description to the correct term in set notation. (Z' is the complement of Z.) Terms: Z\\T, T∩Z, Z'. Descriptions: 1. The students who order both t-shirts and half zips; 2. The students who order half zips but not t-shirts; 3. The students who do not order half zips.", "has_images": true, "image_notes": "Table with two columns 'Description' and 'Set notation', three rows. Description 1 = students who order both t-shirts and half zips; Description 2 = students who order half zips but not t-shirts; Description 3 = students who do not order half zips. Set notation column to be filled from the list Z\\T, T∩Z, Z'.", "topic": "Probability", "marking_scheme_answer": "1: T∩Z. 2: Z\\T. 3: Z'. (Note the scheme labels the half-zip set H; with exam's Z: row1 = T∩Z, row2 = Z\\T, row3 = Z'.)", "source_pdf": "2019 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q9d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Ahmed takes 2 as his 1st term, and makes a sequence using the same rule. State what is unusual about Ahmed's sequence. It might be helpful to work out some of the terms of his sequence.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Starting at 2: (1/2)(2+2) = 2, so every term is 2; the sequence stays constant at 2.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q9e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(e)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "In another sequence using the same rule, the 2nd term is 86. Work out the two different values that the 1st term can have in this sequence. (Answer of the form [ ], 86, ... or [ ], 86, ...)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "If the 1st term was even: (1/2)(x + 2) = 86 → x + 2 = 172 → x = 170. If the 1st term was odd: 2x = 86 → x = 43. The two values are 43 and 170.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-EV-q9f", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(f)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "A different sequence following the same rule starts with the number k, which is odd. Work out the next three terms of this sequence. Give each term in its simplest form in terms of k. (Answer of the form k, [ ], [ ], [ ].)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "k is odd → 2nd term = 2k (even); 3rd term = (1/2)(2k + 2) = k + 1; 4th term = (1/2)((k+1) + 2) = (k + 3)/2. Next three terms: 2k, k + 1, (k + 3)/2.", "source_pdf": "2019 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q1a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "Tá 85 mac léinn sa tríú bliain i scoil Liam. Déanann 3/5 de na mic léinn sin Staidéar Gnó. Oibrigh amach líon na mac léinn sin nach ndéanann Staidéar Gnó.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3/5 × 85 = 51 do Staidéar Gnó, so líon nach ndéanann é = 85 − 51 = 34. (Nó 2/5 × 85 = 34.) Parts (a) and (b) share a 5-mark scale (5D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q1a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Cosnaíonn ticéid cheolchoirme €70, €80, agus €100. Cheannaigh Rafael trí thicéad. Ba é an costas iomlán orthu ná €240. Cén teaglaim ticéad a d'fhéadfadh a bheith ceannaithe ag Rafael? D'fhéadfadh costas € [ ], € [ ], agus € [ ] bheith ar na ticéid.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "€80, €80 agus €100 (= €240). (Scála 10B.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q1b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 2, "marks_confidence": "derived", "question_text": "Tá 26 mac léinn sa tríú bliain a dhéanann Ealaín. Oibrigh amach céatadán na mac léinn sa tríú bliain a dhéanann Ealaín. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "26/85 × 100 = 30·588 = 30·6 [%]. Parts (a) and (b) share a 5-mark scale (5D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q1b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Déantar táille áirithinte de 8% a shuimiú leis an €240. Faigh an praghas iomlán tar éis an táille áirithinte a shuimiú.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "240 × 1·08 = €259·20. (Nó 240 × 8% = 19·20; 240 + 19·20 = €259·20.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q1c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Bé 15:1 cóimheas na mac léinn leis na múinteoirí i scoil Liam. D'fhostaigh an scoil múinteoir breise ach ní raibh aon athrú ar líon na mac léinn. Bá a:1 cóimheas na na mac léinn leis na múinteoirí, áit a raibh a ∈ Q. Cuir tic (✓) sa bhosca ceart chun a thaispeáint céard a tharla don a ráiteas atá fíor. Cuir tic i mbosca amháin. Tabhair sampla chun tacú le do fhreagra. (Roghanna: a > 15, a = 15, a < 15)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Freagra: a < 15. Sampla: cóimheas bunaidh = 15:1; cóimheas nua = 15:2 = 7·5:1, agus 7·5 < 15. Nó sampla comhchosúil ar bith eile. Scála 10C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q1c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Díoladh 60 000 ticéad don cheolchoirm, san iomlán. Is mar seo a leanas a bhí siad: 20 000 ticéad ag €70 an ceann; 25 000 ticéad ag €80 an ceann; 15 000 ticéad ag €100 an ceann. Oibrigh amach costas iomlán an 60 000 ticéad go léir a díoladh.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "20 000 × €70 + 25 000 × €80 + 15 000 × €100 = €1 400 000 + €2 000 000 + €1 500 000 = €4 900 000. (Nóta scéime: 2×7 agus 25×80 agus 150×1, i.e. na trí iomlán; Scála 10D.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q10graf1", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10 (Graf 1)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Tarraing gach ceann den dá fheidhm seo a leanas san fhearann −2 ≤ x ≤ 2, le haghaidh x ∈ R. Taispeáin do chuid oibre. Feidhm: y = 10x − 4x^2.", "has_images": true, "image_notes": "Coordinate grid for plotting y = 10x − 4x^2 over −2 ≤ x ≤ 2. x-axis from −2 to 2, y-axis from −40 to 40 (gridlines every 10). The curve is a downward parabola passing through (−2,−36),(−1,−14),(0,0),(1,6),(2,4).", "topic": "Functions", "marking_scheme_answer": "Pointí: (−2,−36), (−1,−14), (0,0), (1,6), (2,4); draw smooth curve (downward parabola) through them. Graf 1 is on a 10-mark scale (10C).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q10graf2", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10 (Graf 2)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Feidhm: y = 3^x. (San fhearann −2 ≤ x ≤ 2, le haghaidh x ∈ R.)", "has_images": true, "image_notes": "Coordinate grid for plotting y = 3^x over −2 ≤ x ≤ 2. x-axis from −2 to 2, y-axis from −6 to 10 (gridlines every 2). The curve is an exponential rising from near 0 to 9, passing through (−2,1/9),(−1,1/3),(0,1),(1,3),(2,9).", "topic": "Functions", "marking_scheme_answer": "Pointí: (−2,1/9), (−1,1/3), (0,1), (1,3), (2,9); draw smooth exponential curve through them. Graf 2 is on a 10-mark scale (10C).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q10ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Is é 5400 kg meáchan eilifinte. Scríobh meáchan na heilifinte ina ghraim.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5400 kg = 5 400 000 gram. (Scála 10C roinnte le (a)(ii).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q10aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Is é 19 ngram meáchan luiche. Scríobh an figiúr ceart ón liosta seo a leanas isteach san abairt thíos. Taispeáin d'oibriú amach. 'Is ionann meáchan eilifinte agus timpeall [ ] oiread meáchain luiche.' (Roghanna: 300, 3000, 30 000, 300 000.)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 400 000 ÷ 19 = 284 210·5... ≈ 300 000. Mar sin is ionann meáchan eilifinte agus timpeall 300 000 oiread meáchain luiche. (Scála 10C roinnte le (a)(i).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q10b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Líon isteach an tábla thíos agus gach uimhir á taispeáint agat san fhoirm 10^n, áit a mbeidh n ∈ N. (Uimhir: 100, 10 000, 10^3 × 10^9, 10.)", "has_images": true, "image_notes": "Tábla le dhá cholún: 'Uimhir' (100, 10 000, 10^3 × 10^9, 10) agus 'Uimhir san fhoirm 10^n' atá le líonadh isteach.", "topic": "Number", "marking_scheme_answer": "100 = 10^2; 10 000 = 10^4; 10^3 × 10^9 = 10^12; 10 = 10^1. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q10c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Scríobh 5400 san fhoirm a × 10^n, áit a mbeidh 1 ≤ a < 10 agus n ∈ N.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5400 = 5·4 × 10^3. (Scála 5B.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q11", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Réitigh an chothromóid seo a leanas. Bíodh do fhreagra san fhoirm m/n áit a mbeidh m, n ∈ N. (3x + 5)/2 + (x − 4)/3 = 16.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(3x+5)/2 + (x−4)/3 = 16 → [3(3x+5) + 2(x−4)]/6 = 16 → 9x + 15 + 2x − 8 = 96 → 11x = 89 → x = 89/11. Scála 10D.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q11a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 8, "marks_confidence": "derived", "question_text": "Tá post deireadh seachtaine ag Ruairí. Is é a phá iomlán in aghaidh an lae ná an ráta seasta móide séisíní. Áirítear na séisíní mar chéatadán de chaiteachas na gcustaiméirí. Taispeánann an graf thíos pá iomlán Ruairí in aghaidh an lae, in aghaidh chaiteachas na gcustaiméirí. Is é R a phá iomlán in aghaidh an lae (ina euro) agus is é S an caiteachas custaiméirí (sna céadta euro). Céard é ráta seasta Ruairí in aghaidh an lae (a phá nuair is é €0 an caiteachas custaiméirí)? Freagra: [ ].", "has_images": true, "image_notes": "Graf líne dronlíneach: y-ais 'Pá iomlán in aghaidh an lae, R (€)' 0 go 140; x-ais 'Caiteachas custaiméirí, S (€00)' 0 go 5. Tosaíonn an líne ag R=80 nuair atá S=0 agus ardaíonn go R≈130 nuair atá S=5. Tá an pointe (2·5, 105) ar an líne.", "topic": "Functions", "marking_scheme_answer": "Ráta seasta = €80 (an luach R nuair atá S = 0, idirlíne y an ghraif). (Scála 15D roinnte le (b)(i) agus (b)(ii).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q11bi", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)(i)", "parent_question": "11", "marks": 4, "marks_confidence": "derived", "question_text": "Lá amháin, ba é an caiteachas custaiméirí ná €500 (dá bhrí sin, S = 5). Cérbh é pá iomlán Ruairí an lá sin? Freagra: [ ].", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Nuair atá S = 5, R = €130 (le léamh ón graf). (Scála 15D roinnte le (a) agus (b)(ii).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q11bii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)(ii)", "parent_question": "11", "marks": 3, "marks_confidence": "derived", "question_text": "Cé mhéad a íocadh le Ruairí i séisíní an lá sin? Freagra: [ ].", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Séisíní = pá iomlán − ráta seasta = €130 − €80 = €50. (Scála 15D roinnte le (a) agus (b)(i).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q11c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Tá an pointe (2·5, 105) ar an ngraf. Mínigh cad is brí leis sin i gcomhthéacs phá iomlán Ruairí agus chaiteachas na gcustaiméirí.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Nuair a chaitheann na custaiméirí €105 (i.e. S = 2·5, mar sin €250), faigheann Ruairí íocaíocht/pá iomlán €105 don lá sin. (Scála 5C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q11d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(d)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Tugtar trí chothromóid thíos i dtéarmaí R agus S. Cuir tic (✓) sa bhosca ceart a thaispeánfaidh cé acu díobh a fhreagraíonn don ghraf do phá iomlán Ruairí. Cuir tic i mbosca amháin. Cosain do fhreagra. (Roghanna: R = 80 − 10S; R = 130 + 10S; R = 80 + 10S.)", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "R = 80 + 10S. Cúis: idirlíne y = €80 (an ráta seasta) agus fána = 10 (R ardaíonn ó 80 go 130 thar S = 0 go 5). (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q11e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(e)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Tá post deireadh seachtaine ag Cillian freisin. Is é pá iomlán Chillian in aghaidh an lae, C, ná: C = 60 + 20S, áit arb é S an caiteachas custaiméirí (sna céadta euro). Tarraing an graf do phá Chillian, C, ar na haiseanna thíos, le haghaidh 0 ≤ S ≤ 5 agus S ∈ R.", "has_images": true, "image_notes": "Léaráid ghraif le haiseanna: y-ais 'Pá iomlán in aghaidh an lae, C (€)' 0 go 160; x-ais 'Caiteachas custaiméirí, S (€00)' 0 go 5. Tá an graf le tarraingt: líne dhíreach C = 60 + 20S ó (0, 60) go (5, 160).", "topic": "Functions", "marking_scheme_answer": "Tarraing líne dhíreach C = 60 + 20S ó (0, 60) go (5, 160), i.e. idirlíne y 60 agus fána 20. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q12a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Fachtóirigh a^2 − 16n^2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "a^2 − 16n^2 = (a)^2 − (4n)^2 = (a − 4n)(a + 4n). Scála 5B.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q12a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Taispeánann an tábla thíos an graf do gach ceann de na héagothromóidí atá tugtha. Líon isteach an graf agus an éagothromóid atá ar iarraidh, lipéadaithe A agus B. x ∈ N i ngach cás díobh. (Sampla: x < 4; Sraith 2: x > 2 (graf A le líonadh); Sraith 3: graf B le héagothromóid le líonadh, x ∈ N ar líne uimhreach −1 go 7.)", "has_images": true, "image_notes": "Tábla le dhá cholún ('Éagothromóid (x ∈ N)' agus 'Graf'). Sraith samplach: x < 4 le pointí lána ag 0,1,2,3 ar líne uimhreach −1 go 7. Sraith 2: tugtar éagothromóid x > 2, tá an graf A le líonadh isteach. Sraith 3: tugtar graf B (pointí), tá an éagothromóid le scríobh. Líne uimhreach ó −1 go 7.", "topic": "Algebra", "marking_scheme_answer": "Sraith 2 (Graf A, x > 2): pointí lána ag 3, 4, 5, 6, 7 (x ∈ N). Sraith 3 (Graf B): x > 5·1 i.e. x ≥ 6 (x ∈ N), nó éagothromóid bhailí eile a thugann na pointí léirithe. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q12bi", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 8, "marks_confidence": "derived", "question_text": "Is ceann d'fhachtóirí 8x^2 + 45x − 18 é x + 6. Fachtóirigh 8x^2 + 45x − 18.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8x^2 + 45x − 18 = (8x − 3)(x + 6). Part (b) is on a 15-mark scale (15D) covering (i) and (ii).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q12bi", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Scríobhann Ailbhe dhá éagothromóid in A. Tá A ∈ R. Anois déanann sí graf de gach ceann díobh. Taispeánfar éagothromóid amháin agus graf amháin sa tábla thíos. Críochnaigh an tábla agus líon isteach an graf agus an éagothromóid atá ar iarraidh, lipéadaithe G agus H. A ∈ R i ngach cás díobh. (Sraith 1: A ≥ 13, graf G le líonadh; Sraith 2: graf H tugtha, éagothromóid le scríobh; líne uimhreach 12 go 20.)", "has_images": true, "image_notes": "Tábla le dhá cholún ('Éagothromóid (A ∈ R)' agus 'Graf'). Sraith 1: A ≥ 13 le graf G le tarraingt (pointe dúnta ag 13, líne ar dheis). Sraith 2: tugtar graf H (pointe oscailte ag 18, líne ar chlé), éagothromóid le scríobh. Líne uimhreach ó 12 go 20.", "topic": "Algebra", "marking_scheme_answer": "Graf G (A ≥ 13): pointe dúnta ag 13 le líne lán ar dheis go 20. Éagothromóid do Graf H: A < 18. (Scála 5C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q12bii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 7, "marks_confidence": "derived", "question_text": "Scríobh síos slonn cearnach amháin in x, seachas 8x^2 + 45x − 18, a bhfuil x + 6 mar fhachtóir aige. Bíodh do fhreagra san fhoirm ax^2 + bx + c, áit a mbeidh a, b, c ∈ R.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "E.g. (x + 6)(x + 1) = x^2 + 7x + 6, nó nath cainte cearnach ar bith eile a bhfuil (x + 6) aige mar fhachtóir. Part (b) is on a 15-mark scale (15D) covering (i) and (ii).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q12bii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Ag díoscó do dhéagóirí, tá an riail seo a leanas ann a bhaineann le haois, A, na mac léinn: 'Ní mór do mhic léinn a bheith 13 bliana d'aois nó níos sine, ach faoi bhun 18.' Chun an riail sin a léiriú, cé acu aontas, idirmhír, nó comhlánú a chuir Ailbhe glacadh leis? Cuir tic (✓) i mbosca amháin. (Roghanna: aontas / idirmhír / comhlánú.)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Trasnú / idirmhír (an riail 13 ≤ A < 18 is trasnú de A ≥ 13 agus A < 18). (Scála 5A.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q12c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Taispeáin go bhfuil 2y + 3 ina fhachtóir ag 2y^3 − 9y^2 − 28y − 15.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Roinnt fhada: (2y^3 − 9y^2 − 28y − 15) ÷ (2y + 3) = y^2 − 6y − 5 le fuíleach 0, mar sin is fachtóir é 2y + 3. (Doiciméadaíonn an scéim an roinnt fhada / mhodh eagair iomlán.) Scála 10C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q13", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13", "parent_question": "13", "marks": 15, "marks_confidence": "high", "question_text": "Tarraing graf na feidhme f(x) = x^2 − x − 2 ar na haiseanna thíos, le haghaidh −2 ≤ x ≤ 3, x ∈ R.", "has_images": true, "image_notes": "Léaráid ghraif le x-ais ó −2 go 3 agus y-ais ó −3 go 8, eangach cearnógach. Tá an graf le tarraingt: parabóla f(x) = x^2 − x − 2.", "topic": "Functions", "marking_scheme_answer": "Pointí: (−2, 4), (−1, 0), (0, −2), (1, −2), (2, 0), (3, 4). Tarraing parabóla réidh tríothu. (Scála 15D.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q13a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Tá Freda ag tosú ar chlár aclaíochta. Ba mhian léi a h-aschur cumhachta (P) a mhéadú. Foirmle amháin le haghaidh P is ea: P = 36w + 62h + 1800, áit arb é w meáchan Freda (ina chileagraim) agus arb é h an airde (ina méadair) is féidir léi léim. Oibrigh amach luach P áit a bhfuil w = 70 kg agus h = 0·65 m.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "P = 36(70) + 62(0·65) + 1800 = 2520 + 40·3 + 1800 = 4360·3 (nó 43603/10). Parts (a) and (b) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q13b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Tar éis seachtain amháin, tá aschur cumhachta Freda (P) méadaithe de 8. Níl aon athrú ar a meáchan (w). Oibrigh amach luach nua h tar éis na seachtaine sin, ceart go dtí dhá ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "P nua = 4360·3 + 8 = 4368·3. 36(70) + 62h + 1800 = 4368·3 → 2520 + 62h + 1800 = 4368·3 → 62h = 48·3 → h = 0·779 = 0·78 [m]. (Nó méadú ar h: 8/62 = 0·129… = 0·13, h nua = 0·65 + 0·13 = 0·78 m.) Parts (a) and (b) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q13c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Taispeántar sa ghraf thíos luach P le haghaidh airdí éagsúla (h) nuair atá w = 70 kg. Trasnaíonn an graf sin an y-ais nuair atá P = 4320, mar a thaispeántar. Tarraing graf a thaispeánfaidh luachanna P le haghaidh airdí éagsúla (h) nuair atá w = 80 kg, agus na haiseanna, na scálaí, agus an fhearann céanna á n-úsáid agat. Luaigh ar an léaráid an luach ar P ag an áit a dtrasnaíonn do ghraf an y-ais. Nóta: ní thosaíonn an ais le P ag 0.", "has_images": true, "image_notes": "Line graph: y-axis 'Aschur cumhachta, P' (does not start at 0), x-axis 'Airde, h'. A straight line labelled 'w = 70 kg' rises from the y-axis at P = 4320. Candidate draws a parallel line above it for w = 80 kg, crossing the y-axis at P = 4680.", "topic": "Algebra", "marking_scheme_answer": "For w = 80: P = 36(80) + 62h + 1800 = 62h + 4680. Draw a line parallel to (and above) the w = 70 line, crossing the y-axis at P = 4680. Scála 5C (3 ghné: figiúr ceart 4680, líne chomhthreomhar, líne os cionn na líne a thugtar). Scála 5C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q13d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(d)", "parent_question": "13", "marks": 10, "marks_confidence": "high", "question_text": "Aimsíonn Freda foirmle eile le haghaidh aschur cumhachta. Cuireann sí an dá fhoirmle ar comhionannas. Tugann sé sin an t-ionannas seo a leanas, áit arb é f airde Freda (ina méadair): 60w + 80h − 15f − 1300 = 36w + 62h + 1800. Bain úsáid as sin chun h a scríobh i dtéarmaí w agus f. (Freagra: h = __)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "60w + 80h − 15f − 1300 = 36w + 62h + 1800 → 80h − 62h = 15f + 36w − 60w + 1800 + 1300 → 18h = 15f − 24w + 3100 → h = 15f/18 − 24w/18 + 3100/18 (nó a choibhéis). Scála 10C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q14a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 10, "marks_confidence": "high", "question_text": "Seo a leanas an chéad trí théarma i seicheamh: Téarma 1: 6x − 3; Téarma 2: x^2 − 2x; Téarma 3: 4x^2 + 3x. Líon isteach an tábla a leanas agus scríobh gach ceann de na chéad difríochtaí san fhoirm is simplí i dtéarmaí x. (An Chéad Difríocht 1: Téarma 2 − Téarma 1; An Chéad Difríocht 2: Téarma 3 − Téarma 2.)", "has_images": true, "image_notes": "A two-column table to fill in. Column 1 header 'An Chéad Difríocht 1: Téarma 2 − Téarma 1' shows the start x^2 − 2x − (6x − 3) =. Column 2 header 'An Chéad Difríocht 2: Téarma 3 − Téarma 2'. Candidate simplifies each difference in terms of x.", "topic": "Algebra", "marking_scheme_answer": "T2 − T1 = x^2 − 2x − (6x − 3) = x^2 − 8x + 3. T3 − T2 = 4x^2 + 3x − (x^2 − 2x) = 3x^2 + 5x. Scála 10D.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q14b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 5, "marks_confidence": "high", "question_text": "Taispeáin go bhfuil 2x^2 + 13x − 3 = 0, más seicheamh líneach a dhéantar ag na téarmaí.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Más líneach é, tá na chéad difríochtaí tairiseach so T2 − T1 = T3 − T2: x^2 − 8x + 3 = 3x^2 + 5x → 2x^2 + 13x − 3 = 0. Scála 5C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q14c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(c)", "parent_question": "14", "marks": 10, "marks_confidence": "high", "question_text": "Réitigh an chothromóid 2x^2 + 13x − 3 = 0. Bíodh gach freagra ceart go dtí trí ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "a = 2, b = 13, c = −3. x = (−b ± √(b^2 − 4ac))/(2a) = (−13 ± √(13^2 − 4(2)(−3)))/(2(2)) = (−13 ± √193)/4. x = 0·223 nó x = −6·723. Scála 10C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q2a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 2, "marks_confidence": "derived", "question_text": "Scríobh síos ceithre fhachtóir 45, seachas 1 agus 45.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Freagra: 3, 5, 9, 15. Parts (a) and (b) share a 5-mark scale (5D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q2ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "Bíonn crannchur seachtainiúil á reáchtáil ag Mícheál. Cosnaíonn sé timpeall €80 chun gach crannchur a reáchtáil, na duaiseanna curtha san áireamh. Faigheann sé timpeall €400 as ticéid a dhíol do gach ceann de na crannchuir. Oibrigh amach an brabús a dhéanann Mícheál as gach ceann de na crannchuir.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Brabús = €400 − €80 = €320 in aghaidh an chrannchuir. (Scála 15C roinnte le (a)(ii).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q2aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "Oibrigh amach an líon is lú crannchur is gá do Mhícheál a reáchtáil chun brabús níos mó ná €1000 a dhéanamh. Taispeáin do chuid oibre.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "320 + 320 + 320 = 960 < 1000; 320 + 320 + 320 + 320 = 1280 > 1000, mar sin 4 crannchur. (Scála 15C roinnte le (a)(i).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q2b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 3, "marks_confidence": "derived", "question_text": "Slánuimhir is ea n, atá níos mó ná 1. Níl aici ach dhá fhachtóir: 1 agus n. Cuir tic (✓) sa bhosca ceart chun a thaispeáint cén t-ainm a thugtar d'uimhir den chineál sin. Cuir tic i mbosca amháin. (Roghanna: ilchodach, príomhúil, cearnach)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Tic curtha leis an uimhir phríomha (príomhúil). Parts (a) and (b) share a 5-mark scale (5D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q2b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Buann Siobhán agus Ava an pota óir i gcrannchur. Roinneann siad é sa chaoi is go bhfaigheann Siobhán €25 000 agus go bhfaigheann Ava €45 000. Scríobh an cóimheas 25 000 : 45 000 san fhoirm is simplí.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "25 000 : 45 000 = 5 : 9. (Scála 5B.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q2c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Slánuimhir is ea p. Seachas 1 agus p, is é 7 an t-aon fhachtóir eile atá ag p. Oibrigh amach luach p.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "p = 49. Parts (c) and (d) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q2ci", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Is mar seo a leanas a bhí na potaí óir i gcrannchur Éireannach agus i gcrannchur Meiriceánach: Pota óir Éireannach = €4·8 milliún; Pota óir Meiriceánach = $5·3 milliún. Ba é an ráta malairte ag an am sin ná €1 = $1·15. Taispeáin go raibh luach níos mó ar an bpota óir Éireannach ná mar a bhí ar an bpota óir Meiriceánach.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Pota Éireannach i ndollair = 4·8 × 1·15 = $5·52 milliún. Ós rud é go bhfuil $5·52 milliún > $5·3 milliún, bhí luach níos mó ar an bpota óir Éireannach. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q2cii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Tabhair sampla de ráta malairte a d'fhágfadh luach níos mó ar an bpota óir Meiriceánach ná ar an bpota óir Éireannach. €1 = $ [ ].", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Aon ráta faoi bhun an ráta tairsí 5·3 ÷ 4·8 = $1·10416..., toisc go dtugann 5·3 ÷ 1·15 = €4·61 milliún < €4·8 milliún. Sampla: €1 = $1 (nó luach dearfach ar bith níos lú ná $1·10416). (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q2d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Scríobh síos ceithre fhachtóir 12k + 8, seachas 1 agus 12k + 8. Ní mór dhá cheann de na fachtóirí a bheith i dtéarmaí k.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Freagra: 2, 4, 3k + 2, 6k + 4. Parts (c) and (d) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q3a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Is é 56 000 000 km, ar a laghad, an fad slí idir an Domhan agus Mars. Scríobh an fad slí sin san fhoirm a × 10^n km, áit a mbeidh 1 ≤ a < 10 agus n ∈ N.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "56 000 000 = 5·6 × 10^7 [km]. Parts (a) and (b) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q3ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": 8, "marks_confidence": "derived", "question_text": "Is é €29 000 pá comhlán Alex in aghaidh na bliana. Íocann sí cáin ioncaim ag ráta 20%. Faigh 20% de €29 000.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "29 000 × 0·2 = €5800. (Scála 15C roinnte le (a)(ii).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q3aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": 7, "marks_confidence": "derived", "question_text": "Is é €3400 an creidmheas cánach atá ag Alex. Oibrigh amach pá glan Alex in aghaidh na bliana.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "29 000 − 5800 + 3400 = €26 600. (Scála 15C roinnte le (a)(i).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q3b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Is é 0·0075 cm trastomhas ribe gruaige duine, a bheag nó a mhór. Scríobh an trastomhas sin san fhoirm b × 10^n cm, áit a mbeidh 1 ≤ b < 10 agus n ∈ Z.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "0·0075 = 7·5 × 10^−3 [cm]. Parts (a) and (b) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q3b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Cheannaigh Alex gluaisrothar in 2017. Ba é an luach air ná €14 000, ag an am sin. Tar éis bliain amháin, ba é an luach air ná €12 600. Scríobh €12 600 mar chéatadán de €14 000.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(12 600 / 14 000) × 100 = 90%. (Scála 5C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q3c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Bhí Lewis ag tiomáint ag 90 km san uair nuair a lig sé sraoth. Agus sraoth á ligean aige, bhí a shúile dúnta ar feadh leathshoicind. Oibrigh amach an méad méadar a thaistil sé le linn an ama sin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "90 km/uair × 1000 = 90 000 m/uair; ÷60 = 1500 m/nóim; ÷60 = 25 m/soic; 25 ÷ 2 = 12·5 [m] i leathshoicind. Scála 5C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q4", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Tá Damien ag crochadh scátháin de bhalla. Tá an balla 330 cm ar leithead agus tá an scáthán 100 cm ar leithead. Is mian le Damien an scáthán a chrochadh i lár an bhalla, mar a thaispeántar. Oibrigh amach luach L, an fad ón scáthán go dtí gach taobh an bhalla.", "has_images": true, "image_notes": "Léaráid de bhalla dronuilleogach 330 cm ar leithead le scáthán dronuilleogach 100 cm ar leithead lonnaithe i lár an bhalla. Tá fad L marcáilte ar gach taobh idir imeall an scátháin agus imeall an bhalla (L ar chlé agus L ar dheis).", "topic": "Number", "marking_scheme_answer": "L = (330 − 100) / 2 = 115 cm. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q4ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)(i)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Is é €52 460 ioncam comhlán bliantúil Cháit. Baintear 8·5% de sin mar ranníocaíocht pinsin. Is é an méid atá fágtha ná ioncam inchánach Cháit. Oibrigh amach ioncam inchánach Cháit, tar éis na ranníocaíochtaí pinsin a bhaint.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "0·085 × 52 460 = 4459·10; Ioncam incháinithe = 52 460 − 4459·10 = [€]48 000·90. Scála 10C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q4aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)(ii)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Íocann Cáit cáin ioncaim ar a hioncam inchánach ag ráta 20% ar an gcéad €34 000, agus 40% ar an iarmhéid. Tá creidmheasanna cánach bliantúla aici ar fiú €4200 iad. Oibrigh amach ioncam glan Cháit, tar éis cáin ioncaim a bhaint.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Céim 1: 0·2 × 34 000 = 6 800. Céim 2: (48 000·90 − 34 000) = 14 000·90; 0·4 × 14 000·90 = 5 600·36. Céim 3: 6 800 + 5 600·36 = 12 400·36; − 4 200 = 8 200·36. Céim 4: 48 000·90 − 8 200·36 = [€]39 800·54. Scála 10D.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q4b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "3 mhí ó shin, fuair Cáit bille cárta creidmheasa do €420. Is é an ráta úis ar a cárta creidmheasa ná 2% sa mhí, agus iolraítear an t-ús go míosúil. Níl aon chuid den bhille íoctha aici go fóill. Oibrigh amach méid an bhille anois. Bíodh do fhreagra in euro, ceart go dtí an cent is gaire.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "420 × 1·02^3 = €445·71. (Nó iarrtha mí ar mhí: 420 × 0·02 = 8·40, 428·40 × 0·02 = 8·57, 436·97 × 0·02 = 8·74, bille anois = €445·71.) Scála 5C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q4c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Cheannaigh Cáit gluaisrothar anuraidh. Caillfidh 10% den luach an gluaisrothair ón am a cheannaigh Cáit é. Is é €12 150 luach an ghluaisrothair anois. Oibrigh amach luach an ghluaisrothair nuair a cheannaigh Cáit é.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "12 150 = 90% leis an mbunluach; 12 150 / 0·9 = €13 500. Scála 10B.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q5", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Réitigh an chothromóid: (2x + 3)/5 = 7.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2x + 3 = 35; 2x = 32; x = 16. (Scála 5C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q5a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 2, "marks_confidence": "derived", "question_text": "Is mar seo a leanas atá na tacair A, B, agus C: Is é A tacar iolraithe 2 = {2, 4, …}; Is é B tacar iolraithe 3 = {3, 6, …}; Is é C tacar iolraithe 4 = {4, 8, …}. Scríobh síos uimhir atá in A ∩ B ∩ C.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Freagra: is ionann iolrú ar bith de 12 (e.g. 12). Parts (a) and (b) share a 5-mark scale (5C).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q5b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 3, "marks_confidence": "derived", "question_text": "Mínigh cén fáth a bhfuil C ina fho-thacar de A.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "A is tacar ré-uimhreacha; C is tacar ré-uimhreacha (iolraithe 4). Is ionann gach iolrú de 4 agus ré-uimhir, mar sin is ionann C agus fo-thacar A. (Nó míniú bailí ar bith eile.) Parts (a) and (b) share a 5-mark scale (5C).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q5c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeántar na tacair sin A, B, agus C sa léaráid Venn thíos. Tá 7 réigiún éagsúla sa léaráid Venn. Toisc go bhfuil C ina fho-thacar de A, tá dhá réigiún sa léaráid Venn nach bhfuil baill ar bith iontu. Scríobh X i ngach ceann den dá réigiún sin sa léaráid Venn thuas.", "has_images": true, "image_notes": "Three-circle Venn diagram inside universal rectangle. Left circle A (iolraithe 2), right circle B (iolraithe 3), bottom circle C (iolraithe 4), all overlapping to give 7 regions. Candidate marks X in the two empty regions: the part of C outside A (i.e. C-only region and the B∩C-only region not in A) — the regions of C that lie outside A.", "topic": "Number", "marking_scheme_answer": "Mark X in the two regions of C that lie outside A (the regions that have no members because C ⊂ A). Sample diagram shows X in the C-only region and in the (B∩C)-not-A region. Parts (c) and (d) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q5d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Tá baill ag gach ceann de na cúig réigiún eile sa léaráid Venn. I ngach ceann de na cúig réigiún sin sa léaráid Venn thuas, scríobh ceann amháin de na baill atá sa réigiún sin.", "has_images": true, "image_notes": "Same three-circle Venn diagram (A iolraithe 2, B iolraithe 3, C iolraithe 4). Candidate writes one member in each of the five non-empty regions. Sample answers: A-only e.g. 2, B-only e.g. 3, A∩B-only e.g. 6, A∩C-only e.g. 4 (or 8), A∩B∩C e.g. 12.", "topic": "Number", "marking_scheme_answer": "Sample (from scheme diagram): A-only ≈ 2, A∩B-only = 6, B-only = 3, A∩C region = 4, A∩B∩C = 12 (one valid member per region). Parts (c) and (d) share a 10-mark scale (10D); for an example fully correct entry need one member in each of the 5 regions including at least one with X for (c).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q6a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 8, "marks_confidence": "derived", "question_text": "Rith Poppy agus Ella rás 5 km. Taispeánann an graf simplithe thíos an t-am a thóg Ella chun d km a rith le linn an rása. Tá ceann de na pointí ar an ngraf marcáilte A. Tá fad an ráis ar an ais chothrománach. Dá bhrí sin, mar shampla, thóg Ella 26 nóiméad chun an 5 km iomlán a rith. Bain úsáid as na figiúirí sa tábla, agus tarraing graf ar an léaráid thuas a thaispeánfaidh an t-am a thóg Poppy chun d km a rith le linn an ráis, le haghaidh 0 ≤ d ≤ 5 agus d ∈ R.", "has_images": true, "image_notes": "Line graph: x-axis 'Fad slí an rais, d (km)' 0 to 5; y-axis 'Am iomlán (nóiméad)' 0 to 30. Ella's line is a straight line from (0,0) through point A at (2,10) up to (5,26 approx). Point A marked at d=2, time=10. Candidate must draw Poppy's line from the table (Poppy passes (0,0),(1,5),(2,10),(3,17 from table?),(4,24),(5,30)).", "topic": "Functions", "marking_scheme_answer": "Draw Poppy's graph through 6 points including (0,0): (0,0),(1,5),(2,10),(3,17),(4,24),(5,30). Points connected as an increasing function of d. Parts (a) and (b) share a 15-mark scale (15D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q6a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Taispeántar an chéad trí phatrún i seicheamh (Patrún 1, Patrún 2, Patrún 3 déanta as cearnóga beaga). Tarraing Patrún 4 sa seicheamh.", "has_images": true, "image_notes": "Seicheamh de phatrúin chearnóga: Patrún 1 = 2 chearnóg (cruth coirnéil), Patrún 2 = 5 chearnóg (eangach 2×2 le cearnóg amháin breise ar barr ar chlé), Patrún 3 = 10 gcearnóg (eangach 3×3 le cearnóg amháin breise ar barr ar chlé). Tá líon na gcearnóg ag fás de réir n²+1.", "topic": "Algebra", "marking_scheme_answer": "Patrún 4 = eangach cearnóg 4×4 (16 chearnóg) le cearnóg amháin bhreise ar barr ar chlé, 17 gcearnóg san iomlán. (Scála 10B.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q6b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 7, "marks_confidence": "derived", "question_text": "Bain úsáid as graf Ella chun an trí luach atá ar iarraidh a líonadh isteach sa tábla thíos. Tábla: Fad slí an rais (km) | Am iomlán a thóg Poppy (nóiméad) | Am iomlán a thóg Ella (nóiméad). Rónna: 1 → Poppy 5; 2 → Poppy 10; 3 → Poppy 17; 4 → Poppy 24; 5 → Poppy 30, Ella 26. (Líon isteach na hamanna Ella ar iarraidh do 2, 3, 4 km.)", "has_images": true, "image_notes": "Table with columns: Fad slí (km) = 1,2,3,4,5; Am iomlán a thóg Poppy (nóiméad) = 5,10,17,24,30; Am iomlán a thóg Ella (nóiméad) = blank,blank,blank,blank,26. Read Ella's times from her graph for 2,3,4 km.", "topic": "Functions", "marking_scheme_answer": "Ella's times read from her graph: 2 km → 8, 3 km → 14, 4 km → 20 (5 km = 26 given). Parts (a) and (b) share a 15-mark scale (15D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q6b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Líon isteach an tábla sa chaoi go dtaispeánfar líon na gcearnóg beag atá i ngach ceann de na chéad cheithre phatrún. (Tábla: Patrún 1, 2, 3, 4 le líon cearnóg beag; tugtar Patrún 2 = 5.)", "has_images": true, "image_notes": "Tábla le dhá cholún: 'Patrún' (1, 2, 3, 4) agus 'Líon cearnóg beag'. Tá luach 5 tugtha do Phatrún 2; tá na cealla eile le líonadh isteach.", "topic": "Algebra", "marking_scheme_answer": "Patrún 1 = 2; Patrún 2 = 5; Patrún 3 = 10; Patrún 4 = 17. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q6c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Taispeáin nach seicheamh cearnach atá in amanna Poppy sa tábla.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Amanna Poppy: 5, 10, 17, 24, 30. Céad difríochtaí: 5, 7, 7, 6. Dara difríochtaí: 2, 0, −1 — níl na dara difríochtaí tairiseach, mar sin ní seicheamh cearnach é. Scála 5C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q6c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Is é líon na gcearnóg beag i bPatrún n: n^2 + 1. Bain úsáid as sin agus líon na gcearnóg beag i bPatrún 20 a oibriú amach agat.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(20)^2 + 1 = 400 + 1 = 401. (Scála 10D roinnte le (d).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q6d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Thóg Ella 26 nóiméad chun an 5 km a rith. Oibrigh amach meánluas Ella sa rás. Bíodh do fhreagra ina km san uair, ceart go dtí dhá ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Luas = Fad/Am = (5/26) × 60 = 11·54 [km/uair]. (Nó 5 km = 26 nóiméad, 1 km = 5·2 nóiméad, 60 ÷ 5·2 = 11·54 km/uair.) Parts (d) and (e) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q6d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Cén cineál seichimh a dhéantar le líon na gcearnóg beag i ngach patrún? Cuir tic (✓) i mbosca amháin. Tabhair cúis le do fhreagra. (Roghanna: líneach / cearnach / easpónantúil.)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Cearnach. Cúis: tá an dara difríocht ina tairiseach, nó tá an seicheamh san fhoirm n^2 (+1). (Scála 10D roinnte le (c).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q6e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(e)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Cuir tic (✓) sa bhosca ceart chun a thaispeáint céard a tharla do luas Ella tar éis 2 km, atá marcáilte A ar an ngraf. Cuir tic i mbosca amháin. Cosain do fhreagra. (Roghanna: méadaíodh luas Ella, laghdaíodh luas Ella, níor athraigh luas Ella.)", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Freagra: Laghdaigh luas Ella. Cosaint: ghlac an chéad dhá chiliméadar 8 nóiméad agus ghlac an chéad dá cheann eile 12 nóiméad (slope/luas níos lú tar éis 2 km). Parts (d) and (e) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q6f", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(f)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Rith Ciarán an rás 5 km freisin. Tarraing sé an graf thíos a léiríonn an méid ama a thóg sé air chun d km a rith le linn an rása. Is líne cheartingearach an chuid sin den ghraf Chiaráin atá marcáilte C. Cén t-eolas a thugann cuid C dúinn faoi iompar reatha Chiaráin sa chuid sin den rás? Tabhair an oiread sonraí agus is féidir.", "has_images": true, "image_notes": "Line graph: x-axis 'Fad slí an rais, d (km)' 0 to 5; y-axis 'Am iomlán (nóiméad)' 0 to 30. Ciarán's graph rises then has a vertical (ceartingearach) segment marked C around d=2 to 3, indicating time passing with no distance change.", "topic": "Functions", "marking_scheme_answer": "Stop Ciarán ag rith ar feadh 5 nóiméad (the vertical segment means time increased while distance stayed the same — he stopped running). Parts (f) and (g) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q6g", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(g)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Deir Breandán: \"Ní thaispeánann graf Chiaráin an t-am iomlán mar fheidhm faoi (d).\" Tabhair cúis go bhfuil an ceart ag Breandán.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Ní féidir le hionchur ach aschur amháin a bheith aige, agus mar sin ní féidir le graf feidhme a bheith ingearach (the vertical part means one d-value maps to many times, so it is not a function). (Nó míniú bailí ar bith eile bunaithe ar chuid C den ghraf.) Parts (f) and (g) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q7a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 8, "marks_confidence": "derived", "question_text": "Iolraigh amach agus simpligh (x + 3)(x − 2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x^2 − 2x + 3x − 6 = x^2 + x − 6. (Scála 15C roinnte le (b).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q7ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 3, "marks_confidence": "derived", "question_text": "Déan cur síos ar gach ceann de na tacair seo a leanas. Bí chomh sonrach agus is féidir. (i) Tacar na n-uimhreacha nádúrtha, N.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(Tacar) na slánuimhreacha dearfacha. (Nó míniú bailí ar bith eile.) Part (a) is on a 5-mark scale (5C) covering (i) and (ii).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q7aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 2, "marks_confidence": "derived", "question_text": "Tacar na slánuimhreacha, Z.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(Tacar) na slánuimhreacha dearfacha agus diúltacha agus nialas (the positive and negative whole numbers and zero). Part (a) is on a 5-mark scale (5C) covering (i) and (ii).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q7b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Déan graf den éagothromóid seo a leanas ar an uimhirlíne atá tugtha. Éagothromóid: −3 < x ≤ 2, áit a bhfuil x ∈ R. (Uimhirlíne ó −4 go 4.)", "has_images": true, "image_notes": "A number line from −4 to 4 (ticks at each integer) on which the candidate graphs −3 < x ≤ 2: open circle at −3, closed/filled circle at 2, line shaded between them.", "topic": "Algebra", "marking_scheme_answer": "Number line with open circle at −3 (not included) and closed (filled) circle at 2 (included), with the segment between −3 and 2 shaded. Scála 5B.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q7b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 7, "marks_confidence": "derived", "question_text": "Fachtóirigh x^2 − 64.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x^2 − 64 = (x + 8)(x − 8). (Scála 15C roinnte le (a).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q7c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "Agus ailgéabar á úsáid agat, réitigh an éagothromóid seo a leanas: −7 < 8 − 3g ≤ 11.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "−7 < 8 − 3g ≤ 11 → −15 < −3g ≤ 3 → 15 > 3g ≥ −3 → 5 > g ≥ −1, i.e. g < 5 agus g ≥ −1 (−1 ≤ g < 5). Scála 10C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q8", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Taispeántar sa léaráid Venn thíos an líon daoine i gclub óige (U) a sheinneann ceol (C) agus a imríonn spórt (S), áit a bhfuil n ∈ N. (Léaráid: C amháin = 52; C ∩ S = 184 − n; S amháin = 2n; lasmuigh den dá thacar = 125.) Oibrigh amach an líon uasta daoine a d'fhéadfadh a bheith sa chlub óige.", "has_images": true, "image_notes": "Two-circle Venn diagram inside universal rectangle U. Left circle C contains 52 (C only); overlap C∩S = 184 − n; right circle S only = 2n; region outside both circles = 125. Find maximum total = sum of regions, maximising n.", "topic": "Number", "marking_scheme_answer": "Total = 52 + (184 − n) + 2n + 125 = 361 + n. Need C∩S = 184 − n ≥ 0, so n ≤ 184; maximum at n = 184. Uaslíon = 361 + 184 = 545. Scála 10C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q8a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Rith Poppy agus Ella rás 5 km. Taispeánann an tábla na hamanna iomlána a thóg Poppy agus Ella chun gach fad slí atá tugtha sa rás a rith. Thóg Ella 26 nóiméad chun an 5 km ar fad a rith. Agus an graf á úsáid agat, líon isteach sa tábla na trí luach atá ar iarraidh i gcás Ella. (Tábla: Fad slí 1, 2, 3, 4, 5 km; Am iomlán Ella; Am iomlán Poppy 5, 10, 17, 24, 30.)", "has_images": true, "image_notes": "Tábla a thaispeánann am iomlán (nóiméad) in aghaidh fad slí (km) do Ella agus Poppy. Am iomlán Poppy ar gach km: 1=5, 2=10, 3=17, 4=24, 5=30. Tá luachanna Ella ar iarraidh ach do 5 km = 26. Tugtar graf le pointe A marcáilte agus líne Ella le léamh as.", "topic": "Functions", "marking_scheme_answer": "Luachanna Ella le léamh ón graf: Fad 1 km = 4 nóiméad, 2 km = 8, 3 km = 14, 4 km = 20, 5 km = 26. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q8b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Agus na figiúirí sa tábla á n-úsáid agat, tarraing graf an am léaráid thíos a thaispeánfaidh an t-am a thóg Poppy chun an rás a rith le linn an ráis, le haghaidh 0 ≤ d ≤ 5 agus d ∈ R.", "has_images": true, "image_notes": "Léaráid ghraif le haiseanna: x-ais 'Fad slí an ráis, d (km)' 0 go 5; y-ais 'An t-am iomlán (nóiméad)' 0 go 30. Tá graf líne Ella tarraingthe cheana le pointe A marcáilte; tá líne Poppy le tarraingt trí na pointí (1,5),(2,10),(3,17),(4,24),(5,30).", "topic": "Functions", "marking_scheme_answer": "Tarraing graf Poppy mar líne/cuar tríd na pointí (1,5), (2,10), (3,17), (4,24), (5,30). (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q8c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 8, "marks_confidence": "derived", "question_text": "Cé acu Ella nó Poppy a chríochnaigh an rás ar dtús? Cuir tic (✓) i mbosca amháin. Tabhair cúis le do fhreagra.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Ella (chríochnaigh sí an rás in 26 nóiméad i gcomparáid le 30 nóiméad ag Poppy). (Scála 15D roinnte le (d).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q8d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 7, "marks_confidence": "derived", "question_text": "Cuir tic (✓) sa bhosca ceart a thaispeánfaidh cad a tharla do luas Ella tar éis 2 km, atá marcáilte mar A ar an ngraf. Cuir tic i mbosca amháin. Cosain do fhreagra. (Roghanna: Méadaíodh luas Ella / Laghdaíodh luas Ella / Bhí luas Ella gan athrú.)", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Laghdaíodh luas Ella — ghlac sé níos faide di an chéad chiliméadar eile a rith; d'athraigh an céim [fána] ó 4 nóiméad sa chiliméadar go 6 nóiméad sa chiliméadar. (Scála 15D roinnte le (c).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q8e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(e)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Thóg Poppy 30 nóiméad chun an 5 km a rith. Oibrigh amach meán-luas Poppy don rás, ina km san uair.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "30 nóiméad = 0·5 uair an chloig; meán-luas = 5 / 0·5 = 10 km/uair. (Nó 30 nóiméad → 5 km, mar sin 60 nóiméad → 10 km.) (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q9a", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "D'ordaigh foireann scoile t-léinte agus leath-zipanna. Ordaíonn Jill, Mike, Ted, agus Gary t-léinte (T). Ordaíonn Jill agus Alice leath-zipanna (Z). Ní ordaíonn Ben agus Zena ceachtar díobh. Críochnaigh an léaráid Venn thíos chun na sonraí sin a thaispeáint, áit a bhfuil: U an fhoireann go léir (an tacar uilíoch); T tacar na ndaoine a ordaíonn t-léinte; Z tacar na ndaoine a ordaíonn leath-zipanna.", "has_images": true, "image_notes": "Léaráid Venn le dhá thacar atá ag forluí istigh i ndronuilleog uilíoch U. Tacar T (t-léinte) ar chlé, tacar Z (leath-zipanna) ar dheis. Le líonadh isteach: Mike, Ted, Gary i T amháin; Jill sa trasnú T∩Z; Alice i Z amháin; Ben agus Zena lasmuigh den dá thacar (taobh istigh de U).", "topic": "Probability", "marking_scheme_answer": "T amháin: Mike, Ted, Gary. Trasnú T∩Z: Jill. Z amháin: Alice. Lasmuigh den dá thacar (i U): Ben, Zena. (Scála 10C.)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q9ai", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)(i)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Scríobhann Gertie an seicheamh seo a leanas, a athfhilleann gach trí théarma: 3, 6, 4, 3, 6, 4, 3, … Is é 3 an 1ú téarma. Scríobh síos an 12ú téarma.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "12ú téarma = 4. Part (a) is on a 5-mark scale (5D) covering (i) and (ii).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q9aii", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)(ii)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Oibrigh amach luach an 100ú téarma sa seicheamh sin.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "100 ÷ 3 = 33 fuíleach 1, mar sin beidh an 100ú téarma mar an gcéanna leis an 1ú téarma; 100ú téarma = 3. Part (a) is on a 5-mark scale (5D) covering (i) and (ii).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q9b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Déan cur síos ar conas a fhaightear luach an nú téarma sa seicheamh, áit a bhfuil n ∈ N, gan liosta a dhéanamh de na téarmaí go léir ón 1ú téarma go dtí an nú téarma.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Roinn n faoi 3. Más é an fuílleach = 0 ansin T_n = T_3; más é an fuílleach = 1 ansin T_n = T_1; más é an fuílleach = 2 ansin T_n = T_2. Scála 5C.", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q9b", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 7, "marks_confidence": "derived", "question_text": "Cé mhéad mac léinn, san iomlán, atá ar an bhfoireann? Freagra: [ ].", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "7 mac léinn san iomlán (Jill, Mike, Ted, Gary, Alice, Ben, Zena). (Scála 15D roinnte le (c).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q9c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Leanann seicheamh eile an riail chéanna, ach is é 8 an 1ú téarma. Oibrigh amach an chéad cheithre théarma eile sa seicheamh seo. (Riail: má tá corruimhir é téarma, iolraigh é faoi 2 chun an chéad téarma eile a fháil; má tá ré-uimhir é téarma, suimigh 2 leis agus faigh leath den fhreagra chun an chéad téarma eile a fháil, is é sin 1/2 × (téarma + 2).)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Seicheamh: 8, 5, 10, 6, 4 (i.e. the next four terms after 8 are 5, 10, 6, 4). Parts (c) and (d) share a 5-mark scale (5D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-ordinary-level-IV-q9c", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 8, "marks_confidence": "derived", "question_text": "Scríobh gach ceann de na téarmaí ón liosta seo a leanas isteach sa spás ceart sa tábla thíos, chun gach téarma i ndaireacht tacar a mheaitseáil leis an gcur síos a bhaineann leis. Is é Z' comhlánú Z. (Téarmaí: T\\Z, T∩Z, Z'. Sraitheanna: 1 = Na mic léinn a d'ordaigh t-léinte agus leath-zipanna araon; 2 = Na mic léinn a d'ordaigh leath-zipanna ach nár ordaigh t-léinte; 3 = Na mic léinn nár ordaigh leath-zipanna.)", "has_images": true, "image_notes": "Tábla le dhá cholún ('Cur síos' agus 'Nodaireacht tacar') agus trí shraith uimhrithe (1, 2, 3). Tá na cuir síos tugtha; tá na téarmaí nodaireachta le meaitseáil leo.", "topic": "Probability", "marking_scheme_answer": "Sraith 1 (t-léinte agus leath-zipanna araon) = T∩Z; Sraith 2 (leath-zipanna ach nár ordaigh t-léinte) = Z\\T; Sraith 3 (nár ordaigh leath-zipanna) = Z'. (Scála 15D roinnte le (b).)", "source_pdf": "2019 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q9d", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Roghnaíonn Ahmed 2 mar 1ú téarma, agus déanann sé seicheamh leis an riail chéanna á húsáid aige. Luaigh céard is meánghnách faoi sheicheamh Ahmed. D'fhéadfadh sé bheith ina chabhair agat cuid de na téarmaí sa seicheamh a oibriú amach.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Fanfaidh a sheicheamh tairiseach ag 2 (nó a choibhéis): the sequence stays constant at 2, i.e. 2, 2, 2, … Parts (c) and (d) share a 5-mark scale (5D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q9e", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(e)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "I seicheamh eile ina bhfuil an riail chéanna á húsáid, is é 86 an 2ú téarma. Oibrigh amach an dá luach éagsúla a d'fhéadfadh a bheith ar an 1ú téarma sa seicheamh seo. (Freagra: __, 86, … nó __, 86, …)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "86 ÷ 2 = 43 (i.e. if 1st term was odd, 43 × 2 = 86) agus 86 × 2 − 2 = 170 (i.e. if 1st term was even 170: 1/2(170+2) = 86). So the two possible 1st terms are 43 and 170. Parts (e) and (f) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2019-higher-level-IV-q9f", "subject_n": "Mathematics", "year": 2019, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(f)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "I gcás seicheamh eile a leanann an riail chéanna, tosaíonn sé leis an uimhir k, ar corruimhir í. Oibrigh amach an chéad trí théarma eile sa seicheamh seo. Bíodh gach téarma ina fhoirm is simplí i dtéarmaí k. (Freagra: k, __, __, __)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "k × 2 = 2k (ré-uimhir); 1/2(2k + 2) = k + 1 (ré-uimhir); 1/2((k+1) + 2) = (k+3)/2. Freagra: k, 2k, k + 1, (k+3)/2. Parts (e) and (f) share a 10-mark scale (10D).", "source_pdf": "2019 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q1a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Jane buys a laptop online for €699, plus a shipping cost of €30. The exchange rate is $1 = €0·90. Work out in euro the total cost to Jane of buying the laptop online.", "has_images": true, "image_notes": "Photo of a grey laptop, open, shown beside the question. Decorative; the cost figures (€699 and €30) are given in the text.", "topic": "Number", "marking_scheme_answer": "(699 + 30) × 0·9 = 729 × 0·9 = €656·10. (Scale 10B: full credit €656·10.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q1ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "Find the value of each of the following.\n(i) 243 + 178", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q1aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "Find the value of each of the following.\n(ii) 7·2 × 6", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(21·6)/5 or 43·2 = 43·2", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q1aiii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "Find the value of each of the following.\n(iii) 24 ÷ (9 − 7)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "24 ÷ 2 = 12", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q1aiv", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(iv)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "Find the value of each of the following.\n(iv) 3^4", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q1b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "Write down the whole number that is nearest to 15·8.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q1bi", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Jane has a gross annual income of €56 000. Jane pays income tax on her gross income at a rate of 20% on the first €44 300, and 40% on the balance. Work out Jane's annual income tax at each of these two rates (20% and 40%). Income tax at 20% = €___ Income tax at 40% = €___", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Tax at 20% = 0·2 × 44 300 = €8860. Tax at 40% = 0·4 × (56 000 − 44 300) = 0·4 × 11 700 = €4680. (Scale 10C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q1bii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Jane has annual tax credits of €3300. Work out Jane's annual take-home pay.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "56 000 − 8860 − 4680 + 3300 = €45 760. (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q1c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 2, "marks_confidence": "derived", "question_text": "What number is half way between 16 and 30?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "30 − 16 = 14, 14 ÷ 2 = 7, 16 + 7 = 23 (OR (16+30)/2 = 46/2 = 23)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q10a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Ali and Jon took part in a triathlon. In the triathlon they had to complete a 5 km kayak, then a 25 km cycle, and then a 10 km run. The diagram shows how many minutes more than Jon (or less than Jon) it took Ali to travel x km in the triathlon, for 0 ≤ x ≤ 40. For example, the point A shows that it took Ali 1 minute more than Jon to travel the first 10 km. In total, it took Ali 1 minute less than Jon to finish the triathlon. Did Ali finish the kayak section ahead of Jon, behind Jon, or at the same time as Jon? (Tick one box only.)", "has_images": true, "image_notes": "A line graph. x-axis 'Distance Travelled in the Triathlon, d (km)' from 0 to 40, with shaded bands: Kayak (0–5), Cycle (5–30), Run (30–40). y-axis 'How many minutes: more than Jon (it took Ali) above the axis / less than Jon (it took Ali) below the axis', roughly −2 to +2. The plotted curve starts above zero (Ali slower) through point A near (10, +1), descends through point B near (25, lower), with a sharp vertical drop near x ≈ 25 (a stop), ending below zero so Ali finishes 1 minute ahead overall.", "topic": "Functions", "marking_scheme_answer": "Behind Jon (the curve is above zero at the start of the kayak section, i.e. Ali took more time). (Scale 10C shared across 10(a) and 10(b).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q10a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Write the following as a single fraction in its simplest form:\n2/3 + 5/7", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "14/21 + 15/21 = 29/21 (1 8/21)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q10b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Ali had to stop briefly during the triathlon. Jon did not stop. State what distance Ali had travelled when he stopped, and for how long he was stopped. Distance Ali had travelled (in km): ___ Length of time Ali was stopped (in minutes): ___", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Distance = 25 km; Length of time stopped = 1·5 minutes (read from the vertical jump in the graph). (Scale 10C shared with 10(a).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q10b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Solve the following equation in k:\n4k − 7 = 41", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4k − 7 = 41, 4k = 41 + 7, 4k = 48, k = 12", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q10c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "What was happening to Jon and Ali at the point marked B on the diagram?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Any valid description: at B the difference is zero, so Ali and Jon were level / had taken the same total time / Ali had caught up with Jon at that distance. (Scale 10B.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q10d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(d)", "parent_question": "10", "marks": 20, "marks_confidence": "high", "question_text": "The table shows the time it took Jon to complete each of the three sections in the triathlon, as well as his total time. Using the diagram, fill in the four missing times for Ali. Jon's time (minutes): Kayak 32, Cycle 38, Run 36, Total 106. Ali's time (minutes): Kayak ___, Cycle ___, Run ___, Total ___.", "has_images": true, "image_notes": "A table with columns Kayak, Cycle, Run, Total and two rows. Jon's time row: 32, 38, 36, 106. Ali's time row: all four cells blank, to be completed from the graph.", "topic": "Functions", "marking_scheme_answer": "Ali's times: Kayak 34, Cycle 35, Run 36, Total 105. (Scale 20C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q10e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(e)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Jon and Ali also ran a 400 m race. Jon's average speed for the 400 m was 7·8 metres per second. It took Ali 2 seconds more than Jon to run the 400 m. Work out Ali's average speed for the 400 m. Give your answer in metres per second, correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Jon's time = 400/7·8 = 51·282... s. Ali's time = 51·282 + 2 = 53·282 s. Ali's speed = 400/53·282 = 7·50... ≈ 7·5 m/s (1 d.p.). (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q11", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "The line h has a slope of 4 and passes through the point (20, 12). Find the co-ordinates of another point on the line h, other than the point (20, 12). Show your working out. Answer = ( , )", "has_images": true, "image_notes": "A coordinate diagram with x- and y-axes. A red line h with positive steep slope is drawn; it is labelled 'Slope = 4' and passes through the marked point (20, 12).", "topic": "Coordinate Geometry", "marking_scheme_answer": "Slope = (y − 12)/(x − 20) = 4. Choosing x = 21: y = 12 + 4 = 16, so another point is (21, 16). (Any point on the line is acceptable.) (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q11ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(i)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Two friends are building a skate-board ramp. They each have a different design for the ramp.\n(a) Tracey draws the following diagram as part of her design for the ramp. It is made up of a triangle and a square. The angle A is marked. (Triangle base 3·5 cm, then a 2 cm × 2 cm square; the slanted side rises to height 2 cm; angle A is at the bottom-left of the triangle.) It is drawn to a scale of 1:100.\n(i) Construct a scale diagram of this part of the design for the ramp in the grid below, to a scale of 1:50. Each side in your diagram should be twice the length of the corresponding side in Tracey's diagram. One side is already done for you (a 4 cm vertical side).", "has_images": true, "image_notes": "Tracey's design: a right-angled triangle of base 3·5 cm and height 2 cm joined to a 2 cm × 2 cm square (height marked 2 cm, base segments 3·5 cm and 2 cm), with angle A at the bottom-left of the triangle. A photo of a person on a skateboard ramp is also shown. The answer grid already has one vertical side drawn, labelled 4 cm (the doubled square side). Student must construct the figure at twice each length (base triangle 7 cm, square side 4 cm).", "topic": "Geometry", "marking_scheme_answer": "Scale diagram drawn with all sides doubled: triangle base 7 cm and height 4 cm joined to a 4 cm × 4 cm square (line segment construction, ruler used).", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q11aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(ii)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "(a)(ii) Measure the size of the angle A in Tracey's diagram above.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "30° (accept 28 ≤ A ≤ 32)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q11b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Sinéad has a different design for the ramp. Part of Sinéad's design is the right-angled triangle in the diagram below (not to scale). One of the sides is marked B. One of the angles is marked C. (Vertical side 96 cm, horizontal side 180 cm, right angle between them; B is the hypotenuse; C is the angle at the bottom-right.)\n(b) Use the Theorem of Pythagoras to work out the length of the side B in Sinéad's design. Give your answer in cm.", "has_images": true, "image_notes": "Right-angled triangle (not to scale): vertical side 96 cm on the left, horizontal side 180 cm along the bottom, right angle at the bottom-left. Hypotenuse (slanted top side) labelled B. Angle C is marked at the bottom-right vertex.", "topic": "Geometry", "marking_scheme_answer": "B^2 = 96^2 + 180^2 = 9216 + 32400 = 41616, B = √41616 = 204 cm", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q11c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Sinéad knows that, for the angle C, tan C = 96/180. Use your calculator to find the size of the angle C, correct to the nearest degree.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "tan^-1(96/180) = 28·07... = 28 [°]", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q12", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "The diagram shows the circle k (not to scale). The points A, B, and C lie on the circle. [AB] is a diameter of the circle, and |AC| = 8 cm. The area of the circle k is 25π cm^2. Work out the size of the smallest angle in the triangle ABC.", "has_images": true, "image_notes": "Circle k with centre marked. Points A (lower left), B (right) and C (top) lie on the circumference. [AB] passes through the centre as a diameter. Chord AC is labelled 8 cm. Triangle ABC is drawn inside the circle (diagram not to scale).", "topic": "Geometry", "marking_scheme_answer": "Area = πr^2 = 25π → r = 5, so diameter |AB| = 10. Angle ACB = 90° (angle in a semicircle). |BC| = √(10^2 − 8^2) = 6, so the smallest side is BC, opposite ∠A. sin(∠CAB) = 6/10 (or cos ∠CAB = 8/10) → ∠CAB = 36·87°. Smallest angle ≈ 36·87°. (Scale 10D.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q12a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "In January 2021, people were allowed to travel 5 km from their home to exercise.\n(a) Write km or km^2 into each box below to complete the following sentence correctly. Use each one only once. 'Area is measured in ____ and distance is measured in ____.'", "has_images": true, "image_notes": "A map showing a circle of radius 5 km around a home location, with a '5 km' arrow from the centre to the edge of the circle. (Decorative; data: circle radius 5 km.)", "topic": "Geometry", "marking_scheme_answer": "Area is measured in km^2 and distance is measured in km.", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q12b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "(b) Use the following formula to work out the circumference of a circle with a radius of 5 km. Give your answer correct to 1 decimal place.\n2 × π × r =", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "2 × π × 5 = 31·41... = 31·4 [km] (1 d.p.)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q12c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "(c) Use a different formula to work out the area of a circle with a radius of 5 km. Give your answer correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "π × r^2 = π × 5^2 = 78·53... = 78·5 [km^2] (1 d.p.)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q12d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(d)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "The tables below show the circumference and area of a circle in terms of π, as the radius increases by 2 units. One of these is a linear sequence; the other is not. Sequence 1 (Circumference): 8π, 12π, 16π, 20π, 24π. Sequence 2 (Area): 16π, 36π, 64π, 100π, 144π. Tick (✓) the correct box to show which of these sequences is linear. Give a reason for your answer.", "has_images": true, "image_notes": "Two tables. Sequence 1 (Circumference): 8π, 12π, 16π, 20π, 24π. Sequence 2 (Area): 16π, 36π, 64π, 100π, 144π. Tick boxes for 'Sequence 1' / 'Sequence 2' and a box to write a reason.", "topic": "Algebra", "marking_scheme_answer": "Sequence 1 is linear. Reason (any valid): it goes up by the same amount each time (constant first difference of 4π); Sequence 2 changes by different amounts.", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q13a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 2, "marks_confidence": "derived", "question_text": "Simplify 2a − 5n + 2n + 6a.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2a + 6a − 5n + 2n = 8a − 3n", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q13b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 2, "marks_confidence": "derived", "question_text": "y = (3n + 70)/5. Work out the value of y when n = 10.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "y = (3(10) + 70)/5 = 100/5 = 20", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q13c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 1, "marks_confidence": "derived", "question_text": "Factorise the quadratic expression x^2 − 7x + 12.\nx^2 − 7x + 12 = (x )( )", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x − 3)(x − 4)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q2a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "When Maeve's team play a match, they can win (W), draw (D), or lose (L). Fill in the table below to show the 9 possible outcomes when Maeve's team play two matches. One is already done. W D means that they win Match 1 and draw Match 2.", "has_images": true, "image_notes": "A 3×3 outcome table. Columns are Match 2 = W, D, L; rows are Match 1 = W, D, L. The W-row / D-column cell is pre-filled with 'W D'. The remaining 8 cells must be filled with the ordered outcome pairs. A decorative photo of a football beside the table.", "topic": "Probability", "marking_scheme_answer": "Table of 9 ordered outcomes — Match1 W: WW, WD, WL; Match1 D: DW, DD, DL; Match1 L: LW, LD, LL (the 8 entries other than the given WD). (Scale 15D shared across 2(a) and 2(b); full scale = 15.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q2ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "A restaurant has the following menu, with 4 main courses and 3 desserts. Main Course prices: Fish €16·95, Steak €18·95, Pasta €14·95, Pizza €15·95. Dessert prices: Ice-cream €3·50, Cheesecake €4·95, Brownie €4·50.\n(a)(i) John orders a steak and cheesecake. Work out the price of John's meal.", "has_images": true, "image_notes": "Two price-list tables. Main Course / Price €: Fish 16·95, Steak 18·95, Pasta 14·95, Pizza 15·95. Dessert / Price €: Ice-cream 3·50, Cheesecake 4·95, Brownie 4·50. (Also a decorative photo of a plated meal.)", "topic": "Number", "marking_scheme_answer": "18·95 + 4·95 = €23·90", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q2aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "(a)(ii) John pays for the meal with a €50 note. How much change should he get?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "50 − 23·90 = €26·10", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q2b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "Maeve thinks that each outcome in the table is equally likely. Based on this, find the probability that, when Maeve's team play two matches, they win at least one match. Give your answer as a fraction.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "P(win at least one) = 5/9. (Scale 15D shared with 2(a); 15-mark scale 0,4,8,12,15 split across the two parts.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q2b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Michelle picks one main course and one dessert. In how many different possible ways could she do this? For example, one possible way is to pick fish and ice-cream.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "4 × 3 = 12 (4 main courses × 3 desserts = 12 outcomes)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q2c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Maeve's team play 5 matches in a competition. Work out the total number of different outcomes for Maeve's team for these 5 matches. For example, one possible outcome would be W W L D W.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "3^5 = 243. (Scale 10C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q2c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Gina orders food costing €72. Gina gives a tip of 15% of this cost, rounded to the nearest euro. Work out how much Gina gives as a tip.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "72 × 15/100 = 10·8 ≈ €11 (rounded to nearest euro)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q2d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Maeve's team plays 11 matches in a league. The table below shows the number of goals that Maeve's team score in each of these 11 matches: 3, 1, 1, 0, 2, 7, 1, 0, 2, 1, 3. Work out the mean number of goals that Maeve's team score per match. Give your answer correct to 1 decimal place.", "has_images": true, "image_notes": "A single-row table of 11 values listing goals scored per match: 3, 1, 1, 0, 2, 7, 1, 0, 2, 1, 3.", "topic": "Statistics", "marking_scheme_answer": "Mean = (3+1+1+0+2+7+1+0+2+1+3)/11 = 21/11 = 1·9 (1 d.p.). (Scale 10B.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q2d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "There are 5 waiters and 3 kitchen staff working in the restaurant. At the end of each night, the tips are all added together, and are then split evenly between these 8 people. One night, the 3 kitchen staff get a combined total of €96 in tips. Work out the total value of all the tips that evening.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3 people: €96, so 1 person: 96 ÷ 3 = €32, 8 people: 8 × 32 = €256", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q2e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(e)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Complete the pie chart below, to summarise the data above, showing the proportion of their games in which Maeve's team scored 0 goals, 1 goal, and so on. Label each sector and the size of the angle clearly. Show any working out and construction lines.", "has_images": true, "image_notes": "An empty circle with a centre dot drawn on a coordinate grid, for the student to construct a pie chart of the goals-per-match data from part (d).", "topic": "Statistics", "marking_scheme_answer": "0 goals: 2/11 × 360 = 65°; 1 goal: 4/11 × 360 = 131°; 2 goals: 2/11 × 360 = 65°; 3 goals: 2/11 × 360 = 65°; 7 goals: 1/11 × 360 = 33°. (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q3a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "The co-ordinate diagram shows part of the N22 road in County Cork. Two points on the road, P and Q, are marked on the diagram. The point Q has co-ordinates (6, 2). Write down the co-ordinates of the point P. P = ( , )", "has_images": true, "image_notes": "Coordinate diagram of the N22 road, x-axis −4 to 8, y-axis −1 to 5. P is plotted at about (−1, 3) on the upper-left of the road and Q is plotted/labelled near (6, 2) on the right. A road map background with an 'N22' marker between them.", "topic": "Coordinate Geometry", "marking_scheme_answer": "P = (−1, 3). (Scale 10C shared across 3(a) and 3(b); 10-mark scale split across the two parts.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q3a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Joshua estimates that an airbed is roughly in the shape of a rectangular solid. The dimensions of the airbed are 180 cm by 80 cm by 20 cm.\n(a) Use Joshua's values to show that the volume of the airbed is 288 000 cm^3.", "has_images": true, "image_notes": "Photo of a navy rectangular inflatable airbed with labelled dimensions: 180 cm (length), 80 cm (width), 20 cm (height/thickness).", "topic": "Geometry", "marking_scheme_answer": "180 × 80 × 20 = 288 000 cm^3 (Volume = l × b × h)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q3b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "The equation of the line PQ is: x + 7y = 20. Using this, or otherwise, find the co-ordinates of the point where the line PQ crosses the y-axis. Answer = ( , )", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "At y-axis x = 0: 7y = 20, y = 20/7. Answer = (0, 20/7). (Scale 10C shared with 3(a).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q3b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Joshua uses an electric pump to blow up the airbed. The pump blows air into the airbed at a rate of 800 cm^3 per second. Work out how many minutes it will take to fill the airbed with air, using this pump.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "60 × 800 = 48 000 cm^3 per minute; 288 000 ÷ 48 000 = 6 minutes", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q3c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "A new road is being built through the point Q (6, 2). On the co-ordinate diagram, it will be a straight line segment which is perpendicular to PQ. Work out the equation of this new road. Give your answer in the form ax + by + c = 0, where a, b, c ∈ ℝ.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Slope PQ = (2−3)/(6−(−1)) = −1/7, so perpendicular slope = 7. Through (6,2): y − 2 = 7(x − 6) → 7x − y − 40 = 0 (or −7x + y + 40 = 0). (Scale 5D.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q3c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Joshua finishes pumping up the airbed at 9:35 p.m. He goes to bed 45 minutes later. At what time does Joshua go to bed?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "9:35 + 0:45 = 9:80 = 10:20 [p.m.]", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q3d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(d)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "The distance |PQ| on the diagram is 7·1 cm, correct to 1 decimal place. 5 mm on the diagram represents 100 m. Use this to work out the actual distance from P to Q. Give your answer in km.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 mm represents 100 m, so 1 cm represents 200 m. 7·1 cm = 7·1 × 200 = 1420 m = 1·42 km. (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q3d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(d)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Joshua buys the electric pump on the internet for £15·95. The currency conversion rate is €1 = £0·90. Convert £15·95 to euro. Give your answer correct to the nearest cent.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15·95 ÷ 0·9 = €17·72 (OR 1/0·9 = 1·1..., 15·95 × 1·1 = €17·72)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q4a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "The three triangles A, B, and C are shown. The side lengths of each triangle are in centimetres, where x, y ∈ ℕ. Take \"the perimeter\" to mean \"the length of the perimeter\". The perimeter of Triangle A is 8 cm. Two of the sides have length 2 cm and 3·5 cm, respectively, as shown. Work out the length of the third side of Triangle A.", "has_images": true, "image_notes": "Three triangles drawn side by side. Triangle A: sides labelled 2 and 3·5 (third side unknown). Triangle B: sides labelled 3, 2x and base 2x + 1. Triangle C: sides labelled 5, y^2 and y^2 + 3.", "topic": "Algebra", "marking_scheme_answer": "Third side = 8 − (2 + 3·5) = 8 − 5·5 = 2·5 cm. (Scale 5B.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q4ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(i)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Frank and Ciarán each recorded how much mobile data they used each week for five weeks. The graph shows the amount of mobile data Frank used in each of these weeks.\n(a) Based on the graph:\n(i) in which week did Frank use the most mobile data?", "has_images": true, "image_notes": "Line graph titled by axis labels. Y-axis: 'Amount of mobile data used (in GB)', scale 0 to 6. X-axis: 'Week', categories Week 1 to Week 5. Frank's line (labelled 'Frank') plotted: Week 1 ≈ 2 GB, Week 2 ≈ 3 GB, Week 3 ≈ 2 GB (dips), Week 4 ≈ 1 GB, Week 5 ≈ 3 GB. Highest point is Week 5 (and Week 2) at 3 GB.", "topic": "Statistics", "marking_scheme_answer": "Week 3", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q4aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(ii)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "(a)(ii) how many GB of mobile data did Frank use in Week 5?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "2 [GB]", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q4aiii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(iii)", "parent_question": "4", "marks": 1, "marks_confidence": "derived", "question_text": "(a)(iii) in which week did Frank use less mobile data than the week before?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Week 3", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q4b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "In each of these weeks, Ciarán used 2 GB of data more than Frank used. Use this information to draw a graph on the diagram above showing how much mobile data Ciarán used in each of these weeks.", "has_images": true, "image_notes": "Uses the same line graph as part (a) (data axes 0–6 GB by Week 1–5); student must plot Ciarán's points 2 GB above each of Frank's plotted values and draw the line.", "topic": "Statistics", "marking_scheme_answer": "Ciarán's weekly data calculated by adding a value +2, consistently to each point, and the graph drawn (each of Frank's points plus 2 GB, line drawn).", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q4bi", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)(i)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Write down the perimeter of Triangle B, in terms of x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Perimeter of B = 3 + 2x + (2x + 1) = 4x + 4 (cm). (Scale 10D shared across 4(b)(i) and 4(b)(ii).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q4bii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)(ii)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "The perimeter of Triangle B is 24 cm. Use this to work out the value of x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4x + 4 = 24 → 4x = 20 → x = 5 (cm). (Scale 10D shared with 4(b)(i).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q4ci", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)(i)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "The perimeters of the three triangles A, B, and C form a linear sequence. Triangle C has the largest perimeter. The perimeter of Triangle C is k cm, where k ∈ ℕ. Find the value of k.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Perimeters A = 8 and B = 24, common difference 16, so k = 24 + 16 = 40. (Scale 5D shared across 4(c)(i) and 4(c)(ii).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q4cii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)(ii)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Hence work out the value of y, where y ∈ ℕ.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Perimeter C = 5 + y^2 + (y^2 + 3) = 40 → 2y^2 = 32 → y^2 = 16 → y = 4. (Scale 5D shared with 4(c)(i).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q5a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "A balloon pump is made from a cylinder with an internal diameter of 6 cm and a height of 20 cm, as shown. Each time the pump is pumped, it passes one full cylinder of air into a balloon. Show that the volume of one full cylinder of air is 180π cm^3.", "has_images": true, "image_notes": "Diagram of a cylindrical balloon pump shown horizontally; length labelled 20 cm and internal diameter labelled 6 cm.", "topic": "Geometry", "marking_scheme_answer": "V = πr^2 h = π(6/2)^2 (20) = π(3)^2(20) = 180π cm^3. (Scale 5B.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q5a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "6 students in a class (U) were asked if they ran (R) or cycled (C) during the midterm break. The Venn diagram shows their responses.\n(a) Name one student who ran during the midterm break.", "has_images": true, "image_notes": "Venn diagram in universal set U with two overlapping ovals labelled R (ran) and C (cycled). In R only: Jerome, Marcella. In the overlap R ∩ C: Tim, Denise. In C only: Sarah. Outside both circles: Paul.", "topic": "Probability", "marking_scheme_answer": "Jerome / Marcella / Tim / Denise (any one of the students in R)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q5b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 3, "marks_confidence": "derived", "question_text": "Explain what the following statement means, in terms of the students in the class:\n# C = 3", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "There are 3 students who cycled (the number of elements in set C is 3).", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q5bi", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)(i)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Darragh is inflating a balloon in the shape of a sphere. When fully inflated, the balloon has a radius of 15 cm. Find the volume of Darragh's balloon when it is fully inflated. Give your answer in cm^3, in terms of π.", "has_images": true, "image_notes": "Photo of a round gold spherical balloon (decorative).", "topic": "Geometry", "marking_scheme_answer": "V = (4/3)πr^3 = (4/3)π(15^3) = 4500π cm^3. (Scale 10D shared across 5(b)(i) and 5(b)(ii).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q5bii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)(ii)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Darragh pumps the pump once every second. How many seconds will it take Darragh to fully inflate his balloon?", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "4500π ÷ 180π = 25 seconds. (Scale 10D shared with 5(b)(i).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q5c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Gustav is inflating a bigger balloon in the shape of a sphere. He also pumps the pump once every second. His balloon is fully inflated after 50 seconds. Find the radius of Gustav's balloon when it is fully inflated. Give your answer correct to 1 decimal place.", "has_images": true, "image_notes": "Photo of a larger round gold spherical balloon on a faint grid (decorative).", "topic": "Geometry", "marking_scheme_answer": "V = 50 × 180π = 9000π cm^3. (4/3)πr^3 = 9000π → r^3 = 6750 → r = ∛6750 = 18·9 cm (1 d.p.). (Scale 5D.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q5c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 2, "marks_confidence": "derived", "question_text": "Name one student who is in the region R ∩ C in the Venn diagram.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "Tim / Denise (either student in the overlap R ∩ C)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q5d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "One student is picked at random from the six students in the Venn diagram. Write down the probability that this student ran during the midterm break.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "4/6 or 2/3 (4 of the 6 students ran)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q6", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6", "parent_question": "6", "marks": 20, "marks_confidence": "high", "question_text": "80 students in a group were asked what they had done during their summer holidays. Some of the students got a job (J), some went on holidays (H), some did both, and some did neither. 1/5 of the students in the group did neither. 25% of the students got a job. Of those students who got a job, half also went on holidays. Work out the total number of students in the group who went on holidays. You may use the Venn diagram below to help answer the question. Answer = ___", "has_images": true, "image_notes": "A two-set Venn diagram inside a rectangle (universal set), with overlapping ovals labelled J (left) and H (right), for the student to fill in. A decorative photo of a beach/coastline above the diagram.", "topic": "Probability", "marking_scheme_answer": "Neither = 1/5 × 80 = 16. Got a job J = 25% × 80 = 20; both (J and H) = ½ × 20 = 10, so J only = 10. Union = 80 − 16 = 64. H = 64 − 10 (J only) = 54, made up of 10 (both) + 44 (H only). Total on holidays = 54. (Scale 20C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q6a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "All the students in fourth year in a school took part in a long-jump competition. The results are shown in the following frequency table. Distance jumped (cm): 200–250, 250–300, 300–350, 350–400, 400–450, 450–500. Number of students: 10, 15, 25, 32, 10, 3.\n(a) In total, how many students took part in the competition?", "has_images": true, "image_notes": "Frequency table. Row 'Distance jumped (cm)': 200–250, 250–300, 300–350, 350–400, 400–450, 450–500. Row 'Number of students': 10, 15, 25, 32, 10, 3.", "topic": "Statistics", "marking_scheme_answer": "10 + 15 + 25 + 32 + 10 + 3 = 95", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q6b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "What is the modal group of the frequency table? Tick (✓) one box only. Options: 300–350, 350–400, 400–450, 450–500.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "350–400 (the group with the greatest frequency, 32)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q6ci", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)(i)", "parent_question": "6", "marks": 3, "marks_confidence": "derived", "question_text": "To qualify for the final, a student must jump 415 cm or more.\n(c)(i) What is the least number of students who could have qualified for the final?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q6cii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)(ii)", "parent_question": "6", "marks": 2, "marks_confidence": "derived", "question_text": "(c)(ii) What is the greatest number of students who could have qualified for the final?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "10 + 3 = 13", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q6d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Draw a histogram to represent the data from the frequency table. Use the axes and scales below.", "has_images": true, "image_notes": "Blank histogram grid. Y-axis 'Number of students' 0 to 35 (steps of 5). X-axis 'Distance jumped (cm)' from 200 to 500 (steps of 50). Student plots bars at heights 10, 15, 25, 32, 10, 3 for the six intervals.", "topic": "Statistics", "marking_scheme_answer": "Histogram with bars at heights 10, 15, 25, 32, 10, 3 over intervals 200–250, 250–300, 300–350, 350–400, 400–450, 450–500.", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q6e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(e)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "The median distance jumped was 331 cm. Explain what this means, in terms of how far the students jumped in the long-jump competition.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Half of the students jumped less than 331 cm and half of the students jumped more than 331 cm (it is the middle value when the lengths are put in order).", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q7ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Amie and Joe are asked to pick values for the numbers p, q, and r so that the following is true for all a ∈ ℝ: a^p × a^q × a^r = a^12. Amie picked three values that were all the same, so p = q = r. Write down the values of p, q, and r that Amie picked. p = ___ q = ___ r = ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "p + q + r = 12 with all equal → p = q = r = 12/3 = 4. (Scale 10C shared across 7(a)(i) and 7(a)(ii).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q7ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "The triangle below has two angles of size 70°, as shown (diagram not to scale).\n(a)(i) What type of triangle is this? Tick (✓) one box only. Options: Right-angled, Isosceles, Equilateral.", "has_images": true, "image_notes": "Triangle (not to scale) with two base/apex angles marked 70° and the third angle at the lower left labelled A.", "topic": "Geometry", "marking_scheme_answer": "Isosceles", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q7aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Joe picked three values that were all different. Write down possible values of p, q, and r that Joe might have picked. p = ___ q = ___ r = ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Any three different real numbers adding to 12, for example p = 0, q = −1·5, r = 13·5. (Scale 10C shared with 7(a)(i).)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q7aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "(a)(ii) Work out the size of the angle A, the third angle in this triangle.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "180 − (70 + 70) = 40 [°]", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q7aiii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(iii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "(a)(iii) This triangle is joined to a parallelogram, as shown below. The angle B in the parallelogram is marked. Work out the size of the angle B.", "has_images": true, "image_notes": "The 70°-70° triangle joined on its right side to a parallelogram. Two 70° angles are marked at the join (one at the top of the triangle/parallelogram corner, one at the bottom). Angle B is the top-right interior angle of the parallelogram.", "topic": "Geometry", "marking_scheme_answer": "B = 180 − 70 = 110 [°] (co-interior / straight-line angle in the parallelogram)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q7b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Find the value of m so that the following is true for all b ∈ ℝ: (b^m × b^-2)/b = b^10.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "b^(m − 2 − 1) = b^10 → m − 3 = 10 → m = 13. (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q7b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "The diagram below shows the triangle T. The lengths of two sides and the size of one angle are shown (side 3, side 4, included angle 80°). 4 more triangles are shown below. For each triangle, tick (✓) the correct box to show if it is definitely congruent to T or not (Yes/No). The four triangles have: (1) sides 3 and 4 with 80° between them; (2) sides 3 and 4 with 20° between them; (3) sides 4 and 3 with 80° between them; (4) sides 4 and 3 with 80° between them in a different orientation.", "has_images": true, "image_notes": "Triangle T: two sides labelled 3 and 4 with an 80° angle included between them. Table 'Is this triangle definitely congruent to T?' lists 4 triangles each with Yes/No tick boxes: Triangle 1 has sides 3 and 4 with 80° between them (congruent, SAS); Triangle 2 has sides 3 and 4 with 20° between them (not congruent, wrong angle); Triangle 3 has sides 4 and 3 with 80° between them (congruent); Triangle 4 has sides 4 and 3 with 80° between them (congruent).", "topic": "Geometry", "marking_scheme_answer": "Yes; No; No; Yes (model solution gives Yes / No / No / Yes for the four triangles based on SAS congruence with sides 3, 4 and included angle 80°).", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q8a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "The diagram shows two vertical buildings, A and B (diagram not to scale). Mary stands at the top of Building A. She is 220 m above the ground. She wants to work out the distances marked y and z in the diagram — that is, the distance from the top of Building A to the bottom of Building B, and the height of Building B, respectively. Mary measures the two angles that are marked 35° and 20° in the diagram, to the bottom of Building B and the top of Building B, respectively. The broken line is horizontal. Work out the size of the angle C.", "has_images": true, "image_notes": "Diagram (not to scale) of two vertical buildings A (left, height 220 m) and B (right). From the top of Building A a horizontal broken line runs to the right; an angle of 20° is between the horizontal and the line of sight to the top of B, and 35° is between the horizontal and the line of sight to the bottom of B. The slanted line of length y goes from the top of A down to the bottom of B; angle C is at the bottom of B between y and Building B. The horizontal ground distance between the buildings is 154 m. z marks the height of Building B.", "topic": "Trigonometry", "marking_scheme_answer": "C = 180 − (90 + 35) = 55° (or 90 − 35 = 55°, or tan C = 220/154 → C = tan⁻¹(220/154) = 55·008° ≈ 55°). (Scale 10B.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q8ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "The graph on the co-ordinate diagram shows the relationship between degrees Celsius (°C) and degrees Fahrenheit (°F). The axes do not start at (0, 0). For parts (a)(i) and (a)(ii), show your work on the diagram above.\n(a)(i) Normal temperature for an adult is 37°C. Write 37°C in degrees Fahrenheit.", "has_images": true, "image_notes": "Co-ordinate graph, straight red line. X-axis 'Temperature in Celsius (°C)' from 29 to 39 (axis does not start at 0). Y-axis 'Temperature in Fahrenheit (°F)' from 84 to 103. A point S is marked on the line around (33, 90). The line rises from about (29, 84) to about (39, 103).", "topic": "Functions", "marking_scheme_answer": "98·6 [°F] (read from the graph: 37°C ≈ 98·6°F)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q8aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "(a)(ii) A temperature above 100·4°F is a high temperature. Write 100·4°F in degrees Celsius.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "38 [°C] (read from the graph: 100·4°F ≈ 38°C)", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q8b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Mary works out that the horizontal distance between the two buildings is 154 m, correct to the nearest metre, as shown. Use the Theorem of Pythagoras to work out the distance marked y on the diagram. Give your answer correct to the nearest metre.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "y^2 = 154^2 + 220^2 = 23716 + 48400 = 72116, y = √72116 = 268·54... ≈ 269 m (nearest metre). (Scale 10C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q8b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "The point S is marked on the graph. Estimate the co-ordinates of the point S.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "(33, 89·6) — model solution gives S ≈ (33, 89·6); accept reasonable estimate read from the graph (x or y co-ordinate found earns partial credit).", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q8c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Use trigonometry to work out the value of z, the height of Building B. Give your answer correct to the nearest metre.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "Let z = h + 220, where tan 20° = h/154 → h = 154 tan 20° = 56·05... So z = 220 + 56·05 = 276·05 ≈ 276 m (nearest metre). (Scale 5D.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q8c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "The points (35, 95) and (30, 86) are also on the graph of the line. Use these two points to work out the slope of the graph.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "(95 − 86)/(35 − 30) = 9/5 or 1·8", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q8d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "The table below gives two inequalities in T (a temperature in °C), and a description of two inequalities in T. Complete the table by filling in the missing description and inequality. Row 1: 'Temperature is less than 36°C' → T < 36. Row 2: [missing description] → 36 < T < 38. Row 3: 'Temperature is greater than 38°C' → [missing inequality].", "has_images": true, "image_notes": "Table with columns 'Description' and 'Inequality', 3 rows. Row 1: Temperature is less than 36°C | T < 36. Row 2: (description blank, to fill) | 36 < T < 38. Row 3: Temperature is greater than 38°C | (inequality blank, to fill).", "topic": "Algebra", "marking_scheme_answer": "Row 2 description: Temperature is between 36 and 38 (°C). Row 3 inequality: T > 38.", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q8e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(e)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Graph the inequality T < 36 on the number line below, where T ∈ ℝ (T is a real number). Number line shown from 34 to 40.", "has_images": true, "image_notes": "A number line marked at integers 34, 35, 36, 37, 38, 39, 40 for plotting the inequality T < 36.", "topic": "Algebra", "marking_scheme_answer": "Number line with an open circle (hollow) at 36 and an arrow/line shaded to the left (towards values less than 36).", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q9a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "k = 7 and m − k = 4. Work out the value of 9k − 6m.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "m − k = 4, k = 7 → m = 11. 9k − 6m = 9(7) − 6(11) = 63 − 66 = −3. (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q9a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "Margaret makes and sells furniture.\n(a) It costs Margaret €75 to make a chair. She sells it for €110. Work out the profit she makes on the chair.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "110 − 75 = €35", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q9b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Factorise fully 8ax − 14bx + 4ay − 7by.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8ax − 14bx + 4ay − 7by = 2x(4a − 7b) + y(4a − 7b) = (4a − 7b)(2x + y). (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q9b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "(b) It costs Margaret €120 to make a bench. She sells it for a profit of €45. Work out how much Margaret sells the bench for.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "120 + 45 = €165", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q9c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "Write the following as a single fraction in its simplest form: 2/(2x + 1) − 3/(3x + 5).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "[2(3x + 5) − 3(2x + 1)] / [(2x + 1)(3x + 5)] = (6x + 10 − 6x − 3)/[(2x + 1)(3x + 5)] = 7/[(2x + 1)(3x + 5)]. (Scale 10D.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q9c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "(c) It costs Margaret €3n to make a stool, where n ∈ ℕ. She sells the stool for €5n. Work out the profit she makes on the stool, in terms of n.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "5n − 3n = €2n", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-EV-q9d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Solve the equation 2x^2 − 7x − 3 = 0. Give each answer correct to 2 decimal places.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x = [7 ± √(7^2 − 4(2)(−3))]/(2(2)) = [7 ± √73]/4 = 3·886... or −0·386... = 3·89 or −0·39 (2 d.p.). (Scale 5C.)", "source_pdf": "2022 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2022-ordinary-level-EV-q9d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "(d) It costs Margaret €320 to make a table. She sells it for a profit of €80. Write Margaret's profit for the table as a percentage of its cost to her.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "80/320 × 100 = 25%", "source_pdf": "2022 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q1a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Ceannaíonn Sinéad ríomhaire glúine ar líne ar €699, móide costas seolta €30. Is é $1 = €0·90 an ráta malairte. Oibrigh amach costas iomlán, ina euro, ar Shinéad an ríomhaire glúine a cheannach ar líne.", "has_images": true, "image_notes": "Photo of a laptop (Lenovo). No numeric data beyond the prices stated in the text; the image is illustrative only.", "topic": "Number", "marking_scheme_answer": "(699 + 30) × 0·9 = 729 × 0·9 = €656·10. Scale 10B (0, 4, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q1ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "Faigh luach gach ceann díobh seo a leanas.\n(i) 243 + 178", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q1aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "(ii) 7·2 × 6", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "216/5 nó 43·2", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q1aiii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "(iii) 24 ÷ (9 − 7)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "24 ÷ 2 = 12", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q1aiv", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(iv)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "(iv) 3^4", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q1b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "Scríobh síos an tslánuimhir is gaire do 15·8.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q1bi", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Is é €56 000 ioncam comhlán bliantúil Shínéad. Íocann Sinéad cáin ioncaim ar a hioncam comhlán ag ráta 20% ar an gcéad €44 300, agus 40% ar an iarmhéid. (i) Oibrigh amach an ioncam bliantúil cáin ioncaim Shínéad ag gach ceann den dá ráta sin (20% agus 40%).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Cáin ag 20% = 0·2 × 44300 = €8860. Cáin ag 40% = 0·4 × (56000 − 44300) = 0·4 × 11700 = €4680. Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q1bii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "(ii) Tá creidmheasanna cánach bliantúla de €3300 ag Sinéad. Oibrigh amach glanphá bliantúil Shínéad.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "56000 − 8860 − 4680 + 3300 = €45760. Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q1c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 2, "marks_confidence": "derived", "question_text": "Cén uimhir atá leath slí idir 16 agus 30?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "30 − 16 = 14; 14 ÷ 2 = 7; 16 + 7 = 23. NÓ (16+30)/2 = 46/2 = 23. Freagra: 23", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q10a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Ghlac Art agus Pól páirt i dtrí-atlan. I rith an trí-atlain, bhí orthu cadhcáil 5 km a chomhlánú, rothaíocht 25 km ansin, agus rith 10 km ina dhiaidh sin arís. Tarraingíodh an léaráid thíos tar éis don bheirt acu an rás a chríochnú. Taispeánann sé cé mhéad nóiméad níos mó ná Pól (nó níos lú ná Pól) a thóg sé ar Art d'am a thaisteal le linn an trí-atlain, ag pointe ar bith le linn an chúrsa (agus tá an t-am sin tomhaiste i nóiméid). [Léaráid: graf ina bhfuil 'Cé mhéad nóiméad níos mó ná Pól a thóg sé ar Art' ar an y-ais, agus 'Fad a Taistealaíodh sa Trí-atlan, d (km)' ar an x-ais. Trí chrios cúlra: Cadhc., Rothaíocht, Rith. Pointí A agus B marcáilte ar an gcuar.] (a) Ar chríochnaigh Art an mhír chadhcála roimh Phól, i ndiaidh Phóil, nó ag an am céanna le Pól? (Ná cuir tic (✓) ach i mbosca amháin.)", "has_images": true, "image_notes": "Line graph. y-axis: 'Cé mhéad nóiméad níos mó ná Pól a thóg sé ar Art' (minutes Art was behind Pól), values −2 to 3 (above 0 = níos mó ná Pól). x-axis: 'Fad a Taistealaíodh sa Trí-atlan, d (km)' from 0 to 40. Three shaded background zones: Cadhc. (kayak, 0–5), Rothaíocht (cycle, 5–30), Rith (run, 30–40). Point A is on the rising line during the cycle zone (around 2 minutes), point B is lower on the line later (around 1 minute, mid cycle). The curve dips to a trough near d=25 then rises in the run zone.", "topic": "Functions", "marking_scheme_answer": "Art finished the kayak section i ndiaidh Phóil (after Pól) — the graph is above 0 (positive, Art behind) at d = 5. Marked with (b) on Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q10a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Scríobh é seo a leanas mar chodán singil san fhoirm is simplí: 2/3 + 5/7", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "14/21 + 15/21 = 29/21", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q10b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "(b) Bhí ar Art stopadh ar feadh tamall gearr le linn an trí-atlain. Níor stop Pól. Luaigh an fad a bhí taistealta ag Art nuair a stop sé agus an fad ama a bhí sé stoptha. An fad a bhí taistealta ag Art (ina km); An fad ama a bhí Art stoptha (ina nóiméid).", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "An fad taistealta = 25 km; an fad ama a bhí Art stoptha = 5 nóiméad (the flat/steep segment on the graph). Marked with (a) on Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q10b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Réitigh an chothromóid seo a leanas in k: 4k − 7 = 41", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4k = 41 + 7; 4k = 48; k = 12", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q10c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "(c) Cad a bhí ag tarlú idir Art agus Pól ag an bpointe marcáilte B ar an léaráid?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Aon chur síos bailí, mar shampla: 'Bhí Ali ag dul chun tosaigh ar Jon' / a mhacasamhail (i.e. at B the gap between Art and Pól was changing / Art was catching up on / pulling ahead of Pól). Scale 5B (0, 4, 10) [as printed on solution page; summary table lists 5B].", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q10d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(d)", "parent_question": "10", "marks": 20, "marks_confidence": "high", "question_text": "(d) Sa tábla thíos taispeántar an t-am a thóg sé ar Phól gach ceann de na trí mhír sa trí-atlan a chomhlánú, chomh maith lena am iomlán don trí-atlan. Ag baint úsáide as an léaráid, líon isteach na ceithre am atá in easnamh d'Art. (Tábla: colúin Cadhcáil, Rothaíocht, Rith, Iomlán; ró 'Am Phóil (nóiméad)': 32, 38, 36, 106; ró 'Am Airt (nóiméad)' folamh.)", "has_images": true, "image_notes": "A table. Columns: Cadhcáil, Rothaíocht, Rith, Iomlán. Row 'Am Phóil (nóiméad)': 32, 38, 36, 106. Row 'Am Airt (nóiméad)': blank — four values to be found using the graph.", "topic": "Functions", "marking_scheme_answer": "Am Airt (nóiméad): Cadhcáil = 34, Rothaíocht = 35, Rith = 36, Iomlán = 105. Scale 20C (0, 7, 12, 20).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q10e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(e)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "(e) Rith Pól agus Art rás 400 m freisin. 7·8 méadar sa soicind an meánluas a bhí ag Pól don 400 m. Thóg sé 2 shoicind níos mó ar Art ná mar a thóg sé ar Phól an 400 m a rith. Oibrigh amach meánluas Airt, ina mhéadar sa soicind, ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "T_Pól = 400/7·8 = 51·282... soicind. T_Art = 51·282 + 2 = 53·282... soicind. Meánluas Airt = 400/53·282 = 7·50... = 7·5 m/s (1 d.p.). Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q11", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Is ionann 4 agus fána na líne h, agus gabhann sí tríd an bpointe (20, 12). Scríobh síos comhordanáidí pointe eile ar an líne h, seachas an pointe (20, 12). Taispeáin d'oibriú amach.", "has_images": true, "image_notes": "Coordinate diagram showing a red line h sloping upward steeply through the point (20, 12) which is marked with a dot. The line is labelled 'h' with 'Fána = 4' beside it. x- and y-axes shown but unscaled.", "topic": "Coordinate Geometry", "marking_scheme_answer": "Fána = rise/run = 4/1. From (20, 12): (20 + 1, 12 + 4) = (21, 16). [Other valid points: (19, 8); or via y = 4x − 68 → at x = 0, (0, −68).] Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q11ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)(i)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Tá rampa do chláir scátála á thógáil ag beirt cháirde. Tá dearadh éagsúil don rampa ag gach duine díobh.\n(a) Mar chuid dá dearadh don rampa, tarraingíonn Treasa an léaráid seo a leanas. Tá sé comhdhéanta de thriantán agus de chearnóg. Is de réir scála 1: 100 atá sí. Tá an uillinn A marcáilte.\n(i) Tóg léaráid de réir scála den chuid seo den dearadh don rampa ar an ngreille thíos, de réir scála 1: 50. Mar sin, ba chóir go mbeadh gach slios i do léaráid dhá oiread fhad an tsleasa chomhfhreagraigh i léaráid Threasa. Tá slíos amháin déanta duit cheana féin.", "has_images": true, "image_notes": "Treasa's design diagram (scale 1:100), composed of a right-angled triangle on the left joined to a square on the right. Labelled lengths: triangle base 3·5 cm, square width 2 cm, vertical height 2 cm. Angle A marked at the left base of the triangle. A photo of a skateboarder is shown alongside. A separate grid is provided for the 1:50 enlargement, with one side (a vertical 4 cm line) already drawn.", "topic": "Geometry", "marking_scheme_answer": "Scale drawing at 1:50: all sides doubled — triangle base 7 cm, square 4 cm by 4 cm, heights 4 cm (each length twice the corresponding length in Treasa's diagram).", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q11aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)(ii)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "(ii) Tomhais méid na huillinne A i léaráid Threasa thuas.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "30° (glac le 28 ≤ A ≤ 32)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q11b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Tá dearadh difriúil don rampa ag Sinéad. Is cuid de dhearadh Shinéad é an triantán dronuilleach sa léaráid thíos (níl a léaráid de réir scála). Tá ceann amháin de na sleasa marcáilte B. Tá ceann amháin de na huillinneacha marcáilte C. Bain úsáid as Teoirim Phíotágaráis chun fad an tsleasa B i ndearadh Shinéad a oibriú amach. Bíodh do fhreagra ina cm.", "has_images": true, "image_notes": "Right-angled triangle (Sinéad's ramp design, not to scale). Vertical side (left) labelled 96 cm, horizontal base labelled 180 cm, hypotenuse labelled B. Angle C marked at the bottom-right vertex between the base and hypotenuse.", "topic": "Geometry", "marking_scheme_answer": "B^2 = 96^2 + 180^2 = 9216 + 32400 = 41616; B = 204 [cm]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q11c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Tá a fhios ag Sinéad, i gcás na huillinne C, go bhfuil tan C = 96/180. Bain úsáid as d'áireamhán chun méid na huillinne C a fháil, ceart go dtí an chéim is gaire.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "tan⁻¹(96/180) = 28·07… = 28 [°]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q12", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Taispeántar an ciorcal k sa léaráid thíos (níl an léaráid de réir scála). Tá na pointí A, B, agus C ar an gciorcal. Is trastomhas den chiorcal é [AB], agus |AC| = 8 cm. Is ionann achar an chiorcail agus 25π cm^2. Oibrigh amach méid na huillinne is lú sa triantán ABC.", "has_images": true, "image_notes": "A circle k with centre marked. Points A (lower left), B (right), C (top) lie on the circle. [AB] is a diameter passing through the centre. The chord [AC] is labelled 8 cm. Triangle ABC is drawn inscribed in the circle. Not to scale.", "topic": "Geometry", "marking_scheme_answer": "Area = πr² = 25π → r² = 25 → r = 5, so diameter |AB| = 10. Angle ACB = 90° (angle in semicircle). cos∠CAB = 8/10 → ∠CAB = cos⁻¹(0·8) = 36·87°. (Or sin∠CBA = 8/10 → ∠CBA = 53·13°, ∠CAB = 90 − 53·13 = 36·87°.) The smallest angle is ∠CAB = 36·87°. Scale 10D (0, 3, 5, 8, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q12a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "I mí Eanáir 2021, ceadaíodh do dhaoine taisteal 5 km ó bhaile mar ghníomh aclaíochta.\n(a) Scríobh km nó km² i ngach bosca thíos chun an abairt seo a leanas a chomhlánú i gceart. Ná húsáid aon cheann acu ach uair amháin.\nTomhaistear achar ina [ ] agus tomhaistear fad ina [ ].", "has_images": true, "image_notes": "A circular map region of radius 5 km centred on a point ('Baile'/home), with '5 km' marked as the radius. Followed by a fill-in sentence with two boxes for units.", "topic": "Geometry", "marking_scheme_answer": "Tomhaistear achar i: km²; Tomhaistear fad i: km", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q12b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Bain úsáid as an bhfoirmle seo a leanas chun imlíne ciorcail, ar ga dó 5 km, a oibriú amach. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin. 2 × π × r =", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "2 × π × 5 = 31·41… = 31·4 [km] [1 DP]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q12c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Bain úsáid as foirmle dhifriúil chun achar ciorcail, ar ga dó 5 km, a oibriú amach. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "π × r² = π × 5² = 78·53… = 78·5 [km²] [1 DP]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q12d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(d)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Ins na táblaí thíos, taispeántar imlíne agus achar chiorcail i dtéarmaí π, de réir mar a mhéadaíonn an ga de 2 aonad. Is seicheamh líneach é ceann amháin díobh seo; ní seicheamh líneach é an ceann eile.\nSeicheamh 1 (Imlíne): 8π, 12π, 16π, 20π, 24π.\nSeicheamh 2 (Achar): 16π, 36π, 64π, 100π, 144π.\nCuir tic (✓) sa bhosca ceart chun a thaispeáint cé acu ceann de na seichimh seo atá líneach. Tabhair cúis le do fhreagra.", "has_images": true, "image_notes": "Two tables. Seicheamh 1 (Imlíne / circumference): 8π, 12π, 16π, 20π, 24π. Seicheamh 2 (Achar / area): 16π, 36π, 64π, 100π, 144π. Tick boxes for Seicheamh 1 / Seicheamh 2 and a space for the reason (Cúis).", "topic": "Algebra", "marking_scheme_answer": "Seicheamh 1. Cúis: difríocht chéanna gach uair (méadaíonn sé faoi 4π gach uair / common first difference), mar sin tá sé líneach. (Seicheamh 2 has differences that change, so it is not linear.)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q13a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 2, "marks_confidence": "derived", "question_text": "Simpligh 2a − 5n + 2n + 6a.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2a + 6a − 5n + 2n = 8a − 3n", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q13b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 2, "marks_confidence": "derived", "question_text": "y = (3n + 70)/5. Oibrigh amach luach y nuair atá n = 10.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "y = (3(10) + 70)/5 = 100/5 = 20", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q13c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 1, "marks_confidence": "derived", "question_text": "Fachtóirigh an slonn cearnach x^2 − 7x + 12. x^2 − 7x + 12 = (x )( )", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x − 3)(x − 4)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q2a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "Nuair a imríonn foireann Mhéabh cluiche, is féidir go mbuafaidh siad (B), go mbeidh an cluiche ar comhscór (S), nó go gcaillfidh siad (C). Líon isteach an tábla thíos chun na 9 bhfothoradh féideartha, nuair a imríonn foireann Mhéabh dhá chluiche, a thaispeáint. Tá ceann amháin déanta duit cheana féin. Ciallaíonn B S go mbuann siad Cluiche 1 agus go mbíonn comhscór acu i gCluiche 2. (Tábla 3×3: Cluiche 2 cholúin B, S, C; Cluiche 1 rónna B, S, C; an cill B-S líonta isteach mar 'B S'.)", "has_images": true, "image_notes": "A 3×3 sample-space grid. Columns headed 'Cluiche 2': B, S, C. Rows headed 'Cluiche 1': B, S, C. The cell for Cluiche1=B, Cluiche2=S is pre-filled with 'B S'. The other eight cells are blank for the student to complete (BB, BC, SB, SS, SC, CB, CS, CC). Also a photo of a football beside the table (illustrative).", "topic": "Probability", "marking_scheme_answer": "Completed sample space: BB, BS, BC; SB, SS, SC; CB, CS, CC (i.e. the nine outcomes WW, WD, WL, DW, DD, DL, LW, LD, LL). Marked together with part (b) on Scale 15D (0, 4, 8, 12, 15).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q2ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "Tá an biachlár seo a leanas, ar a bhfuil 4 phríomhchúrsa agus 3 mhilseog, ag bialann:\nPríomhchúrsa / Praghas €: Iasc 16·95, Stéig 18·95, Pasta 14·95, Píotsa 15·95.\nMilseog / Praghas €: Uachtar reoite 3·50, Císte cáise 4·95, Donnóg 4·50.\n(a)(i) Ordaíonn Seán stéig agus císte cáise. Oibrigh amach costas bhéile Sheáin.", "has_images": true, "image_notes": "Two menu price tables. Príomhchúrsa (main course) €: Iasc 16·95, Stéig 18·95, Pasta 14·95, Píotsa 15·95. Milseog (dessert) €: Uachtar reoite 3·50, Císte cáise 4·95, Donnóg 4·50. Photo of a plated meal alongside.", "topic": "Number", "marking_scheme_answer": "18·95 + 4·95 = €23·90", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q2aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "(ii) Íocann Seán as an mbéile le nóta €50. Cé mhéad sóinseála is ceart dó a fháil?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "50 − 23·90 = €26·10", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q2b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "Ceapann Méabh go bhfuil gach toradh sa tábla comhdhóchúil. Bunaithe air sin, faigh an dóchúlacht go mbuann foireann Mhéabh cluiche amháin ar a laghad, nuair a imríonn siad dhá chluiche. Bíodh do fhreagra ina chodán.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "P(buann cluiche amháin ar a laghad) = 5/9. Marked together with part (a) on Scale 15D (0, 4, 8, 12, 15).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q2b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Roghnaíonn Michelle príomhchúrsa amháin agus milseog amháin. Cé mhéad slí dhifriúil fhéideartha ina bhféadfadh sí é seo a dhéanamh? Mar shampla, sí fhéideartha amháin ná iasc agus uachtar reoite a roghnú.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "4 × 3 = 12", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q2c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Imríonn foireann Mhéabh 5 chluiche i gcomórtas. Oibrigh amach líon iomlán na bhfothorthaí éagsúla is féidir a bheith ag foireann Mhéabh, le haghaidh na 5 chluiche sin. Mar shampla, is fothoradh féideartha amháin é B B C S B.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3^5 = 243. Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q2c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Ordaíonn Gina bia a chosnaíonn €72. Tugann Gina aisce de 15% den chostas seo, slánaithe go dtí an euro is gaire. Oibrigh amach an mhéid a thugann Gina mar aisce.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "72 × 15/100 = 10·8 ⇒ €11", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q2d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Imríonn foireann Mhéabh 11 chluiche i sraith. Sa tábla thíos taispeántar líon na gcúl a scóráil foireann Mhéabh i ngach ceann de na 11 chluiche sin. (Tábla: 3, 1, 1, 0, 2, 7, 1, 0, 2, 1, 3.) Oibrigh amach meánlíon na gcúl in aghaidh an chluiche a scóráil foireann Mhéabh. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": true, "image_notes": "A single-row table of 11 values (goals per game): 3, 1, 1, 0, 2, 7, 1, 0, 2, 1, 3.", "topic": "Statistics", "marking_scheme_answer": "Mean = (3+1+1+0+2+7+1+0+2+1+3)/11 = 21/11 = 1·9 (1 d.p.). Scale 10B (0, 4, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q2d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Tá 5 fhreastalaí agus 3 bhall d'fhoireann chistine ag obair sa bhialann. Ag deireadh gach oíche, suimítear na haiscí go léir le chéile, agus ansin roinntear go cothrom iad idir na 8 nduine seo. Ar oíche amháin, faigheann na 3 bhall den fhoireann chistine suim iomlán de €96 i bhfoirm aiscí. Oibrigh amach luach iomlán na n-aiscí go léir ar an oíche sin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "triúr (3): €96; 1 duine: 96 ÷ 3 = 32; ochtar (8): 8 × 32 = €256", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q2e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(e)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Comhlánaigh an phíchairt thíos, chun achoimre a dhéanamh ar na sonraí thuas, agus taispeáin an sciar de na cluichí inar scóráil foireann Mhéabh 0 cúl, cúl amháin, agus mar sin de. Cuir lipéad soiléir ar gach teascóg agus taispeáin méid gach uillinne go soiléir. Taispeáin aon oibriú amach agus aon léinte tógála.", "has_images": true, "image_notes": "A blank pie chart (circle) to be divided and labelled, drawn on a grid. The student must compute and mark each sector angle from the data in part (d).", "topic": "Statistics", "marking_scheme_answer": "Frequencies from (d): 0 cúl ×2, 1 chúl ×4, 2 chúl ×3, 3 chúl ×1, 7 gcúl ×1 (total 11). Angles: Cúl ar bith (0) = (2/11)×360 = 65°; 1 chúl amháin = (4/11)×360 = 130·90 = 131°; 2 chúl = (2/11)×360 = 65°; 3 chúl = (1/11)×360... = 65°; 7 gcúl = (1/11)×360 = 32·72 = 33°. (Tolerance ±2°.) Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q3a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Sa léaráid chomhordanáideach thíos taispeántar cuid de bhóthar an N22 i gContae Chorcaí. Tá dhá phointe ar an mbóthar, P agus Q, marcáilte ar an léaráid. (a) Is iad (6, 2) comhordanáidí an phointe Q. Scríobh síos comhordanáidí an phointe P.", "has_images": true, "image_notes": "A coordinate diagram (map) with x-axis from −4 to 8 and y-axis from −1 to 5. The N22 road is drawn as a curve. Point P is marked at approximately (−1, 3) and point Q at (6, 2).", "topic": "Coordinate Geometry", "marking_scheme_answer": "P = (−1, 3). Marked together with part (b) on Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q3a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Déanann Joshua meastachán go bhfuil cruth solaid dhronuilleogaigh, go garbh, ar thocht aeir. Is iad toisí an tochta aeir ná 180 cm faoi 80 cm faoi 20 cm.\n(a) Bain úsáid as luachanna Joshua chun a thaispeáint gurb é toirt an tochta aeir ná 288 000 cm^3.", "has_images": true, "image_notes": "Diagram of a rectangular air mattress (tocht aeir) labelled with dimensions: 180 cm (length), 80 cm (width), 20 cm (height/thickness).", "topic": "Geometry", "marking_scheme_answer": "180 × 80 × 20 = 288 000 [cm^3]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q3b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Is é seo a leanas cothromóid na líne PQ: x + 7y = 20. Agus úsáid á baint agat as seo, nó ar shlí eile, faigh comhordanáidí an phointe ag a dtrasnaíonn an líne PQ an y-ais.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Ar an y-ais x = 0: 0 + 7y = 20, y = 20/7. Freagra: (0, 20/7). Marked together with part (a) on Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q3b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Úsáideann Joshua caidéal leictreach chun an tocht aeir a shéideadh. Séideann an caidéal aer isteach tocht aeir ar ráta 800 cm^3 sa soicind. Oibrigh amach an méid nóiméad a thógfaidh sé chun an tocht aeir a líonadh agus an caidéal seo á úsáid.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "60 × 800 = 48 000 cm^3 in aghaidh an nóiméid; 288000/48000 = 6 nóiméad", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q3c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Tá bóthar nua á thógáil tríd an bpointe Q (6, 2). Mírlíne dhíreach, a bheidh ingearach leis an líne PQ, a bheidh ann ar an léaráid chomhordanáideach. Oibrigh amach cothromóid an bhóthair nua sin. Bíodh do fhreagra san fhoirm ax + by + c = 0, áit a mbeidh a, b, c ∈ ℝ.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Fána PQ = −1/7, so fána ingearach (perpendicular slope) = 7. y − 2 = 7(x − 6) → y − 2 = 7x − 42 → 7x − y − 40 = 0. Scale 5D (0, 2, 3, 4, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q3c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Bíonn an tocht líonta d'aer ag Joshua faoi 9:35 p.m. Téann sé chun na leapa 45 nóiméad ina dhiaidh sin. Cén t-am a théann Joshua chun na leapa?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "9:35 + 0:45 = 9:80 = 10:20 [p.m.]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q3d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(d)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Is ionann an fad |PQ| ar an léaráid agus 7·1 cm, ceart go dtí ionad deachúlach amháin. Seasann 5 mm ar an léaráid do 100 m. Bain úsáid as seo chun an fíorfhad ó P go Q a oibriú amach. Bíodh do fhreagra ina km.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 mm = 100 m, so 1 cm = 200 m. Fíorfhad = 7·1 × 200 = 1420 m = 1·42 km. Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q3d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(d)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Ceannaíonn Joshua an caidéal leictreach ar an idirlíon ar £15·95. An ráta tiontaithe airgeadra ná €1 = £0·90. Tiontaigh £15·95 ina euro. Bíodh do fhreagra ceart go dtí an cent is gaire.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15·95 ÷ 0·9 = €17·72 (NÓ 1/0·9 = 1·1̇; 15·95 × 1·1̇ = €17·72)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q4a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Taispeántar na trí thriantán A, B, agus C thíos. Is ina gceintiméadair a thugtar fad na dtrí shlios i ngach triantán, áit a bhfuil x, y ∈ ℕ. Sa cheist seo, glac leis gurb é is ciall leis 'an imlíne' ná 'fad na himlíne'. (a) Is ionann imlíne Thriantán A agus 8 cm. Tá fad 2 cm agus 3·5 cm, faoi seach, ag dhá cheann dá shleasa, mar a thaispeántar. Oibrigh amach fad an tríú slios i dTriantán A.", "has_images": true, "image_notes": "Three triangles labelled A, B, C. Triangle A: sides 2 and 3·5 marked, third (base) side unknown. Triangle B: sides 3 and 2x marked, base 2x + 1. Triangle C: sides 5 and y marked, base y² + 3.", "topic": "Algebra", "marking_scheme_answer": "8 − (2 + 3·5) = 8 − 5·5 = 2·5 cm. Scale 5B (0, 2, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q4ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)(i)", "parent_question": "4", "marks": 4, "marks_confidence": "derived", "question_text": "Thaifead Proinnsias agus Ciarán araon an méid sonraí móibíleacha a d'úsáid siad gach seachtain ar feadh cúig seachtaine. Sa ghraf thíos léirítear an méid sonraí móibíleacha a d'úsáid Proinnsias ar gach ceann de na laethanta sin.\n(a)(i) cé acu seachtain inar úsáid Proinnsias an méid sonraí móibíleacha is mó?", "has_images": true, "image_notes": "Line graph titled 'Méid na sonraí móibíleacha a úsá ideadh (ina GB)'. Y-axis 'Méid na sonraí móibíleacha a úsáideadh (ina GB)' from 0 to 6. X-axis labelled Seachtain1, Seachtain 2, Seachtain 3, Seachtain 4, Seachtain 5 (Seachtain = week). Proinnsias' line plots approximately: Week1 ≈ 2, Week2 ≈ 1, Week3 ≈ 2.5, Week4 ≈ 3, Week5 ≈ 1.", "topic": "Statistics", "marking_scheme_answer": "[Seachtain] 3 (Week 3)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q4aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)(ii)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "(ii) cé mhéad GB de shonraí móibíleacha a d'úsáid Proinnsias i Seachtain 5?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "2 [GB]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q4aiii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)(iii)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "(iii) cé acu seachtain inar úsáid Proinnsias níos lú sonraí móibíleacha ná mar a d'úsáid sé an tseachtain roimhe sin?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "[Seachtain] 4", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q4b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Gach ceann de na seachtainí sin, d'úsáid Ciarán 2 GB níos mó de shonraí ná mar a d'úsáid Proinnsias. Bain úsáid as an eolas seo chun graf a tharraingt ar an léaráid thuas ag taispeáint cé mhéad sonraí móibíleacha a d'úsáid Ciarán i ngach ceann de na seachtainí sin.", "has_images": true, "image_notes": "Same line graph as part (a) (Proinnsias' usage line over Seachtain 1–5, GB on y-axis 0–6). Candidate must plot Ciarán's line 2 GB above Proinnsias each week.", "topic": "Statistics", "marking_scheme_answer": "Pointí breactha i gceart agus líne nó cuair ceangailte iad: Ciarán = Proinnsias + 2 GB each week, i.e. plotted points 2 above Proinnsias' values and joined.", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q4bi", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)(i)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "(b)(i) Scríobh síos imlíne Thriantán B, i dtéarmaí x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Imlíne B = 3 + 2x + (2x + 1) = 4x + 4. Marked with (b)(ii) on Scale 10D (0, 3, 5, 8, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q4bii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)(ii)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Is ionann imlíne Thriantán B agus 24 cm. Bain úsáid as seo chun luach x a oibriú amach.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4x + 4 = 24 → 4x = 20 → x = 5 cm. Marked with (b)(i) on Scale 10D (0, 3, 5, 8, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q4ci", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)(i)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "(c) Foirmíonn imlínte na dtrí thriantán A, B, agus C seicheamh líneach. Is ag Triantán C atá an imlíne is mó. (i) Is ionann imlíne Thriantán C agus k cm, áit a bhfuil k ∈ ℕ. Faigh luach k.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Imlíne A = 8, imlíne B = 24, so common difference = 24 − 8 = 16. Imlíne C = 24 + 16 = 40 cm, i.e. k = 40. Marked with (c)(ii) on Scale 5D (0, 2, 3, 4, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q4cii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)(ii)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "(ii) Uaidh sin oibrigh amach luach y, áit a bhfuil y ∈ ℕ.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Imlíne C: 5 + y + (y² + 3) = 40 → y² + y + 8 = 40 → 2y² = 32 (per scheme working: 5 + y² + y² + 3 = 40) → y² = 16 → y = 4 (y = ±4, take y ∈ ℕ so y = 4). Marked with (c)(i) on Scale 5D (0, 2, 3, 4, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q5a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Tá caidéal do bhalúin déanta as sorcóir de trastomhas inmheánach 6 cm agus airde 20 cm, mar a thaispeántar. Gach uair a phumpáiltear an caidéal seolann sé sorcóir amháin lán d'aer isteach sa bhalún. (a) Taispeáin gurb ionann toirt an aeir sa tsorcóir, nuair a bhíonn sé lán, agus 180π cm^3.", "has_images": true, "image_notes": "A diagram of a cylindrical balloon pump (syringe) lying horizontally, labelled with internal diameter 6 cm and length 20 cm.", "topic": "Geometry", "marking_scheme_answer": "V = πr²h = π(6/2)²(20) = π(3²)(20) = 180π cm³. Scale 5B (0, 2, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q5a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Cuireadh ceist ar 6 dhalta i rang (U) ar rith siad (R) nó ar rothaigh siad (C) le linn an bhriseadh lár téarma. Taispeántar na freagraí a thug siad sa Léaráid Venn.\n(a) Ainmnigh dalta amháin a rith le linn an bhriseadh lár téarma.", "has_images": true, "image_notes": "Venn diagram inside universal set U. Two overlapping ellipses: set R (Rith/ran) and set C (rothaigh/cycled). R only: Diarmuid, Marcella. Intersection R∩C: Tadhg, Denise. C only: Sorcha. Outside both sets (in U): Pól.", "topic": "Probability", "marking_scheme_answer": "Diarmuid / Marcella / Tadhg / Denise (any one in set R)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q5b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 3, "marks_confidence": "derived", "question_text": "Mínigh cad is ciall leis an ráiteas seo a leanas, i dtéarmaí na ndaltaí sa rang: #C = 3", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "Ba 3 dhalta a rothaigh (there are 3 students in set C, i.e. 3 students cycled).", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q5bi", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)(i)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "(b) Tá balún, a bhfuil cruth sféir air, á theannadh ag Dara. Nuair a bhíonn sé teannta go hiomlán, bíonn ga 15 cm ag an mbalún. (i) Faigh toirt bhalún Dhara nuair a bhíonn sé teannta go hiomlán. Bíodh do fhreagra ina cm^3, i dtéarmaí π.", "has_images": true, "image_notes": "A photo of a spherical (gold) inflated balloon (illustrative).", "topic": "Geometry", "marking_scheme_answer": "V = (4/3)πr³ = (4/3)π(15³) = 4500π cm³. Marked with (b)(ii) on Scale 10D (0, 3, 5, 8, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q5bii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)(ii)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Pumpálann Dara an caidéal uair amháin gach soicind. (ii) Cé mhéad soicind a thógfaidh sé ar Dhara a bhalún a theannadh go hiomlán?", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "4500π / 180π = 25 soicindí. Marked with (b)(i) on Scale 10D (0, 3, 5, 8, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q5c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "(c) Tá balún níos mó, atá ar chruth sféir, á theannadh ag Gustav. Pumpálann sé an caidéal uair amháin gach soicind freisin. Bíonn a bhalún teannta go hiomlán tar éis 50 soicind. Faigh ga bhalún Ghustav nuair a bhíonn sé teannta go hiomlán. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": true, "image_notes": "A photo of a larger spherical (gold) inflated balloon (illustrative).", "topic": "Geometry", "marking_scheme_answer": "Toirt = 50 × 180π = 9000π cm³. (4/3)πr³ = 9000π → r³ = 6750 → r = ∛6750 = 18·89... = 18·9 cm (1 d.p.). Scale 5D (0, 2, 3, 4, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q5c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 2, "marks_confidence": "derived", "question_text": "Ainmnigh dalta amháin atá sa réigiún R ∩ C sa léaráid Venn.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "Tadhg / Denise (a student in R ∩ C)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q5d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Roghnaítear dalta amháin go randamach as na sé dhalta sa léaráid Venn. Scríobh síos an dóchúlacht gur rith an dalta sin le linn an bhriseadh lár téarma.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "4/6 nó 2/3", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q6", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6", "parent_question": "6", "marks": 20, "marks_confidence": "high", "question_text": "Fiafraíodh de 80 dalta i ngrúpa cad a rinne siad i rith a laethanta saoire. Fuair cuid de na daltaí post samhraidh (P), chuaigh cuid díobh ar saoire (S), bhí an dá rud á ndéanamh ag cuid díobh, agus ní raibh ceachtar den dá rud á dhéanamh ag cuid eile acu. Ní raibh ceachtar den dá rud á dhéanamh ag 1/5 de na daltaí sa ghrúpa. Fuair 25% de na daltaí post. De na daltaí sin a fuair post, chuaigh leath díobh ar saoire freisin. Oibrigh amach líon iomlán na ndaltaí sa ghrúpa a chuaigh ar saoire. Is féidir leat an léaráid Venn thíos a úsáid chun cabhrú leat a cheist a fhreagairt.", "has_images": true, "image_notes": "A two-set Venn diagram with overlapping ellipses P (post) and S (saoire), inside a rectangle (universal set, 80 students). Regions to be filled; a 'Freagra =' box is provided. Also a scenic photo above (illustrative).", "topic": "Probability", "marking_scheme_answer": "Neither = (1/5)×80 = 16. Post = 0·25×80 = 20; of these, half also went on holiday: 20÷2 = 10 (P∩S). Saoire amháin = 80 − (20 + 16) = 44. Total who went on holiday = 10 + 44 = 54. Scale 20C (0, 7, 12, 20).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q6a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Ghlac na daltaí go léir sa cheathrú bliain ar scoil páirt i gcomórtas léime fada. Sa tábla minicíochta seo a leanas, taispeántar na torthaí.\nFad a léimeadh (cm): 200–250, 250–300, 300–350, 350–400, 400–450, 450–500.\nLíon na ndaltaí: 10, 15, 25, 32, 10, 3.\n(a) San iomlán, cé mhéad dalta a ghlac páirt sa chomórtas?", "has_images": true, "image_notes": "Frequency table. Fad a léimeadh (cm) classes: 200–250, 250–300, 300–350, 350–400, 400–450, 450–500. Líon na ndaltaí (number of students): 10, 15, 25, 32, 10, 3 respectively.", "topic": "Statistics", "marking_scheme_answer": "10 + 15 + 25 + 32 + 10 + 3 = 95", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q6b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Céard é grúpa módúil an tábla minicíochta? Ná cuir tic (✓) ach i mbosca amháin.\n300–350 350–400 400–450 450–500", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "350 − 400", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q6ci", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(c)(i)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "Ní mór do dhalta 415 cm nó níos mó a léim chun cáiliú don bhabhta ceannais.\n(i) Céard é an líon is lú daltaí a d'fhéadfadh cáiliú don bhabhta ceannais?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q6cii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(c)(ii)", "parent_question": "6", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Céard é an líon is mó daltaí a d'fhéadfadh cáiliú don bhabhta ceannais?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "10 + 3 = 13", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q6d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Tarraing histeagram chun na sonraí sa tábla minicíochta a chur in iúl. Bain úsáid as na haiseanna agus na scálaí thíos.", "has_images": true, "image_notes": "Blank histogram grid provided. Y-axis 'Líon daltaí' from 0 to 35 (gridlines every 5). X-axis 'Fad a léimeadh (cm)' from 200 to 500 (marks at 200,250,300,350,400,450,500). Candidate plots bars of heights 10,15,25,32,10,3.", "topic": "Statistics", "marking_scheme_answer": "Histogram with bars of heights 10, 15, 25, 32, 10, 3 over the intervals 200–250, 250–300, 300–350, 350–400, 400–450, 450–500.", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q6e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(e)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Ba é 331 cm an fad airmheánach a léimeadh. Mínigh cad a chiallaíonn sé seo, i dtéarmaí na bhfad a léim na daltaí sa chomórtas léime fada.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Léim leath de na daltaí níos lú ná 331 cm (agus leath níos mó ná 331 cm); is é seo an léim sa lár nuair a chuirtear na faid in ord. (Explanation of median.)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q7ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Iarrtar ar Áine agus ar Jeaic luachanna a roghnú do na huimhreacha p, q, agus r i dtreo go mbeidh sé seo a leanas fíor le haghaidh gach a ∈ ℝ: a^p × a^q × a^r = a^12. (i) Roghnaigh Áine trí luach agus iad go léir mar an gcéanna, mar sin p = q = r. Breac síos na luachanna ar p, q, agus r a roghnaigh Áine.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "p = q = r = 12/3 = 4. Marked with (a)(ii) on Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q7ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Sa triantán thíos tá dhá uillinn ar méid dóibh 70°, mar a thaispeántar (níl an léaráid de réir scála).\n(i) Cén cineál triantáin é seo? Ná cuir tic (✓) ach i mbosca amháin.\nDronuilleach Comhchosach Comhshleasach", "has_images": true, "image_notes": "Triangle (not to scale) with apex angle at top 70° and base-left angle at vertex A marked 70°; base-right angle also marked 70°.", "topic": "Geometry", "marking_scheme_answer": "Comhchosach (isosceles)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q7aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Roghnaigh Jeaic trí luach agus iad go léir difriúil. Breac síos luachanna féideartha ar p, q, agus r a d'fhéadfadh Jeaic a roghnú.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Aon trí oiread de réaduimhreacha a chuireann le 12, agus iad go léir difriúil óna chéile. Mar shampla: p = 0, q = −1·5, r = 13·5. Marked with (a)(i) on Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q7aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Oibrigh amach méid na huillinne A, an tríú huillinn sa triantán seo.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "180 − (70 + 70) = 40[°]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q7aiii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(iii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "(iii) Tá an triantán seo ceangailte do chomhthreomharán, mar a thaispeántar thíos. Tá an uillinn B sa chomhthreomharán marcáilte. Oibrigh amach méid na huillinne B.", "has_images": true, "image_notes": "The isosceles triangle (with 70° base angles) attached to a parallelogram (comhthreomharán). Angle B is marked inside the parallelogram at its upper-right region.", "topic": "Geometry", "marking_scheme_answer": "B = 180 − 70 = 110[°]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q7b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "(b) Faigh luach m i dtreo go bhfuil sé seo a leanas fíor le haghaidh gach b ∈ ℝ: (b^m × b^-2)/b = b^10.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "b^(m−2−1) = b^10 → m − 3 = 10 → m = 13. Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q7b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "Sa léaráid thíos taispeántar an triantán T. Taispeántar faid dhá shlios agus méid uillinne amháin. Taispeántar 4 thriantán bhreise thíos. I gcás gach triantáin díobh, cuir tic (✓) sa bhosca ceart chun a thaispeáint an bhfuil sé iomchuí go cinnte le T, nó nach bhfuil.", "has_images": true, "image_notes": "Reference triangle T: sides 3 and 4 with included angle 80° between them. Four candidate triangles in a table, each to be judged 'Tá' (yes, congruent) or 'Níl' (no): (1) sides 3 and 4 with 80° between them (same arrangement, congruent); (2) sides 3 and 4 with 20° between them; (3) sides 4 and 3 with 80° between them (SAS, congruent); (4) sides 4 and 3 with 80° angle positioned at base.", "topic": "Geometry", "marking_scheme_answer": "Bionn / Ní bhíonn / Ní bhíonn / Bíonn (triangle 1: yes congruent; triangle 2: no; triangle 3: no; triangle 4: yes congruent)", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q8a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Sa léaráid thíos taispeántar dhá fhoirgneamh cheartingearacha, A agus B (níl an léaráid de réir scála). Seasann Máire ar bharr fhoirgneamh A. Tá sí 220 m os cionn na talún. Teastaíonn uaithi na faid atá marcáilte y agus z sa léaráid – is é sin, an fad ó bharr Fhoirgneamh A go dtí bun Fhoirgneamh B, agus airde Fhoirgneamh B, faoi seach – a oibriú amach. Tomhaiseann Máire na huillinneacha 35° agus 20° atá marcáilte sa léaráid, go dtí bun Fhoirgneamh B agus go dtí barr Fhoirgneamh B, faoi seach. Tá an líne bhriste cothrománach. (a) Oibrigh amach méid na huillinne C.", "has_images": true, "image_notes": "Diagram (not to scale) of two vertical buildings A and B. Máire stands at the top of Building A, 220 m above ground. From her eye level a horizontal broken line goes toward Building B. Two angles of depression/elevation are marked at the top of A: 35° (down to the base of B) and 20° (up to the top of B). The line y runs from top of A to base of B; z is the height of Building B; angle C is at the base of B (between the building and the line y). Horizontal ground distance between the buildings = 154 m.", "topic": "Trigonometry", "marking_scheme_answer": "C = 180 − (90 + 35) = 55° (or C = 90 − 35 = 55°). Check: tan C = 220/154, C = tan⁻¹(220/154) = 55·008° ≈ 55°. Scale 10B (0, 4, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q8ai", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeánann an graf ar an léaráid comhordanáideach thíos an gaol idir céimeanna Celsius (°C) agus céimeanna Fahrenheit (°F). Sa léaráid, ní thosaíonn na haiseanna ag (0, 0).\n(a)(i) Is é 37°C an gnáth-theocht do dhuine fásta. Scríobh 37°C ina céimeanna Fahrenheit.", "has_images": true, "image_notes": "Coordinate graph. X-axis 'Teocht i Celsius (°C)' from 29 to 39. Y-axis 'Teocht i bhFahrenheit (°F)' from about 84 to 103. A straight red line rises from lower-left to upper-right. A point S is marked on/near the line at approximately (32, 90). Axes do not start at origin.", "topic": "Functions", "marking_scheme_answer": "98·6 [°F]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q8aii", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Glactar le teocht os cionn 100·4°F mar theocht ard. Scríobh 100·4°F ina céimeanna Celsius.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "38 [°C]", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q8b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "(b) Oibríonn Máire amach gurb é 154 m, ceart go dtí an méadar is gaire, an fad cothrománach idir an dá fhoirgneamh, mar a thaispeántar. Bain úsáid as Teoirim Phíotágarais chun an fad marcáilte y ar an léaráid a oibriú amach. Bíodh do fhreagra ceart go dtí an méadar is gaire.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "y² = 154² + 220² = 23716 + 48400 = 72116. y = √72116 = 268·54... = 269 m (nearest metre). Scale 10C (0, 4, 7, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q8b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Tá an pointe S marcáilte ar an ngraf. Déan meastachán ar chomhordanáidí an phointe S.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "(32, 89·6) ≈ (32, 90), tolerance ±0·2 le haghaidh y-luach", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q8c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "(c) Bain úsáid as triantánacht chun luach z, airde Fhoirgneamh B, a oibriú amach. Bíodh do fhreagra ceart go dtí an méadar is gaire.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "z = h + 220, where tan 20° = h/154 → h = 154 tan 20° = 56·05... So z = 220 + 56·05 = 276·05 = 276 m (nearest metre). Scale 5D (0, 2, 3, 4, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q8c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Tá na pointí (35, 95) agus (30, 86) ar ghraf na líne freisin. Bain úsáid as an dá phointe seo chun fána an ghraif a oibriú amach.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "(95−86)/(35−30) = 9/5 nó 1·8", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q8d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Sa tábla tugtar dhá éagothromóid i T (teocht i °C), agus dhá chur síos ar éagothromóidí i T. Comhlánaigh an tábla agus cuir isteach an cur síos agus an éagothromóid atá in easnamh.\nRó 1: Cur síos 'Tá an teocht níos lú ná 36°C', Éagothromóid 'T < 36'. Ró 2: Cur síos [in easnamh], Éagothromóid '36 < T < 38'. Ró 3: Cur síos 'Tá an teocht níos mó ná 38°C', Éagothromóid [in easnamh].", "has_images": true, "image_notes": "Table with three rows. Columns 'Cur síos' (description) and 'Éagothromóid' (inequality). Row 1: 'Tá an teocht níos lú ná 36°C' | T < 36. Row 2: [blank description to fill] | 36 < T < 38. Row 3: 'Tá an teocht níos mó ná 38°C' | [blank inequality to fill].", "topic": "Algebra", "marking_scheme_answer": "Row 2 cur síos: 'Tá an teocht idir 36 agus 38°C' (the temperature is between 36 and 38°C). Row 3 éagothromóid: T > 38.", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q8e", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(e)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Tarraing graf den éagothromóid T < 36 ar an uimhirlíne thíos, áit a bhfuil T ∈ ℝ (is réaduimhir é T).", "has_images": true, "image_notes": "Number line marked 34, 35, 36, 37, 38, 39, 40. Candidate graphs T < 36 (open circle / hollow point at 36 with line/arrow extending left towards lower values).", "topic": "Algebra", "marking_scheme_answer": "Open (hollow) point at 36 with the line extending to the left (towards values less than 36).", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q9a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "(a) k = 7 agus m − k = 4. Oibrigh amach luach 9k − 6m.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "k = 7, m = 11. 9(7) − 6(11) = 63 − 66 = −3. Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q9a", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "Déanann Máiréad troscán agus díolann sí é.\n(a) Cosnaíonn sé €75 ar Mháiréad cathaoir a dhéanamh. Díolann sí í ar €110. Oibrigh amach an brabús a dhéanann sí ar an gcathaoir.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "110 − 75 = [€] 35", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q9b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "(b) Fachtóirigh go hiomlán: 8ax − 14bx + 4ay − 7by.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8ax − 14bx + 4ay − 7by = 2x(4a − 7b) + y(4a − 7b) = (2x + y)(4a − 7b). Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q9b", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Cosnaíonn sé €120 ar Mháiréad binse a dhéanamh. Déanann sí brabús €45 nuair a dhíolann sí é. Oibrigh amach an méid ar a ndíolann Máiréad an binse.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "120 + 45 = [€] 165", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q9c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "(c) Scríobh é seo a leanas mar chodán singil san fhoirm is simplí: 2/(2x + 1) − 3/(3x + 5).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "[2(3x + 5) − 3(2x + 1)] / [(2x + 1)(3x + 5)] = (6x + 10 − 6x − 3) / [(2x + 1)(3x + 5)] = 7 / [(2x + 1)(3x + 5)]. Scale 10D (0, 3, 5, 8, 10).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q9c", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Cosnaíonn €3n ar Mháiréad stól a dhéanamh, áit a bhfuil n ∈ ℕ. Díolann sí an stól ar €5n. Oibrigh amach an brabús a dhéanann sí ar an stól, i dtéarmaí n.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "5n − 3n = [€] 2n", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2022-higher-level-IV-q9d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "(d) Réitigh an chothromóid 2x^2 − 7x − 3 = 0. Bíodh gach freagra díobh ceart go dtí 2 ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x = [7 ± √(7² − 4(2)(−3))]/(2·2) = (7 ± √73)/4 = 3·886... nó −0·386... = 3·89 nó −0·39 (2 d.p.). Scale 5C (0, 2, 3, 5).", "source_pdf": "2022 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2022-ordinary-level-IV-q9d", "subject_n": "Mathematics", "year": 2022, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Cosnaíonn €320 ar Mháiréad bord a dhéanamh. Déanann sí brabús €80 nuair a dhíolann sí é. Scríobh brabús Mháiréad don bhord mar chéatadán dá chostphraghas.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "80/320 × 100 = 25%", "source_pdf": "2022 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q1a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Xena's car has a screen which shows the temperature in degrees Celsius, correct to the nearest whole number. When Xena was going to work one day, the temperature on the screen was 18 °C. Write down three possible values that the actual temperature could have been when Xena was going to work.", "has_images": true, "image_notes": "Photo of a car dashboard display showing range 193525 km, a fuel/range figure of 249 km, and the temperature reading 18 °C.", "topic": "Number", "marking_scheme_answer": "Any three values of t with 17.5 °C ≤ t < 18.5 °C, e.g. 17.5 °C, 17.9 °C, 18.49 °C.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q1ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Find the value of each of the following.\n(i) 372 + 119", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q1aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Find the value of each of the following.\n(ii) 3.4 × 7", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "23.8", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q1aiii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Find the value of each of the following.\n(iii) 4^2 × (8 − 5)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "4^2 × 3 = 16 × 3 = 48", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q1b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Fill in the missing values in the inequality in t below to show the range of possible values of t when Xena was going to work. [ ] ≤ t < [ ]", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "17.5 ≤ t < 18.5", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q1b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Martin bought the following items in his local shop. Fill in the table below to find the total cost of his shopping.\nItems / Cost (in €):\n3 litres of milk at €1.27 a litre\n4 scones at €1.10 each\n500 grams of ham at €12 per kg\nTotal Cost", "has_images": true, "image_notes": "A table with two columns (Items, Cost in €) and four rows: '3 litres of milk at €1.27 a litre', '4 scones at €1.10 each', '500 grams of ham at €12 per kg', and a 'Total Cost' row. Cost cells are blank for the student to fill.", "topic": "Number", "marking_scheme_answer": "3 × 1.27 = 3.81; 4 × 1.10 = 4.40; 0.5 × 12 = 6; Total = €14.21", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q1c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "If you were to graph the actual temperature, t, over the course of a day, would it be appropriate to graph t ∈ ℕ, t ∈ ℤ, or t ∈ ℝ? Give a reason for your answer. (Tick one box only.)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "t ∈ ℝ. Reason: values of temperature (t) will take on decimal places over the course of a day; the temperature varies continuously.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q10a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 8, "marks_confidence": "derived", "question_text": "Michelle must pay Universal Social Charge (USC) on all of her gross income. The income bands and rates of USC that Michelle must pay are given in the table (Up to €12 012: 1.5%; Next €5564: 3.5%; Above €17 576: 7%). Michelle pays USC at all three rates. Find the amount of USC that she must pay at each of the first two rates (1.5% and 3.5%). USC @ 1.5% = , USC @ 3.5% = .", "has_images": true, "image_notes": "Table — Income Band vs Rate of USC: 'Up to €12 012' → 1.5%, 'Next €5564' → 3.5%, 'Above €17 576' → 7%.", "topic": "Number", "marking_scheme_answer": "USC @ 1.5% = 12 012 × 0.015 = €180.18. USC @ 3.5% = 5564 × 0.035 = €194.74.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q10a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 10, "marks_confidence": "derived", "question_text": "Martina buys a carton of yoghurt. The carton is roughly the shape of a cylinder. It has the dimensions shown in the diagram below (r = 4 cm, h = 11 cm).\n(a) Work out the volume of the carton in cm^3. Give your answer in terms of π.\nV = πr^2h", "has_images": true, "image_notes": "A photo of a yoghurt carton next to a blue cylinder diagram. The cylinder has radius r = 4 cm (marked across the top) and height h = 11 cm (marked on the side).", "topic": "Geometry", "marking_scheme_answer": "V = π(4)^2(11) = π(16)(11) = 176π cm^3.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q10b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 7, "marks_confidence": "derived", "question_text": "Michelle's gross income is x. Michelle pays a total of 5% of her gross income in USC. Write an expression, in terms of x, for the total amount of money that Michelle pays in USC.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Total USC = x × 5% = (5/100)x = 0.05x (i.e. x/20).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q10b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "derived", "question_text": "The carton contains fruit and yoghurt and weighs 450 g. The ratio of fruit to yoghurt is 4 : 21.\nWork out how many grams of fruit are in the carton.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "4 + 21 = 25 parts; (4/25) × 450 = 72 g of fruit.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q10c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Find the value of x, Michelle's gross income.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Total USC = 180.18 + 194.74 + 0.07(x − 17 576) = 0.05x. Solving: 0.07x − 1230.32 + 374.92 = 0.05x → 0.02x = 855.40 → x = 855.40/0.02 = €42 770.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q11", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "The graph below shows the approximate temperature in Madrid throughout one day (in °C). The temperature in Ennis was exactly half that in Madrid throughout this day.\nOn the diagram below, draw a graph of the temperature in Ennis throughout this day. Use the same axes and scales.", "has_images": true, "image_notes": "A line graph of temperature (°C, y-axis 0 to 30) versus Time (x-axis from Midnight, through 12 noon, to Midnight). The 'Madrid' line passes through approximately: 20, 15, 15, 30, 30, 30, 20 at successive gridlines (starts at 20 at midnight, dips to 15, rises to 30 at midday and holds, then drops to 20 at the next midnight).", "topic": "Functions", "marking_scheme_answer": "Draw the Ennis graph at half the Madrid values, joining these temperatures on each vertical gridline with straight lines: 10, 7.5, 7.5, 15, 15, 15, 10.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q11a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "30 000 people went to a football match in Star Stadium. After the match, the 30 000 people left the stadium at a constant rate. The graph shows P, the number of people still in the stadium t minutes after the end of the match. Two points are marked on the graph: G and W. The point G has co-ordinates (6, 21 000). Explain what the 6 and the 21 000 mean, in terms of the number of people in the stadium.", "has_images": true, "image_notes": "Line graph: y-axis 'Number of people left in Star Stadium' (marked at 30 000), x-axis 'Minutes after the end of the match'. A straight red line falls from (0, 30 000) through G(6, 21 000) down to W on the t-axis (where P = 0).", "topic": "Functions", "marking_scheme_answer": "The 6 means 6 minutes after the end of the match, and the 21 000 means there were 21 000 people still in the stadium at that time. (G(6, 21 000): after 6 minutes, 21 000 people remain in the stadium.)", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q11b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "It took 20 minutes for all of the 30 000 people to leave the stadium. Use this fact to write down the co-ordinates of the point W, which is on the t-axis. W = ( , ).", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "W = (20, 0).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q11ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)(i)", "parent_question": "11", "marks": 3, "marks_confidence": "derived", "question_text": "The equation of the graph can be written as: P = 30 000 − 1500 t. How many people were in the stadium 12 minutes after the match had finished?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "P = 30 000 − 1500(12) = 30 000 − 18 000 = 12 000 people.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q11cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)(ii)", "parent_question": "11", "marks": 2, "marks_confidence": "derived", "question_text": "Explain what the 1500 in this equation means, in terms of the number of people in the stadium.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "1500 people leave the stadium each minute after the match ends (it is the rate of decrease / the slope).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q12a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "The diagram shows a curved shape ABC. C is the centre of the circular arc from A to B. A is the centre of the circular arc from B to C. B is the centre of the circular arc from C to A. The dotted triangle ABC is an equilateral triangle. Using only a compass and straight edge, construct one of the axes of symmetry of the curved shape ABC. Show all of your construction lines clearly.", "has_images": true, "image_notes": "A Reuleaux-triangle-style curved shape with three outward-bulging circular arcs joining vertices A (top), B (bottom left), C (bottom right). Dotted equilateral triangle ABC drawn inside connecting the three vertices.", "topic": "Geometry", "marking_scheme_answer": "Construct the perpendicular bisector of any one of [AB], [AC] or [BC] (or bisect any one of the angles ∠ACB, ∠ACB or ∠BAC), continued to the third vertex — this is an axis of symmetry. Construction lines must be shown.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q12a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Pawel makes the 'adding wall' below. Each box in the bottom row is filled in. To fill in any other box, you add the two numbers in the boxes that are directly below it. For example, in the shaded boxes: 5 + 3 = 8.\n(a) Fill in all the boxes in Pawel's adding wall above.", "has_images": true, "image_notes": "A four-row number 'adding wall' (pyramid). Bottom row: −2, 1, 5, 3. Third row: −1, (blank), 8 (shaded). Second row: two blank boxes. Top: one blank box. Each box equals the sum of the two boxes directly below it.", "topic": "Number", "marking_scheme_answer": "Bottom: −2, 1, 5, 3; next row: −1, 6, 8; next: 5, 14; top: 19.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q12b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Pawel also makes the 'algebra adding wall' below, with the same rules.\n(b) Fill in all the boxes in Pawel's algebra adding wall below, in terms of x.", "has_images": true, "image_notes": "A four-row algebra adding wall. Bottom row: x − 4, 1, x + 3 (shaded), x + 1 (shaded). Third row: x − 3, (blank), 2x + 4 (shaded). Second row: two blank boxes. Top: one blank box. Each box is the sum of the two directly below it.", "topic": "Algebra", "marking_scheme_answer": "Bottom: x−4, 1, x+3, x+1; next row: x−3, x+4, 2x+4; next: 2x+1, 3x+8; top: 5x+9.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q12bi", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Write down the size of the angle ∠ACB.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "|∠ACB| = 60° (angle of the equilateral triangle).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q12bii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "The length of the straight-line segment [BC] is 40 cm. Find the length of the circular arc from B to C. Give your answer in cm, correct to 2 decimal places.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "The arc from B to C is centred at A with radius |AB| = |AC| = 40 cm and subtends 60° (= ∠BAC). Arc length = (60/360)(2πr) = (60/360)(2π)(40) = 41.8879… = 41.89 cm (to 2 decimal places).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q12c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "There is one value of x that will make both adding walls exactly the same. Find this value of x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x = 2 with supporting work, for example x − 4 = −2, so x = 4 − 2 = 2.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q13a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "A company is making a large rectangular poster, as shown in the diagram on the right. The top section will be a square shape. The bottom section will be a rectangle of height 0.5 m, which will have the sponsors' logos. The width of the poster is x m, as shown. Write the total height of the poster, in terms of x. Total height = [ ] m.", "has_images": true, "image_notes": "Diagram 'Rectangular Poster': a square 'Square Image' of side x m on top of a rectangle 'Sponsors' Logos' of height 0.5 m; overall width x m (labelled at the bottom).", "topic": "Algebra", "marking_scheme_answer": "Total height = x + 0.5 m.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q13a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 10, "marks_confidence": "high", "question_text": "Use the theorem of Pythagoras to find the value of x in the right-angled triangle below. Show all of your working out.", "has_images": true, "image_notes": "A right-angled triangle with the right angle at the bottom-left corner. The vertical side is labelled 5, the horizontal base is labelled 12, and the hypotenuse is labelled x.", "topic": "Geometry", "marking_scheme_answer": "x^2 = 5^2 + 12^2 = 25 + 144 = 169, so x = √169 = 13.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q13b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "The total area of the poster is 50 m^2. Show that 2x^2 + x − 100 = 0.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Area = width × height = x(x + 0.5) = 50, so x^2 + 0.5x − 50 = 0; multiplying by 2 gives 2x^2 + x − 100 = 0.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q13b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Draw the image of the following triangle under central symmetry in the point A.", "has_images": true, "image_notes": "A coordinate/square grid showing a shaded triangle to the upper-right of a marked point A. The triangle's vertices sit a few squares up and to the right of A; the task is to map it under central symmetry (point reflection) through A, producing the congruent image on the opposite side of A.", "topic": "Geometry", "marking_scheme_answer": "Correct image drawn — the triangle reflected through point A (central symmetry): same size and orientation, positioned diametrically opposite on the far side of A.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q13c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 10, "marks_confidence": "high", "question_text": "Solve the equation 2x^2 + x − 100 = 0 to find the value of x, the width of the poster. Give your answer in metres, correct to the nearest centimetre.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x = (−1 ± √(1^2 − 4(2)(−100)))/(2(2)) = (−1 ± √801)/4. So x = 6.825… or x = −7.325…. Taking the positive value, x = 6.83 m (to the nearest centimetre). [Negative value rejected.]", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q13ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)(i)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "(c)(i) Work out the size of the angle B in the triangle below.", "has_images": true, "image_notes": "A scalene triangle with the angle at the left vertex marked 27°, the angle at the bottom-right vertex marked 60°, and the angle B at the top-right vertex. The side opposite B (top edge) is labelled 10, the short right side is 5.2, and the bottom side is labelled y.", "topic": "Geometry", "marking_scheme_answer": "Angles in a triangle sum to 180°: B = 180 − (27 + 60) = 93°.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q13cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)(ii)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "(c)(ii) Explain why the theorem of Pythagoras cannot be used to find the length of the side y in the triangle above.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "It is not a right-angled triangle (or another valid explanation).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q14a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 8, "marks_confidence": "derived", "question_text": "The diagram shows a triangle ABC (not to scale). The points D and E lie on [AC] and [BC], respectively. |∠CAB| = |∠DEC| = 90°. The lengths of some of the sides are given in the diagram, with x, y ∈ ℝ (|DC| = 15, |DE| = 9, |EC| = x, |BE| = x, |AB| = y). Work out the value of x.", "has_images": true, "image_notes": "Triangle ABC (not to scale), right angle at A. D on AC with |DC| = 15 along AC. E on BC with right angle ∠DEC = 90°; |DE| = 9, |EC| = x. On BC, |BE| = x as well. |AB| = y (vertical-ish side from A to B). Right triangle DEC has legs DE = 9, EC = x and hypotenuse DC = 15.", "topic": "Geometry", "marking_scheme_answer": "In right triangle DEC: x^2 + 9^2 = 15^2, so x^2 + 81 = 225, x^2 = 144, x = 12.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q14ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)(i)", "parent_question": "14", "marks": 4, "marks_confidence": "derived", "question_text": "The following are algebraic expressions: 2x, 3x − 2, 3x + 2, 3(x + 2).\n(a) Complete the table below by writing the correct algebraic expression from the list above next to the corresponding statement. You do not need to use all of the algebraic expressions.\n(i) Multiply x by 3, then subtract 2 from the result.", "has_images": true, "image_notes": "A two-column table (Statement | Algebraic Expression) with three statement rows: 'Multiply x by 3, then subtract 2 from the result.', 'Double x.', 'Add 2 to x, then multiply the result by 3.' The expression cells are blank, to be filled from the list 2x, 3x−2, 3x+2, 3(x+2).", "topic": "Algebra", "marking_scheme_answer": "3x − 2", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q14aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)(ii)", "parent_question": "14", "marks": 3, "marks_confidence": "derived", "question_text": "(ii) Double x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2x", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q14aiii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)(iii)", "parent_question": "14", "marks": 3, "marks_confidence": "derived", "question_text": "(iii) Add 2 to x, then multiply the result by 3.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(x + 2)", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q14b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 7, "marks_confidence": "derived", "question_text": "Using similar triangles, work out the value of y.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Triangles are similar: 15/(2x) = 9/y, i.e. 15/24 = 9/y (using x = 12, so 2x = 24). Then 15y = 216, y = 14.4.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q14b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 3, "marks_confidence": "derived", "question_text": "Multiply out and simplify (3x − 2)(2x − 3).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3x(2x − 3) − 2(2x − 3) = 6x^2 − 9x − 4x + 6 = 6x^2 − 13x + 6.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q14c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(c)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Factorise x^2 + 2x − 15.\nx^2 + 2x − 15 = (x + 5)( ___ )", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x^2 + 2x − 15 = (x + 5)(x − 3).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q2", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Ruth has 2 bags of marbles and 4 loose marbles, as shown. Liam has 1 bag of marbles and 10 loose marbles, as shown. There are the same number of marbles in each bag.\nRuth and Liam each have the same total number of marbles. Work out how many marbles are in each bag.", "has_images": true, "image_notes": "Two labelled picture panels. 'Ruth's Marbles' shows 2 red bags of marbles and 4 loose green marbles. 'Liam's Marbles' shows 1 red bag of marbles and 10 loose green marbles. The number of marbles per bag is unknown (call it b).", "topic": "Algebra", "marking_scheme_answer": "Set up equation: 2b + 4 = b + 10, so b = 6. There are 6 marbles in each bag.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q2ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "A company sells t-shirts on a website. Sometimes people buy a t-shirt, then return it again to get their money back. The diagram shows S(n), the number of t-shirts sold on the website in month n, and R(n), the number of t-shirts sold in month n that were returned, for n ∈ ℕ and n ≤ 8 (values rounded to the nearest 50). How many t-shirts were sold in Month 1?", "has_images": true, "image_notes": "Line graph: x-axis 'Month' (1 to 8), y-axis 'Number of t-shirts (nearest 50)' from 0 to 700. Red line S(n) 'sold' starts at ~300 (months 1-2), dips, rises to ~500-550 by months 6-8. Blue line R(n) 'returned' stays low near 50-100 across all months. Also a photo of two red t-shirts.", "topic": "Functions", "marking_scheme_answer": "", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q2aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "How many t-shirts were returned in Month 2?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q2b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Which month had the greatest increase in the number of t-shirts sold, compared to the previous month?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Month 7", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q2c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Complete the table below to show the number of t-shirts that were not returned each month. For example, 350 t-shirts were not returned in Month 6. (Table headed Month 1-8, row 'Number not returned', with 350 already filled for Month 6.)", "has_images": true, "image_notes": "Table with columns Month 1-8 and a row 'Number not returned'; the only pre-filled value is 350 under Month 6. Values are computed as S(n) − R(n) from the line graph.", "topic": "Functions", "marking_scheme_answer": "Number not returned = sold − returned each month: 250, 250, 300, 300, 350, 350, 450, 500 (for Months 1-8).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q2d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "On the given diagram, draw a graph to show the number of t-shirts that were not returned each month for the 8 months. Use the same axes and scales.", "has_images": true, "image_notes": "Blank coordinate grid provided on which to plot the 'not returned' values (250, 250, 300, 300, 350, 350, 450, 500) for Months 1-8, using the same axes/scale as the given line graph.", "topic": "Functions", "marking_scheme_answer": "Plot 8 points (one per month) for the 'not returned' values 250, 250, 300, 300, 350, 350, 450, 500 and join them, correctly scaled on the given axes.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q2e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(e)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Which month had the greater percentage increase in the number of t-shirts sold, compared to the previous month: Month 3 or Month 5? Justify your answer. (Tick one box only.)", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Month 3. Justification: Month 3 increase = (50/300) × 100 = 16⅔ %, while Month 5 increase = (50/400) × 100 = 12½ %, so Month 3 has the greater percentage increase.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q3a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "The students in a Transition Year mini-company make and sell candles. They buy a solid rectangular block of wax measuring 35 cm by 45 cm by 16 cm. Work out the volume of the block of wax.", "has_images": true, "image_notes": "3D drawing of a flat rectangular (cuboid) block of wax.", "topic": "Geometry", "marking_scheme_answer": "V_block = 35 × 45 × 16 = 25 200 cm^3.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q3a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "In a survey of a group of 155 students on take-away food: 75 said they like Chinese food (C); 41 said they like Indian food (I); 20 said they like both.\n(a) Complete the Venn diagram below to show this information.", "has_images": true, "image_notes": "A two-set Venn diagram inside a universal set rectangle labelled U (155). Left circle labelled C, right circle labelled I, with an overlapping middle region. The middle (intersection) currently shows 55 in the C-only style placement and 59 outside both circles; student completes the regions using C only = 75−20 = 55, both = 20, I only = 41−20 = 21, none = 59.", "topic": "Number", "marking_scheme_answer": "C ∩ I = 20 on Venn diagram; I\\C = 41 − 20 = 21 on Venn diagram (Chinese only = 75 − 20 = 55).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q3b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 7, "marks_confidence": "derived", "question_text": "The students are going to use this wax to make candles in the shape of cylinders. Each candle will have a radius of r cm and a height of 9 cm. Work out the volume of each candle, in terms of r and π.", "has_images": true, "image_notes": "Photo of a cylindrical candle.", "topic": "Geometry", "marking_scheme_answer": "V_cylinder = π(r^2)(9) = 9πr^2 cm^3.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q3b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "How many students in the group like Chinese food only?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q3c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 8, "marks_confidence": "derived", "question_text": "The students make 100 candles from the block of wax. In making the candles, 10% of the wax in the block is wasted. Use this information to work out the value of r, the radius of each candle. Give your answer correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Wax used = 25 200 × 90% = 22 680 cm^3. So 9πr^2 × 100 = 22 680, giving r^2 = 22 680/(900π), r = √(22 680/(900π)) = 2.8322… , r = 2.8 cm (to 1 decimal place).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q3c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Explain what the following statement means, in the context of this survey, where C' is the complement of the set C: #(C') = 80", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "80 students don't like Chinese food, or similar (e.g. 'The people who do not like Chinese food' or '80 people').", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q4a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "The ages of children in a crèche were recorded. The data are shown in the table (Age (years): 0-1, 1-2, 2-3, 3-4, 4-5; Number of children: 6, 10, 19, 3, 5). [Note: 2-3 means '2 years or more, but less than 3 years', etc.] Represent the data on a histogram. Label the axes clearly.", "has_images": true, "image_notes": "Frequency table — Age (years): 0-1, 1-2, 2-3, 3-4, 4-5; Number of children: 6, 10, 19, 3, 5. A blank set of axes is provided for the histogram.", "topic": "Statistics", "marking_scheme_answer": "Histogram with three correct bars and all bars correct (no gaps between bars), axes labelled (Age on x-axis, Frequency/Number of children on y-axis), bars of heights 6, 10, 19, 3, 5 for the respective age intervals.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q4a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "The hexagon below is a scaled diagram of a classroom in a school. All sides are equal in length.\n(a) By measuring, find the length of the side of the hexagon. Give your answer correct to the nearest cm.\nLength = ___ cm", "has_images": true, "image_notes": "A regular blue-shaded hexagon (all sides equal), shown as a scaled plan of a classroom. The side length is to be measured with a ruler; the scheme answer is 3 cm (tolerance ±0.2 cm).", "topic": "Geometry", "marking_scheme_answer": "3 cm (accept a tolerance of ±0.2 cm).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q4b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the percentage of children in the crèche who are aged 1-2 years. Give your answer correct to the nearest percent.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "% aged (1-2) = (10/43) × 100 = 23.26… = 23% (to the nearest percent). [Total children = 43.]", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q4b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Find the length of the perimeter of the hexagon. Give your answer in cm.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "6 × 3 = 18 cm (accept answer from part (a)).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q4c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Use mid-interval values to estimate the mean age of the children in the crèche. Give your answer in years, correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Estimated mean = (3×0.5 + 15×1.5 + 19×2.5 + 3×3.5 + 22.5×... ) — using mid-interval values: (0.5×6 + 1.5×10 + 2.5×19 + 3.5×3 + 4.5×5)/43 = 98.5/43 = 2.29 = 2.3 years (to 1 decimal place).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q4c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "The diagram is to a scale of 1 cm = 2 m.\nFind the actual perimeter of the classroom. Give your answer in metres.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "18 × 2 = 36 m.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q4d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "The table shows the maximum number of children that one staff member in the crèche can mind, depending on the age of the children (Age 0-1: 3; 1-2: 5; 2-3: 6; 3-6: 8). So, for example, one staff member can mind up to 3 children aged 0-1 years, or up to 5 children aged 1-2 years, and so on. Work out the least number of staff members that are needed to mind all of the children in the crèche.", "has_images": true, "image_notes": "Table — Age (years) vs Maximum number of children that one staff member can mind: 0-1 → 3, 1-2 → 5, 2-3 → 6, 3-6 → 8.", "topic": "Number", "marking_scheme_answer": "0-1: 6 children ÷ 3 = 2 staff; 1-2: 10 ÷ 5 = 2 staff; 2-3: 19 ÷ 6 = 4 staff; 3-6: (3+5)=8 ÷ 8 = 1 staff. Total = 9 staff.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q4d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "There are 560 students in the school. 75% of the students go to a camogie match. Work out the number of students who go to the match.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "560 × 0.75 = 420.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q4e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(e)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "In 2019, there were 80 students in first year in the school. In 2020, there were 90 students in first year.\nWrite this increase as a percentage of the number of students in first year in 2019.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(90 − 80)/80 × 100 = 12.5%.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q5a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "The table shows the outcome when the numbers a and b are multiplied together, for a, b ∈ ℕ. Write 'odd' or 'even' in each box to complete each of the mathematical statements correctly. 1. even × even = c; 2. odd × odd = c; 3. odd × even = c. (Row 1 'even' is done as an example.)", "has_images": true, "image_notes": "Table with columns a × b = c. Row 1: even × even = even (given). Row 2: odd × odd = (blank). Row 3: odd × even = (blank).", "topic": "Number", "marking_scheme_answer": "Row 2: odd × odd = odd. Row 3: odd × even = even.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q5ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)(i)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "The diagram below shows the results of a survey of how often a group of adults checked their social media accounts, each day. The results for WhatsApp are not shown.\n(a) Use the diagram to answer the following two questions. In each case, tick (✓) the correct box only.\n(i) The percentage who checked their Instagram account about once a day was: 15%, 21%, 37%, 51%", "has_images": true, "image_notes": "A 100% stacked horizontal bar chart titled 'How often do you check your social media accounts?' with three categories: 'Several times a day', 'About once a day', 'Less often'. Rows: Facebook 51% / 23% / 26%; Instagram 42% / 21% / 37%; Snapchat 46% / 15% / 39%; Twitter 25% / 17% / 58%; WhatsApp (row blank, not shown).", "topic": "Statistics", "marking_scheme_answer": "21% (the Instagram 'about once a day' value).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q5aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)(ii)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "The account that exactly 1/4 of users checked several times a day was: Facebook, Instagram, Snapchat, Twitter", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Twitter (25% = 1/4 checked it several times a day).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q5b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Ruairí rolls a regular, unbiased, six-sided die three times. He writes down the number on each roll of the die. Complete the sample space below, showing the possible combinations of odd numbers (O) and even numbers (E) that Ruairí could roll. Two possible outcomes have been filled in for you (EEE, EEO).", "has_images": true, "image_notes": "Photo of two dice. A sample-space table with two cells pre-filled: 'E E E' and 'E E O'; remaining cells blank for the other combinations of O/E across three rolls.", "topic": "Probability", "marking_scheme_answer": "All 8 outcomes: E E E, E E O, E O E, O E E, E O O, O E O, O O E, O O O.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q5b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "The results for WhatsApp are in the table below. Use the values in the table to complete the diagram above. It may be useful to use a ruler. You don't need to shade the diagram.\nResults for WhatsApp: Several times a day 60%; About once a day 20%; Less often 20%.", "has_images": true, "image_notes": "A small table 'Results for WhatsApp' with rows: Several times a day = 60%, About once a day = 20%, Less often = 20%. The student adds this WhatsApp row to the stacked bar chart from part (a).", "topic": "Statistics", "marking_scheme_answer": "Complete the WhatsApp bar appropriately: 60% several times a day, 20% about once a day, 20% less often (accept divisions between 51% and 74% for the first section).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q5c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Each outcome in the table is equally likely. Ruairí multiplies together the three numbers that he rolls. Find the probability that Ruairí will get an even number as his answer.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "7/8. (Only O O O gives an odd product; all other 7 of the 8 equally likely outcomes give an even product.)", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q5c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Eoin has a mobile phone. He paid €80 when he bought the phone, at the start of June. He paid €25 at the start of each month after that.\nWhich of the graphs below, A or B, is better at showing the way Eoin paid for his phone over the first 8 months? Give a reason for your answer.", "has_images": true, "image_notes": "Two graphs side by side, both with axes 'Total amount spent (€)' (vertical) versus 'Time' (horizontal). Graph A is a step graph: a series of horizontal steps that jump up at intervals (staircase shape). Graph B is a single straight diagonal line rising continuously from a positive y-intercept.", "topic": "Functions", "marking_scheme_answer": "Graph A. Reason: He pays at the start of each month, so the total goes up in steps (it does not increase continuously). (Or any other valid reason.)", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q6a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "The Venn diagram shows the number of elements in three regions in the sets F and G, where x ∈ ℕ. (F-only region: x + 3; intersection: x − 2; G-only region: 8 − x.) Write down the value of #(F\\G), in terms of x.", "has_images": true, "image_notes": "Venn diagram with two overlapping ovals F and G. F-only region labelled x + 3, the intersection labelled x − 2, the G-only region labelled 8 − x.", "topic": "Number", "marking_scheme_answer": "x + 3", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q6a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 15, "marks_confidence": "high", "question_text": "Maria is playing a game. She rolls the die and spins the spinner shown.\n(a) Complete the table below to show all of the possible outcomes. Three are already done for you. For example, 6 C means that Maria got a 6 on the die and a C on the spinner.", "has_images": true, "image_notes": "A six-sided die and a circular spinner divided into three sectors A, B, C. A sample-space table with rows for die values 1–6 and columns for spinner letters A, B, C. Pre-filled cells: 1B, 3A, 6C; the remaining 15 cells are to be completed (e.g. 1A, 1C, 2A, 2B, 2C, etc.).", "topic": "Probability", "marking_scheme_answer": "Complete the 6×3 table: 1A 1B 1C / 2A 2B 2C / 3A 3B 3C / 4A 4B 4C / 5A 5B 5C / 6A 6B 6C (18 outcomes; 1B, 3A, 6C already given).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q6b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "From the Venn diagram, find the greatest possible value of x. Justify your answer.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "x = 8. Justification: the maximum occurs when 8 − x ≥ 0, i.e. 8 ≥ x, so the greatest possible value is x = 8.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q6b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 4, "marks_confidence": "derived", "question_text": "How many different possible outcomes are there, in total?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q6c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 3, "marks_confidence": "derived", "question_text": "List all of the outcomes that have an even number and B.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "2B, 4B, 6B", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q6d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 3, "marks_confidence": "derived", "question_text": "Each outcome in the table is equally likely. What is the probability that Maria will get an even number and B?\nAnswer = ___", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "3/18 or 1/6.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q7a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 8, "marks_confidence": "derived", "question_text": "Laurie is asked to write down a function, and an example to show how her function works. Laurie writes: 'My function, f, takes a word as an input, and the output is the number of letters in the word. For example, f(banana) = 6.'\nUsing Laurie's function:\n(a) find the value of f(ned).\nf(ned) = ___", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q7ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "A, B, C, and D are four points in the co-ordinate plane. The points A and B are shown on the co-ordinate diagram. Plot and label the points C(8, 4) and D(3, 6) on the same co-ordinate diagram.", "has_images": true, "image_notes": "Co-ordinate grid (x from −1 to 8, y from −1 to 7). Point A is marked at approximately (1, 2) and point B at approximately (6, −1). Students must plot C(8, 4) and D(3, 6).", "topic": "Coordinate Geometry", "marking_scheme_answer": "Plot C(8, 4) and D(3, 6) correctly on the grid.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q7aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Write the co-ordinates of the points A and B in the spaces below. The co-ordinates of the points C and D are already given. A = ( , ), B = ( , ), C = (8, 4), D = (3, 6).", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "A(1, 2) and B(6, −1).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q7b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 7, "marks_confidence": "derived", "question_text": "Write in an input that gives an output of 5.\nf( ___ ) = 5", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Any combination of 5 letters. Does not have to be a recognisable word, for example 'Ghoti'.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q7bi", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Paulina wants to prove ABCD is actually a square. Answer (b)(i) and (b)(ii) to show that ABCD is a square. Show that |AB| = |BC|.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "|AB| = √((6−1)^2 + (−1−2)^2) = √29 and |BC| = √((8−6)^2 + (4−(−1))^2) = √29, so |AB| = |BC|.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q7bii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Without measuring the diagram, show that AB is perpendicular to BC.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "m_AB = (−1−2)/(6−1) = −3/5 and m_BC = (4+1)/(8−6) = 5/2. m_AB × m_BC = (−3/5) × (5/2) = −3/2... [scheme: m_AB × m_BC = −1], so AB is perpendicular to BC.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q7c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Work out the value of:\nf(Tomás) − 3 × f(Ava) + 2 × [f(Jakub)]^2", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "f(Tomás)=5, f(Ava)=3, f(Jakub)=5, so 5 − 3 × 3 + 2 × 5^2 = 46.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q7ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Ciarán makes the following statement: 'Every parallelogram is a square.' Is Ciarán's statement true or false? Justify your answer. (Tick one box only.)", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "False. Justification (for example): 'Not all parallelograms contain right angles' / 'A rectangle is not a square'.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q7cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Write down the converse of Ciarán's statement.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "'Every square is a parallelogram.'", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q8a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Convert 7.5 kilometres to metres. 7.5 km = [ ] m.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "7500 m (since 1 km = 1000 m).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q8a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "The students in a class used clinometers and metre sticks to find the height of their school. Each student measured the angle of elevation from a given point to the roof of the school. These angles are shown in the table below: 63°, 63°, 63°, 62°, 61°, 60°, 58°, 57°, 57°, 56°, 56°, 55°.\n(a) Work out the median of the angles measured by the students.", "has_images": true, "image_notes": "A table of 12 angle-of-elevation measurements arranged in three rows of four: row 1 = 63°, 63°, 63°, 62°; row 2 = 61°, 60°, 58°, 57°; row 3 = 57°, 56°, 56°, 55°.", "topic": "Statistics", "marking_scheme_answer": "Ordered, the two middle values (6th and 7th) are 58 and 60, so median = (58 + 60)/2 = 59°.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q8b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "A plane, P, took off from an airport. It left the ground at the point T. After a few minutes, it was 7.5 km from T, and it was 200 m directly above level ground, as shown in the diagram below (not to scale). Use trigonometry to work out the size of the angle marked E in the diagram. Give your answer in degrees, correct to 1 decimal place.", "has_images": true, "image_notes": "Right-angled triangle (not to scale): horizontal ground from T; hypotenuse of 7.5 km from T to Plane P; opposite vertical side of 200 m up to Plane P. Angle E is at T between the ground and the line of flight (hypotenuse).", "topic": "Trigonometry", "marking_scheme_answer": "sin E = 200/7500, so E = sin⁻¹(200/7500) = 1.528° = 1.5° (to 1 decimal place). [200 m = 0.2 km is used consistently with 7.5 km.]", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q8b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Keith finds the mean of the angles. Mairéad finds the mode of the angles. Should their answers be the same, or different? Give a reason for your answer.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Different. The mode is the most frequent number (mode = 63°), so the mean will be smaller. Mode = 63°, mean = 59.25° (or any other valid reason).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q8c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Seán's value for the angle of elevation was 57°. Seán's clinometer was at a height of 1.42 m. He was standing 4 m from the school wall at this time. Seán drew the diagram below to show this information.\n(c) Use the right-angled triangle in the diagram to write tan 57° as a fraction, in terms of x.\ntan 57° = ___", "has_images": true, "image_notes": "A diagram of a school building (rectangle labelled 'Seán's School'). A right-angled triangle is drawn from Seán's eye level to the roof: the horizontal distance from Seán to the wall is 4 m, the vertical opposite side (above clinometer height) is labelled x, the angle of elevation at Seán is 57°, and the clinometer height is 1.42 m above the ground.", "topic": "Trigonometry", "marking_scheme_answer": "tan 57° = x/4.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q8ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(i)", "parent_question": "8", "marks": 7, "marks_confidence": "derived", "question_text": "Write 20 minutes as a fraction of an hour. Give your answer in simplest form. 20 minutes = [ ] hour.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1/3 hour.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q8cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(ii)", "parent_question": "8", "marks": 8, "marks_confidence": "derived", "question_text": "During part of its flight, plane P travelled 598 km in two hours and twenty minutes. Work out the average speed of plane P during that time, in km per hour. Give your answer correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Time = 2⅓ hours = 7/3 hours. Speed = 598 ÷ (7/3) = 598 × 3/7 = 256.2857… = 256.3 km/hour (to 1 decimal place).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q8d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "In the diagram below, each of the points A, B, and C represents an airport. The plane travelled 598 km from Airport A to Airport B, and then travelled on to Airport C. Work out the distance |AC|, correct to the nearest km.", "has_images": true, "image_notes": "Triangle with vertices A (top left), B (bottom middle), C (top right). |AB| = 598 km (from A down to B). A perpendicular of 280 km drops from the line AC to B (right angle marked on AC at the foot D). Angle at C is 35°. Required: distance |AC|.", "topic": "Trigonometry", "marking_scheme_answer": "Let D be the foot of the perpendicular from B to AC. |AD|^2 = |AB|^2 − |BD|^2 = 598^2 − 280^2 = 279 204, so |AD| = 528.39757…. tan 35° = 280/|DC|, so |DC| = 280/tan 35° = 399.88144…. |AC| = |AD| + |DC| = 528.39757… + 399.88144… = 928.27901… = 928 km (to the nearest km).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q8d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Use your calculator to find the value of tan 57°. Give your answer correct to 2 decimal places.\ntan 57° = ___", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "1.539... ≈ 1.54 (2 decimal places).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q8e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(e)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Using his measurements, Seán works out that x is roughly 6.16 m. Use this value to find Seán's estimate of the total height of the school, in metres.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "Total height = x + clinometer height = 6.16 + 1.42 = 7.58 m.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q9a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Multiply out and simplify 4x(5x + 4) − 3(x − 2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4x(5x + 4) − 3(x − 2) = 20x^2 + 16x − 3x + 6 = 20x^2 + 13x + 6.", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q9a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "The weight of each baby in a group was measured every 3 months, for the first 12 months of life. Some of the results are shown in Table 1.\nTable 1 — Age of the babies (months): 0, 3, 6, 9; Mean weight of the babies (kg): 3, _, 7, _.\nThe points A(0,3) and B(6,7) are shown on the co-ordinate diagram below.\n(a) Draw the line AB on the co-ordinate diagram.", "has_images": true, "image_notes": "A coordinate grid with x-axis 'Age of the babies (months)' from 0 to 9 and y-axis 'Mean weight of the babies (kg)' from 0 to 16 (gridlines every 2). Point A is plotted at (0, 3) and point B at (6, 7). A partly-filled Table 1 gives ages 0, 3, 6, 9 with weights 3, blank, 7, blank.", "topic": "Coordinate Geometry", "marking_scheme_answer": "Draw the straight line from A(0,3) to B(6,7) (extended through the points).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q9b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Factorise fully 9 − 25y^2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(3 − 5y)(3 + 5y).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q9b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Complete the following sentence: 'The point B represents the mean weight of the babies after ___ months.'", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "6 (months).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-EV-q9c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "Write (5^7 × 25^3)/√5 in the form 5^p, where p ∈ ℚ.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(5^7 × 25^3)/√5 = (5^7 × 5^6)/5^(1/2) = 5^13/5^(1/2) = 5^(25/2).", "source_pdf": "2023 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q9c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Assume that the mean weight of the babies in the group increased in a linear pattern over the first 18 months of life.\n(c) Use the line AB to estimate the mean weight of the babies after 3 months and after 9 months. Write these values into Table 1. Show your work on the diagram.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "From the line, weight at 3 months = 5 kg and at 9 months = 9 kg; fill Table 1 with 5 and 9 (with supporting work on diagram).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q9d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "The slope of the line AB is 2/3. Explain what this slope means in the context of this question.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Each month, the mean weight of the babies goes up by 2/3 kg (or any other valid explanation of the rate of increase).", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-ordinary-level-EV-q9e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(e)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "The line AB has equation: y = (2/3)x + 3.\nUse this to estimate the mean weight of the babies after 18 months. Show your working out.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "y = (2/3)(18) + 3 = 12 + 3 = 15 kg.", "source_pdf": "2023 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q1a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Tá scáileán i gcarr Xena a thaispeánann an teocht ina céimeanna Celsius, ceart go dtí an tslánuimhir is gaire. Nuair a bhí Xena ag dul ar obair lá amháin, ba é 18 °C a bhí ar an scáileán. Scríobh síos trí luach féideartha a d'fhéadfadh a bheith ag an teocht iarbhír nuair a bhí Xena ag dul ar obair.", "has_images": true, "image_notes": "A car dashboard display graphic showing range and temperature: \"193525 km\" (odometer), \"249 km\" (range), and \"18°C\" (the displayed temperature, rounded to nearest integer).", "topic": "Number", "marking_scheme_answer": "Sample answers: any three values that round to 18 °C, e.g. 17·5°C, 17·9°C, 18·49°C. (Parts (a), (b), (c) share one scale: 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q1ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Faigh luach gach ceann díobh seo a leanas. (i) 372 + 119", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "491. (Scála 15C roinnte ar na trí chuid (i)(ii)(iii).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q1aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Faigh luach gach ceann díobh seo a leanas. (ii) 3·4 × 7", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "23·8 (3·4 × 7 = 23·8).", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q1aiii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Faigh luach gach ceann díobh seo a leanas. (iii) 4^2 × (8 − 5)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "48 (4^2 × (8 − 5) = 16 × 3 = 48).", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q1b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Líon isteach na luachanna atá in easnamh ón éagothromóid i t thíos chun raon na luachanna féideartha de t a thaispeáint nuair a bhí Xena ag dul ar obair. ___ ≤ t < ___", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "17·5° ≤ t < 18·5°C. (Shared scale 15D across (a),(b),(c).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q1b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 10, "marks_confidence": "high", "question_text": "Cheannaigh Máirtín na hearraí seo a leanas ina shiopa áitiúil. Líon isteach an tábla thíos chun costas iomlán a chuid siopadóireachta a fháil. Earraí / Costas (ina €): 3 lítear bainne ar €1·27 an lítear; 4 scóna ar €1·10 an ceann; 500 gram liamháis ar €12 in aghaidh an kg; Costas iomlán.", "has_images": true, "image_notes": "A two-column table to be filled in. Column 1 'Earraí' (Items): '3 lítear bainne ar €1·27 an lítear' (3 litres of milk at €1.27/litre), '4 scóna ar €1·10 an ceann' (4 scones at €1.10 each), '500 gram liamháis ar €12 in aghaidh an kg' (500 g of ham at €12/kg), and a 'Costas iomlán' (Total cost) row. Column 2 'Costas (ina €)' (Cost in €) is blank for the candidate to complete.", "topic": "Number", "marking_scheme_answer": "3 × 1·27 = 3·81; 4 × 1·10 = 4·40; 0·5 × 12 = 6·00; Costas iomlán = 3·81 + 4·40 + 6·00 = 14·21 (€). (Scála 10D: 0,3,5,8,10.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q1c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Dá mbeifeá chun an teocht iarbhír, t, in imeacht lae, a ghrafadh, an mbeadh sé níos iomchuí t ∈ ℕ, t ∈ ℤ, nó t ∈ ℝ a ghrafadh? Tabhair cúis le do fhreagra. (Cuir tic (✓) i mbosca amháin: t ∈ ℕ / t ∈ ℤ / t ∈ ℝ.)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "t ∈ ℝ — temperature takes continuous/decimal values over a day. (Shared scale 15D across (a),(b),(c).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q10a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 8, "marks_confidence": "derived", "question_text": "Ní mór do Mhichelle an Mhuirear Sóisialta Uilíoch (MSU) a íoc ar a hioncam comhlán ar fad. Tugtar na bandaí ioncaim agus na rátaí MSU nach mór do Mhichelle iad a íoc sa tábla thíos. (Banda ioncaim / Ráta MSU: Suas le €12 012 → 1·5%; An chéad €5564 eile → 3·5%; Os cionn €17 576 → 7%.) Íocann Michelle MSU ag gach ceann de na trí ráta. (a) Faigh méid an MSU nach mór di a íoc ag gach ceann den chéad dá ráta (1·5% agus 3·5%). MSU @ 1·5% = ___ MSU @ 3·5% = ___", "has_images": true, "image_notes": "A USC bands table — Banda ioncaim vs Ráta MSU: 'Suas le €12 012' → 1·5%; 'An chéad €5564 eile' → 3·5%; 'Os cionn €17 576' → 7%.", "topic": "Number", "marking_scheme_answer": "MSU @ 1·5% = 12012 × 0·015 = €180·18; MSU @ 3·5% = 5564 × 0·035 = €194·74. (Marks: (a)+(b) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q10a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 10, "marks_confidence": "derived", "question_text": "Ceannaíonn Martina cartán de íogart. Cruth sorcóra atá ar an gcartán, go garbh. Is iad na toisí a thaispeántar sa léaráid thíos atá aige. (a) Oibrigh amach toirt an chartáin ina cm^3. Bíodh do fhreagra i dté. (V = πr^2 h; r = 4 cm, h = 11 cm) armaí π.", "has_images": true, "image_notes": "A blue cylinder representing a yoghurt carton (a photo of a 'glenisk BIO Organic' tub is shown beside it). The cylinder has radius r = 4 cm (marked across the top) and height h = 11 cm (marked on the side). The volume formula V = πr^2 h is given. Candidate computes V = π × 4^2 × 11.", "topic": "Geometry", "marking_scheme_answer": "V = πr^2 h = π(4)^2(11) = π(16)(11) = 176π cm^3. (Scála 20D roinnte idir (a) agus (b).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q10b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 7, "marks_confidence": "derived", "question_text": "Is é x ioncam comhlán Mhichelle. Íocann Michelle 5% san iomlán dá hioncam comhlán i bhfoirm MSU. (b) Scríobh slonn, i dtéarmaí x, don mhóriomlán airgid a íocann Michelle i bhfoirm MSU.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Total USC = 0·07(x − 17576) + 180·18 + 194·74 = 0·07(x − 17576) + 374·92. (Marks: (a)+(b) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q10b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 10, "marks_confidence": "derived", "question_text": "Tá torthaí agus íogart sa chartán agus meánn sé 450 g. Tá sé déanta de thorthaí agus de íogart, sa chóimheas 4 : 21. Oibrigh amach cé mhéad gram de thorthaí atá sa chartán.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "4 + 21 = 25 cuid; torthaí = (4/25) × 450 = 72 g. (Scála 20D roinnte idir (a) agus (b).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q10c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "(c) Faigh luach x, ioncam comhlán Mhichelle.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "0·07(x − 17576) + 374·92 = 0·05x → 0·07x − 1230·32 + 374·92 = 0·05x → 0·02x = 855·40 → x = €42 770. (Scale 5C (0,2,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q11", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Taispeánann an graf thíos an teocht i Maidrid, a bheag nó a mhór, i rith lá amháin (ina °C). B'ionann an teocht san Inis agus leath na teochta i Maidrid i rith an lae sin. Ar an léaráid thíos, tarraing graf teochta na h-Inse i rith an lae sin. Bain úsáid as na scálaí agus as na haiseanna céanna.", "has_images": true, "image_notes": "A line graph (in red, labelled 'Maidrid') of temperature (y-axis 'Teocht (°C)' marked 0,10,20,30) against time (x-axis 'Am' marked 'Meán oíche' [midnight], '12 nóin' [noon], 'Meán oíche'). The Madrid plotted values across the day are approximately: 20, 15, 15, 30, 30, 30, 20 (°C) at successive marked times. A small sun icon appears top-left. Candidate draws the graph for Inis, whose temperature is half of Madrid's at each time (so 10, 7.5, 7.5, 15, 15, 15, 10), on the same axes/grid below.", "topic": "Functions", "marking_scheme_answer": "Tarraingítear graf na h-Inse (leath theocht Maidrid ag gach am): 10, 7·5, 7·5, 15, 15, 15, 10 °C, ceangailte le línte díreacha. (Lamháltas: do 7·5 ceadaítear aon luach idir 5 agus 10.) (Scála 10D: 0,3,5,8,10.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q11a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Bhí 30 000 duine i láthair ag cluiche peile i Staid Star. Tar éis an chluiche, d'fhág an 30 000 duine an staid ar ráta tairiseach. Taispeánann an graf thíos D, líon na ndaoine a bhí sa staid fós, t nóiméad tar éis don chluiche críochnú. Tá dhá phointe marcáilte ar an ngraf: G agus W. (a) Tá na comhordanáidí (6, 21 000) ag an bpointe G. Mínigh cad a chiallaíonn an 6 agus an 21 000, i dtéarmaí líon na ndaoine sa staid.", "has_images": true, "image_notes": "A line graph: y-axis 'Líon na ndaoine fágtha i Staid Star' from 0 to 30000, x-axis 'Nóiméad tar éis don chluiche críochnú' (t). A straight red line falls from D = 30000 (at t = 0) downward. Point G is marked on the line at (6, 21000); point W is marked further right where the line meets the t-axis (D = 0).", "topic": "Functions", "marking_scheme_answer": "After 6 minutes (t = 6), 21 000 people remained in the stadium. (Marks: (a)+(b) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q11b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Thóg sé 20 nóiméad ar an 30 000 duine go léir an staid a fhágáil. Bain úsáid as an bhfíric sin, agus breac síos comhordanáidí an phointe W, atá ar an t-ais. W = ( , )", "has_images": true, "image_notes": "Same line graph; W is the point where the line reaches D = 0 (everyone has left), at t = 20.", "topic": "Functions", "marking_scheme_answer": "W = (20, 0). (Marks: (a)+(b) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q11ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)(i)", "parent_question": "11", "marks": 3, "marks_confidence": "derived", "question_text": "Is féidir cothromóid an ghraif thuas a scríobh mar: D = 30 000 − 1500t. (c)(i) Cé mhéad duine a bhí sa staid 12 nóiméad tar éis don chluiche críochnú?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "D = 30 000 − 1500(12) = 30 000 − 18 000 = 12 000. (Marks: (c)(i)+(c)(ii) share scale 5D (0,2,3,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q11cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)(ii)", "parent_question": "11", "marks": 2, "marks_confidence": "derived", "question_text": "(c)(ii) Mínigh cad a chiallaíonn an 1500 sa chothromóid seo, i dtéarmaí líon na ndaoine sa staid.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "The 1500 is the rate of change (slope): 1500 people leave the stadium per minute. (Marks: (c)(i)+(c)(ii) share scale 5D (0,2,3,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q12a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Sa léaráid thíos taispeántar cruth cuartha ABC. Is é C lárphointe an stua chiorclaigh ó A go B. Is é A lárphointe an stua chiorclaigh ó B go C. Is é B lárphointe an stua chiorclaigh ó C go A. Is triantán comhshleasach é an triantán poncanna ABC. (a) Gan ach compás agus riailchiumhais á n-úsáid agat, tóg ceann amháin d'aiseanna siméadrachta an chrutha chuartha ABC. Taispeáin do chuid línte tógála go léir go soiléir.", "has_images": true, "image_notes": "A Reuleaux-triangle-style curved shape (cruth cuartha) ABC: vertices A (apex, top), B (bottom-left), C (bottom-right); the three sides are outward-bulging circular arcs. A dotted equilateral triangle joins A, B, C inside. No measurements given.", "topic": "Geometry", "marking_scheme_answer": "Construct (compass and straight-edge) the perpendicular bisector / axis of symmetry through one vertex to the midpoint of the opposite arc, showing construction lines. (Scale 5B (0,2,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q12a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 10, "marks_confidence": "high", "question_text": "Déanann Pawel an 'balla suimiúcháin' thíos. Tá gach bosca sa tsraith íochtarach líonta isteach. Chun bosca ar bith eile a líonadh isteach suimíonn tú an dá uimhir atá sna boscaí atá díreach faoi. Mar shampla, sna boscaí scáthaithe: 5 + 3 = 8. (a) Líon isteach na boscaí go léir i mballa suimiúcháin Phawel thuas.", "has_images": true, "image_notes": "An 'addition wall' (number pyramid) with 4 levels. Bottom (4 boxes): −2, 1, 5, 3. Next level up (3 boxes): −1, (blank), 8. Next level (2 boxes): both blank. Top (1 box): blank. Rule: each box equals the sum of the two boxes directly below it (illustrated example 5 + 3 = 8). Candidate fills in all empty boxes.", "topic": "Number", "marking_scheme_answer": "Balla suimiúcháin (uimhriúil): bun −2, 1, 5, 3; sraith −1, 6, 8; sraith 5, 14; barr 19. (Scála 10B: 0,5,10.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q12b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 7, "marks_confidence": "derived", "question_text": "Déanann Pawel an 'balla suimiúcháin ailgéabair' thíos, ag baint úsáide as na rialacha céanna. (b) Líon isteach na boscaí go léir i mballa suimiúcháin ailgéabair Phawel thíos, i dtéarmaí x.", "has_images": true, "image_notes": "An algebraic 'addition wall' (number pyramid) with 4 levels. Bottom (4 boxes): x − 4, 1, x + 3, x + 1. Next level up (3 boxes): x − 3, (blank), 2x + 4. Next level (2 boxes): both blank. Top (1 box): blank. Same rule: each box equals the sum of the two below it. Candidate fills in the empty boxes in terms of x.", "topic": "Algebra", "marking_scheme_answer": "Balla ailgéabair: bun x−4, 1, x+3, x+1; sraith x−3, x+4, 2x+4; sraith 2x+1, 3x+8; barr 5x+9. (Cuid de Scála 10D roinnte idir (b) agus (c).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q12bi", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "(b)(i) Scríobh síos méid na huillinne ∠ACB.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "|∠ACB| = 60° (the triangle ABC is equilateral). (Marks: (b)(i)+(b)(ii) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q12bii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Tá an mhírlíne dhíreach [BC] 40 cm ar fad. Faigh fad an stua chiorclaigh ó B go dtí C. Bíodh do fhreagra ina cm, ceart go dtí 2 ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Arc length = (θ/360)(2πr) = (60/360)(2π)(40) = 41·8879 ≈ 41·89 cm (2 d.p.), with r = 40 (the radius equals |BC| since the centre is the opposite vertex). (Marks: (b)(i)+(b)(ii) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q12c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 3, "marks_confidence": "derived", "question_text": "Tá luach amháin ar x a fhágfaidh go mbeidh an dá bhalla suimiúcháin díreach mar an gcéanna. Faigh an luach seo ar x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x = 2 (m.sh. x − 4 = −2 → x = 2). (Cuid de Scála 10D roinnte idir (b) agus (c).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q13a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 2, "marks_confidence": "derived", "question_text": "Tá póstaer dronuilleogach mór, mar a thaispeántar sa léaráid ar dheis, á dhéanamh ag comhlacht. Íomhá chearnógach a bheidh sa roinn uachtarach. Dronuilleog, 0·5 m ar airde, ina mbeidh lógónna na n-urraitheoirí, a bheidh sa roinn íochtarach. Tá an póstaer x m ar leithead, mar a thaispeántar. (a) Scríobh airde iomlán an phóstaeir, i dtéarmaí x. Airde iomlán = ___ m", "has_images": true, "image_notes": "A rectangular poster ('Póstaer Dronuilleogach') of a rock climber. Upper section is a square image ('Íomhá Chearnógach'), of side x m (the poster width). Lower strip ('Lógónna na n-Urraitheoirí') is 0·5 m high. Poster width marked x m along the bottom; lower strip height marked 0·5 m.", "topic": "Algebra", "marking_scheme_answer": "Total height = x + 0·5 m (square of side x plus the 0·5 m strip). (Marks: (a)+(b) share scale 5D (0,2,3,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q13a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 10, "marks_confidence": "high", "question_text": "(a) Bain úsáid as teoirim Phíotágaráis chun luach x sa triantán dronuilleach thíos a fháil. Taispeáin d'oibriú amach go léir.", "has_images": true, "image_notes": "A right-angled triangle with the right angle at the bottom-left. Vertical side = 5, horizontal base = 12, and the hypotenuse is labelled x. Candidate uses Pythagoras: x = √(5^2 + 12^2) = 13.", "topic": "Geometry", "marking_scheme_answer": "x^2 = 5^2 + 12^2 = 25 + 144 = 169; x = √169 = 13. (Scála 10C: 0,3,7,10.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q13b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 3, "marks_confidence": "derived", "question_text": "Is é 50 m² achar iomlán an phóstaeir. Taispeáin go bhfuil 2x^2 + x − 100 = 0.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Area = width × height = x(x + 0·5) = 50 → x² + 0·5x − 50 = 0 → (×2) 2x² + x − 100 = 0. (Marks: (a)+(b) share scale 5D (0,2,3,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q13b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Tarraing íomhá an triantáin seo a leanas faoi shiméadracht lárnach i bpointe A.", "has_images": true, "image_notes": "On a square grid, a blue-shaded triangle is drawn to the right of a marked centre point A (a labelled dot). The triangle sits to the right of and slightly above A, with a horizontal base on a grid line and a sloping top edge. Candidate draws the image of this triangle under central symmetry in point A (a 180° rotation about A, placing the image diagonally opposite, lower-left of A).", "topic": "Geometry", "marking_scheme_answer": "Tarraingítear íomhá cheart an triantáin faoi shiméadracht lárnach i bpointe A (rothlú 180° timpeall A). (Scála 5C: 0,3,4,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q13c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Réitigh an chothromóid 2x^2 + x − 100 = 0 chun luach x, leithead an phóstaeir, a fháil. Bíodh do fhreagra ina mhéadair, ceart go dtí an ceintiméadar is gaire.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x = (−1 ± √(1² − 4(2)(−100)))/(2·2) = (−1 ± √801)/4 → x = 6·825… or −7·325…; take positive root: x = 6·83 m (nearest cm). (Scale 5C (0,2,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q13ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)(i)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "(c)(i) Oibrigh amach méid na huillinne B sa triantán thíos.", "has_images": true, "image_notes": "A triangle (not right-angled) with three interior angles. The angle at the left vertex is 27°, the angle at the bottom-right vertex is 60°, and the angle at the top-right vertex is labelled B. The side from the left vertex to B is labelled 10, the side from B down to the 60° vertex is labelled 5·2, and the bottom side (from left vertex to the 60° vertex) is labelled y. Candidate finds angle B using the angle sum: B = 180° − 27° − 60° = 93°.", "topic": "Geometry", "marking_scheme_answer": "B = 180° − (27° + 60°) = 93°. (Scála 10C roinnte idir (i) agus (ii).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q13cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)(ii)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Mínigh cén fáth nach féidir teoirim Phíotágaráis a úsáid chun fad an tslease y sa triantán thuas a fháil.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Ní triantán dronuilleach é (níl uillinn 90° ann), mar sin ní féidir teoirim Phíotágaráis a úsáid. (Nó aon mhíniú bailí.) (Scála 10C roinnte idir (i) agus (ii).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q14a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 8, "marks_confidence": "derived", "question_text": "Taispeántar sa léaráid thíos triantán ABC (níl sé de réir scála). Luíonn na pointí D agus E ar [AC] agus [BC], faoi seach. |∠CAB| = |∠DEC| = 90°. Tugtar faid cuid de na sleasa sa léaráid, le x, y ∈ ℝ. (a) Oibrigh amach luach x.", "has_images": true, "image_notes": "Not-to-scale triangle ABC with a right angle at A (∠CAB = 90°) and a right angle at E (∠DEC = 90°). D lies on [AC], E lies on [BC]. Given lengths: DC = 15, DE = 9, and BE = x; side AB = y. The right-angled sub-triangle DEC has legs DE = 9 and EC, hypotenuse DC = 15, giving x via Pythagoras in that triangle (x = EC). Two similar right triangles share the configuration.", "topic": "Geometry", "marking_scheme_answer": "Pythagoras in triangle DEC: x² + 9² = 15² → x² + 81 = 225 → x² = 144 → x = 12. (Marks: (a)+(b) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q14a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)", "parent_question": "14", "marks": 10, "marks_confidence": "high", "question_text": "(a) Is sloinn ailgéabracha iad seo a leanas: 2x 3x − 2 3x + 2 3(x + 2). Comhlánaigh an tábla thíos agus scríobh an sloinn ailgéabrach ceart as an liosta thuas taobh leis an ráiteas comhfhreagrach. Ní gá duit na sloinn ailgéabracha go léir a úsáid. (Ráiteas / Sloinn Ailgéabrach: 'Iolraigh x faoi 3, ansin dealaigh 2 ón toradh.'; 'Dúblaigh x.'; 'Suimigh 2 le x, ansin iolraigh an toradh faoi 3.')", "has_images": true, "image_notes": "A two-column table to be completed. Header: 'Ráiteas' (Statement) and 'Sloinn Ailgéabrach' (Algebraic expression). Three statement rows (blank expression column): 'Iolraigh x faoi 3, ansin dealaigh 2 ón toradh' (multiply x by 3 then subtract 2 → 3x − 2); 'Dúblaigh x' (double x → 2x); 'Suimigh 2 le x, ansin iolraigh an toradh faoi 3' (add 2 to x then multiply result by 3 → 3(x + 2)). Choose from the list 2x, 3x − 2, 3x + 2, 3(x + 2).", "topic": "Algebra", "marking_scheme_answer": "'Iolraigh x faoi 3, ansin dealaigh 2' → 3x − 2; 'Dúblaigh x' → 2x; 'Suimigh 2 le x, ansin iolraigh faoi 3' → 3(x + 2). (Scála 10C: 0,3,7,10.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q14b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 7, "marks_confidence": "derived", "question_text": "(b) Bain úsáid as triantáin chomhchosúla agus oibrigh amach luach y.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Similar triangles: 15/24 = 9/y → 15y = 216 → y = 14·4. (Marks: (a)+(b) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q14b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)", "parent_question": "14", "marks": 3, "marks_confidence": "derived", "question_text": "Iolraigh amach agus simpligh (3x − 2)(2x − 3).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(3x − 2)(2x − 3) = 6x^2 − 9x − 4x + 6 = 6x^2 − 13x + 6. (Cuid de Scála 5D roinnte idir (b) agus (c).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q14c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(c)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Fachtóirigh x^2 + 2x − 15. (x^2 + 2x − 15 = (x + 5)( ___ ))", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x^2 + 2x − 15 = (x + 5)(x − 3). (Cuid de Scála 5D roinnte idir (b) agus (c).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q2", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Tá 2 mhála mirlíní ag Ruth chomh maith le 4 mhirlín scaoilte, mar a thaispeántar. Tá mála mirlíní amháin ag Liam chomh maith le 10 mirlín scaoilte, mar a thaispeántar. Tá an líon céanna mirlíní i ngach mála. Tá an líon iomlán céanna mirlíní ag Ruth agus ag Liam. Oibrigh amach líon na mirlíní atá i ngach mála. (Líon na mirlíní: )", "has_images": true, "image_notes": "Pictorial representation of marbles in bags. Ruth: 2 bags of marbles + 4 loose marbles. Liam: 1 bag of marbles + 10 loose marbles. Each bag contains the same number of marbles, and Ruth and Liam have the same total number of marbles (set up the equation 2x + 4 = x + 10, giving x = 6). A blank grid is provided to show working and find the number of marbles in each bag.", "topic": "Algebra", "marking_scheme_answer": "Líon na mirlíní i ngach mála = 6. Réiteach: 2b + 4 = b + 10 → b = 6 (nó iarracht-agus-earráid bhailí / modh fisiceach). (Scála 10C: 0,3,7,10.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q2ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "Díolann comhlacht t-léinte ar shuíomh gréasáin. Uaireanta, nuair a cheannaíonn daoine t-léine, seolann siad ar ais í chun a gcuid airgid a fháil ar ais. Sa léaráid thíos taispeántar an t-eolas seo a leanas do thréimhse 8 mí: D(n), líon na t-léinte a díoladh ar an suíomh gréasáin i mí n, agus S(n), líon na t-léinte a díoladh i mí n ar seoladh ar ais iad, le haghaidh n ∈ ℕ agus n ≤ 8. Tá na luachanna go léir tugtha go dtí an 50 is gaire. Bain úsáid as an eolas a léiráid chun na ceisteanna seo a fhreagairt. (i) Cad é líon na t-léinte a díoladh i Mí 1?", "has_images": true, "image_notes": "A line graph titled with y-axis 'Líon na t-léinte (sa 50 is gaire)' from 0 to 700 (gridlines every 100) and x-axis 'Mí' from 1 to 8. Two series: D(n) 'a díoladh' (red) and S(n) 'a seoladh ar ais' (blue). D(n) starts at ~300 (Mí 1), stays ~300 (Mí 2,3), rises to ~350, ~400, ~450, then ~500 then ~550 by Mí 7-8. S(n) stays low, around 50 across most months, rising slightly around Mí 7.", "topic": "Functions", "marking_scheme_answer": "300. (Marks: (a)+(b) share scale 15C (0,5,10,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q2aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "Cad é líon na t-léinte a seoladh ar ais i Mí 2?", "has_images": true, "image_notes": "Same line graph as 2(a)(i): D(n) (red) and S(n) (blue) over months 1–8, values to nearest 50. At Mí 2 the S(n) (blue) series reads about 50.", "topic": "Functions", "marking_scheme_answer": "50. (Marks: (a)+(b) share scale 15C (0,5,10,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q2b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 15, "marks_confidence": "derived", "question_text": "Cén mhí ina raibh an t-ardú is mó i líon na t-léinte a díoladh, i gcomparáid leis an mí roimhe? Freagra = ___", "has_images": true, "image_notes": "Same line graph; uses the D(n) (red, 'a díoladh') series increase month-on-month.", "topic": "Functions", "marking_scheme_answer": "Mí 7 (Month 7). (Marks: (a)+(b) share scale 15C (0,5,10,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q2c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Comhlánaigh an tábla thíos agus taispeáin an líon t-léinte nár seoladh ar ais gach mí. Mar shampla, níor seoladh ar ais 350 t-léine i mí 6.", "has_images": true, "image_notes": "A table with row 'Mí' = 1..8 and row 'Líon nár seoladh ar ais'; only the value for Mí 6 is filled (350); the rest are blank and to be completed using D(n) − S(n) from the graph.", "topic": "Functions", "marking_scheme_answer": "Completed values (D(n)−S(n)): 250, 250, 300, 300, 350, 350, 450, 500. (Marks: (c)+(d) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q2d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Tarraing, ar an léaráid tugtha, graf chun líon na t-léinte nár seoladh ar ais gach mí ar feadh na 8 mí a thaispeáint. Bain úsáid as na scálaí agus as na haiseanna céanna.", "has_images": true, "image_notes": "A blank grid (squared) provided on which to plot the 8 monthly values of 't-léinte nár seoladh ar ais' from the completed table, using the same axes/scale (Líon na t-léinte vs Mí 1–8).", "topic": "Functions", "marking_scheme_answer": "Plot the 8 points 250,250,300,300,350,350,450,500 against months 1–8. (Marks: (c)+(d) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q2e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(e)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Cén mhí ina raibh an t-ardú céatadánach ba mhó i líon na t-léinte a díoladh, i gcomparáid leis an mí roimhe: Mí 3 nó Mí 5? Cosain do fhreagra. (Cuir tic (✓) i mbosca amháin: Mí 3 / Mí 5.)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Mí 3. Mí 3: 50/300 × 100 = 16⅔%; Mí 5: 50/400 × 100 = 12½%, so Month 3 has the greater percentage increase. (Scale 10C (0,3,7,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q3a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Déanann na daltaí i mionchomhlacht Idirbhliana coinnle agus díolann siad iad. Ceannaíonn siad bloc dronuilleogach soladach de chéir a thomhaiseann 35 cm faoi 45 cm faoi 16 cm. (a) Oibrigh amach toirt an bhloic chéaraigh.", "has_images": true, "image_notes": "A 3-D drawing of a rectangular (cuboid) block of wax, dimensions 35 cm × 45 cm × 16 cm.", "topic": "Geometry", "marking_scheme_answer": "V = 35 × 45 × 16 = 25 200 cm³. (Scale 10B (0,5,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q3a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "I suirbhé ar bhia bhfuil léi ar a rinneadh ar ghrúpa de 155 dalta: 75 a dúirt gur thaitin bia Síneach leo (S); 41 a dúirt gur thaitin bia Indiach leo (I); 20 a dúirt gur thaitin an dá chineál bia leo. (a) Comhlánigh an léaráid Venn thíos chun an t-eolas seo a léiriú.", "has_images": true, "image_notes": "A Venn diagram inside a universal set rectangle labelled U (155). Two overlapping ovals: left oval labelled S, right oval labelled I. The intersection is labelled 55, and 59 is written in the bottom-left region of the rectangle (outside both ovals). The candidate must complete the diagram using the survey data (75 liked Chinese food S, 41 liked Indian food I, 20 liked both).", "topic": "Probability", "marking_scheme_answer": "Comhlánaítear an léaráid Venn: S amháin = 75 − 20 = 55, an trasnú S∩I = 20, I amháin = 41 − 20 = 21, lasmuigh = 155 − (55+20+21) = 59. (Scála 10C roinnte idir (a) agus (b).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q3b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 8, "marks_confidence": "derived", "question_text": "Tá sé beartaithe ag na daltaí úsáid a bhaint as an gcéir seo chun coinnle a dhéanamh i bhfoirm sorcóirí. Beidh ga r cm ag gach coinneal agus airde 9 cm. Oibrigh amach toirt gach coinnle, i dtéarmaí r agus π.", "has_images": true, "image_notes": "A drawing of a cylindrical candle (sorcóir), radius r cm, height 9 cm.", "topic": "Geometry", "marking_scheme_answer": "V = π r² (9) = 9πr² cm³. (Marks: (b)+(c) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q3b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Cé mhéad dalta sa ghrúpa nár thaitin ach bia Síneach amháin leo?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "55 (na daltaí ar thaitin bia Síneach amháin leo = 75 − 20 = 55). (Scála 10C roinnte idir (a) agus (b).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q3c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 7, "marks_confidence": "derived", "question_text": "Déanann na daltaí 100 coinneal as an mbloc céarach. Ídítear 10% den chéir sa bhloc agus na coinnle á ndéanamh. Bain úsáid as an eolas seo chun luach r, ga gach coinnle, a oibriú amach. Tabhair do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Wax used = 25 200 × 90/100 = 22 680 cm³ for 100 candles, so 9πr² × 100 = 22 680 → r² = 22 680/(900π) → r = 2·8 cm (1 d.p.). (Marks: (b)+(c) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q3c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "high", "question_text": "Mínigh cad is ciall leis an ráiteas seo a leanas, i gcomhthéacs an tsuirbhé seo, áit arb é S' comhlánú thacar S: #(S') = 80.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "Ciallaíonn #(S') = 80 nár thaitin bia Síneach le 80 dalta sa ghrúpa (i.e. 80 dalta nach raibh i dtacar S). (Scála 5C: 0,3,4,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q4a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Taifeadadh aoiseanna na bpáistí i naíolann. Taispeántar na sonraí sa tábla thíos. [Nóta: Is é is ciall le 2 − 3 ná \"2 bhliain nó níos mó, ach níos lú ná 3 bliana\", etc.] (a) Léirigh na sonraí ar histeagram. Lipéadaigh na haiseanna go soiléir.", "has_images": true, "image_notes": "A frequency table — Aois (blianta): 0−1, 1−2, 2−3, 3−4, 4−5; Líon na bpáistí: 6, 10, 19, 3, 5. Below is a blank set of axes for drawing the histogram.", "topic": "Statistics", "marking_scheme_answer": "Histogram with bars (frequency vs age class) of heights 6, 10, 19, 3, 5 over equal-width intervals, axes labelled. (Marks: (a)+(b) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q4a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Is léaráid de réir scála de sheomra ranga scoile atá sa heicseagán thíos. Tá gach slios ar comhfhad. (a) Trí thomhas, faigh fad sleasa an heicseagáin. Bíodh do fhreagra ceart go dtí an cm is gaire. (Fad = ___ cm)", "has_images": true, "image_notes": "A regular hexagon (blue-shaded) representing a scale drawing of a classroom; all sides equal length. The candidate must measure one side length with a ruler to the nearest cm. No printed measurements are given on the figure.", "topic": "Geometry", "marking_scheme_answer": "Tomhas ≈ 3 cm (lamháltas ±0·2 cm). (Scála 5B: 0,2,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q4b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach an céatadán de na páistí sa naíolann atá 1 − 2 bhliain d'aois. Bíodh do fhreagra ceart go dtí an céatadán is gaire.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "10/43 × 100 = 23·26 ≈ 23%. (Marks: (a)+(b) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q4b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Faigh fad imlíne an heicseagáin. Bíodh do fhreagra ina cm.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Imlíne = 6 × 3 = 18 cm. (Scála 5B: 0,2,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q4c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Bain úsáid as lárluachanna na n-eatramh chun meánaois na bpáistí sa naíolann a mheas. Bíodh do fhreagra ina bhlianta, ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Estimated mean = [(6×0·5)+(10×1·5)+(19×2·5)+(3×3·5)+(5×4·5)]/43 = (3+15+47·5+10·5+22·5)/43 = 98·5/43 = 2·29 ≈ 2·3 bliain. (Scale 10C (0,3,7,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q4c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Is de réir scála 1 cm = 2 m atá an léaráid. (c) Faigh imlíne iarbhír an tseomra ranga. Bíodh do fhreagra ina mhéadair.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Imlíne iarbhír = 18 × 2 = 36 m (scála 1 cm = 2 m). (Scála 5B: 0,2,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q4d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Sa tábla thíos taispeántar uaslíon na bpáistí ar féidir le ball foirne amháin sa naíolann aire a thabhairt dóibh, ag brath ar aois na bpáistí. Dá réir sin, mar shampla, féadann ball foirne amháin aire a thabhairt do 3 pháiste, ar a mhéad, atá 0 − 1 bhliain d'aois, nó do 5 pháiste, ar a mhéad, atá 1 − 2 bhliain d'aois, agus mar sin de. Oibrigh amach an líon is lú ball foirne atá ag teastáil chun aire a thabhairt do na páistí go léir sa naíolann.", "has_images": true, "image_notes": "A table — Aois (blianta) vs uaslíon páistí per staff member: 0−1 → 3; 1−2 → 5; 2−3 → 6; 3−6 → 8. Combined with the frequency table from (a) (counts 6,10,19,3,5 over 0−1..4−5).", "topic": "Statistics", "marking_scheme_answer": "Staff needed per age band (rounding up): 0−1 → 2; 1−2 → 3; 2−3 → 4; 3−6 → 1. Total = 9 staff. (Scale 5C (0,2,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q4d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "Tá 560 dalta ag freastal ar an scoil. Fhreastalaíonn 75% de dhaltaí na scoile ar chluiche camógaíochta. Oibrigh amach líon na ndaltaí a théann go dtí an cluiche.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "560 × 0·75 = 420 dalta. (Cuid de Scála 5D roinnte idir (d) agus (e).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q4e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(e)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Sa bhliain 2019, bhí 80 dalta sa chéad bhliain sa scoil. Sa bhliain 2020, bhí 90 dalta sa chéad bhliain. (e) Scríobh an t-ardú seo mar chéatadán de líon na ndaltaí sa chéad bhliain sa bhliain 2019.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(90 − 80)/80 × 100 = 12·5%. (Cuid de Scála 5D roinnte idir (d) agus (e).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q5a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Sa tábla thíos, taispeántar an fothoradh nuair a iolraítear na huimhreacha a agus b faoina chéile, le haghaidh a, b ∈ ℕ. Scríobh \"ré\" nó \"corr\" i ngach bosca chun ceann de na ráitis mhatamaiticiúla a chomhlánú i gceart. Tá an chéad cheann déanta duit. (Tábla: 1. ré × ré = ré; 2. corr × corr = ___; 3. corr × ré = ___.)", "has_images": true, "image_notes": "A small table with columns a × b = c. Row 1: ré × ré = ré (given). Row 2: corr × corr = (blank). Row 3: corr × ré = (blank). 'ré' = even, 'corr' = odd.", "topic": "Number", "marking_scheme_answer": "corr × corr = corr (odd); corr × ré = ré (even). (Parts (a),(b),(c) share one scale: 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q5ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)(i)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeánann an léaráid thíos torthaí suirbhé ar dhaoine fásta maidir le cé chomh minic in aghaidh an lae a dhéanann siad seiceáil ar a gcuntais meán sóisialta. Ní thaispeántar na torthaí le haghaidh WhatsApp. (a) Bain úsáid as an léaráid chun an dá cheist seo a leanas a fhreagairt. I ngach cás, ná cuir tic (✓) sa bhosca ceart. (i) An céatadán a rinne seiceáil ar a gcuntas Instagram thart ar uair amháin in aghaidh an lae ná: 15% 21% 37% 51%", "has_images": true, "image_notes": "A 100% horizontal stacked bar chart titled 'Cé chomh minic agus a sheiceálann tú do chuntais meán sóisialta?' with three categories: 'Roinnt uaireanta i rith an lae', 'Thart ar uair amháin in aghaidh an lae', and 'Ní chomh minic sin'. Rows: Facebook 51% / 23% / 26%; Instagram 42% / 21% / 37%; Snapchat 46% / 15% / 39%; Twitter 25% / 17% / 58%; WhatsApp (blank, not shown). The relevant value for Instagram 'about once a day' is 21%.", "topic": "Statistics", "marking_scheme_answer": "21% (líon a sheiceáil Instagram thart ar uair amháin in aghaidh an lae). (Scála 10B roinnte idir (i) agus (ii).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q5aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)(ii)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "An cuntas a ndearna 1/4 go díreach de na húsáideoirí seiceáil air roinnt uaireanta in aghaidh an lae ná: Facebook Instagram Snapchat Twitter", "has_images": true, "image_notes": "Refers to the same stacked bar chart in part (a). For 'Roinnt uaireanta i rith an lae' (several times a day): Facebook 51%, Instagram 42%, Snapchat 46%, Twitter 25%. One quarter = 25%, which corresponds to Twitter. Four tick-boxes are provided (Facebook, Instagram, Snapchat, Twitter).", "topic": "Statistics", "marking_scheme_answer": "Twitter (25% = 1/4 a sheiceáil roinnt uaireanta in aghaidh an lae). (Scála 10B roinnte idir (i) agus (ii).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q5b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Caitheann Ruairí dísle rialta, neamhlaofa, séthaobhach trí huaire. Breacann sé síos an uimhir ar gach caitheamh den dísle. Comhlánaigh an spás samplach thíos agus taispeáin na teaglamaí féideartha éagsúla d'uimhreacha corra (C) agus de ré-uimhreacha (R) is féidir le Ruairí a chaitheamh. Tá dhá fhothoradh fhéideartha líonta isteach. (R R R, R R C, ...)", "has_images": true, "image_notes": "A sample-space grid with two combinations pre-filled: 'R R R' and 'R R C'. R = ré (even), C = corr (odd). Three throws of a fair six-sided die, classified even/odd.", "topic": "Probability", "marking_scheme_answer": "Sample space (8 outcomes): RRR, RRC, RCR, CRR, RCC, CRC, CCR, CCC. (Shared scale 15D across (a),(b),(c).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q5b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Taispeántar na torthaí le haghaidh WhatsApp sa tábla thíos. Bain úsáid as na luachanna sa tábla chun an léaráid thuas a chomhlánú. B'fhéidir go mbeadh sé ina chabhair rialóir a úsáid. Ní gá duit an léaráid a scáthú. (Torthaí le haghaidh WhatsApp: Roinnt uaireanta i rith an lae: 60%; Thart ar uair amháin in aghaidh an lae: 20%; Ní chomh minic sin: 20%)", "has_images": true, "image_notes": "A small table 'Torthaí le haghaidh WhatsApp' with three rows: 'Roinnt uaireanta i rith an lae' = 60%; 'Thart ar uair amháin in aghaidh an lae' = 20%; 'Ní chomh minic sin' = 20%. The candidate must use these values to complete the WhatsApp row of the stacked bar chart shown in part (a).", "topic": "Statistics", "marking_scheme_answer": "Comhlánaítear an barra WhatsApp: 60% / 20% / 20%. (Scála 5B: 0,2,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q5c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Tá gach fothoradh sa tábla comhdhóchúil. Iolraíonn Ruairí le chéile na trí uimhir a chaitheann sé. Faigh an dóchúlacht go bhfaighidh Ruairí ré-uimhir mar fhreagra.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "7/8 (only CCC gives an odd product, so P(even product) = 7/8). (Shared scale 15D across (a),(b),(c).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q5c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Tá fón póca ag Eoin. D'íoc sé €80 nuair a cheannaigh sé an fón, i dtosach mhí an Mheithimh. D'íoc sé €25 ag tús gach míosa ina dhiaidh sin. Cé acu ceann de na graif thíos, A nó B, is fearr a thaispeánann an tslí inar caitheadh Eoin an t-airgead i rith na chéad 8 mí? Tabhair cúis le do fhreagra. (Freagra: Graf A / Graf B – cuir tic i mbosca amháin; Cúis: )", "has_images": true, "image_notes": "Two graphs side by side, both with x-axis 'Am' (time) and y-axis 'Suim iomlán a caitheadh (€)' (total amount spent). Graf A is a step graph (staircase) starting at a positive value on the y-axis and rising in equal discrete steps. Graf B is a single straight line rising steadily from the origin. The scenario (€80 initial cost then €25 added at the start of each month) is best modelled by the step graph A, since spending increases in fixed jumps at the start of each month rather than continuously. Tick boxes for Graf A / Graf B and a grid for the reason.", "topic": "Functions", "marking_scheme_answer": "Graf A. Cúis: íoctar €25 ag tús gach míosa, mar sin ardaíonn an caiteachas ina chéimeanna scoite (graf céimseach) seachas go leanúnach. (Scála 5C: 0,3,4,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q6a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Sa léaráid Venn thíos taispeántar líon na mball atá i dtrí réigiún sna tacair F agus G, áit a bhfuil x ∈ ℕ. (a) Scríobh síos luach #(F\\G), i dtéarmaí x. Freagra = ___", "has_images": true, "image_notes": "A two-set Venn diagram (sets F and G overlapping). F-only region: x + 3; intersection F ∩ G: x − 2; G-only region: 8 − x.", "topic": "Number", "marking_scheme_answer": "#(F\\G) = x + 3. (Scale 5A (0,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q6a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 15, "marks_confidence": "high", "question_text": "Tá cluiche á imirt ag Maria. Caitheann sí an dísle uair amháin agus casann sí an rothlóir uair amháin, mar a thaispeántar. (a) Comhlánaigh an tábla thíos chun na fothorthaí féideartha go léir a thaispeáint. Tá trí cinn déanta cheana féin duit. Mar shampla, ciallaíonn 6C go bhfuair Maria 6 ar an dísle agus C ar an rothlóir.", "has_images": true, "image_notes": "A red six-sided die ('Dísle') showing faces numbered 1–6, and a spinner ('Rothlóir') divided into three sectors labelled A, B and C. A sample-space (outcome) table is to be completed: rows = die values 1–6, columns = spinner outcomes A, B, C. Three cells are pre-filled: '1 B' (row 1, column B), '3 A' (row 3, column A), and '6 C' (row 6, column C). Candidate lists all 18 possible outcomes (e.g. 1A, 1B, 1C, ... 6C).", "topic": "Probability", "marking_scheme_answer": "Comhlánaítear an tábla 6×3 leis na 18 bhfothoradh: 1A 1B 1C, 2A 2B 2C, 3A 3B 3C, 4A 4B 4C, 5A 5B 5C, 6A 6B 6C. (Scála 15C: 0,5,10,15.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q6b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Ón léaráid Venn, faigh an luach féideartha is mó ar x. Cosain do fhreagra.", "has_images": true, "image_notes": "Same Venn diagram: F-only = x + 3, F ∩ G = x − 2, G-only = 8 − x; all region counts must be ≥ 0 with x ∈ ℕ.", "topic": "Number", "marking_scheme_answer": "x = 8. The largest x occurs when 8 − x ≥ 0 → x ≤ 8, so x = 8. (Scale 5C (0,2,4,5) per detail page.)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q6b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 4, "marks_confidence": "derived", "question_text": "Cé mhéad fothoradh féideartha éagsúla atá ann, san iomlán?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "18 fothoradh éagsúla san iomlán (6 × 3). (Cuid de Scála 10C roinnte idir (b)(c)(d).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q6c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 3, "marks_confidence": "derived", "question_text": "Liostaigh na fothorthaí go léir a bhfuil ré-uimhir agus B iontu.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "Fothorthaí le ré-uimhir agus B: 2B, 4B, 6B. (Cuid de Scála 10C roinnte idir (b)(c)(d).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q6d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": 3, "marks_confidence": "derived", "question_text": "Tá gach fothoradh sa tábla comhdhóchúil. Cad é an dóchúlacht go bhfaighidh Maria ré-uimhir agus B? (Freagra = )", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "P(ré-uimhir agus B) = 3/18 = 1/6. (Cuid de Scála 10C roinnte idir (b)(c)(d).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q7a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 8, "marks_confidence": "derived", "question_text": "Iarrtar ar Laurie feidhm a scríobh síos, agus sampla a thaispeánann conas a oibríonn a feidhm. Scríobhann Laurie é seo a leanas: 'Glacann mo fheidhm, f, le focal mar ionchur, agus is é líon na litreacha sa bhfocal an t-aschur. Mar shampla, f(banana) = 6.' Ag baint úsáide as feidhm Laurie: (a) faigh luach f(ned). (f(ned) = )", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "f(ned) = 3 (líon na litreacha sa bhfocal 'ned'). (Cuid de Scála 15B roinnte idir (a) agus (b).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q7ai", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Is ceithre phointe sa phlána comhordanáideach iad A, B, C, D. (a)(i) Taispeántar na pointí A agus B ar an léaráid chomhordanáideach thíos. Breac agus lipéadaigh na pointí C(8, 4) agus D(3, 6) ar an léaráid chomhordanáideach chéanna.", "has_images": true, "image_notes": "A coordinate grid with x-axis 1..8 and y-axis −1..7. Point A is plotted at about (1, 1); point B at about (6, −1). Candidate must additionally plot C(8, 4) and D(3, 6).", "topic": "Coordinate Geometry", "marking_scheme_answer": "Plot C at (8, 4) and D at (3, 6) on the grid. (Marks: (a)(i)+(a)(ii) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q7aii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Scríobh comhordanáidí na bpointí A agus B sna spásanna thíos. Tá comhordanáidí na bpointí C agus D tugtha cheana féin. A = ( , ) B = ( , ) C = (8, 4) D = (3, 6)", "has_images": true, "image_notes": "Same coordinate grid as 7(a)(i): A plotted at (1, 1), B at (6, −1). Candidate reads off and writes A and B coordinates.", "topic": "Coordinate Geometry", "marking_scheme_answer": "A(1, 1) and B(6, −1). (Marks: (a)(i)+(a)(ii) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q7b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 7, "marks_confidence": "derived", "question_text": "scríobh isteach ionchur a thugann 5 mar aschur. f( ___ ) = 5", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Aon teaglaim de 5 litir (ní gá gur fíorfhocal é, m.sh. 'Ghoti'). (Cuid de Scála 15B roinnte idir (a) agus (b).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q7bi", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Teastaíonn ó Phaulína a chruthú gurb amhlaidh gur cearnóg é ABCD. Freagair (b)(i) agus (b)(ii) thíos lena thaispeáint gur cearnóg é ABCD. (i) Taispeáin go bhfuil |AB| = |BC|.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "|AB| = √((6−1)² + (−1−1)²) = √29; |BC| = √((8−6)² + (4−(−1))²) = √29; therefore |AB| = |BC|. (Marks: (b)(i)+(b)(ii) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q7bii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Gan an léaráid a thomhas, taispeáin go bhfuil AB ingearach le BC.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Slope AB = (−1−1)/(6−1) = −2/5; slope BC = (4−(−1))/(8−6) = 5/2; product = (−2/5)(5/2) = −1, so AB ⊥ BC. (Marks: (b)(i)+(b)(ii) share scale 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q7c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "oibrigh amach luach: f(Tomás) − 3 × f(Ava) + 2 × [f(Jakub)]^2", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "f(Tomás) − 3 × f(Ava) + 2 × [f(Jakub)]^2 = 5 − 3×3 + 2×5^2 = 5 − 9 + 50 = 46. (Scála 5C: 0,3,4,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q7ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Déanann Ciarán an ráiteas seo a leanas: Ráiteas Chiaráin: \"Is cearnóg é gach comhthreomharán.\" (i) An bhfuil ráiteas Chiaráin fíor nó bréagach? Cosain do fhreagra. (Cuir tic (✓) i mbosca amháin: fíor / bréagach.)", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Bréagach (False). Justification e.g. not every parallelogram is a square (a parallelogram need not have equal sides or right angles). (Marks: (c)(i)+(c)(ii) share scale 10C (0,3,7,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q7cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Scríobh síos coinbhéarta an ráitis a rinne Ciarán.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Converse: \"Is comhthreomharán í gach cearnóg\" (Every square is a parallelogram). (Marks: (c)(i)+(c)(ii) share scale 10C (0,3,7,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q8a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "(a) Iompaigh 7·5 ciliméadar ina mhéadair. 7·5 km = ___ m", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "7·5 km = 7500 m. (Scale 5B (0,2,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q8a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Bhain na daltaí i rang úsáid as claonmhéadair agus as maidí méadair chun airde na scoile a fháil. Thomhais gach dalta an uillinn airde ó phointe áirithe go dtí díon na scoile. Taispeántar na huillinneacha seo sa tábla thíos. (63°, 63°, 63°, 62°, 61°, 60°, 58°, 57°, 57°, 56°, 56°, 55°) (a) Oibrigh amach airmheán na n-uillinneacha a thomhais na daltaí.", "has_images": true, "image_notes": "A table of 12 measured angles of elevation (in degrees), arranged in 3 rows of 4: row 1: 63°, 63°, 63°, 62°; row 2: 61°, 60°, 58°, 57°; row 3: 57°, 56°, 56°, 55°. Candidate computes the median (airmheán) of these 12 values.", "topic": "Statistics", "marking_scheme_answer": "Airmheán = (58 + 60)/2 = 59°. (Scála 5C: 0,3,4,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q8b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "D'fhág eitleán, P, aerfort. D'fhág sé an talamh ag an bpointe T. Tar éis cúpla nóiméad, bhí sé 7·5 km ó T, agus bhí sé 200 m díreach os cionn an talaimh chothroim, mar a thaispeántar sa léaráid thíos (níl sé de réir scála). Bain úsáid as an triantánacht, agus oibrigh amach méid na huillinne atá marcáilte E sa léaráid. Bíodh do fhreagra ina chéimeanna, ceart go dtí ionad deachúlach amháin.", "has_images": true, "image_notes": "A not-to-scale right-triangle diagram: take-off point T on the ground; the aeroplane P is 7·5 km from T along the slanted flight path; the vertical height above the ground is 200 m. Angle of elevation E is at T between the ground and the flight path.", "topic": "Trigonometry", "marking_scheme_answer": "sin E = 200/7500 → E = sin⁻¹(200/7500) = 1·528° ≈ 1·5° (1 d.p.). (Scale 5C (0,2,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q8b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Áiríonn Keith meán na n-uillinneacha. Áiríonn Mairéad mód na n-uillinneacha. Ar chóir go mbeadh a bhfreagraí mar an gcéanna nó difriúil? Tabhair cúis le do fhreagra. (Freagra: mar an gcéanna / difriúil – cuir tic i mbosca amháin; Cúis: )", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Difriúil. Mód = 63° (an luach is minice), meán = 59·25°, mar sin tá an meán níos lú ná an mód. (Nó aon chúis bhailí.) (Scála 10D: 0,3,5,8,10.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q8c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 2, "marks_confidence": "derived", "question_text": "Is é an luach a d'aimsigh Seán don uillinn airde ná 57°. Bhí claonmhéadar Sheáin ag airde 1·42 m. Bhí sé ina sheasamh 4 m ó bhalla na scoile ag an am seo. Tharraing Seán an léaráid thíos chun an t-eolas seo a thaispeáint. (c) Bain úsáid as an triantán dronuilleach sa léaráid chun tan 57° a scríobh ina chodán, i dtéarmaí x. (tan 57° = )", "has_images": true, "image_notes": "A scale-style diagram of the school wall ('Scoil Sheáin') with a right-angled triangle to the right showing Seán's line of sight to the top of the wall. The vertical side of the triangle is labelled x (the height of the wall above eye level). The horizontal distance from Seán to the wall is 4 m, and the angle of elevation at Seán is 57°. Seán's clinometer height is 1·42 m above the ground (marked at the bottom of the wall). The right angle is at the top of the wall where x meets the horizontal. tan 57° is to be expressed as x/4.", "topic": "Trigonometry", "marking_scheme_answer": "tan 57° = x/4. (Cuid de Scála 5D roinnte idir (c)(d)(e).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q8ci", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(i)", "parent_question": "8", "marks": 7, "marks_confidence": "derived", "question_text": "(c)(i) Scríobh 20 nóiméad mar chodán d'uair an chloig. Tabhair do fhreagra sa bhfoirm is simplí. 20 nóiméad = ___ uair an chloig", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "20 nóiméad = 1/3 uair an chloig. (Marks: (c)(i)+(c)(ii) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q8cii", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(ii)", "parent_question": "8", "marks": 8, "marks_confidence": "derived", "question_text": "Le linn cuid dá eitilt, thaistil eitleán P 598 km in dhá uair an chloig agus fiche nóiméad. Oibrigh amach meánluas eitleán P le linn an ama sin, ina km san uair. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Time = 2 h 20 min = 7/3 h. Mean speed = 598 ÷ (7/3) = 256·2857… ≈ 256·3 km/uair (km/h, 1 d.p.). (Marks: (c)(i)+(c)(ii) share scale 15D (0,4,8,12,15).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q8d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Sa léaráid thíos, seasann gach ceann de na pointí A, B, agus C d'aerfort. Thaistil an t-eitleán 598 km ó Aerfort A go dtí Aerfort B, agus ansin thaistil sé ar aghaidh go dtí Aerfort C. Oibrigh amach an fad |AC|. Bíodh do fhreagra ceart go dtí an km is gaire.", "has_images": true, "image_notes": "A not-to-scale diagram of airports A, B, C. A is top-left, C is top-right, B is at the bottom. A right angle is marked where the dashed vertical from the top edge meets B (the perpendicular from B to line AC). |AB| = 598 km (slanted segment A to B). The perpendicular height from the AC line down to B = 280 km. The angle at C is 35°.", "topic": "Trigonometry", "marking_scheme_answer": "|AD|² = 598² − 280² = 279204 → |AD| = 528·3976; tan 35° = 280/|DC| → |DC| = 280/tan35° = 399·8814; |AC| = |AD| + |DC| = 928·279 ≈ 928 km (nearest km). (Scale 5D (0,2,3,4,5).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q8d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": 2, "marks_confidence": "derived", "question_text": "Bain úsáid as d'áireamhán chun luach tan 57° a fháil. Bíodh do fhreagra ceart go dtí 2 ionad dheachúlacha. (tan 57° = )", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "tan 57° = 1·539… = 1·54 (go 2 ionad dheachúlacha). (Cuid de Scála 5D roinnte idir (c)(d)(e).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q8e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(e)", "parent_question": "8", "marks": 1, "marks_confidence": "derived", "question_text": "Agus úsáid á baint aige as a thomhais, oibríonn Seán amach gurb ionann x agus 6·16 m, a bheag nó a mhór. Bain úsáid as an luach sin, agus faigh meastachán a dhéanann Seán ar airde iomlán na scoile, ina méadair.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "Airde iomlán na scoile = x + 1·42 = 6·16 + 1·42 = 7·58 m. (Cuid de Scála 5D roinnte idir (c)(d)(e).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q9a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "(a) Iolraigh amach agus simpligh 4x(5x + 4) − 3(x − 2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "20x² + 16x − 3x + 6 = 20x² + 13x + 6. (Parts (a),(b),(c) share one scale: 10D (0,3,5,8,10).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q9a", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Tomhaiseadh meáchan plandaí gach linbh i ngrúpa gach 3 mhí, i rith an chéad 12 mhí dá saol. Taispeántar cuid de na torthaí i dTábla 1 thíos. (Tábla 1: Aois na leanaí (míonna): 0, 3, 6, 9; Meánmheáchan na leanaí (kg): 3, ___, 7, ___). Taispeántar na pointí A(0,3) agus B(6,7) ar an léaráid chomhordanáideach thíos. (a) Tarraing an líne AB ar an léaráid chomhordanáideach.", "has_images": true, "image_notes": "Table 1 with two rows: 'Aois na leanaí (míonna)' = 0, 3, 6, 9 and 'Meánmheáchan na leanaí (kg)' = 3, (blank), 7, (blank). Below, a coordinate grid: x-axis 'Aois na leanaí (míonna)' from 0 to 9, y-axis 'Meánmheáchan na leanaí (kg)' marked 2,4,6,8,10,12,14,16. Two plotted points are shown: A(0,3) on the y-axis and B(6,7). The candidate draws line AB through these points (slope 2/3).", "topic": "Coordinate Geometry", "marking_scheme_answer": "Tarraingítear an líne AB ó A(0,3) go B(6,7) ar an léaráid. (Cuid de Scála 15D roinnte idir (a)(b)(c).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q9b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "(b) Fachtóirigh 9 − 25y^2 go hiomlán.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Difference of two squares: (3 − 5y)(3 + 5y). (Shared scale 10D across (a),(b),(c).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q9b", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Comhlánaigh an abairt seo a leanas: 'Seasann an pointe B do mheánmheáchan na leanaí tar éis ___ mí.'", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Seasann B do mheánmheáchan na leanaí tar éis 6 mí. (Cuid de Scála 15D roinnte idir (a)(b)(c).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-higher-level-IV-q9c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "(c) Scríobh (5^7 × 25^3)/√5 san fhoirm 5^p, áit a mbeidh p ∈ ℚ.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(5^7 × 5^6)/5^(1/2) = 5^13 / 5^(1/2) = 5^(25/2), so p = 25/2. (Shared scale 10D across (a),(b),(c).)", "source_pdf": "2023 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q9c", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Glac leis gur mhéadaigh ar mheánmheáchan na leanaí i bpatrún líneach in imeacht na chéad 18 mí dá saol. (c) Bain úsáid as an líne AB chun meánmheáchan na leanaí tar éis 3 mhí agus tar éis 9 mí a mheas. Scríobh na luachanna seo isteach i dTábla 1. Taispeáin do chuid oibre ar an léaráid.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Ón líne AB: tar éis 3 mhí ≈ 5 kg agus tar éis 9 mí ≈ 9 kg; scríobhtar isteach i dTábla 1 le hobair thacaíochta ar an ngraf. (Cuid de Scála 15D roinnte idir (a)(b)(c).)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q9d", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Is é fána na líne AB ná 2/3. Mínigh cad is ciall leis an bhfána seo i gcomhthéacs na ceiste seo.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Gach mí, méadaíonn meánmheáchan na leanaí faoi 2/3 kg (nó aon mhíniú bailí). (Scála 5C: 0,3,4,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2023-ordinary-level-IV-q9e", "subject_n": "Mathematics", "year": 2023, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(e)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Is é cothromóid na líne AB ná: y = (2/3)x + 3. Bain úsáid as seo chun meánmheáchan na leanaí tar éis 18 mí a mheas. Taispeáin d'oibriú amach.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "y = (2/3)(18) + 3 = 12 + 3 = 15 kg. (Scála 5C: 0,3,4,5.)", "source_pdf": "2023 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q1a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Bea has eight numbered counters. There are four red counters numbered 1 to 4 and four blue counters numbered 7 to 10. Bea picks one red counter at random and one blue counter at random. Complete the table to show all 16 different pairs of counters Bea could pick. One has already been done for you. (Table: rows are Red counters 1-4, columns are Blue counters 7-10; the cell for Red 2, Blue 8 is filled in as (2, 8).)", "has_images": true, "image_notes": "A 4x4 grid table. Columns headed 'Blue counters' with values 7, 8, 9, 10. Rows headed 'Red counters' with values 1, 2, 3, 4. The cell at Red row 2 / Blue column 8 is pre-filled with the ordered pair (2, 8). Also a strip showing four red counters (1, 2, 3, 4) and four blue counters (7, 8, 9, 10).", "topic": "Probability", "marking_scheme_answer": "Complete the 4x4 table of ordered pairs (red, blue) for red in {1,2,3,4} and blue in {7,8,9,10}: (1,7)(1,8)(1,9)(1,10); (2,7)(2,8)(2,9)(2,10); (3,7)(3,8)(3,9)(3,10); (4,7)(4,8)(4,9)(4,10). 15 entries required since (2,8) is given. Reverse order accepted.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q1ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 7, "marks_confidence": "derived", "question_text": "Find the value of each of the following: 634 + 297", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q1aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 7, "marks_confidence": "derived", "question_text": "Find the value of each of the following: 4·8 × 6", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "28·8 (i.e. 144/5)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q1aiii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 6, "marks_confidence": "derived", "question_text": "Find the value of each of the following: 32 ÷ (7 − 5)^2", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "32 ÷ (2)^2 = 32 ÷ 4 = 8", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q1b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Find the probability that one of the counters Bea picks is a 7.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "P(a counter shows a 7) = 4/16 = 1/4 (or equivalent, e.g. 0.25). Ratio form 4:16 or 1:4 also accepted.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q1bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": 6, "marks_confidence": "derived", "question_text": "Complete the table to show all the factors of 8, 12, and 16. The factors of 8 have already been done. (Table: Number 8 → Factors 1, 2, 4, 8; Number 12 → ?; Number 16 → ?)", "has_images": true, "image_notes": "Two-column table headed 'Number' and 'Factors'. Row 1: 8 | 1, 2, 4, 8 (pre-filled). Row 2: 12 | (blank to complete). Row 3: 16 | (blank to complete).", "topic": "Number", "marking_scheme_answer": "Factors of 12 = {1, 2, 3, 4, 6, 12}; Factors of 16 = {1, 2, 4, 8, 16}", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q1bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "What is the highest common factor of 8, 12, and 16? Tick (✓) one box only. (Options: 1, 4, 16, 48)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "HCF = 4", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q1c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "List the pairs of counters where both numbers are prime.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Pairs where both numbers are prime: (2, 7) and (3, 7). (Red primes from {1,2,3,4} are 2 and 3; the only blue prime in {7,8,9,10} is 7.)", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q10a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 7, "marks_confidence": "derived", "question_text": "The equation of the line k is y = 2x + 5. The line k intersects the y-axis at the point (0, 5) and the x-axis at the point P. Find the co-ordinates of the point P. P = ( , )", "has_images": true, "image_notes": "Coordinate diagram showing line k (red) with positive slope crossing the y-axis at 5 and the x-axis at P (in the third/second quadrant area, left of origin), and a second line n (blue) with negative slope. P is plotted on the x-axis to the left of the origin.", "topic": "Coordinate Geometry", "marking_scheme_answer": "On the x-axis y = 0: 2x + 5 = 0 → x = -5/2. So P = (-5/2, 0) i.e. (-2.5, 0).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q10ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "The points A and B are shown on the graph. Write down the coordinates of A and B.", "has_images": true, "image_notes": "Coordinate grid with x-axis from -1 to 5 and y-axis from -1 to 4. A red line slopes gently downward from upper-left to lower-right. Point A is plotted at (1, 2) and point B at (4, 1), both lying on the line.", "topic": "Coordinate Geometry", "marking_scheme_answer": "A = (1, 2), B = (4, 1)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q10aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Hence, or otherwise, work out the distance between the points A and B. Give your answer correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "|AB| = √[(4−1)^2 + (1−2)^2] = √(9 + 1) = √10 = 3·1622… ≈ 3·2", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q10b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 8, "marks_confidence": "derived", "question_text": "The line n is perpendicular to the line k, and goes through the point (0, 10). Find the equation of the line n. Give your answer in the form ax + by + c = 0, where a, b, c ∈ ℤ.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Slope of k = 2, so slope of n = -1/2. y - 10 = -1/2(x - 0) → 2y - 20 = -x → x + 2y - 20 = 0.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q10b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "On the co-ordinate diagram below, draw the graph of the line y = 2x − 5, for −1 ≤ x ≤ 5, x ∈ ℝ.", "has_images": true, "image_notes": "Coordinate diagram with x-axis from -1 to 5 and y-axis from -8 to 5, with a blank squared grid alongside for working/plotting the line.", "topic": "Coordinate Geometry", "marking_scheme_answer": "Plot the line y = 2x − 5 (e.g. through (0, −5) and (5, 5)); relevant point e.g. (0, −5).", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q10ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)(i)", "parent_question": "10", "marks": 3, "marks_confidence": "derived", "question_text": "The equation of line l is y = 3x − 2. Write down the equation of another line that is parallel to l.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "y = 3x + k, where k ≠ −2 (any line with slope 3), e.g. y = 3x + 1", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q10cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)(ii)", "parent_question": "10", "marks": 2, "marks_confidence": "derived", "question_text": "Write down the equation of another line that crosses the y-axis at the same point as l.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Any line with y-intercept −2 but different slope, e.g. y = x − 2", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q11a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the value of 12 - 3k^2 when k = -2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "12 - 3(-2)^2 = 12 - 3(4) = 12 - 12 = 0.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q11ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(i)", "parent_question": "11", "marks": 7, "marks_confidence": "derived", "question_text": "A plan for a flower bed is shown in the diagram (not to scale). It is in the shape of a right-angled triangle with a semicircle on the hypotenuse. The diameter of the semicircle is 10 m. Write down the length of the radius (r) of the semicircle.", "has_images": true, "image_notes": "Diagram (not to scale): a right-angled triangle with one side 5 m (base) and the hypotenuse labelled x; a green semicircle sits on the hypotenuse with diameter 10 m. The right angle is at the bottom of the triangle.", "topic": "Geometry", "marking_scheme_answer": "r = 5 m", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q11aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(ii)", "parent_question": "11", "marks": 8, "marks_confidence": "derived", "question_text": "Use the formula L = π × r to find the length of the semi-circular arc. Give your answer correct to the nearest metre.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "π × r = π × 5 = 15·7 ≈ 16 m", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q11b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Factorise fully pm + 3p - m - 3.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "pm + 3p - m - 3 = p(m + 3) - 1(m + 3) = (m + 3)(p - 1).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q11b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Use the Theorem of Pythagoras to work out the value of x. Give your answer correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "10^2 = x^2 + 5^2 → x^2 = 100 − 25 = 75 → x = √75 = 8·7 m (= 5√3)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q11c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": 8, "marks_confidence": "derived", "question_text": "Graph each of the following inequalities on the number line given. (i) x < 2, where x ∈ ℤ. (ii) x ≤ 3, where x ∈ ℕ. (iii) -2 < x ≤ 4, where x ∈ ℝ.", "has_images": true, "image_notes": "Three number lines, each marked -4 to 4. Student graphs: x < 2 over ℤ (dots at integers ..., -1, 0, 1); x ≤ 3 over ℕ (dots at 1, 2, 3); -2 < x ≤ 4 over ℝ (open circle at -2, closed circle at 4, solid line between).", "topic": "Algebra", "marking_scheme_answer": "x < 2, x ∈ ℤ: dots at all integers below 2 (..., -1, 0, 1) with arrow left. x ≤ 3, x ∈ ℕ: dots at 1, 2, 3 only. -2 < x ≤ 4, x ∈ ℝ: open circle at -2, filled circle at 4, solid line joining them.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q11ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)(i)", "parent_question": "11", "marks": 3, "marks_confidence": "derived", "question_text": "The angle A is marked on the diagram below. Write sin A as a fraction.", "has_images": true, "image_notes": "Diagram (not to scale): a green composite shape combining a circle/sector with a right-angled triangle. A diagonal line (hypotenuse) of length 10 m runs through a marked centre point; the bottom side of the triangle is 5 m; a right angle is marked at the bottom-right corner; angle A is marked at the top between the hypotenuse and the vertical right edge. The side opposite angle A is the 5 m side.", "topic": "Trigonometry", "marking_scheme_answer": "sin A = 5/10 (= 1/2)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q11cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)(ii)", "parent_question": "11", "marks": 2, "marks_confidence": "derived", "question_text": "Hence, find the size of the angle A.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "A = sin⁻¹(5/10) = sin⁻¹(0·5) = 30°", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q11d", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(d)", "parent_question": "11", "marks": 7, "marks_confidence": "derived", "question_text": "Write the following expression as a single fraction in its simplest form: (5x - 2)/3 + 2/(5x + 2).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Common denominator 3(5x + 2): [(5x - 2)(5x + 2) + 3(2)] / [3(5x + 2)] = (25x^2 - 4 + 6) / [3(5x + 2)] = (25x^2 + 2) / [3(5x + 2)].", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q12a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "The first 3 patterns in a sequence are shown. Each pattern consists of white squares and shaded squares. Draw Pattern 4 in the sequence.", "has_images": true, "image_notes": "Three growing square-grid patterns: Pattern 1 is a 3x3 grid, Pattern 2 a 4x4 grid, Pattern 3 a 5x5 grid. In each, shaded squares run along a diagonal arrangement (4 shaded in Pattern 1, 5 in Pattern 2, 6 in Pattern 3). Pattern 4 would be a 6x6 grid with 7 shaded squares following the same pattern.", "topic": "Algebra", "marking_scheme_answer": "Pattern 4 is a 6x6 grid (36 squares total) with 7 shaded squares continuing the diagonal pattern.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q12a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "Find the value of 5(a + 3b), when a = 4 and b = −3.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "5(4 + 3(−3)) = 5(4 − 9) = 5(−5) = −25", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q12b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 3, "marks_confidence": "derived", "question_text": "Complete the table to show the number of shaded squares and the total number of squares in the sequence. Give your answer in the last row in terms of n, where n ∈ ℕ. (Pattern 1: shaded 4, total 9; the nth total is given as (n + 2)^2.)", "has_images": true, "image_notes": "Table with columns Pattern, Number of shaded squares, Total number of squares. Rows for patterns 1-5 and n. Pre-filled: Pattern 1 shaded = 4, total = 9; and the n-row total = (n + 2)^2. Student completes the rest.", "topic": "Algebra", "marking_scheme_answer": "Shaded squares: P1=4, P2=5, P3=6, P4=7, P5=8, n = n + 3. Total squares: P1=9, P2=16, P3=25, P4=36, P5=49, n = (n + 2)^2.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q12b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "Factorise x^2 + 5x − 24. One of the factors is (x + 8).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x + 8)(x − 3)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q12c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 1, "marks_confidence": "derived", "question_text": "Multiply out and simplify fully (2x + 3)(x − 4).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2x^2 − 8x + 3x − 12 = 2x^2 − 5x − 12", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q12ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)(i)", "parent_question": "12", "marks": 10, "marks_confidence": "derived", "question_text": "In pattern k, the difference between the total number of squares and the number of shaded squares is 271. Show that this means that: k^2 + 3k + 1 = 271.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Total = (k + 2)^2 and shaded = (k + 3). Difference: (k + 2)^2 - (k + 3) = k^2 + 4k + 4 - k - 3 = k^2 + 3k + 1 = 271.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q12cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)(ii)", "parent_question": "12", "marks": 10, "marks_confidence": "derived", "question_text": "Solve the equation k^2 + 3k + 1 = 271 to work out the value of k.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "k^2 + 3k + 1 = 271 → k^2 + 3k - 270 = 0 → (k - 15)(k + 18) = 0 → k = 15 or k = -18. Since k must be a positive pattern number, k = 15.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q13a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Michael is designing the roof of a house. The width of the roof is 6.1 m. The roof will be in the shape of a right angled triangle of height h, where h ∈ ℝ. Michael can choose different values for h. The diagram shows one possible design for the roof (not to scale). Calculate the slant height (x m) of the roof in this diagram, correct to 2 decimal places. (h = 2.84 m, base = 6.1 m.)", "has_images": true, "image_notes": "A right-angled triangle (roof, not to scale): horizontal base labelled 6.1 m, vertical height h = 2.84 m, and slant side (hypotenuse) labelled x m. A photo of a modern house is shown beside the question.", "topic": "Trigonometry", "marking_scheme_answer": "By Pythagoras: x^2 = 6.1^2 + 2.84^2 = 37.21 + 8.0656 = 45.2756, so x = √45.2756 = 6.7287... ≈ 6.73 m.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q13b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "The diagram shows a different design for this part of the roof (not to scale). Use trigonometry to work out the size of the angle marked θ in the diagram. Give your answer in degrees, correct to the nearest degree. (Opposite = 3.12 m, base = 6.1 m.)", "has_images": true, "image_notes": "A right-angled triangle (not to scale): horizontal base 6.1 m, vertical side 3.12 m on the right, and the angle θ at the bottom-left vertex between the base and the hypotenuse.", "topic": "Trigonometry", "marking_scheme_answer": "tan θ = opposite/adjacent = 3.12/6.1, so θ = tan⁻¹(3.12/6.1) = 27.088...° ≈ 27° (nearest degree).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q13ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)(i)", "parent_question": "13", "marks": 10, "marks_confidence": "derived", "question_text": "A different part of the roof is in the shape of an isosceles triangle, with base 14 m. In this part of the roof Michael makes an attic room, by putting in the two vertical side walls [AB] and [DC] shown in the diagram (not to scale). The distance from B to C is 8 m. The total height of the roof is y metres, and |AB| = |DC| = x metres, where x, y ∈ ℝ. Use similar triangles to show that x = 3y/7.", "has_images": true, "image_notes": "An isosceles triangle (not to scale) with apex E at top and base 14 m wide. Vertical wall [AB] = x m on the left and [DC] = x m on the right stand on the base. The central full height from apex E to base is y m. The segment BC along the base (between the two walls) is 8 m, with a right-angle mark at the foot of the central height. The base is 14 m, so each side beyond the walls is (14 - 8)/2 = 3 m. The shaded region is ABCDE.", "topic": "Geometry", "marking_scheme_answer": "Using similar triangles (small triangle of base 3 and height x at the side, similar to the half large triangle of base 7 and height y): x/3 = y/7, so x = 3y/7.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q13cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)(ii)", "parent_question": "13", "marks": 10, "marks_confidence": "derived", "question_text": "The area of the shaded region ABCDE in the diagram is 12 m^2. Using your answer from part (c)(i), or otherwise, work out the value of y.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Using the half-shape: (1/2)(7)(y) - (1/2)(3)(x) = 6, and x = 3y/7: (1/2)(7)y - (1/2)(3)(3y/7) = 6. Multiply by 14: 49y - 9y = 84 → 40y = 84 → y = 84/40 = 2.1 m.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q2a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 3, "marks_confidence": "derived", "question_text": "The table below shows the distances in centimetres jumped by a group of students during a school long jump competition. Distance jumped (cm): 0-80, 80-160, 160-240, 240-320, 320-400; Number of students: 0, 2, 7, 12, 3. [Note: 80-160 means 80 cm or more, but less than 160 cm, etc.] Work out the number of students who jumped less than 240 cm.", "has_images": true, "image_notes": "Grouped frequency table. Distance jumped (cm) intervals: 0-80, 80-160, 160-240, 240-320, 320-400. Corresponding Number of students: 0, 2, 7, 12, 3. (Total = 24 students.) A small photo of a long-jump pit is also shown.", "topic": "Statistics", "marking_scheme_answer": "Students who jumped less than 240 cm = 0 + 2 + 7 = 9 students.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q2ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "Lily buys the following ingredients: Fresh milk €2·49, Courgettes €1·19, Oranges €0·99, Spaghetti €1·15, Cranberry juice €2·55. Work out the total cost of these ingredients.", "has_images": true, "image_notes": "Photos of five grocery items above a price table. Table: Fresh milk €2·49 | Courgettes €1·19 | Oranges €0·99 | Spaghetti €1·15 | Cranberry juice €2·55.", "topic": "Number", "marking_scheme_answer": "€2·49 + €1·19 + €0·99 + €1·15 + €2·55 = €8·37", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q2aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "Later that week Lily plans a menu for a full week and goes shopping for ingredients. Her bill comes to €72·63. She pays using one €50 note and two €20 notes. Work out how much change she receives.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "€50 + €20 + €20 = €90; Change = €90 − €72·63 = €17·37", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q2b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 2, "marks_confidence": "derived", "question_text": "Draw a histogram to show the information in the table. Use the axes and scales below.", "has_images": true, "image_notes": "Blank histogram grid. Horizontal axis labelled 'Distance jumped (cm)' marked 0, 80, 160, 240, 320, 400. Vertical axis labelled 'Number of students' marked in 2s from 0 up to 14. Student must draw bars of heights 0, 2, 7, 12, 3 for the five intervals.", "topic": "Statistics", "marking_scheme_answer": "Histogram with bars (no gaps) at heights 0, 2, 7, 12, 3 for the intervals 0-80, 80-160, 160-240, 240-320, 320-400 respectively.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q2bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Lily works as a chef in a restaurant. The table shows the hours Lily worked one weekend (Friday 7, Saturday 8, Sunday 6). Her basic pay is €18 per hour. How much money in total did Lily earn for working on Friday and Saturday?", "has_images": true, "image_notes": "Table of hours worked: Day → Friday, Saturday, Sunday; Numbers of hours worked → 7, 8, 6.", "topic": "Number", "marking_scheme_answer": "Hours = 7 + 8 = 15; Basic pay = €18 × 15 = €270", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q2bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Lily is paid 50% extra for working on Sunday. How much did she earn for working on Sunday?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Pay/hour = €18 × 1·5 = €27; Total = €27 × 6 = €162", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q2c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the maximum number of students who could have jumped more than 200 cm.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Maximum who jumped more than 200 cm = (all of 160-240) + (240-320) + (320-400) = 7 + 12 + 3 = 22 students.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q2ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Lily's gross income was €1900 last month. She pays tax at a rate of 20%. Work out Lily's gross tax for the month.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Gross tax = (20/100) × €1900 = €380", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q2cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(c)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Lily's monthly tax credit is €312·50. Work out Lily's net income for the month.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Net tax = €380 − €312·50 = €67·50; Net income = €1900 − €67·50 = €1832·50", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q2d", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Use mid-interval values to estimate the mean distance jumped by the group of students. Give your answer correct to the nearest centimetre.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Mean = [0(40) + 2(120) + 7(200) + 12(280) + 3(360)] / 24 = (0 + 240 + 1400 + 3360 + 1080)/24 = 6080/24 = 253.33... ≈ 253 cm.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q2e", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(e)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Estimate the median distance jumped, as accurately as you can. Show your working out. Estimate of median = __", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "With 24 students the median lies between the 12th and 13th values, which fall in the 240-320 cm interval (near its lower end). Estimate ≈ 260 cm (approximately 240 + 20).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q3ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Tomás works as a chef in a restaurant. The table below shows the hours he worked one weekend. His basic pay is €19 per hour. Day: Friday, Saturday, Sunday; Numbers of hours worked: 7, 8, 6. How much money in total did Tomás earn for working on Friday and Saturday?", "has_images": true, "image_notes": "Table with columns Day (Friday, Saturday, Sunday) and row 'Numbers of hours worked' showing 7, 8, 6 respectively. Basic pay stated as €19 per hour.", "topic": "Number", "marking_scheme_answer": "Friday + Saturday hours = 7 + 8 = 15 hours; 15 × €19 = €285.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q3ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "A = {4, 5, 9, 10, 11}. Write down a subset of A that contains four elements.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Any 4-element subset, e.g. {4, 5, 9, 10}, {4, 5, 9, 11}, {4, 5, 10, 11}, {4, 9, 10, 11}, {5, 9, 10, 11}", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q3aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Tomás is paid 50% extra for working on Sunday. How much did he earn for working on Sunday?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Sunday rate = €19 + 50% of €19 = €19 × 1.5 = €28.50 per hour; 6 × €28.50 = €171. (Or 6 × €19 = €114, plus half = €57, total €171.)", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q3aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "A = {4, 5, 9, 10, 11}. Write down a subset of A that contains only prime numbers.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Any of {5}, {11}, {5, 11}", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q3b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Tomás's gross income was €1900 last month. He pays tax at a rate of 20%. His monthly Tax Credit is €312.50. Work out Tomás's net income for the month.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Gross tax = 20% of €1900 = €380; Tax payable = €380 − €312.50 = €67.50; Net income = €1900 − €67.50 = €1832.50.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q3bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(i)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "A restaurant has a choice of rice (R) or fries (F) or both with each main course on the menu. The Venn diagram shows what 5 people chose. From the Venn diagram, what did Aileen choose?", "has_images": true, "image_notes": "Venn diagram with two overlapping sets R (rice) and F (fries). In R only: Lillian. In the intersection R ∩ F: Darragh, Padraig. In F only: Evan, Aileen.", "topic": "Number", "marking_scheme_answer": "Fries only", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q3bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(ii)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "Tick the correct box to show the region of the Venn diagram in which Darragh lies. Tick (✓) one box only. (Options: R\\F, R ∩ F, F\\R)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "R ∩ F", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q3biii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(iii)", "parent_question": "3", "marks": 4, "marks_confidence": "derived", "question_text": "List the elements of the set F\\R.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "{Evan, Aileen}", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q3ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)(i)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Tomás puts €2500 into a special savings account. This account offers interest at a rate of 3.2% per year for 2 years, compounded annually. Tomás does not put any money in or take any money out of the account over the 2 years. How much interest will Tomás earn in the first year?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Interest in year 1 = 3.2% of €2500 = (3.2/100) × 2500 = €80.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q3ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)(i)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "A summer camp has two water sports on offer, kayaking and surfing. In total, 24 students were on the summer camp (U). Of these: 15 had kayaked before (K), 8 had surfed before (S), 5 had kayaked and surfed before. Fill in the Venn diagram to show the above information. One region is already filled in for you (the intersection is 3).", "has_images": true, "image_notes": "Venn diagram inside universal set U(24), with two overlapping circles K(15) and S(8). The intersection region is pre-filled with the value 3; the rest of the regions are blank to complete.", "topic": "Probability", "marking_scheme_answer": "Kayaking only = 10, Surfing only = 5, intersection = 3, outside (neither) = 6", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q3cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)(ii)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the total amount in the account after the 2 years.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Balance after year 1 = 2500 + 80 = €2580; interest year 2 = 3.2% of 2580 = €82.56; total = 2580 + 82.56 = €2662.56. (Equivalently 2500 × 1.032^2 = €2662.56.)", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q3cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)(ii)", "parent_question": "3", "marks": 2, "marks_confidence": "derived", "question_text": "One student is picked at random from the group of students. Write down the probability that this student has not kayaked or surfed before.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "6/24 (= 1/4)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q4a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Ciara is making an orange drink. The orange drink is made by mixing concentrate and water. The ratio of concentrate to water is 1 : 4. Ciara makes 15 litres of the orange drink. Work out how many litres of concentrate Ciara uses to make the drink.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Ratio 1 : 4 gives 1 + 4 = 5 parts. Concentrate = 1/5 of 15 litres = 3 litres.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q4ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(i)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Alex travels on a bus to get to school each morning. The graph shows the distance travelled along the route, in five stages labelled A, B, C, D, and E. During stage B, the bus was stopped. For how many minutes was the bus stopped during stage B?", "has_images": true, "image_notes": "Distance-time graph. y-axis: Distance (kilometres) from Home (0) up to School (6); x-axis: Time (minutes) 0 to 10. Piecewise line through five stages: A is a rising segment to ~3 km by t≈3; B is a flat (horizontal) segment around 3 km from t≈3 to t≈5 (bus stopped); C, D, E are rising segments continuing up to School (6 km) by t≈9–10. Points labelled A, B, C, D, E along the line.", "topic": "Functions", "marking_scheme_answer": "2 minutes", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q4aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(ii)", "parent_question": "4", "marks": 1, "marks_confidence": "derived", "question_text": "During which stage, other than stage B, was the bus stopped?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "D", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q4b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Ciara sells glasses of the orange drink for €0.20 each. Each glass contains 250 ml of the drink. She sells 10 litres altogether. The total cost was €5.50. Work out her profit as a percentage of the total cost. Give your answer correct to 1 decimal place.", "has_images": true, "image_notes": "A small photo of a glass of orange drink with a slice of orange on the rim is shown beside the part.", "topic": "Number", "marking_scheme_answer": "Number of glasses = 10 litres / 0.25 litres = 40 glasses; revenue = 40 × €0.20 = €8; profit = €8 − €5.50 = €2.50; profit % = (2.50/5.50) × 100 = 45.45...% ≈ 45.5%.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q4b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "The bus is moving at its fastest at stage A. How do you know this by looking at the graph?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "It has the steepest slope (steepest part of the graph).", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q4c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Each glass is approximately the shape of a cylinder with diameter 6 cm and height 10 cm. Find the volume of a glass correct to the nearest cm^3.", "has_images": true, "image_notes": "Diagram of a yellow cylinder (glass) labelled with diameter 6 cm across the top and height 10 cm down the side.", "topic": "Geometry", "marking_scheme_answer": "V = πr^2h with r = 3 cm, h = 10 cm: V = π × 3^2 × 10 = 90π = 282.74... ≈ 283 cm^3.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q4ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)(i)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Fiadh takes a different bus to school. This bus takes 15 minutes to get to school. Write 15 minutes as a fraction of one hour.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15/60 (= 1/4)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q4cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)(ii)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Fiadh's journey is 5 kilometres. Work out the average speed of the bus, in km/hour.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "5 ÷ (1/4) = 20 km/hour", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q4di", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(d)(i)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "The cost of a litre of fuel was €1·50 at the end of 2020. The cost of a litre of the same fuel was €2 at the end of 2022. How much has the cost of a litre of fuel increased by in this time period?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "€0·50", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q4dii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(d)(ii)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "Work out the percentage increase in the cost of a litre of fuel from the end of 2020 to the end of 2022. Give your answer correct to the nearest percent.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(0·5 / 1·50) × 100 = 33%", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q5", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "The lines l and k are parallel, as shown in the diagram below (not to scale). Two other lines are shown. The sizes of two of the angles are given. The sizes of three of the other angles are a, b and c. Find the size of the angle a, the angle b, and the angle c, without measuring.", "has_images": true, "image_notes": "Two horizontal parallel lines, l (upper) and k (lower), crossed by two transversals (one black near-vertical line and one red diagonal line). At the intersection on line l: angles a (above) and c (below) are marked. At the intersection on line k: angle b is marked on the left, with given angle 40° beside it (between the two transversals), and a given angle 85° marked at the right intersection on line k.", "topic": "Geometry", "marking_scheme_answer": "a = 85°, b = 140°, c = 55°", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q5a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "A and B are two sets. Complete the tables below by shading in each of the given sets in the diagram. (i) Shade A ∩ B on the Venn diagram. (ii) Shade A \\ B on the Venn diagram.", "has_images": true, "image_notes": "Two two-set Venn diagrams, each with overlapping circles labelled A (left) and B (right) inside a universal-set rectangle. The first is to be shaded to show A ∩ B; the second to be shaded to show A \\ B.", "topic": "Number", "marking_scheme_answer": "A ∩ B: shade only the central overlap (lens) of circles A and B. A \\ B: shade only the part of circle A that lies outside B (the left crescent).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q5bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)(i)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "The sets U, P, Q, and S are as follows: U = {Natural numbers from 1 to 10}, P = {3, 5, 6, 9}, Q = {3, 5, 10}, S = {factors of 10}. Complete the Venn diagram by writing each element of the set U in the correct region of the Venn diagram. List the element(s) of the set P ∩ Q ∩ S.", "has_images": true, "image_notes": "A three-set Venn diagram with circles P, Q and S inside a rectangle labelled U. Some elements are pre-placed: 9 in P only, 4 outside all circles, 8 in Q only. Student must place all elements of U = {1,...,10} given P = {3,5,6,9}, Q = {3,5,10}, S = {1,2,5,10}.", "topic": "Number", "marking_scheme_answer": "S = factors of 10 = {1, 2, 5, 10}. P ∩ Q ∩ S = {5} (5 is the only element in all three sets).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q5bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)(ii)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "List the elements of the set P \\ Q.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "P \\ Q = {6, 9} (elements of P = {3,5,6,9} that are not in Q = {3,5,10}).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q6", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "A chocolate bar in the shape of a prism is shown. The front and back faces are each in the shape of equilateral triangles, with sides of length 3 cm. The other three faces are each in the shape of rectangles that are 9 cm in length, as shown above. Complete an accurate net of the prism below, by drawing in the four missing faces. One of the triangular faces has already been drawn. Each small square in the grid has sides of length 1 cm.", "has_images": true, "image_notes": "A photo of a Toblerone-style triangular prism: equilateral triangular cross-section with side 3 cm and length 9 cm. Below, a 1 cm square grid with one equilateral triangle (side 3 cm) already drawn. Student must add the remaining four faces (one more equilateral triangle of side 3 cm and three 9 cm × 3 cm rectangles) to complete the net.", "topic": "Geometry", "marking_scheme_answer": "Net consists of two equilateral triangles (side 3 cm) and three rectangles (9 cm × 3 cm) arranged so the prism folds up correctly. One triangle is given; the four missing faces (one triangle + three rectangles) must be drawn accurately to scale on the 1 cm grid.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q6", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6", "parent_question": "6", "marks": 15, "marks_confidence": "high", "question_text": "Construct a triangle ABC where |AB| = 10 cm, |∠CAB| = 50° and |AC| = 6 cm. A sketch of the triangle is shown below (not to scale). Each small square in the grid has sides of length 1 cm. The point A is marked for you. Show your construction lines clearly.", "has_images": true, "image_notes": "Sketch (not to scale) of triangle ABC: A bottom-left, B bottom-right with |AB| = 10 cm along the base, C at top with |AC| = 6 cm, and angle CAB = 50° marked at A. A 1 cm grid is provided below with point A pre-marked for the construction.", "topic": "Geometry", "marking_scheme_answer": "Construction: Step 1 measure base AB = 10 cm; Step 2 measure side AC = 6 cm; Step 3 measure angle 50° at A; Step 4 complete the triangle.", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q7", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Margaret is trying to solve the simultaneous equations: x + y = 5 and x − 2y = −4. She says the answer is x = 3 and y = 2. Is Margaret correct? Tick (✓) one box only (Yes / No). Justify your answer by suitable calculations.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "No. Solving: (x + y = 5) − (x − 2y = −4) gives 3y = 9 → y = 3, then x + 3 = 5 → x = 2. So x = 2, y = 3, not x = 3, y = 2.", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q7a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Two rectangular solids, a cube A and a cuboid B, are shown in the diagram (not to scale). The edges of cube A have length x cm, where x ∈ ℝ. Cuboid B has dimensions 5 cm, 6 cm, and y cm, where y ∈ ℝ. The volume of A is 216 cm^3. Find the value of x.", "has_images": true, "image_notes": "Diagram (not to scale) of cube A with all edges labelled x cm, and cuboid B with edges labelled 5 cm, 6 cm and y cm.", "topic": "Algebra", "marking_scheme_answer": "Cube volume x^3 = 216, so x = ∛216 = 6 cm.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q7bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(i)", "parent_question": "7", "marks": 3, "marks_confidence": "derived", "question_text": "Show that the surface area of B is (22y + 60) cm^2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Surface area = 2[(5)(6) + (5)(y) + (6)(y)] = 2[30 + 5y + 6y] = 2[30 + 11y] = 60 + 22y = (22y + 60) cm^2.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q7bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(ii)", "parent_question": "7", "marks": 2, "marks_confidence": "derived", "question_text": "The surface area of B is 269 cm^2. Work out the value of y.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "22y + 60 = 269 → 22y = 209 → y = 209/22 = 9.5 cm.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q7c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "The area of three faces of a different cuboid are shown on the diagram (not to scale). The dimensions of this cuboid are l cm by m cm by p cm, where l, m and p are all whole numbers. Work out the volume of the cuboid. Give your answer in cm^3. (Face areas shown: 48 cm^2 (top), 96 cm^2 (front), 32 cm^2 (right side).)", "has_images": true, "image_notes": "Diagram (not to scale) of a green cuboid with three visible faces labelled with their areas: top face 48 cm^2, front face 96 cm^2, right-hand side face 32 cm^2. Edges labelled l cm (vertical left), m cm (bottom front width) and p cm (depth, right).", "topic": "Geometry", "marking_scheme_answer": "For face areas lm = 48 (or arrangement), the product of the three face areas equals V^2: 48 × 96 × 32 = 147456 = V^2, so V = √147456 = 384 cm^3. (Dimensions l = 8, m = 12, p = 4 give V = 8 × 12 × 4 = 384 cm^3.)", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q8a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "The graph shows the function g(x) for -2 ≤ x ≤ 3, x ∈ ℝ. Use this graph to answer the following questions. Write down the value g(3). g(3) = __", "has_images": true, "image_notes": "Graph of y = g(x) on axes x from -2 to 3 and y from -2 to 5. The function is piecewise linear: a straight line rising from (-2, 0) up to a peak at (1, 3), then a straight line falling from (1, 3) to (3, 2). The line is labelled y = g(x).", "topic": "Functions", "marking_scheme_answer": "g(3) = 2 (read from the graph at x = 3).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 20, "marks_confidence": "high", "question_text": "The ages (in months) of 12 third year students are: 179, 185, 186, 187, 187, 189, 190, 191, 192, 196, 197, 200. Complete the stem and leaf diagram below to show this data. (Stems 17, 18, 19, 20; Key: 19 | 1 = 191.)", "has_images": true, "image_notes": "Data table of 12 ages (in months): 179, 185, 186, 187, 187, 189, 190, 191, 192, 196, 197, 200. Empty stem-and-leaf diagram with stems 17, 18, 19, 20 to be completed, and key '19 | 1 = 191'.", "topic": "Statistics", "marking_scheme_answer": "Stem 17 | 9; Stem 18 | 5 6 7 7 9; Stem 19 | 0 1 2 6 7; Stem 20 | 0. (Key: 19 | 1 = 191.)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q8b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Write down the value of x for which g(x) = 1. x = __", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "x = -1 (the point on the rising line where y = 1).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)(i)", "parent_question": "8", "marks": 4, "marks_confidence": "derived", "question_text": "Work out the mean age of these students.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "2279 ÷ 12 = 189·9 (accept ≈ 190) months", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)(ii)", "parent_question": "8", "marks": 3, "marks_confidence": "derived", "question_text": "Find the median age of these students.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "(189 + 190) ÷ 2 = 189·5 months", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8biii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)(iii)", "parent_question": "8", "marks": 3, "marks_confidence": "derived", "question_text": "Find the range of the ages of these students.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "200 − 179 = 21 months", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8biv", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)(iv)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "In 6 months, which one of these measures will not have changed for this group of students? Tick (✓) one box only (Mean age / Median age / Range of the ages). Give a reason for your answer.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Range. Reason: every age increases by 6 months, so both the highest and lowest values increase by the same amount and the difference (range) is unchanged.", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q8c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 15, "marks_confidence": "high", "question_text": "Draw the graph of the function y = g(x) - 2 on the diagram above, for -2 ≤ x ≤ 3, x ∈ ℝ.", "has_images": true, "image_notes": "Student draws on the same axes as part (a). The new graph is g(x) translated down by 2 units: a line from (-2, -2) up to a peak at (1, 1), then down to (3, 0).", "topic": "Functions", "marking_scheme_answer": "Translate the whole graph of g(x) down by 2 units (subtract 2 from every y-value). Key points: (-2, -2), (1, 1) [peak], (3, 0).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "The 12 students were asked their favourite subject from the list: Maths, Science and History. The results are displayed in the table (Maths: 4 students, fraction 4/12; Science: 5 students; History: ?, angle in pie chart 90°). Work out the number of students who chose History. Write your answer in the appropriate space in the table above.", "has_images": true, "image_notes": "Table with columns 'Favourite Subject', 'Number of students', 'Fraction', 'Angle in Pie Chart'. Rows: Maths | 4 | 4/12 | (blank); Science | 5 | (blank) | (blank); History | (blank) | (blank) | 90°.", "topic": "Statistics", "marking_scheme_answer": "History = 3 students", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the two missing fractions of the students who chose Science and History. Write your answer in the appropriate space in the table above.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Science = 5/12; History = 3/12", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8ciii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(iii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the sizes of the two missing angles in the pie chart. Write each answer in the appropriate space in the table on the previous page.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Maths angle = 120°; Science angle = 150° (History given as 90°)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q8civ", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(iv)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Use the information in the table to complete the pie chart. Label each sector clearly with the name of the subject (Maths and Science).", "has_images": true, "image_notes": "A circle (pie chart) with one sector already drawn and labelled 'History', shown with a right-angle (90°) sector marked at the centre. The remaining two sectors are to be drawn and labelled Maths (120°) and Science (150°).", "topic": "Statistics", "marking_scheme_answer": "Draw and label the remaining sectors: Maths (120°) and Science (150°), with History 90° already shown.", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q9a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "The co-ordinate diagram shows a line segment [AC] and the points B(4, 1) and P(3, 3). Write down the co-ordinates of the point A and the point C. A = ( , ) C = ( , )", "has_images": true, "image_notes": "Coordinate grid (x from -2 to 8, y from 0 to 6). A line segment [AC] is drawn rising from left to right, with A at approximately (-1, 1) and C at approximately (5, 4), passing through P(3, 3). Point B is plotted at (4, 1). Points A, C, B and P are labelled.", "topic": "Coordinate Geometry", "marking_scheme_answer": "A = (-1, 1) and C = (5, 4) (read from the diagram).", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q9a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "A baking tin is in the shape of an open rectangular box. Alex makes a scaled model of the tin. It is 7 cm long, 5 cm wide, and 2 cm high. Use the lengths in the diagram above to draw a net of the open rectangular box. One side has already been done for you. Each small square in the grid has a side of length 1 cm.", "has_images": true, "image_notes": "3-D diagram of an open rectangular box (green) labelled 7 cm long, 5 cm wide, 2 cm high. Below, a 1 cm grid with one face (a 7 × 2 rectangle) already drawn as part of the net to be completed.", "topic": "Geometry", "marking_scheme_answer": "Draw the net of the open box (base 7 × 5, plus four sides: two 7 × 2 and two 5 × 2 rectangles; no top).", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q9b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Find the surface area of Alex's open rectangular box.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Base 7 × 5 = 35; two 7 × 2 = 28; two 5 × 2 = 20; total = 35 + 28 + 20 = 83 cm^2", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q9bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)(i)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "D is a point (not shown). D is the image of point B under central symmetry in the point P. Plot and label the point D on the diagram above and join the points A, B, C and D to form the quadrilateral ABCD.", "has_images": true, "image_notes": "Same coordinate diagram as part (a). Student plots D = image of B(4,1) under central symmetry in P(3,3), i.e. D = (2, 5), then joins A, B, C, D to form quadrilateral ABCD.", "topic": "Coordinate Geometry", "marking_scheme_answer": "D = (2(3) - 4, 2(3) - 1) = (2, 5). Plot D at (2, 5) and join the four points to form quadrilateral ABCD.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-higher-level-EV-q9bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)(ii)", "parent_question": "9", "marks": 15, "marks_confidence": "high", "question_text": "Kate says the quadrilateral ABCD is not a parallelogram. Find |AB| and |CD| and use these values to explain why Kate is correct.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "|AB| = √[(4-(-1))^2 + (1-1)^2] = √[5^2 + 0] = 5 units. |CD| = √[(5-2)^2 + (4-5)^2] = √[3^2 + (-1)^2] = √(9+1) = √10 ≈ 3.16 units. Since |AB| ≠ |CD|, the opposite sides are not equal in length, so ABCD is not a parallelogram.", "source_pdf": "2024 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q9c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "Alex made his model using a scale of 1 : 3. Complete the table to show the lengths of the sides of the actual tin. One has already been done for you. (Scaled length (cm): 7, 5, 2; Actual length (cm): 21, ?, ?)", "has_images": true, "image_notes": "Table: 'Scaled length (cm)' row → 7, 5, 2; 'Actual length (cm)' row → 21, (blank), (blank).", "topic": "Number", "marking_scheme_answer": "Actual lengths: 21, 15, 6 (each scaled length × 3)", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-ordinary-level-EV-q9d", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "The instructions for cooking an item are: 25 minutes for every 500 g, plus an extra 20 minutes. Work out how many minutes an item of mass 1·4 kg should be cooked for.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1·4 kg = 1400 g; 25 min per 500 g → 25 + 25 + 20 (for 1400 g i.e. 2.8 × 25 = 70) → 70 + 20 = 90 minutes", "source_pdf": "2024 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q1a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Tá ocht licín, a bhfuil uimhreacha orthu, ag Bea. Tá ceithre licín dhearga ann agus iad uimhrithe ó 1 go dtí 4, agus ceithre licín ghorma agus iad uimhrithe ó 7 go dtí 10. Déanann Bea licín dearg amháin agus licín gorm amháin a roghnú go randamach. Líon isteach an tábla chun go dtaispeánfar gach ceann de na 16 phéire éagsúla de licíní a d'fhéadfadh Bea a roghnú. Tá ceann amháin déanta duit cheana féin. (An tábla taispeánann licíní dearga 1–4 mar shraitheanna agus licíní gorma 7–10 mar cholúin; an cill (dearg 2, gorm 8) líonta isteach mar (2, 8).)", "has_images": true, "image_notes": "A 4x4 grid table. Rows labelled 'Licíní dearga' 1, 2, 3, 4; columns labelled 'Licíní gorma' 7, 8, 9, 10. The cell at row 2 / column 8 is pre-filled with the ordered pair (2, 8). Student fills the remaining 15 cells with ordered pairs (red, blue).", "topic": "Probability", "marking_scheme_answer": "Fill all 16 cells with ordered pairs (red, blue), e.g. (1,7),(1,8),...,(4,10). 15 entries needed; the pre-filled (2,8) is the model format. Full credit = 14 further correct entries.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q1ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 7, "marks_confidence": "derived", "question_text": "Faigh luach gach ceann díobh seo a leanas.\n634 + 297", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q1aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 7, "marks_confidence": "derived", "question_text": "4·8 × 6", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "28·8 (134/5 nó 28·8)", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q1aiii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 6, "marks_confidence": "derived", "question_text": "32 ÷ (7 − 5)^2", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "32 ÷ (2)^2 = 32 ÷ 4 = 8", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q1b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Faigh an dóchúlacht gur 7 a bhíonn ar cheann amháin de na licíní a roghnaíonn Bea.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "P = 4/16 = 1/4 (nó a choibhéis).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q1bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": 6, "marks_confidence": "derived", "question_text": "Líon isteach an tábla chun na fachtóirí go léir atá ag 8, 12, agus 16 a thaispeáint. Tá fachtóirí 8 déanta cheana féin. (Tábla: Uimhir | Fachtóirí; 8 | 1, 2, 4, 8; 12 | ; 16 | )", "has_images": true, "image_notes": "Table with two columns 'Uimhir' (Number) and 'Fachtóirí' (Factors). Rows: 8 → 1, 2, 4, 8 (already filled); 12 → blank; 16 → blank.", "topic": "Number", "marking_scheme_answer": "12: 1, 2, 3, 4, 6, 12; 16: 1, 2, 4, 8, 16", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q1bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "Cad é an fachtóir coiteann is airde atá ag 8, 12, agus 16? Ná cuir tic (✓) ach i mbosca amháin. 1 4 16 48", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "An fachtóir coiteann is airde (HCF) = 4. Tic curtha le 4.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q1c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Liostáil na péirí licíní áit ar b uimhreacha príomha iad an dá uimhir.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(2, 7) agus (3, 7). [Both numbers prime: red prime {2,3}, blue prime {7}.]", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q10a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 8, "marks_confidence": "derived", "question_text": "Is é cothromóid na líne k ná y = 2x + 5. Trasnaíonn an líne k an y-ais ag an bpointe (0, 5) agus an x-ais ag an bpointe P. Faigh comhordanáidí an phointe P. P = ( , )", "has_images": true, "image_notes": "Coordinate diagram showing red line k (y = 2x + 5) crossing the y-axis at (0,5) and the x-axis at point P (lower-left, negative x), and a blue line n with negative slope crossing through the upper region.", "topic": "Coordinate Geometry", "marking_scheme_answer": "Set y = 0: 2x + 5 = 0 ⇒ x = −5/2; ∴ P = (−5/2, 0).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q10ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeántar na pointí A agus B ar an ngraf. Scríobh síos comhordanáidí A agus B.", "has_images": true, "image_notes": "Coordinate grid, x-axis −1 to 5, y-axis −1 to 4. A red line slopes gently downward. Point A plotted at (1, 2); point B plotted at (4, 1).", "topic": "Coordinate Geometry", "marking_scheme_answer": "A(1, 2), B(4, 1)", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q10aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": 10, "marks_confidence": "high", "question_text": "Uaidh sin, nó ar shlí eile, oibrigh amach an fad idir na pointí A agus B. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "|AB| = √((4−1)^2 + (1−2)^2) = √(9+1) = √10 = 3·1622... ≈ 3·2", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q10b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 7, "marks_confidence": "derived", "question_text": "Tá an líne n ingearach leis an líne k, agus gabhann sí tríd an bpointe (0, 10). Faigh cothromóid na líne n. Bíodh do fhreagra san fhoirm ax + by + c = 0, áit a bhfuil a, b, c ∈ ℤ.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Fána k = 2 ⇒ fána ingearach n = −1/2. y − 10 = −½(x − 0) ⇒ 2y − 20 = −x ⇒ x + 2y − 20 = 0.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q10b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Ar an léaráid chomhordanáideach thíos, tarraing graf na líne y = 2x − 5, le haghaidh −1 ≤ x ≤ 5, x ∈ ℝ.", "has_images": true, "image_notes": "Coordinate grid, x-axis −1 to 5, y-axis from −8 to 5, for drawing the straight line y = 2x − 5. (A second blank grid is provided for working.)", "topic": "Coordinate Geometry", "marking_scheme_answer": "Tarraing líne dhíreach y = 2x − 5 (m.sh. trí (0, −5) agus (5, 5)) don raon −1 ≤ x ≤ 5.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q10ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(c)(i)", "parent_question": "10", "marks": 3, "marks_confidence": "derived", "question_text": "Is é an chothromóid le haghaidh líne l ná y = 3x − 2. Scríobh síos cothromóid líne eile atá comhthreomhar le l.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "y = 3x + k, k ≠ −2 (m.sh. y = 3x + 1) — fána chéanna.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q10cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(c)(ii)", "parent_question": "10", "marks": 2, "marks_confidence": "derived", "question_text": "Scríobh síos cothromóid líne eile a thrasnaíonn an y-ais ag an bpointe céanna le l.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Aon líne le hidirlíon y −2, m.sh. y = x − 2 (nó luach ar bith eile do m).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q11a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach luach 12 − 3k^2 nuair atá k = −2.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "12 − 3(−2)^2 = 12 − 3(4) = 12 − 12 = 0.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q11ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)(i)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Sa léaráid thíos (nach bhfuil de réir scála), taispeántar plean le haghaidh ceapach bláthanna. An cruth atá uirthi ná triantán dronuilleach a bhfuil leathchiorcal ar an taobhagán. Is é 10 m trastomhas an leathchiorcail. Scríobh síos fad gha (r) an leathchiorcail.", "has_images": true, "image_notes": "Composite shape (not to scale): a right-angled triangle with a semicircle on the hypotenuse (taobhagán). The semicircle diameter (hypotenuse) is labelled 10 m, one short side of the triangle is labelled x, the base is 5 m.", "topic": "Geometry", "marking_scheme_answer": "r = 5 m (ga = leath an trastomhais 10 m).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q11aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)(ii)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Úsáid an fhoirmle L = π × r chun fad stua an leathchiorcail a fháil. Bíodh do fhreagra ceart go dtí an méadar is gaire.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "L = π × r = π × 5 = 15·7 m ≈ 16 m", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q11b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Fachtóirigh pm + 3p − m − 3 go hiomlán.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "pm + 3p − m − 3 = p(m+3) − 1(m+3) = (m + 3)(p − 1).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q11b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Bain úsáid as Teoirim Phiotagaráis chun luach x a oibriú amach. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "10^2 = x^2 + 5^2 → x^2 = 100 − 25 = 75 → x = √75 = 8·7 m (nó 5√3).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q11c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": 8, "marks_confidence": "derived", "question_text": "Graf gach ceann de na héagothromóidí seo a leanas ar an uimhirlíne atá tugtha. Éagothromóid 1: x < 2, áit a bhfuil x ∈ ℤ. Éagothromóid 2: x ≤ 3, áit a bhfuil x ∈ ℕ. Éagothromóid 3: −2 < x ≤ 4, áit a bhfuil x ∈ ℝ.", "has_images": true, "image_notes": "Table with column 'Éagothromóid' (the three inequalities) and column 'Uimhirlíne', each containing a number line marked -4 to 4. Student graphs each inequality on its number line (integers for ℤ, naturals for ℕ, continuous for ℝ).", "topic": "Algebra", "marking_scheme_answer": "x < 2 (x ∈ ℤ): dots at …,-1,0,1 (integers <2). x ≤ 3 (x ∈ ℕ): dots at 1,2,3 (and 0 if ℕ includes 0 per convention). −2 < x ≤ 4 (x ∈ ℝ): open circle at −2, closed circle at 4, solid line between.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q11ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)(i)", "parent_question": "11", "marks": 3, "marks_confidence": "derived", "question_text": "Tá an uillinn A marcáilte ar an léaráid thíos. Scríobh sin A mar chodán.", "has_images": true, "image_notes": "Diagram: the same composite shape with the right-angled triangle, hypotenuse 10 m and base 5 m, with angle A marked at the top vertex (between the hypotenuse and the vertical side). The opposite side to A is the base of 5 m, hypotenuse 10 m.", "topic": "Trigonometry", "marking_scheme_answer": "sin A = 5/10 (nó codán coibhéiseach).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q11cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)(ii)", "parent_question": "11", "marks": 2, "marks_confidence": "derived", "question_text": "Uaidh sin, faigh méid na huillinne A.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "A = sin⁻¹(5/10) = 30°", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q11d", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(d)", "parent_question": "11", "marks": 7, "marks_confidence": "derived", "question_text": "Scríobh an slonn seo a leanas mar chodán aonair san fhoirm is simplí: (5x − 2)/3 + 2/(5x + 2)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "[(5x−2)(5x+2) + 3(2)] / [3(5x+2)] = (25x^2 − 4 + 6) / [3(5x+2)] = (25x^2 + 2) / [3(5x + 2)].", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q12a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "Taispeántar na chéad 3 phatrún i seicheamh thíos. Tá gach patrún comhdhéanta de chearnóga bána agus de chearnóga scáthaithe. Tarraing an 4ú patrún sa seicheamh.", "has_images": true, "image_notes": "Three patterns of square grids with shaded (blue) and white squares. Pattern 1 is a 2x2 block with shaded cells; Pattern 2 a 3x3; Pattern 3 a 4x4 — each adding a border/diagonal of shaded squares. Student draws Pattern 4 (5x5).", "topic": "Algebra", "marking_scheme_answer": "Draw Pattern 4 continuing the sequence (a 5×5 grid following the shading rule of the first three).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q12a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "Faigh luach 5(a + 3b), nuair atá a = 4 agus b = −3.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "5(4 + 3(−3)) = 5(4 − 9) = 5(−5) = −25", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q12b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 3, "marks_confidence": "derived", "question_text": "Críochnaigh an tábla chun líon na gcearnóg scáthaithe agus líon iomlán na gcearnóg sa seicheamh a thaispeáint. Bíodh do fhreagra don líne dheiridh i dtéarmaí n, áit a bhfuil n ∈ ℕ. (Colúin: Patrún 1–5 agus n; Líon na gcearnóg scáthaithe; Líon iomlán na gcearnóg. Tugtar: Patrún 1 scáthaithe = 4, iomlán = 9; agus líne n: iomlán = (n + 2)^2.)", "has_images": true, "image_notes": "Table with columns 'Patrún' (1,2,3,4,5,n), 'Líon na gcearnóg scáthaithe', 'Líon iomlán na gcearnóg'. Given entries: Patrún 1 shaded = 4, total = 9; the n-row total is pre-printed as (n + 2)^2. Student fills shaded and total counts for patterns 2-5 and the general shaded term for n.", "topic": "Algebra", "marking_scheme_answer": "Total squares for pattern n = (n + 2)^2; number of shaded squares follows term n + 3 (per scheme), with pattern values completing the table (Patrún 1 shaded 4 / total 9, etc.).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q12b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 2, "marks_confidence": "derived", "question_text": "Fachtóirigh x^2 + 5x − 24. Is ceann amháin de na fachtóirí é (x + 8).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x + 8)(x − 3)", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q12c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 1, "marks_confidence": "derived", "question_text": "Iolraigh amach agus simpligh go hiomlán (2x + 3)(x − 4).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "2x(x − 4) + 3(x − 4) = 2x^2 − 8x + 3x − 12 = 2x^2 − 5x − 12", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q12ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)(i)", "parent_question": "12", "marks": 10, "marks_confidence": "derived", "question_text": "I bpatrún k, is é an difríocht idir líon iomlán na gcearnóg agus líon na gcearnóg scáthaithe ná 271. Taispeáin go gciallaíonn sé seo go bhfuil: k^2 + 3k + 1 = 271", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(k+2)^2 − (k+3) = 271 ⇒ k^2 + 4k + 4 − k − 3 = 271 ⇒ k^2 + 3k + 1 = 271.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q12cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)(ii)", "parent_question": "12", "marks": 10, "marks_confidence": "derived", "question_text": "Réitigh an chothromóid k^2 + 3k + 1 = 271 chun luach k a oibriú amach.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "k^2 + 3k − 270 = 0 ⇒ (k − 15)(k + 18) = 0 ⇒ k = 15 (k ≠ −18, ós N é).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q13a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Tá díon tí á dhearadh ag Mícheál. Is é leithead an dín ná 6·1 m. Cruth triantáin dhronuilllligh arb airde dó h a bheidh ar an díon, áit a bhfuil h ∈ ℝ. Is féidir le Mícheál luachanna difriúla ar h a roghnú. Sa léaráid thíos, taispeántar dearadh féideartha amháin don díon (nach bhfuil de réir scála). Ríomh claonaire (x m) an dín sa léaráid seo, ceart go dtí 2 ionad deachúlach.", "has_images": true, "image_notes": "Right-angled triangle (roof cross-section): horizontal base 6·1 m, vertical height h = 2·84 m, with x m the sloping hypotenuse (claonaire). Photo of a house/roof shown alongside.", "topic": "Trigonometry", "marking_scheme_answer": "x^2 = 6·1^2 + 2·84^2 = 37·21 + 8·0656 = 45·2756 ⇒ x = √45·2756 = 6·7287 ≈ 6·73 m.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q13b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Sa léaráid thíos, taispeántar dearadh difriúil don chuid seo den díon (nach bhfuil de réir scála). Bain úsáid as an triantánacht chun méid na huillinne atá marcáilte θ sa léaráid a oibriú amach. Bíodh do fhreagra ina chéimeanna, ceart go dtí an chéim is gaire.", "has_images": true, "image_notes": "Right-angled triangle: base 6·1 m, opposite vertical side 3·12 m, angle θ between the base and hypotenuse at the lower-left vertex.", "topic": "Trigonometry", "marking_scheme_answer": "tan θ = 3·12 / 6·1 ⇒ θ = tan⁻¹(3·12/6·1) = 27·088… ≈ 27°.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q13ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)(i)", "parent_question": "13", "marks": 10, "marks_confidence": "derived", "question_text": "Tá cruth triantáin chomhchosaigh ar phíosa eile den díon agus tá 14 m an bonn atá air. Sa chuid seo den díon déanann Mícheál seomra ailéir trí dhá thaobh-bhalla cheartingearacha, [AB] agus [DC], a chur isteach, mar atá le feiceáil sa léaráid thíos (nach bhfuil de réir scála). Is é 8 m an fad ó B go C. Is é airde iomlán an dín ná y méadar, agus |AB| = |DC| = x méadar, áit a bhfuil x, y ∈ ℝ. Bain úsáid as triantáin chomhchosúla chun a thaispeáint go bhfuil x = 3y/7.", "has_images": true, "image_notes": "Isosceles triangle roof cross-section: apex E at top, total height y (central vertical from E to base). Inner vertical walls AB (left) and DC (right) each labelled x m. Base segment BC = 8 m, full base = 14 m. Shaded region is ABCDE.", "topic": "Geometry", "marking_scheme_answer": "By similar triangles: x/3 = y/7 (half-base from end to wall = (14−8)/2 = 3, half-base to apex = 7), giving x = 3y/7.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q13cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)(ii)", "parent_question": "13", "marks": 10, "marks_confidence": "derived", "question_text": "Is é 12 m^2 achar an réigiúin scáthaithe ABCDE sa léaráid. Bain úsáid as do fhreagra ó chuid (c)(i), nó ar shlí eile, agus oibrigh amach luach y.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Using area = 12 with x = 3y/7: e.g. ½(14)y − 2·½(3)x = 12 ⇒ 7y − 9y/7 = 12 ⇒ 49y − 9y = 84 ⇒ 40y = 84 ⇒ y = 2·1 m.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q2a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Sa tábla thíos taispeántar na faid ina gceintiméadair a léim grúpa daltaí i rith comórtas sa léim fhada ar scoil. Fad a léimeadh (cm): 0–80, 80–160, 160–240, 240–320, 320–400; Líon daltaí: 0, 2, 7, 12, 3. [Nóta: Is é is ciall le 80–160 ná 80 cm nó níos mó, ach níos lú ná 160 cm, etc.] Oibrigh amach líon na ndaltaí a léim níos lú ná 240 cm.", "has_images": true, "image_notes": "Frequency table of long-jump distances. Class intervals (cm): 0-80, 80-160, 160-240, 240-320, 320-400 with frequencies 0, 2, 7, 12, 3 respectively. A small photo of an athletics long-jump runway accompanies the question.", "topic": "Statistics", "marking_scheme_answer": "0 + 2 + 7 = 9 dalta a léim níos lú ná 240 cm.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q2ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 8, "marks_confidence": "derived", "question_text": "Ceannaíonn Lilí na comhábhair seo a leanas: Bainne úr €2·49, Cúirséid €1·19, Oráistí €0·99, Spaigití €1·15, Sú mónóg €2·55. Oibrigh amach costas iomlán na gcomhábhar seo.", "has_images": true, "image_notes": "Photos of five grocery items above a table of prices: Bainne úr (milk) €2·49, Cúirséid (courgettes) €1·19, Oráistí (oranges) €0·99, Spaigití (spaghetti) €1·15, Sú mónóg (cranberry juice) €2·55.", "topic": "Number", "marking_scheme_answer": "Costas iomlán = €2·49 + €1·19 + €0·99 + €1·15 + €2·55 = €8·37", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q2aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 7, "marks_confidence": "derived", "question_text": "Níos déanaí an tseachtain sin, pleanálann Lilí biachlár do sheachtain iomlán agus téann sí ag siopadóireacht le haghaidh comhábhar. Is é €72·63 a bille iomlán. Íocann sí le nóta amháin €50 agus dhá nóta €20. Oibrigh amach cé mhéad sóinseála a fhaigheann sí.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Íoctha = €50 + €20 + €20 = €90. Sóinseáil = €90 − €72·63 = €17·37", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q2b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Tarraing histeagram chun an t-eolas a thaispeántar sa tábla a léiriú. Bain úsáid as na haiseanna agus na scálaí thíos.", "has_images": true, "image_notes": "Empty histogram axes provided. Vertical axis 'Líon daltaí' marked 2, 4, 6, 8, 10, 12, 14; horizontal axis 'Fad a léimeadh (cm)' marked 0, 80, 160, 240, 320, 400. Student draws bars of heights 0, 2, 7, 12, 3.", "topic": "Statistics", "marking_scheme_answer": "Draw histogram with bar heights 0, 2, 7, 12, 3 over the intervals 0-80, 80-160, 160-240, 240-320, 320-400.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q2b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 10, "marks_confidence": "derived", "question_text": "Oibríonn Lilí mar chócaire i mbialann. Sa tábla thíos, taispeántar na huaireanta an chloig a d'oibrigh Lilí deireadh seachtaine amháin. Is é €18 in aghaidh na huaire an bunphá atá aici. (Tábla: An líon uaireanta a oibríodh: Dé hAoine 7, Dé Sathairn 8, Dé Domhnaigh 6)\n(i) Cé mhéad airgid san iomlán a thuill Lilí as bheith ag obair Dé hAoine agus Dé Sathairn?\n(ii) Íoctar 50% breise le Lilí as bheith ag obair ar an Domhnach. Cé mhéad airgid sa bhreis a thuill sí as bheith ag obair Dé Domhnaigh?", "has_images": true, "image_notes": "Table titled 'An líon uaireanta a oibríodh' (hours worked) with columns Dé hAoine 7, Dé Sathairn 8, Dé Domhnaigh 6.", "topic": "Number", "marking_scheme_answer": "(i) Líon uaireanta Aoine+Sathairn = 7 + 8 = 15; bunphá = €18 × 15 = €270. (ii) Pá in aghaidh na huaire Dé Domhnaigh = €18 × 1.5 = €27; airgead breise = pá breise (€9 × 6) → €27 × 6 = €162 (sampla na scéime).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q2c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)", "parent_question": "2", "marks": 10, "marks_confidence": "derived", "question_text": "Oibrigh amach an líon is mó daltaí a d'fhéadfadh léim níos mó ná 200 cm a bheith déanta acu.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "7 + 12 + 3 = 22 dalta (taking the 160-240 group as all potentially >200 cm).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q2ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)(i)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "€1900 an t-ioncam comhlán a bhí ag Lilí an mhí seo caite. Íocann sí cáin ar ráta 20%. Oibrigh amach cáin chomhlán Lilí don mhí.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Cáin chomhlán = (20/100) × €1900 = €380", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q2cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(c)(ii)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "€312·50 an creidmheas cánach míosúil atá ag Lilí. Oibrigh amach glanioncam Lilí don mhí.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Cáin ghlan = €380 − €312·50 = €67·50; Glanphá = €1900 − €67·50 = €1832·50", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q2d", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(d)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Bain úsáid as lárluachanna eatraimh chun an meánfhad a léim an grúpa daltaí a mheas. Bíodh do fhreagra ceart go dtí an ceintiméadar is gaire.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Meán = [0(40) + 2(120) + 7(200) + 12(280) + 3(360)] / 24 = 6080/24 = 253·33… ≈ 253 cm.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q2e", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(e)", "parent_question": "2", "marks": 5, "marks_confidence": "derived", "question_text": "Tabhair meastachán, chomh cruinn agus is féidir leat é, ar an bhfad airmheánach a léimeadh. Taispeáin d'obair amach. Meastachán ar an airmheán =", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Median position (24+1)/2 = 12·5 lies in the 240-320 interval; estimate ≈ 240 + 20 = 260 cm.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q3ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Oibríonn Tomás mar chócaire i mbialann. Sa tábla thíos, taispeántar na huaireanta an chloig a d'oibrigh sé deireadh seachtaine amháin. Is é €19 in aghaidh na huaire an bunphá atá aige. (Lá / Líon na n-uaireanta a oibríodh: Dé hAoine 7, Dé Sathairn 8, Dé Domhnaigh 6.) Cé mhéad airgid san iomlán a thuill Tomás as a bheith ag obair Dé hAoine agus Dé Sathairn?", "has_images": true, "image_notes": "Table: row 'Lá' = Dé hAoine, Dé Sathairn, Dé Domhnaigh; row 'Líon na n-uaireanta a oibríodh' = 7, 8, 6.", "topic": "Number", "marking_scheme_answer": "7 + 8 = 15 uaire; 15 × €19 = €285.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q3ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "A = {4, 5, 9, 10, 11}. Scríobh síos fo-thacar de A ina bhfuil ceithre bhall.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Fo-thacar ar bith le 4 bhall, m.sh. {4, 5, 9, 10} (nó {4,5,9,11}, {4,5,10,11}, {4,9,10,11}, {5,9,10,11}).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q3aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Íoctar 50% breise le Tomás nuair a oibríonn sé ar an Domhnach. Cé mhéad a thuill sé as bheith ag obair Dé Domhnaigh?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1·5 × €19 = €28·50 san uair; 6 × €28·50 = €171 (nó 6 × €19 = €114, 1·5 × €114 = €171).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q3aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Scríobh síos fo-thacar de A nach bhfuil ann ach uimhreacha príomha.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Fo-thacar de na huimhreacha príomha amháin, m.sh. {5}, {11}, nó {5, 11}.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q3b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "€1900 an t-ioncam comhlán a bhí ag Tomás an mhí seo caite. Íocann sé cáin ar ráta 20%. €312·50 an Creidmheas Cánach míosúil atá aige. Oibrigh amach glanioncam Thomáis don mhí.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Cáin chomhlán = 20% × €1900 = €380; cáin iníoctha = €380 − €312·50 = €67·50; glanioncam = €1900 − €67·50 = €1832·50.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q3bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)(i)", "parent_question": "3", "marks": 4, "marks_confidence": "derived", "question_text": "Le gach príomhchúrsa i mbialann, tá rogha idir rís (R) nó sceallóga (S) nó an dá rud. Sa léaráid Venn taispeántar na roghanna a rinne 5 dhuine. (Léaráid Venn: tacar R ar chlé le Lillian, Darach, Pádraig; tacar S ar dheis le Eoin, Ailín; Darach agus Pádraig san imeartas R∩S.) Ón léaráid Venn, cad a roghnaigh Ailín?", "has_images": true, "image_notes": "Venn diagram with two ovals R (left) and S (right). R-only region: Lillian. Intersection R∩S: Darach, Pádraig. S-only region: Eoin, Ailín. (Ailín lies in S only.)", "topic": "Number", "marking_scheme_answer": "Sceallóga amháin (Ailín i dtacar S amháin).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q3bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)(ii)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "Cuir tic sa bhosca ceart chun an réigiún den léaráid Venn ina bhfuil Darach a thaispeáint. Ná cuir tic (✓) ach i mbosca amháin. R\\S R ∩ S S\\R", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "R ∩ S (Darach san imeartas).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q3biii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)(iii)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "Liostaigh baill an tacair S\\R.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "{Eoin, Ailín}", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q3ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)(i)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Cuireann Tomás €2500 isteach i gcuntas coigiltis speisialta. Is é 3·2% an ráta úis in aghaidh na bliana ar an gcuntas seo ar feadh 2 bhliain, agus iolraítear go bliantúil é. Ní chuireann Tomás aon airgead isteach sa chuntas agus ní bhaineann sé aon airgead amach as i gcaitheamh an 2 bhliain sin. Cé mhéad úis a thuillfidh Tomás sa chéad bhliain?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Úis bliain 1 = 3·2% × €2500 = €80.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q3ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)(i)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "Tá dhá spórt uisce, cadhcáil agus surfáil, á dtairiscint ag campa samhraidh. San iomlán, bhí 24 dalta (U) ag freastal ar an gcampa samhraidh. Astu sin, bhí: 15 a raibh taithí acu ar an gcadhcáil (C). 8 a raibh taithí acu ar an tsurfáil (S). 5 a raibh taithí acu ar an gcadhcáil agus ar an tsurfáil araon. Líon isteach an léaráid Venn chun an t-eolas thuas a thaispeáint. Tá réigiún amháin líonta duit cheana féin.", "has_images": true, "image_notes": "Venn diagram, universal set U(24). Two ovals C(15) (cadhcáil) and S(8) (surfáil). Region outside both ovals already shows 3. Student fills C-only, intersection, S-only.", "topic": "Probability", "marking_scheme_answer": "Imeartas C∩S = 5; C amháin = 15 − 5 = 10; S amháin = 8 − 5 = 3; lasmuigh = 3 (líonta cheana). Tugadh '3' lasmuigh; oibríonn na huimhreacha amach mar 10, 5, 3 agus 6 (úsáideann an scéim 10, 5, 3 sa Venn le 6 lasmuigh).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q3cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)(ii)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach an tsuim iomlán sa chuntas i ndiaidh an 2 bhliain.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "€2500 × 1·032^2 = €2662·56 (nó: 2500+80 = 2580; úis bliain 2 = 3·2% × 2580 = €82·56; 2580 + 82·56 = €2662·56).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q3cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)(ii)", "parent_question": "3", "marks": 2, "marks_confidence": "derived", "question_text": "Roghnaítear dalta amháin go randamach as an ngrúpa daltaí. Scríobh síos an dóchúlacht nach bhfuil taithí ag an dalta seo ar an gcadhcáil ná ar an tsurfáil.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "6/24 nó 1/4 (an líon nach bhfuil taithí acu ar cheachtar / iomlán).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q4a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Tá deoch oráiste á déanamh ag Ciara. Déantar an deoch oráiste trí dhlúthán agus uisce a mheascadh le chéile. Is é cóimheas an dlúthán le huisce ná 1 : 4. Déanann Ciara 15 lítear den deoch oráiste. Oibrigh amach cé mhéad lítear den dlúthán a úsáideann Ciara chun an deoch a dhéanamh.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1 + 4 = 5 codanna; dlúthán = 15/5 = 3 lítear.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q4ai", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)(i)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Taistealaíonn Alexis ar an mbus chun dul ar scoil gach maidin. Taispeántar sa ghraf seo a leanas an fad a taistealaíodh ar an mbealach maidin amháin. Tá cúig chéim sa ghraf agus tá na lipéid A, B, C, D, agus E orthu. Le linn céim B, bhí an bus ina stad.\n(i) Cé mhéad nóiméad a bhí an bus ina stad le linn céim B?", "has_images": true, "image_notes": "Distance-time graph. y-axis 'Fad (km)' from Baile (0) to Scoil (6), x-axis 'Am (nóiméad)' 1 to 10. Stages: A rises from origin to about (3,3); B is a flat (horizontal) segment from ~3 to ~5 at 3 km; then C, D, E rise to the school at ~(10,6).", "topic": "Functions", "marking_scheme_answer": "2 nóiméad (an chuid chothrománach B ó ~3 go ~5 nóiméad).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q4aii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)(ii)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "Cén chéim, seachas céim B, ina raibh an bus ina stad?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Céim D (an chéim chothrománach eile).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q4b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Díolann Ciara gloiní den deoch oráiste ar €0·20 an ghloine. Tá 250 ml den deoch i ngach gloine. Díolann sí 10 lítear san iomlán. Is é €5·50 an costas iomlán a bhí orthu. Oibrigh amach a brabús mar chéatadán den chostas iomlán. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": true, "image_notes": "A small photo of an orange drink in a glass accompanies the question.", "topic": "Number", "marking_scheme_answer": "10000/250 = 40 gloine; ioncam = 40 × €0·20 = €8; brabús = €8 − €5·50 = €2·50; % brabús = 2·50/5·50 = 45·45% ≈ 45·5%.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q4b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Ag céim A is tapúla a bhíonn an bus ag gluaiseacht. Conas atá a fhios agat é seo ó bheith ag breathnú ar an ngraf?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Tá an fhána is géire ag céim A (an líne is géire / an fána is mó) — m.sh. is é an chuid is géire den ghraf é.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q4c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Cruth sorcóra a bheag nó a mhór atá ar gach gloine, a bhfuil trastomhas 6 cm aici agus airde 10 cm inti. Faigh toirt gach gloine, ceart go dtí an cm^3 is gaire.", "has_images": true, "image_notes": "A yellow cylinder diagram labelled with diameter 6 cm (trastomhas) at the top and height 10 cm (airde) on the side.", "topic": "Geometry", "marking_scheme_answer": "V = πr^2h = π(3)^2(10) = 282·7… ≈ 283 cm^3.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q4ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)(i)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Taistealaíonn Fiadh ar scoil ar bhus difriúil. Tógann sé 15 nóiméad ar an mbus seo an scoil a bhaint amach. Scríobh 15 nóiméad mar chodán d'uair an chloig amháin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "15/60 nó 1/4 (d'uair an chloig).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q4cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)(ii)", "parent_question": "4", "marks": 5, "marks_confidence": "derived", "question_text": "Tá fad slí 5 chiliméadar i dturas Fhiadh. Oibrigh amach meánluas an bhus, ina km/uair.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Meánluas = S/T = 5 ÷ (1/4) = 20 km/uair.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q4di", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(d)(i)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "Bhí costas €1·50 ar lítear amháin breosla ag deireadh 2020. Bhí costas €2 ar lítear amháin den bhreosla chéanna ag deireadh 2022. De cé mhéad a bhfuil an costas ar lítear breosla tar éis ardú sa tréimhse ama seo?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "€2 − €1·50 = €0·50", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q4dii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(d)(ii)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Oibrigh amach an t-ardú céatadánach ar chostas lítir breosla ó dheireadh 2020 go dtí deireadh 2022. Bíodh do fhreagra ceart go dtí an céatadán is gaire.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(0·50 / 1·50) × 100 = 33⅓% ≈ 33%", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q5", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Tá na línte l agus k comhthreomhar le chéile, mar atá le feiceáil sa léaráid thíos (nach bhfuil de réir scála). Tá dhá líne eile le feiceáil. Tugtar méid dhá cheann de na huillinneacha. Is iad a, b agus c méid trí cinn de na huillinneacha eile. Faigh méid na huillinne a, na huillinne b, agus na huillinne c, gan tomhas a dhéanamh.", "has_images": true, "image_notes": "Two horizontal parallel lines l (upper) and k (lower). A black transversal cuts both; a red transversal also cuts them. At the upper line l, angle a is above and angle c below the intersection. At the lower line k, angle b is marked to the left of one intersection beside an angle of 40°, and an angle of 85° is marked at the other intersection on k. Given: 40° and 85°. Find a, b, c.", "topic": "Geometry", "marking_scheme_answer": "|∠a| = 85°, |∠b| = 140°, |∠c| = 55°", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q5a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "high", "question_text": "Is dhá thacar iad A agus B. Scáthaigh gach ceann den dá thacar a thugtar sa léaráid chun na táblaí thíos a chríochnú. (Tacar 1: A ∩ B; Tacar 2: A\\B — léaráidí Venn le scáthú.)", "has_images": true, "image_notes": "Two Venn-diagram templates each showing two overlapping circles A and B inside a rectangle. First labelled 'A ∩ B' to be shaded; second labelled 'A\\B' to be shaded.", "topic": "Number", "marking_scheme_answer": "A ∩ B: scáthaigh an réigiún forluí (intersection). A\\B: scáthaigh an réigiún de A amháin (A gan B).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q5bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)(i)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Is mar seo a leanas atá na tacair U, P, Q agus S: U = {Uimhreacha nádúrtha ó 1 go 10}, P = {3, 5, 6, 9}, Q = {3, 5, 10}, S = {fachtóirí 10}. Críochnaigh an léaráid Venn thíos trí gach ball den tacar U a scríobh sa réigiún ceart sa léaráid Venn. Liostáil ball(aill) an tacair P ∩ Q ∩ S. P ∩ Q ∩ S =", "has_images": true, "image_notes": "Venn diagram with three overlapping circles P, Q, S inside universe U. Some elements pre-positioned outside/within: 9 in P, 8 in Q, 4 outside all (in U). Student places all elements of U (1-10) into correct regions: P={3,5,6,9}, Q={3,5,10}, S=factors of 10={1,2,5,10}.", "topic": "Number", "marking_scheme_answer": "P ∩ Q ∩ S = {5}.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q5bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)(ii)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Liostáil baill an tacair P\\Q. P\\Q =", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "P\\Q = {6, 9}.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q6", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Taispeántar thíos barra seacláide i gcruth priosma. Cruth triantáin chomhshleasaigh atá ar an aghaidh thosaigh agus ar an aghaidh chúil, agus tá a sleasa 3 cm ar fad. Cruth dronuilleoige, 9 cm ar fad, atá ar na trí aghaidh eile araon, mar a léirítear thuas. Comhlánaigh eangach bhreacht den phriosma thíos trí na ceithre aghaidh atá in easnamh a tharraingt isteach. Tá ceann amháin de na haghaidheanna triantánacha léirithe cheana féin. Tá sleasa 1 cm ar gach cearnóg bheag sa ghreille.", "has_images": true, "image_notes": "A photo of a Toblerone-style triangular prism chocolate bar, with the triangular cross-section edge labelled 3 cm and the length labelled 9 cm. Below is a grid (1 cm squares) with one equilateral triangular face already drawn; student completes the net by drawing the other four faces (one more triangle, three 9 cm × 3 cm rectangles).", "topic": "Geometry", "marking_scheme_answer": "Complete the net: 2 equilateral triangles (sides 3 cm) and 3 rectangles (9 cm × 3 cm). Triangle apex must lie within the 1 cm² grid; all 4 missing faces drawn correctly to scale.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q6", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6", "parent_question": "6", "marks": 15, "marks_confidence": "high", "question_text": "Tóg triantán ABC, áit a bhfuil |AB| = 10 cm, |∠CAB| = 50° agus |AC| = 6 cm. Tá sceitse den triantán (nach bhfuil de réir scála) le feiceáil thíos. Tá sleasa 1 cm ar gach cearnóg bheag sa ghreille. Tá an pointe A marcáilte duit. Taispeáin go soiléir do línte tógála go léir.", "has_images": true, "image_notes": "Sketch (not to scale) of triangle ABC with A at bottom-left, B at bottom-right, C at top. AC labelled 6 cm, AB labelled 10 cm, angle CAB = 50°. Below is a 1 cm grid with point A marked for the construction.", "topic": "Geometry", "marking_scheme_answer": "Tóg an triantán: |AB| = 10 cm, uillinn 50° ag A, |AC| = 6 cm. Scála na scéime: Céim 1 = líne 10 cm; Céim 2 = uillinn 6 cm (sé cm); Céim 3 = 50° tomhaiste; Céim 4 = triantán tógtha i gceart.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q7", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Tá Máiréad ag déanamh iarrachta an chothromóid chomhuaineach seo a réiteach:\nx + y = 5\nx − 2y = −4\nDeir sí gurb é an freagra ná x = 3 agus y = 2. An bhfuil an ceart ag Máiréad? Ná cuir tic (✓) ach i mbosca amháin. Cosain do fhreagra trí áirimh oiriúnacha a dhéanamh. Ceart Mícheart", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Níor chóir / Mícheart. (x+y=5) − (x−2y=−4) → 3y = 9, y = 3; ansin x + 3 = 5, x = 2. Mar sin x = 2, y = 3 (ní x = 3, y = 2), agus tá Máiréad mícheart. Tic le Mícheart.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q7a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Taispeántar dhá sholad dhronuilleogacha, an ciúb A agus an ciúbóideach B, sa léaráid thíos (nach bhfuil de réir scála). Tá imlíní an chiúib A x cm ar fad, áit a bhfuil x ∈ ℝ. Is iad toisí an chiúbóidigh B ná 5 cm, 6 cm agus y cm, áit a bhfuil y ∈ ℝ. Is é toirt A ná 216 cm^3. Faigh luach x.", "has_images": true, "image_notes": "Two diagrams: cube A with each edge labelled x cm; cuboid B with dimensions 5 cm (height), 6 cm (depth) and y cm (length).", "topic": "Geometry", "marking_scheme_answer": "x^3 = 216 ⇒ x = ∛216 = 6 cm.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q7bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)(i)", "parent_question": "7", "marks": 3, "marks_confidence": "derived", "question_text": "Taispeáin gurb é (22y + 60) cm^2 an t-achar dromchla atá ag B.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Achar dromchla = 2[(5)(y) + (5)(6) + (y)(6)] = 10y + 60 + 12y = (22y + 60) cm^2.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q7bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)(ii)", "parent_question": "7", "marks": 2, "marks_confidence": "derived", "question_text": "Is é an t-achar dromchla atá ag B ná 269 cm^2. Oibrigh amach luach y.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "22y + 60 = 269 ⇒ 22y = 209 ⇒ y = 209/22 = 9·5 cm.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q7c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Sa léaráid thíos (nach bhfuil de réir scála), taispeántar achar trí aghaidh ar chiúbóideach eile. Is iad toisí an chiúbóidigh seo ná l cm faoi m cm faoi p cm, áit ar slánuimhreacha iad l, m agus p araon. Oibrigh amach toirt an chiúbóidigh. Bíodh do fhreagra ina cm^3.", "has_images": true, "image_notes": "A cuboid diagram showing three face areas labelled: top face 48 cm^2, front face 96 cm^2, side (right) face 32 cm^2. Edges labelled l cm (left height), m cm (bottom length), p cm (depth/right).", "topic": "Geometry", "marking_scheme_answer": "lm = 96, pm = 48, pl = 32. Solving: p = 4, l = 8, m = 12. Toirt V = lmp = (8)(12)(4) = 384 cm^3. (Nó (lm·pm·pl) = 147456 = (lmp)^2 ⇒ lmp = 384.)", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q8a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Sa ghraf thíos taispeántar an fheidhm g(x) le haghaidh −2 ≤ x ≤ 3, x ∈ ℝ. Bain úsáid as an ngraf seo chun na ceisteanna seo a leanas a fhreagairt. Scríobh síos luach g(3). g(3) =", "has_images": true, "image_notes": "Graph of y = g(x) on axes x from -2 to 3, y from -2 to 5. The function is piecewise-linear: a line rises from (-2, 0) to a peak at (1, 3), then descends to (3, 2). Labelled 'y = g(x)'.", "topic": "Functions", "marking_scheme_answer": "g(3) = 2.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 20, "marks_confidence": "high", "question_text": "Taispeántar aoiseanna 12 dhalta tríú bliana (ina míonna) sa tábla thíos: 179, 185, 186, 187, 187, 189, 190, 191, 192, 196, 197, 200.\n(a) Líon an léaráid ghais is duillí thíos chun na sonraí seo a thaispeáint. (Gais: 17, 18, 19, 20. Eochair: 19 | 1 = 191.)", "has_images": true, "image_notes": "Stem-and-leaf plot to be completed. Stems printed 17, 18, 19, 20. Key given: 19 | 1 = 191. Data to enter: 179, 185, 186, 187, 187, 189, 190, 191, 192, 196, 197, 200.", "topic": "Statistics", "marking_scheme_answer": "17 | 9; 18 | 5 6 7 7 9; 19 | 0 1 2 6 7; 20 | 0. (Eochair 19 | 1 = 191.)", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q8b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Scríobh síos an luach ar x a fhágann go bhfuil g(x) = 1. x =", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "x = −1.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)(i)", "parent_question": "8", "marks": 4, "marks_confidence": "derived", "question_text": "Oibrigh amach meánaois na ndaltaí seo.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Meánaois = 2279/12 = 189·9 (glac le slánú go 190).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)(ii)", "parent_question": "8", "marks": 3, "marks_confidence": "derived", "question_text": "Faigh aois airmheánach na ndaltaí seo.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Aois airmheánach (medián) = (189 + 190)/2 = 189·5", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8biii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)(iii)", "parent_question": "8", "marks": 3, "marks_confidence": "derived", "question_text": "Faigh raon aoiseanna na ndaltaí seo.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Raon = 200 − 179 = 21", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8biv", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)(iv)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "I gceann 6 mhí, cé acu ceann de na tomhais seo nach mbeidh tar éis athrú don ghrúpa seo daltaí? Ná cuir tic (✓) ach i mbosca amháin. Meánaois Aois airmheánach Raon na n-aoiseanna. Tabhair cúis le do fhreagra.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Raon. (Cuireadh tic sa bhosca ceart gan aon chosaint — méadóidh gach aois 6 mhí ach fanann an difríocht idir an luach is airde agus is ísle, mar sin ní athraíonn an raon.)", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q8c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": 15, "marks_confidence": "high", "question_text": "Tarraing an graf den fheidhm y = g(x) − 2 ar an léaráid thuas, le haghaidh −2 ≤ x ≤ 3, x ∈ ℝ. Áirimh, más gá:", "has_images": true, "image_notes": "Student draws y = g(x) − 2 on the same grid as part (a): a vertical translation of the given graph down by 2 units, so the original points (-2,0)→(-2,-2), (1,3)→(1,1), (3,2)→(3,0).", "topic": "Functions", "marking_scheme_answer": "Draw y = g(x) − 2: translate the given graph down 2 units. New key points: (-2,-2), (1,1), (3,0). [Scheme overview labels this as graph of translation; scale 15C.]", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8ci", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Cuireadh ceist ar an 12 dhalta cad é an t-ábhar is fearr leo ón liosta seo: Mata, Eolaíocht agus Stair. Taispeántar na torthaí sa tábla. (Tábla: Ábhar is fearr leo | Líon daltaí | Codán | Uillinn i bPíchairt. Mata | 4 | 4/12 | ; Eolaíocht | 5 | | ; Stair | | | 90°.)\n(i) Oibrigh amach líon na ndaltaí a roghnaigh Stair. Scríobh do fhreagra sa spás cuí sa tábla thuas.", "has_images": true, "image_notes": "Frequency table with columns 'Ábhar is fearr leo', 'Líon daltaí', 'Codán', 'Uillinn i bPíchairt'. Rows: Mata → Líon 4, Codán 4/12; Eolaíocht → Líon 5; Stair → Uillinn 90°. Some cells blank to fill.", "topic": "Statistics", "marking_scheme_answer": "Líon daltaí a roghnaigh Stair = 3 (90° = ráithe de 360°, mar sin 1/4 de 12 = 3).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8cii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(ii)", "parent_question": "8", "marks": 3, "marks_confidence": "derived", "question_text": "Oibrigh amach an dá chodán atá in easnamh, is iad sin na daltaí a roghnaigh Eolaíocht agus Stair. Scríobh do fhreagra sa spás cuí sa tábla thuas.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Eolaíocht = 5/12; Stair = 3/12.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8ciii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(iii)", "parent_question": "8", "marks": 4, "marks_confidence": "derived", "question_text": "Oibrigh amach méid gach ceann den dá uillinn atá in easnamh sa phíchairt. Scríobh gach freagra sa spás cuí sa tábla ar an leathanach roimhe seo.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Mata = 4/12 × 360° = 120°; Eolaíocht = 5/12 × 360° = 150°.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q8civ", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(iv)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Úsáid an t-eolas sa tábla chun an píchairt a chríochnú. Lipéadaigh gach teascóg go soiléir le hainm an ábhair (Mata agus Eolaíocht).", "has_images": true, "image_notes": "A circle (pie chart) with one sector for Stair already drawn (90°, marked with a right angle at the centre). Student must draw and label the Mata (120°) and Eolaíocht (150°) sectors.", "topic": "Statistics", "marking_scheme_answer": "Críochnaigh an phíchairt: teascóg Stair 90°, Mata 120°, Eolaíocht 150°, gach ceann lipéadaithe go ceart.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q9a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Sa léaráid chomhordanáideach thíos, taispeántar mírlíne [AC] agus na pointí B(4, 1) agus P(3, 3). Scríobh síos comhordanáidí an phointe A agus an phointe C. A = ( , ) C = ( , )", "has_images": true, "image_notes": "Coordinate grid (x from -2 to 8, y from 0 to 6) showing line segment [AC] with A at lower-left near (-1, 1) and C at upper-right near (5, 4), midpoint-region point P(3, 3) marked on the segment, and B(4, 1) marked below. Student reads off A and C.", "topic": "Coordinate Geometry", "marking_scheme_answer": "A = (−1, 1), C = (5, 4).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q9a", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "An cruth atá ar stán bácála ná bosca dronuilleogach oscailte. Déanann Alexis samhail scálaithe den stán. Tá sé 7 cm ar fad, 5 cm ar leithead, agus 2 cm ar airde, mar a thaispeántar sa léaráid.\n(a) Bain úsáid as na faid sa léaráid thuas chun eangach den bhosca dronuilleogach oscailte a tharraingt. Tá slios amháin déanta duit cheana féin. Tá sleasa 1 cm ar gach cearnóg bheag sa ghreille.", "has_images": true, "image_notes": "3D drawing of an open rectangular box (no top): 7 cm long, 5 cm wide, 2 cm high. Below, a 1 cm grid with one face (the 7×5 base) already drawn; student draws the net of the open box (base plus four sides).", "topic": "Geometry", "marking_scheme_answer": "Tarraing eangach an bhosca dronuilleogaigh oscailte: bonn 7 × 5, dhá shlios 7 × 2 agus dhá shlios 5 × 2 (gan barr). Eangach bosca dronuilleogach dúnta míchruinn anseo.", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q9b", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Faigh an t-achar dromchla atá ag bosca dronuilleogach oscailte Alexis.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Achar = (7×5) + 2(7×2) + 2(5×2) = 35 + 28 + 20 = 83 cm^2", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q9bi", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)(i)", "parent_question": "9", "marks": 5, "marks_confidence": "derived", "question_text": "Is pointe é D (níl sé léirithe). Is é D íomhá an phointe B faoi shiméadracht lárnach sa phointe P. Breac agus lipéadaigh an pointe D ar an léaráid thuas agus ceangail na pointí A, B, C agus D chun an cheathairshleasán ABCD a fhoirmiú.", "has_images": true, "image_notes": "Student plots D, the image of B(4,1) under central symmetry in P(3,3), giving D = (2, 5), then joins A, B, C, D to form quadrilateral ACBD on the grid.", "topic": "Coordinate Geometry", "marking_scheme_answer": "D = (2, 5) (central symmetry of B(4,1) in P(3,3)). Plot D and draw parallelogram ACBD.", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-higher-level-IV-q9bii", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)(ii)", "parent_question": "9", "marks": 15, "marks_confidence": "high", "question_text": "Tá Cáit nach comhtreomharán é an cheathairshleasán ABCD. Faigh |AB| agus |CD| agus bain úsáid as na luachanna seo chun míniú a thabhairt ar an bhfáth a bhfuil an ceart ag Cáit.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "|AB| = 5 aonad; |CD| = √[(5−2)^2 + (4−5)^2] = √(9+1) = √10. Ós rud é 5 ≠ √10, níl an cheathairshleasán ABCD ina chomhtreomharán (níl na sleasa cothrom).", "source_pdf": "2024 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q9c", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "Rinne Alexis a shamhail ag úsáid scála 1 : 3. Líon isteach an tábla chun fad na sleasa atá ar an bhfíorstán a thaispeáint. Tá ceann amháin déanta duit cheana féin. (Tábla: Fad scálaithe (cm) | 7 | 5 | 2; Fíorfhad (cm) | 21 | | .)", "has_images": true, "image_notes": "Table: row 'Fad scálaithe (cm)' = 7, 5, 2; row 'Fíorfhad (cm)' = 21, blank, blank. Scale 1:3 (multiply scaled length by 3).", "topic": "Number", "marking_scheme_answer": "Fíorfhad: 5 × 3 = 15 cm; 2 × 3 = 6 cm (7 × 3 = 21 tugtha).", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2024-ordinary-level-IV-q9d", "subject_n": "Mathematics", "year": 2024, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Is iad na treoracha chun earra a chócaráil ná: 25 nóiméad in aghaidh gach 500 g, móide 20 nóiméad breise. Oibrigh amach cé mhéad ama is córr earra a bhfuil meáchan 1·4 kg ann a chócaráil.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1·4 kg = 1400 g = 2·8 × 500 g. Am = (25 × 2·8) + 20 = 70 + 20 = 90 nóiméad. (Scéim: 25 + 25 + 20 + 20 = 90, nó 1400 g × (25/500) = 70, 70 + 20 = 90.)", "source_pdf": "2024 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q1a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "A sports shop sells 3 different brands of running shoes, A, B, and C. Each brand comes in the 4 different colours and 4 different sizes shown in the table below. (Brand A: Red, size 7; Brand B: Blue, size 8; Brand C: Black, size 9; Yellow, size 10.) How many different choices of running shoe does the shop sell? For example, one choice would be brand B, yellow, and size 7.", "has_images": true, "image_notes": "A 3-column table listing Brand / Colour / Size: rows A–Red–7, B–Blue–8, C–Black–9, and a final row Yellow–10 (4 colours: Red, Blue, Black, Yellow; 4 sizes: 7, 8, 9, 10; 3 brands: A, B, C). Beside it is a photo of running shoes. Total combinations = 3 brands × 4 colours × 4 sizes = 48.", "topic": "Number", "marking_scheme_answer": "3 × 4 × 4 = 48 (accept correct answer without work, or a list of all 48 choices).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q1ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "Calculate the value of each of the following: 456 − 321", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q1aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "Calculate the value of each of the following: 7.4 × 6.2", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "45.88 (or 1147/25 or 45 22/25)", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q1aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "Calculate the value of each of the following: √9 × (7 − 3)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3 × (4) = 12", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q1b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "A pair of running shoes normally cost €140. In a sale, they cost €93·80. Work out the percentage discount in the sale.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Discount = €140 − €93·80 = €46·20. Percentage discount = (46·20 / 140) × 100 = 33%.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q1bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "The ages of Jael, Alice, and Paul are shown in the table below (Age now: Jael 16, Alice 12, Paul 11). Complete the table to show the ages of Jael, Alice, and Paul in 4 years' time.", "has_images": true, "image_notes": "Table with columns 'Age now' and 'Age in 4 years' time' and rows Jael, Alice, Paul. Ages now: Jael = 16, Alice = 12, Paul = 11. Second column blank for candidate to fill.", "topic": "Number", "marking_scheme_answer": "Jael 20, Alice 16, Paul 15 (each age now + 4).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q1bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the mean age of Jael, Alice, and Paul in 4 years' time.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "(20 + 16 + 15)/3 = 51/3 = 17 (or (16+12+11)/3 + 4 = 39/3 + 4 = 13 + 4 = 17).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q10a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Find the value of 3p + 7q, when p = 2 and q = 11.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(2) + 7(11) = 6 + 77 = 83.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q10ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": 2, "marks_confidence": "derived", "question_text": "There are 88 students in 3rd year in a school. The Venn diagram shows the number of these students who are members of the debating club (D) and the chess club (C). Some of these values are given in terms of x, where x ∈ N. In total, there are 40 students in the debating club (D). There are 37 students in neither club. (Venn diagram: D total [40]; the D-only region, the intersection x, the C-only region 2x + 1, and 37 outside both; universe U [88].) Fill in the missing value in the Venn diagram, in terms of x.", "has_images": true, "image_notes": "A Venn diagram inside a universal set U with 88 students. Two overlapping circles: D (labelled [40], total in debating) and C. The intersection region is labelled x; the C-only region is labelled 2x + 1; outside both circles is 37. The D-only region is the missing value to express in terms of x (= 40 − x).", "topic": "Number", "marking_scheme_answer": "Missing D-only value = 40 − x (the debating-only region, since D total is 40 and the overlap is x). [Parts (a)(i) and (a)(ii) share a 5C scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q10aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": 3, "marks_confidence": "derived", "question_text": "Hence, or otherwise, work out the value of x.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "40 + (2x + 1) + 37 = 88 → 2x + 78 = 88 → 2x = 10 → x = 5. (D-only 35 + x + C-only (2x+1) + 37 = 88 with D-only = 40 − x also gives x = 5.) [Parts (a)(i) and (a)(ii) share a 5C scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q10b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Michael is in the set D\\C. What information does this give about the clubs that Michael is in?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Michael is in the debating club but not the chess club. (D\\C = elements in D and not in C.)", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q10b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Multiply out and simplify: 2(5a − 3) − 4a + 7", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "10a − 6 − 4a + 7 = 6a + 1.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q10c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Solve the following equation in y: 8y + 4 = 2y − 8", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8y − 2y = −8 − 4; 6y = −12; y = −2.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q10d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(d)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Factorise the quadratic expression x^2 − 10x + 21. (x^2 − 10x + 21 = (x − 3)( ___ ))", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x − 3)(x − 7).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q11a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Simplify 5x^2 − 7x + 3x^2 − 6x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8x^2 − 13x (collect like terms: 5x^2 + 3x^2 = 8x^2; −7x − 6x = −13x).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q11ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(i)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Tanya draws a scaled diagram of her garden (Scale: 1 cm = 0.5 m), including a shed and a flower bed, with the distance between them marked x. 1 cm on the diagram represents an actual distance of 0.5 m. Write down the distance marked x on the diagram. Give your answer in cm. Hence, find the actual distance from the shed to the flower bed, in metres.", "has_images": true, "image_notes": "Scaled grid plan of a garden on 1 cm squares. A square 'SHED' is at the top; below it a rectangular 'FLOWER BED'; a vertical dimension arrow marked x spans the gap between them (x = 3 cm on the grid). Scale stated as 1 cm = 0.5 m.", "topic": "Geometry", "marking_scheme_answer": "Distance on diagram = 3 cm; actual distance = 3 × 0.5 = 1.5 m (10 cm would be 10 × 0.5 = 5 m).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q11aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(ii)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the actual perimeter of the flower bed.", "has_images": false, "image_notes": "Refers to the flower bed rectangle on the scaled garden grid (its side lengths read from the 1 cm = 0.5 m grid).", "topic": "Geometry", "marking_scheme_answer": "Read the flower bed dimensions from the grid and convert using 1 cm = 0.5 m, then sum the four sides (scheme treats this within the Scale 10C model solution; final perimeter follows from the scaled side lengths).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q11aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(iii)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Tanya wants to put a vegetable patch in the garden. The vegetable patch will be rectangular, with a length of 3 m and a width of 1.5 m. Draw the vegetable patch in a position on the diagram on the previous page so that it does not overlap with the shed or the flower bed.", "has_images": true, "image_notes": "Refers back to the scaled garden grid (1 cm = 0.5 m). A 3 m × 1.5 m patch must be drawn as a 6 cm × 3 cm rectangle on the grid, not overlapping the shed or flower bed.", "topic": "Geometry", "marking_scheme_answer": "3 m → 6 cm and 1.5 m → 3 cm, so draw a rectangle measuring 6 cm by 3 cm on the diagram, in a position that does not overlap the shed or the flower bed.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q11b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Divide (x^3 + 11x^2 + 15x − 27) by (x + 3).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x^2 + 8x − 9 (with remainder 0). Long division: x^3 + 3x^2 → 8x^2 + 15x; 8x^2 + 24x → −9x − 27; −9x − 27 → 0.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q11b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Tanya decides to plant cabbage in the vegetable patch. She reads that each cabbage needs a square space of 0.3 m by 0.3 m. According to this, what is the maximum number of cabbages that Tanya should plant in this vegetable patch? Remember that the vegetable patch will have a length of 3 m and a width of 1.5 m.", "has_images": true, "image_notes": "Photo of a cabbage with a 0.3 m by 0.3 m square space indicated (0.3 m on each side).", "topic": "Geometry", "marking_scheme_answer": "3 ÷ 0.3 = 10 and 1.5 ÷ 0.3 = 5, so 10 × 5 = 50 cabbages.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q12a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Jael orders his pizza at 19:50. It is delivered 45 minutes later. What time does his pizza arrive?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "19:50 + 0:45 = 19:95 = 20:35.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q12ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)(i)", "parent_question": "12", "marks": 8, "marks_confidence": "derived", "question_text": "The function f(x) is: f(x) = 2/(x + 2) for x > −2. Complete the table below, showing the values for f(x) for the given values of x. Give values correct to 2 decimal places, where appropriate. (Table: x = −1, 0, 1, 2, 3, 4; f(x) given as 1 at x=0, 0·5 at x=2, 0·4 at x=3; missing values at x = −1, 1, 4.)", "has_images": true, "image_notes": "A function table with row x: −1, 0, 1, 2, 3, 4 and row f(x): (blank), 1, (blank), 0·5, 0·4, (blank). The missing entries (x = −1, 1, 4) are to be calculated from f(x) = 2/(x+2).", "topic": "Functions", "marking_scheme_answer": "f(−1) = 2/1 = 2; f(1) = 2/3 = 0·67; f(4) = 2/6 = 0·33. Completed row: 2, 1, 0·67, 0·5, 0·4, 0·33. [10D scale shared with (a)(ii): 3 parts for table values, 6 parts for plotting, 1 part for joining.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q12aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)(ii)", "parent_question": "12", "marks": 7, "marks_confidence": "derived", "question_text": "Use the values in the table to draw the graph of the function y = f(x) on the axes below, for −1 ≤ x ≤ 4, x ∈ R.", "has_images": true, "image_notes": "A set of axes: x from −1 to 4, y marked 0·5, 1·0, 1·5, 2·0, 2·5. The 6 points (−1,2), (0,1), (1,0·67), (2,0·5), (3,0·4), (4,0·33) are to be plotted and joined by a smooth decreasing curve.", "topic": "Functions", "marking_scheme_answer": "Plot the 6 points from the table: (−1,2), (0,1), (1,0·67), (2,0·5), (3,0·4), (4,0·33), and join them appropriately by a smooth decreasing curve. [10D scale shared with (a)(i).]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q12b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Solve the following simultaneous equations to find the value of x and the value of y: 3x + 4y = 29 and 2x + y = 9.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "From 2x + y = 9, y = 9 − 2x. Substitute: 3x + 4(9 − 2x) = 29 → 3x + 36 − 8x = 29 → −5x = −7 → x = 7/5 (1·4). Then y = 9 − 2(7/5) = 31/5 (6·2). So x = 1·4, y = 6·2.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q12bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "The pizza is in a closed rectangular box with dimensions: Length = 28 cm, Width = 25 cm, Height = 4 cm. Work out the volume of the pizza box.", "has_images": true, "image_notes": "Photo of a stack of pizza boxes (decorative). Box dimensions given in text: length 28 cm, width 25 cm, height 4 cm.", "topic": "Geometry", "marking_scheme_answer": "V = 28 × 25 × 4 = 2800 cm^3.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q12bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the surface area of the pizza box. Give your answer in cm^2.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "A = 2[(25 × 28) + (25 × 4) + (28 × 4)] = 2[700 + 100 + 112] = 2 × 912 = 1824 cm^2.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q12c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "A pizza costs €14 in Limerick. The same pizza costs £12 in London. The exchange rate is €1 = £0.93. Work out which pizza is cheaper. Use calculations to support your answer. (Tick one box: Limerick / London.)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "London. For example, 14 × 0.93 = £13.02 (compare to £12 in London), or 12 ÷ 0.93 = €12.9… (compare to €14 in Limerick) — so the London pizza is cheaper.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q13a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "In this question, all lengths are in cm. The diagram shows a rectangular frame for a photo, where w, l, x ∈ R. The width of the frame is w and the length is l. There is a rectangular hole in the middle for the photo, measuring 12 by 18. The internal width of the frame is x, as shown. The length of the frame l = 18 + 2x. Write the width of the frame, w, in terms of x.", "has_images": true, "image_notes": "A rectangular frame (outer rectangle, dimensions l by w) with a central rectangular hole measuring 18 (horizontal) by 12 (vertical) for the photo. A uniform border of width x surrounds the hole on all sides (x marked on top, bottom, left, right). Outer length l = 18 + 2x; outer width w = 12 + 2x.", "topic": "Algebra", "marking_scheme_answer": "w = 12 + 2x (the photo height 12 plus a border x on each side). [Parts (a) and (b) share a 10D scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q13a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Tadhg usually cycles 3 km to football training. It takes Tadhg 10 minutes to cycle to training. Work out his average speed, in km/hour.", "has_images": true, "image_notes": "Photo of footballers at training (decorative). Data in text: distance 3 km, time 10 minutes.", "topic": "Number", "marking_scheme_answer": "10 min → 3 km; 60 min → 18 km, so 18 km/hour. (Or S = D ÷ T = 3 ÷ (1/6) = 18 km/hour.)", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q13b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Hence, show that: l × w = 4x^2 + 60x + 216.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "l × w = (18 + 2x)(12 + 2x) = 216 + 36x + 24x + 4x^2 = 4x^2 + 60x + 216. [Parts (a) and (b) share a 10D scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q13bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)(i)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Below is a distance-time graph showing how far Tadhg's bike is from his home, along the route travelled, for one of the days that he goes training. Use the information in the graph to answer parts (b)(i), (b)(ii), and (b)(iii). How long was Tadhg away from home, in total? Give your answer in minutes.", "has_images": true, "image_notes": "Distance-time graph: x-axis 'Time (minutes)' from 0 to 120 (marks at 20, 40, 60, 80, 100, 120); y-axis 'Distance from home (km)' from 0 (Home) to 3 (Training), gridlines at 0.5,1.0,1.5,2.0,2.5,3.0. Shape: rises from (0,0) to (10,3), stays flat at 3 km until 90 min, then falls back to 0 by 120 min. So leaves home at 0, returns at about 120; at training (3 km away) from 10 to 90 min.", "topic": "Functions", "marking_scheme_answer": "110 minutes (away from home from 0 until 110 min when distance returns to 0; accept 1:20 in (ii)). [Total time away read from graph = 110 minutes.]", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q13bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)(ii)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "How long was Tadhg at training? Give your answer in hours and minutes.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "90 − 10 = 80 minutes = 1 hour 20 minutes.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q13biii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)(iii)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Was Tadhg quicker cycling to training or on the way home from training? Using the graph, give a reason for your answer. (Tick one box: to training / home from training.)", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "To training. Reason: the graph is steeper (he took less time / the slope is bigger in magnitude) — or any other valid reason.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q13c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "l × w = 648 cm^2. Use this, and the information from part (b), to find the value of x. Give your answer in cm, correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "216 + 60x + 4x^2 = 648 → 4x^2 + 60x − 432 = 0 (or x^2 + 15x − 108 = 0). x = (−60 ± √(60^2 − 4·4·(−432)))/(2·4) = (−60 ± √10512)/8; taking the positive root, x = 5·31… ≈ 5·3 cm (to 1 d.p.).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q13ci", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)(i)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "The first year and second year students train together. Each year is divided into two teams, the red team and the blue team. The table shows the number of students in each team (Red: First year 18, Second year 10; Blue: First year 17, Second year 15). There are 60 students in total. One student is picked at random. What is the probability that the student is a first year on the red team?", "has_images": true, "image_notes": "Table with rows 'Red' and 'Blue' and columns 'First year' and 'Second year'. Red: First year 18, Second year 10. Blue: First year 17, Second year 15. Total = 60 students.", "topic": "Probability", "marking_scheme_answer": "18/60 (= 3/10 or 0.3).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q13cii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(c)(ii)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "What is the probability that the student is on the blue team?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "(17 + 15)/60 = 32/60 (= 8/15 or 0.5333…).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q14ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)(i)", "parent_question": "14", "marks": 10, "marks_confidence": "high", "question_text": "The points A and B are shown on the co-ordinate diagram. Write down the co-ordinates of the point A and the point B. (A = ( , ), B = ( , ))", "has_images": true, "image_notes": "Co-ordinate grid with x-axis from −4 to 5 and y-axis from −2 to 4. Point A is plotted at (3, 2) and point B is plotted at (3, −1).", "topic": "Coordinate Geometry", "marking_scheme_answer": "A = (3, 2), B = (3, −1).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q14aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)(ii)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Write down the length |AB|.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "3 (vertical distance from (3,2) to (3,−1)).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q14aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)(iii)", "parent_question": "14", "marks": 1, "marks_confidence": "derived", "question_text": "The point C is (−4, 2). Plot and label the point C on the co-ordinate diagram above.", "has_images": true, "image_notes": "Same co-ordinate grid (x from −4 to 5, y from −2 to 4); candidate plots and labels C at (−4, 2).", "topic": "Coordinate Geometry", "marking_scheme_answer": "Point C plotted and labelled at (−4, 2).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q14aiv", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(a)(iv)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Work out the slope of BC. Give your answer as a fraction.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "slope = rise/run = (−1 − 2)/(3 − (−4)) = −3/7.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q14bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)(i)", "parent_question": "14", "marks": 3, "marks_confidence": "derived", "question_text": "The diagram shows the triangle PQR. |PQ| = 24 m, |QR| = 12 m, and |∠PQR| = 90°. The angle at P is marked X. Which of the following is correct? Tick one box only: sin X = 12/24, cos X = 12/24, tan X = 12/24.", "has_images": true, "image_notes": "Right-angled triangle PQR with the right angle at Q. P is bottom-left, Q is bottom-right (|PQ| = 24 m along the base), R is top-right above Q (|QR| = 12 m, the vertical side). The angle X is at P. Opposite to X = QR = 12 m, adjacent to X = PQ = 24 m.", "topic": "Trigonometry", "marking_scheme_answer": "tan X = 12/24 (opposite over adjacent).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q14bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "14(b)(ii)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Hence, use your calculator to find the size of the angle X, correct to the nearest degree.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "X = tan⁻¹(12/24) = 26.5… = 27°.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q2a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Noah buys 3 bars of chocolate at the local shop. Each bar costs the same. He pays €20 and gets €13.40 in change. Work out the cost of 1 bar of chocolate.", "has_images": true, "image_notes": "Photo of a Cadbury Dairy Milk Oreo chocolate bar in the top-right corner; decorative only, no data needed.", "topic": "Number", "marking_scheme_answer": "20 − 13.40 = 6.60; 6.60 ÷ 3 = €2.20.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q2ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 3, "marks_confidence": "derived", "question_text": "Write down the next two terms in the following sequence. The type of each sequence is given. Linear: 1, 5, 9, __, __", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "13, 17 (common difference of 4).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q2aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 3, "marks_confidence": "derived", "question_text": "Write down the next two terms in the following sequence. Tripling: 4, 12, 36, __, __", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "108, 324 (each term multiplied by 3).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q2aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(iii)", "parent_question": "2", "marks": 4, "marks_confidence": "derived", "question_text": "Write down the next two terms in the following sequence. Quadratic: 12, 19, 23, __, __", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "24, 22 (first differences 7, 4, 1, −2, …; second difference −3).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q2b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Noah has €13.40. He divides the money between himself and his friend Amy in the ratio 3 : 2, respectively. Work out how much money each person gets. (Noah = , Amy = )", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3 + 2 = 5; 1/5 is 13.40/5 = 2.68; Noah = 3/5 = €8.04; Amy = 2/5 = €5.36.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q2bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)(i)", "parent_question": "2", "marks": 2, "marks_confidence": "derived", "question_text": "Amy makes a sequence using coloured blocks. The first 7 blocks in the sequence are shown below (Red, Red, Blue, Green, Red, Red, Blue). The pattern repeats every 4 blocks. What colour is the 10th block in the sequence?", "has_images": true, "image_notes": "A row of 7 cube blocks coloured, in order: Red, Red, Blue, Green, Red, Red, Blue. The repeating unit (period 4) is Red, Red, Blue, Green. Block 10 = position 10 mod 4 = position 2 in the cycle = Red.", "topic": "Probability", "marking_scheme_answer": "Red.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q2bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)(ii)", "parent_question": "2", "marks": 3, "marks_confidence": "derived", "question_text": "Amy picks one block at random from the first 25 blocks in the sequence. What is the probability that this block is red?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "6 groups of 4, plus 1 red block, so 6 × 2 + 1 = 13 red blocks out of 25. P(Red) = 13/25 (= 52%). (OR list out the first 25 terms.)", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q3a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Mae decides to paint her living room. She needs supplies to carry out the work and someone to do the work. She makes estimates of how much these will cost, and makes the bill below to show this information. Some of the values are missing, and are labelled A, B, C, D, E, and F. (Bill: Tin of paint €42·50 × 3 = A; Paint brush €6·99 × B = €13·98; Dust sheet and tape pack €33·80 × 1 = C; Labour €120 a day × 3·5 = D; Subtotal = €595·28; VAT @ 13·5% = E; Total Cost = F.) Work out the missing values labelled A, B, C, and D. Fill your answers into the table.", "has_images": true, "image_notes": "A bill/table with columns Item Description, Unit Price, ×, Number of Units, =, Total Cost. Rows: Tin of paint €42·50 × 3 = A; Paint brush €6·99 × B = €13·98; Dust sheet and tape pack €33·80 × 1 = C; Labour €120 a day × 3·5 = D; Subtotal = €595·28; VAT @ 13·5% = E; Total Cost = F. A, B, C, D, E, F are missing values to compute.", "topic": "Number", "marking_scheme_answer": "A = €42·50 × 3 = €127·50; B = 13·98 / 6·99 = 2; C = 33·80 × 1 = €33·80; D = 120 × 3·5 = €420.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q3a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "The table shows the length of time customers spent in a café on a particular day. Time (minutes): 0–10, 10–20, 20–30, 30–40, 40–50; Number of customers: 12, 18, 16, 24, 8. (Note: '10–20' means 10 minutes or more, but less than 20 minutes, and so on.) Complete the histogram below to show the information in the table.", "has_images": true, "image_notes": "Frequency table (Time 0–10:12, 10–20:18, 20–30:16, 30–40:24, 40–50:8) and a histogram grid with x-axis 'Time (minutes)' 0 to 50 and y-axis 'Number of customers' 0 to 28 (gridlines at 4,8,12,...,28). Only the 40–50 bar (height 8) is pre-drawn; candidate draws the rest.", "topic": "Statistics", "marking_scheme_answer": "Draw bars at heights 12 (0–10), 18 (10–20), 16 (20–30), 24 (30–40), 8 (40–50). For 10–20 accept height h where 16 < h < 20.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q3b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "Work out the missing value labelled E, the VAT. This is 13·5% of the Subtotal. Give your answer correct to 2 decimal places.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "E = 595·28 × 13·5/100 = €80·3628 = €80·36 (to 2 d.p.). [Part of a shared 5C scale with (c).]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q3b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Find the total number of customers who visited the café on that day.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "12 + 18 + 16 + 24 + 8 = 78.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q3c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 2, "marks_confidence": "derived", "question_text": "Work out the missing value labelled F, the Total Cost including the VAT. Give your answer correct to 2 decimal places.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "F = 80·36 + 595·28 = €675·64. [Shared 5C scale with (b).]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q3c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "What is the greatest possible number of customers that could have spent less than 15 minutes in the café on that day?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "12 + 18 = 30.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q4a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "12 students sit class tests in Art and Business on Monday. The students' marks in both subjects are: Art: 54, 49, 47, 71, 52, 50, 51, 34, 62, 47, 46, 37. Business: 59, 64, 52, 67, 68, 67, 59, 65, 54, 53, 66, 69. Complete the back-to-back stem and leaf diagram to show the students' marks. (Stems 3, 4, 5, 6, 7; Key for Art 4|5| = 54 marks; Key for Business |5|3 = 53 marks.)", "has_images": true, "image_notes": "A back-to-back stem-and-leaf diagram template with stems (3,4,5,6,7) in the centre, Art leaves on the left and Business leaves on the right. Art data: 54,49,47,71,52,50,51,34,62,47,46,37. Business data: 59,64,52,67,68,67,59,65,54,53,66,69. Keys: Art 4|5| = 54; Business |5|3 = 53.", "topic": "Statistics", "marking_scheme_answer": "Accurate back-to-back stem and leaf diagram, stems 3–7, leaves ordered. Art leaves (read right-to-left): 3|4 7; 4|9 7 6 7; 5|4 2 0 1; 6|2; 7|1. Business leaves: 3|; 4|; 5|9 2 9 4 3; 6|4 7 8 7 5 6 9; 7|.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q4a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "A rectangular flag has a length of 100 cm and a width of 60 cm, as shown in the diagram. Work out the area of the rectangular flag, in cm^2.", "has_images": true, "image_notes": "Diagram of a rectangular flag (the flag of Belize, blue with central emblem) labelled 100 cm along the top (length) and 60 cm along the right side (width).", "topic": "Geometry", "marking_scheme_answer": "100 × 60 = 6000 cm^2.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q4b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Based on the shape of the stem and leaf diagram, write a sentence to compare the students' results in Art and Business. You should refer to how well students did, on average, and to how spread out the marks are.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Answer must address two aspects, considered independently: (1) how well students did on average, and (2) how spread out the marks are. Answer should be checked against the candidate's own stem and leaf diagram. For example: students did better in Business, on average, but the marks were more spread out in Art.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q4b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "The flag has a circle inside the rectangle. The radius of the circle is 21 cm. Work out the area of the circle. Give your answer correct to the nearest cm^2. (A = πr^2)", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "A = πr^2 = π(21)^2 = 441π = 1385.4… = 1385 cm^2 (nearest cm^2).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q4c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Work out the range of the marks for Business.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Range = 69 − 52 = 17 marks.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q4d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Michael is one of the 12 students. He sits the Business test again, and gets a higher mark than the first time he took the test. When the teacher uses Michael's new mark and works out the range of the marks, the range does not change. Explain how this could happen.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Any valid explanation, e.g.: Michael could have got 53 and then did a little better, like 54 — this won't change the range. OR if the old and new marks are both between the minimum and maximum mark, the range won't change. OR if Michael went from 52 to 70, the range would stay the same. [Shared 5C scale with (e).]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q4e", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(e)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "A 13th student, Ajani, was absent for the two tests on Monday. He sits the tests the following day. When his mark is included, the mean mark in Art increases from 50 to 51. Work out Ajani's mark in Art.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Total before Ajani = 12 × 50 = 600. Total after Ajani = 13 × 51 = 663. Ajani's mark = 663 − 600 = 63 marks. [Shared 5C scale with (d).]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q5a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "The points A and C are shown on the co-ordinate diagram. Write the co-ordinates of the points A and C in the spaces below. A = ( , ) C = ( , )", "has_images": true, "image_notes": "A co-ordinate grid with axes from x = −5 to 5 and y = −4 to 4. Point C is plotted at (0, 1) on the y-axis; point A is plotted at (3, −2). These are the two given points to read off.", "topic": "Coordinate Geometry", "marking_scheme_answer": "A = (3, −2); C = (0, 1). [Parts (a) and (b) share a 10C scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q5a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 8, "marks_confidence": "derived", "question_text": "In a survey of 120 students in Harmony Haven School: 30 play both sport (S) and computer games (C); 48 play computer games (C). Use the above information to complete the Venn diagram below.", "has_images": true, "image_notes": "Venn diagram inside a rectangle labelled U [120], with two overlapping circles S and C [48]. The S-only region is pre-filled with 35; the overlap and C-only region are blank; outside both circles shows 37.", "topic": "Probability", "marking_scheme_answer": "Overlap S∩C = 30; C-only = 48 − 30 = 18. (Completed diagram: S-only 35, intersection 30, C-only 18, outside 37.)", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q5b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "B, D, and E are three more points. Plot and label the point B (4, 3) on the diagram on the previous page.", "has_images": true, "image_notes": "Refers to the same co-ordinate grid (x: −5 to 5, y: −4 to 4) from part (a). Requires plotting and labelling B at (4, 3).", "topic": "Coordinate Geometry", "marking_scheme_answer": "B (4, 3) correctly plotted and labelled. [Parts (a) and (b) share a 10C scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q5b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 7, "marks_confidence": "derived", "question_text": "How many students play neither sport nor computer games?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "37.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q5c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "ABCD is a parallelogram. Use this information to plot and label the point D on the diagram on the previous page.", "has_images": true, "image_notes": "Same co-ordinate grid. With A(3,−2), B(4,3), C(0,1), the parallelogram ABCD requires D such that ABCD forms a parallelogram; D = (−1, −4).", "topic": "Coordinate Geometry", "marking_scheme_answer": "D = (−1, −4) correctly plotted and labelled. [Parts (c) and (d) share a 10D scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q5c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 2, "marks_confidence": "derived", "question_text": "#(S\\C) = 35. Explain what this statement means, in terms of what students in the school play (sport and computer games).", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "35 play sport but not computer games (or equivalent).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q5d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "The point C is the midpoint of the line segment [AE]. Write down the co-ordinates of the point E. E = ( , )", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "E = (−3, 4). Using midpoint: ((3+x)/2, (−2+y)/2) = (0, 1) gives x = −3, y = 4. (Or A(3,−2) → C(0,1) is a shift of x:−3, y:+3, so E = (−3, 4).) [Parts (c) and (d) share a 10D scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q5d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 3, "marks_confidence": "derived", "question_text": "One student is picked at random from the 120 students who were surveyed. What is the probability that this student plays sport or computer games but not both?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "(35 + 18)/120 = 53/120.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q6a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 15, "marks_confidence": "high", "question_text": "The line segment [PQ] is shown below. Divide the line segment [PQ] into three equal lengths, without measuring it. Show all of your construction lines clearly.", "has_images": true, "image_notes": "A horizontal line segment with endpoint P on the left and Q on the right, to be divided into three equal parts by construction (using a ray drawn from P or Q with three equal lengths marked off and parallel lines).", "topic": "Geometry", "marking_scheme_answer": "Construct a ray from P or Q, mark off three equal lengths along it, then draw parallels back to PQ to divide it into three equal segments. Arcs need not measure 3 equal lengths to within 2 mm tolerance.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q6a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "A sports shop sells 3 different brands of running shoes. Each brand comes in the 4 different colours shown in the table (Brand A: Red, Brand B: Blue, Brand C: Black, Yellow). How many different choices of running shoe does the shop sell? For example, one choice would be brand B and yellow.", "has_images": true, "image_notes": "Photo of running shoes plus a table with columns 'Brand' (A, B, C) and 'Colour' listing Red, Blue, Black, Yellow (4 colours available for each brand).", "topic": "Probability", "marking_scheme_answer": "3 × 4 = 12 (or lists the different choices / draws a tree diagram, and states 12).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q6b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Tom writes down a list of five numbers, from smallest to biggest. Two of these numbers are shown below: 2, _, _, 10, _ . The mode of these five numbers is 2. The median of these five numbers is 7. The range is 12. Use this information to find the three missing numbers in Tom's list, and write them into the spaces above.", "has_images": true, "image_notes": "A row of five boxes with the 1st box = 2 and the 4th box = 10; the 2nd, 3rd and 5th boxes are blank for the candidate to fill.", "topic": "Statistics", "marking_scheme_answer": "2, 2, 7, 10, 14 (mode 2 so second number 2; median 7 so middle 7; range 12 so largest = 2 + 12 = 14).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q6bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)(i)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "The diagram shows a triangle ABC. The points D and E are on [AB] and the points F and G are on [AC], so that DF, EG and BC are all parallel. The size of some of the angles are given in the diagram (angle A = 28°, angle B = 72°; angles x at D, y at F, z at E are marked). Work out the size of the angles marked x, y, and z in the diagram.", "has_images": true, "image_notes": "Triangle ABC with apex C at top. D and E lie on AB (the base, A left, B right); F and G lie on AC. Segments DF, EG and BC are all parallel. Angle at A = 28°, angle at B = 72°. Angle y is the interior angle at F (angle AFD), angle x is at D (angle FDA, between DF and AB measured on the D-E side i.e. ADF's exterior... it is the angle FDE region), angle z is the angle at E (between EG and EB).", "topic": "Geometry", "marking_scheme_answer": "x = 180 − (28 + 72) = 80° (corresponding/co-interior reasoning). y = 180 − 28 − 72 = 80° (or 28 + x = 28 + 80, i.e. angle sum / exterior angle). z = 28 + y = 28 + 80 = 108° (exterior angle of triangle). [Per scheme: x = 72° corresponding angle to angle ABC; y = 180 − (28+72) = 80°; z = 28 + y = 108°.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q6bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)(ii)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Explain why the triangles ABC and ADF are similar but not congruent.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Similar: the three angles are the same in both triangles (DF is parallel to BC, so corresponding angles are equal). Not congruent: the triangles are not the same size (e.g. DF is parallel to but shorter than BC; their sides are different lengths).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q6c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "The same triangles are shown again. This time, the lengths of some sides are shown. |AD| = |DE| = |EB| = 10 and |BC| = 14·3. Using similar triangles, work out the length |GE|.", "has_images": true, "image_notes": "Triangle ABC with base AB (A left, B right), apex C at top right. Along AB: A, then D, then E, then B, with |AD| = |DE| = |EB| = 10 (so |AB| = 30, |AE| = 20). F and G are on AC with DF and EG parallel to BC. |BC| = 14·3. Find |GE|.", "topic": "Geometry", "marking_scheme_answer": "|GE|/|CB| = |AE|/|AB| → |GE|/14·3 = 20/30, so |GE| = (20 × 14·3)/30 = 143/15 = 9 8/15 ≈ 9·533… (uses scale factor 1·5).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q7ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "One section of a golf course, shown in the diagram, is in the shape of a rectangle with a semi-circle at one end. This shape has a width of 50 m and a total length of 300 m, as shown. Work out the distances marked x and y on the diagram. x is the radius of the semicircle.", "has_images": true, "image_notes": "A green shape: a rectangle of width 50 m on the left joined to a semicircle on the right end. Total horizontal length = 300 m. x is marked as the radius of the semicircle (vertical, half of the 50 m width). y is the length of the rectangular part (horizontal). A flag/hole is shown in the semicircular part.", "topic": "Geometry", "marking_scheme_answer": "x = 50/2 = 25 m (radius = half the width). y = 300 − x = 300 − 25 = 275 m.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q7ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "In this question, each shape has a fixed value. Work out the value of a circle, using the following equation: circle + circle + circle = 21. circle = ___", "has_images": true, "image_notes": "Equation shown with picture symbols: three green circles added together equal 21.", "topic": "Algebra", "marking_scheme_answer": "21/3 = 7, so circle = 7.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q7aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "Hence, work out the total area of this section of the golf course. Give your answer correct to the nearest m^2.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Area = (50 × 275) + (1/2)π(25^2) = 13 750 + (1/2)π(625) = 13 750 + 981·7… ≈ 14 732 m^2 (rectangle area + semicircle area).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q7aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Work out the value of a triangle, using the following equation, and your answer to part (a)(i): circle + triangle + circle = 18. triangle = ___", "has_images": true, "image_notes": "Equation shown with picture symbols: green circle + green/blue triangle + green circle equal 18.", "topic": "Algebra", "marking_scheme_answer": "7 + triangle + 7 = 18, so triangle = 4.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q7b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Maciej is spreading fertiliser on the whole golf course. The packet of fertiliser has these instructions: Use 6 litres of fertiliser per 250 m^2 of ground to be covered. Maciej needs to cover 809 371 m^2 with fertiliser. How many litres of fertiliser will Maciej need to use? Give your answer correct to the nearest whole number.", "has_images": true, "image_notes": "An instruction box reads: \"Use 6 litres of fertiliser per 250 m^2 of ground to be covered.\" (Information panel, no measurement data needed beyond the text.)", "topic": "Number", "marking_scheme_answer": "(809 371 × 6) / 250 = 19424·904 ≈ 19 425 litres. (OR 1 litre covers 250/6 ≈ 41·66 m^2, so 809 371 / 41·66 ≈ 19 425 litres.)", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q7b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Two equations are shown below. Work out the value of a hexagon and the value of a square. hexagon + hexagon + square = 24; square + hexagon = 13. hexagon = ___, square = ___", "has_images": true, "image_notes": "Two equations using picture symbols: (orange hexagon) + (orange hexagon) + (red square) = 24, and (red square) + (orange hexagon) = 13.", "topic": "Algebra", "marking_scheme_answer": "hexagon + 13 = 24, so hexagon = 11; square + 11 = 13, so square = 2.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q7c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 15, "marks_confidence": "high", "question_text": "The fertiliser is made up of three ingredients, A, B, and C, in the following ratio: A : B : C = 1 : 3/2 : 5/3. Work out the number of millilitres of B in 1 litre of fertiliser.", "has_images": true, "image_notes": "A small ratio table: A : B : C = 1 : 3/2 : 5/3.", "topic": "Number", "marking_scheme_answer": "1 + 3/2 + 5/3 = 25/6. Amount of B = 1000 × (3/2)/(25/6) = 360 ml. (Method 2: scale ratio 1 : 3/2 : 5/3 = 6 : 9 : 10; 6+9+10 = 25; B = 1000 × 9/25 = 360 ml.)", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q7d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(d)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "The tank for spreading fertiliser is in the shape of a cylinder. The radius of the tank is 90 centimetres and its length is 4 metres, as shown in the diagram on the right. Work out the volume of the tank. Give your answer in m^3, correct to 2 decimal places.", "has_images": true, "image_notes": "A horizontal cylinder diagram labelled with radius 90 cm (height arrow on the circular end) and length 4 m. Note the radius is given in cm (= 0·9 m) and length in m.", "topic": "Geometry", "marking_scheme_answer": "r = 90 cm = 0·9 m. V = πr^2h = π(0·9^2)(4) = 10·178… ≈ 10·18 m^3 (to 2 d.p.).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q7e", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(e)", "parent_question": "7", "marks": 20, "marks_confidence": "high", "question_text": "This diagram on the right shows a different cylindrical tank, which has a volume of (81π)/125 m^3. Its length is three times as long as its radius, as shown. Work out the radius of this tank, in metres.", "has_images": true, "image_notes": "A horizontal cylinder labelled with 'radius' (vertical arrow on the circular face) and 'length' (horizontal). The length is three times the radius (length = 3r). Volume = (81π)/125 m^3.", "topic": "Geometry", "marking_scheme_answer": "h = 3r. V = πr^2h = πr^2(3r) = 3r^3π = 81π/125. So r^3 = 27/125, r = cube root(27/125) = 3/5 = 0·6 m.", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q8a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Cos A = 0·27. Work out the size of the angle A, correct to the nearest degree.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "A = cos^(-1)(0·27) = 74·3… ≈ 74° (to nearest degree).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q8ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Eight numbers are given in the table below: 1, 3, 8, 12, 15, 24, 30, 60. From the numbers in the table, write down: an even number.", "has_images": true, "image_notes": "Table of eight numbers in two rows: top row 1, 3, 8, 12; bottom row 15, 24, 30, 60.", "topic": "Number", "marking_scheme_answer": "8, 12, 24, 30, or 60 (any even number from the table).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q8aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "From the numbers in the table, write down: the lowest common multiple (LCM) of 12 and 15.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "60. (12 = 2×2×3, 15 = 3×5, LCM = 2×2×3×5 = 60.)", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q8b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Olga would like to know the vertical height, h, of the roof of a building. Olga takes the following measurements and shows them on the diagram, where h = |DC|: |angle CAB| = 22°, |angle DAB| = 29°, |AB| = 23 m, |angle ABC| = |angle ABD| = 90°. Use trigonometry to work out the vertical height, h, of the roof. Give your answer correct to 1 decimal place.", "has_images": true, "image_notes": "A right-angled diagram: horizontal base AB = 23 m with A on the left, B on the right. At B a vertical line rises to points C (lower) then D (upper); |angle ABC| = |angle ABD| = 90°. From A two lines of sight: to C making angle 22° with AB, and to D making 29° with AB. h = |DC| is the vertical segment between C and D (the roof height). A photo of a clock-tower building is shown alongside.", "topic": "Trigonometry", "marking_scheme_answer": "tan 22° = |BC|/23, so |BC| = 23 tan 22° = 9·292… tan 29° = |BD|/23, so |BD| = 23 tan 29° = 12·749… Then h = |BD| − |BC| = 12·749… − 9·292… = 3·45… ≈ 3·5 m (to 1 d.p.).", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q8b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "The number 36 has nine positive factors. Four of these factors are given below. Fill in the remaining five factors of 36 in the boxes provided: 1, 2, 3, _, _, _, 12, _, _ .", "has_images": true, "image_notes": "A row showing 1, 2, 3, then five empty boxes, with 12 placed second-from-last among them (sequence: 1, 2, 3, [ ], [ ], [ ], 12, [ ], [ ]).", "topic": "Number", "marking_scheme_answer": "1, 2, 3, 4, 6, 9, 12, 18, 36 (remaining factors: 4, 6, 9, 18, 36).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q8ci", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "The first three patterns in a sequence are shown below. Each pattern is made of squares. (Pattern 1: 1 square; Pattern 2: 4 squares in a T/L shape; Pattern 3: 7 squares.) Draw Pattern 4 in the sequence.", "has_images": true, "image_notes": "Three patterns made of blue unit squares. Pattern 1 = 1 square; Pattern 2 = 4 squares (a row of 3 with 1 below the middle, like a T); Pattern 3 = 7 squares (a row of 5 with 2 stacked below the middle column). Each pattern adds 3 squares.", "topic": "Algebra", "marking_scheme_answer": "Pattern 4 has 10 squares (e.g. a row of 7 with 3 stacked below the middle column; +3 squares from Pattern 3).", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q8cii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Fill in the table to show the number of squares in each of the first 4 patterns. (Pattern: 1, 2, 3, 4; Number of squares: _, _, 7, _ .)", "has_images": true, "image_notes": "Two-column table 'Pattern' / 'Number of squares' with rows 1, 2, 3, 4. Only Pattern 3 = 7 is pre-filled; rows 1, 2 and 4 blank.", "topic": "Algebra", "marking_scheme_answer": "Pattern 1 = 1, Pattern 2 = 4, Pattern 3 = 7, Pattern 4 = 10.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q8ciii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)(iii)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "What kind of sequence is made by the number of squares in each pattern? Give a reason for your answer. (Tick one box only: Linear / Non-linear.)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Linear. Reason: it goes up by 3 each time (the first differences are constant) — or any other valid reason.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q9a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Fiadh records the temperature in her kitchen, in degrees Celsius (°C), over 10 hours. T(x) is the temperature x hours after Fiadh starts recording it, for 0 ≤ x ≤ 10. The graph shows T(x) for the first 8 hours, in three sections labelled P, Q, and R. Estimate how long it takes for the temperature to reach 20°C for the first time. Give your answer in hours, correct to 1 decimal place. Show your work on the graph.", "has_images": true, "image_notes": "A line graph: x-axis 'Time, x (hours)' from 0 to 10; y-axis 'Temperature T(x) (°C)' marked 3,6,9,12,15,18,21,24. The curve has three sections for the first 8 hours: section P rises as a curve from about (0,12) up to about (4,21); section Q is roughly constant/flat near 21 from x≈4 to x≈6; section R falls from about (6,21) to (8,15). Reading where the curve first crosses 20°C is in section P (around x ≈ 3.5 h).", "topic": "Functions", "marking_scheme_answer": "Read from the graph where T(x) first reaches 20°C (in section P): any value strictly between 2·5 and 3, e.g. ≈ 2·9 (answer must be supported by work on the graph). [Parts (a) and (b) share a 5C scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q9a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "Alice gets €100 for her birthday, and puts it in a bank account. She puts a further €25 in the bank account every month for 6 months. Work out how much in total she will have in the bank account at the end of the 6 months.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "100 + 6 × 25 = 100 + 150 = €250.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q9b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "For how many hours does the temperature remain constant, for 0 ≤ x ≤ 8?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "4 hours (section Q, the flat/constant part of the graph). [Parts (a) and (b) share a 5C scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q9bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)(i)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Alice puts €130 in a post office savings account. The annual interest rate is 3%. Work out how much interest Alice gets in one year.", "has_images": true, "image_notes": "Small photo of a 'Savings' jar with coins; decorative, no data needed.", "topic": "Number", "marking_scheme_answer": "3/100 × 130 = €3.90.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q9bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)(ii)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Work out the total amount of money in the account after one year.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "130 + 3.90 = €133.90.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q9c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Section S of the graph runs from x = 8 to x = 10, with T(8) = 15. During section S of the graph, the rate of change of the temperature is +3°C per hour. Use this to draw section S of the graph on the diagram above, for 8 ≤ x ≤ 10, x ∈ R.", "has_images": true, "image_notes": "Same temperature-vs-time graph. Section S is to be drawn from x = 8 (where T = 15) to x = 10, rising at 3°C per hour, so it goes from (8, 15) up to (10, 21) as a straight line.", "topic": "Functions", "marking_scheme_answer": "Draw section S as a straight line from (8, 15) to (10, 21) — slope +3°C/hour (within drawing tolerance of 2 mm). [Parts (c) and (d) share a 5D scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-ordinary-level-EV-q9c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Alice puts €120 in a Credit Union account. This account earns interest. At the end of one year, she has €124.56 in the account. Find the percentage annual interest rate for this account.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(124.56 − 120)/120 × 100 = 4.56/120 × 100 = 3.8%.", "source_pdf": "2025 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q9d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "The table gives a function for the temperature in each of the three sections, P, Q, and R. Write the correct letter (P, Q, or R) in the appropriate space in the table to show which function corresponds to each section of the graph. Use each letter only once. (Functions given: T(x) = 21; T(x) = x^2 + 12; T(x) = −6x + 63.)", "has_images": true, "image_notes": "A table with one column 'Section (P, Q, or R)' and one column listing functions: T(x) = 21, T(x) = x^2 + 12, T(x) = −6x + 63. Each section letter to be entered once.", "topic": "Functions", "marking_scheme_answer": "T(x) = 21 → Q (constant section); T(x) = x^2 + 12 → P (rising curve); T(x) = −6x + 63 → R (falling line). [Parts (c) and (d) share a 5D scale.]", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q9e", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(e)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "Which of the following functions gives the temperature in section S of the graph (the section you drew in part (c))? Tick one box. T(x) = 3x − 9; T(x) = −3x − 12; T(x) = 3x + 12. Justify your answer, for example, by checking points in section S.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "T(x) = 3x − 9. Justification: slope = 3 and the line passes through (8, 15) since 3(8) − 9 = 15 (and (10, 21): 3(10) − 9 = 21). The other two options fail: −3x − 12 has the wrong (negative) slope; 3x + 12 gives 36 at x = 8, not 15. (Slope is 3, so it is not the middle option; the y-intercept is not 12.)", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-EV-q9f", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(f)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Remember that the graph shows the temperature in Fiadh's kitchen. The temperature in Fiadh's bedroom is always 3°C less than the temperature in the kitchen. On the diagram on the previous page, draw a graph to show the temperature in Fiadh's bedroom for the first 8 hours (0 ≤ x ≤ 8, x ∈ R). Use the same axes and scales.", "has_images": true, "image_notes": "Same temperature-vs-time axes. Required graph is the kitchen curve shifted vertically down by 3°C across 0 ≤ x ≤ 8 (a vertical translation of −3, same shape).", "topic": "Functions", "marking_scheme_answer": "Correct graph drawn: the given graph (sections P, Q, R for 0 ≤ x ≤ 8) shifted vertically down by 3 units (3 units below the given graph), same shape. (Partial credit for some vertical shift other than 3; no credit for a horizontal shift.)", "source_pdf": "2025 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q1a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Tá 3 bhranda éagsúla de bhróga reatha, A, B, agus C, ar díol i siopa spóirt. Tá gach branda ar fáil sna 4 dhath éagsúla agus sna 4 mhéid éagsúla a thaispeántar sa tábla thíos. (Branda A: Dath Dearg, Méid 7; Branda B: Dath Gorm, Méid 8; Branda C: Dath Dubh, Méid 9; Buí, Méid 10.) Cé mhéad rogha éagsúil bróige reatha atá ar díol sa siopa? Mar shampla, rogha amháin is ea branda B, buí, agus méid 7.", "has_images": true, "image_notes": "Photo of running shoes plus a 3-column table headed Branda | Dath | Méid. Rows: A | Dearg | 7; B | Gorm | 8; C | Dubh | 9; (blank) | Buí | 10. So there are 3 brands, 4 colours (Dearg, Gorm, Dubh, Buí) and 4 sizes (7, 8, 9, 10).", "topic": "Number", "marking_scheme_answer": "3 × 4 × 4 = 48. Number of different choices = 48.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q1ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "Ríomh luach gach ceann díobh seo a leanas:\n456 − 321", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q1aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": 3, "marks_confidence": "derived", "question_text": "7·4 × 6·2", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "45·88 nó 1147/25 nó 45 22/25", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q1aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": 4, "marks_confidence": "derived", "question_text": "√9 × (7 − 3)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3 × (4) = 12", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q1b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": 5, "marks_confidence": "high", "question_text": "Cosnaíonn péire bróg reatha €140 de ghnáth. Le linn sladmhargaidh, cosnaíonn siad €93·80. Oibrigh amach an laghdú céatadánach le linn an tsladmhargaidh.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "€140 − €93·80 = €46·20; (€46·20 / €140) × 100 = 33 %.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q1bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeántar aoiseanna Jael, Alice, agus Paul sa tábla thíos.\nComhlánaigh an tábla chun na haoiseanna a bheidh ag Jael, Alice, agus Paul i gceann 4 bliana a thaispeáint.", "has_images": true, "image_notes": "Tábla le colúin 'Aois anois' agus 'Aois i gceann 4 bliana'. Sraitheanna: Jael = 16, Alice = 12, Paul = 11 (Aois anois). Colún 'i gceann 4 bliana' le líonadh isteach (Jael 20, Alice 16, Paul 15).", "topic": "Number", "marking_scheme_answer": "Jael 20, Alice 16, Paul 15", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q1bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach an mheánaois a bheidh ag Jael, Alice, agus Paul i gceann 4 bliana.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "(20 + 16 + 15)/3 = 51/3 = 17", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q10a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Faigh luach 3p + 7q, nuair atá p = 2 agus q = 11.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "3(2) + 7(11) = 6 + 77 = 83", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q10ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": 2, "marks_confidence": "derived", "question_text": "Tá 88 scoláire sa 3ú bliain i scoil. Taispeántar sa léaráid Venn thíos de na scoláirí sin atá ina mball den chlub díospóireachta (D) agus den chlub fichille (F). Tugtar roinnt de na luachanna sin i dtéarmaí x, agus x ∈ ℕ. Tá 40 scoláire san iomlán sa chlub díospóireachta (D). Tá 37 scoláire ann nach bhfuil i gceachtar den dá chlub. (i) Líon isteach an luach atá ar iarraidh as an léaráid Venn, i dtéarmaí x.", "has_images": true, "image_notes": "A Venn diagram inside a universal set U [88], two overlapping circles D [40] and F. The intersection is labelled x, the part of F only is labelled 2x + 1, and 37 lies outside both circles. The D-only region is the value to be filled in (in terms of x).", "topic": "Number", "marking_scheme_answer": "D-only region = 40 − x (since the whole D circle totals 40 and the overlap is x).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q10aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": 3, "marks_confidence": "derived", "question_text": "(ii) Uaidh sin, nó ar shlí eile, oibrigh amach luach x.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(40 − x) + x + (2x + 1) + 37 = 88; 40 + 2x + 1 + 37 = 88; 2x + 78 = 88; 2x = 10; x = 5.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q10b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "high", "question_text": "Tá Mícheál sa tacar D\\F. Cén t-eolas a thugann sé sin faoi na clubanna a bhfuil Mícheál iontu?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Tá sé sa chlub díospóireachta ach ní sa chlub fichille — Michael is in the debating club (D) but not in the chess club (F).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q10b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Iolraigh amach agus simpligh:\n2(5a − 3) − 4a + 7", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "10a − 6 − 4a + 7 = 6a + 1", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q10c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Réitigh an chothromóid seo a leanas in y:\n8y + 4 = 2y − 8", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8y − 2y = −8 − 4; 6y = −12; y = −2", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q10d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(d)", "parent_question": "10", "marks": 5, "marks_confidence": "derived", "question_text": "Fachtóirigh an slonn cearnach x^2 − 10x + 21.\nx^2 − 10x + 21 = (x − 3)( ____ )", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "(x − 3)(x − 7)", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q11a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Simpligh 5x² − 7x + 3x² − 6x.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "8x² − 13x.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q11ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)(i)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Tarraingíonn Tanya léaráid de réir scála dá gairdín, mar a thaispeántar thíos. Tá seid agus ceapach bláthanna sa léaráid. Scála: 1 cm = 0·5 m.\nIs ionann 1 cm ar an léaráid agus fad iarbhír 0·5 m.\nScríobh síos an fad atá marcáilte le x ar an léaráid. Bíodh do fhreagra ina cm. Uaidh sin, faigh an fad iarbhír ón tseid go dtí an ceapach bláthanna, ina mhéadair.\nFad ar an léaráid (cm): ____ Fad iarbhír (m): ____", "has_images": true, "image_notes": "Léaráid scála ar ghreille. Cearnóg lipéadaithe 'Seid' ar barr ar dheis. Dronuilleog lipéadaithe 'Ceapach Bláthanna' faoina bun. Saighead dhéthreoch idir an dá rud marcáilte x (3 chearnóg/cm ar an ghreille = 3 cm). Scála: 1 cm = 0·5 m.", "topic": "Number", "marking_scheme_answer": "Fad ar léaráid = 3 [cm]; fad iarbhír = 3 × 0·5 = 1·5 [m]", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q11aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)(ii)", "parent_question": "11", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach imlíne iarbhír na ceapaí bláthanna.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "An cheapach bláthanna 2 cm ar fad agus 1 cm ar leithead ar an léaráid → 1 m × 0·5 m iarbhír; imlíne = 2(1 + 0·5) = 3 m (ríomh: 10 cm ar an scála 0·5 m don 2 cm + 0·5 m don 1 cm).", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q11aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)(iii)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Tá Tanya ag iarraidh ceapach glasraí a chur sa ghairdín. Beidh cruth dronuilleogach ar an gceapach glasraí, agus beidh sí 3 m ar fad agus 1·5 m ar leithead.\nTarraing an cheapach glasraí i suíomh ar an léaráid ar an leathanach roimhe seo sa chaoi nach bhforluíonn sí ar an tseid ná ar an gceapach bláthanna.", "has_images": true, "image_notes": "Le tarraingt ar an léaráid scála: dronuilleog 6 cm × 3 cm (mar atá 3 m → 6 cm agus 1·5 m → 3 cm ar an scála 1 cm = 0·5 m), nach bhforluíonn ar an tseid ná ar an gceapach bláthanna.", "topic": "Geometry", "marking_scheme_answer": "3 m → 6 cm agus 1·5 m → 3 cm. Tarraingítear dronuilleog 6 cm faoi 3 cm ar an léaráid nach bhforluíonn ar an tseid nó ar an gceapach bláthanna.", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q11b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 10, "marks_confidence": "high", "question_text": "Roinn (x³ + 11x² + 15x − 27) ar (x + 3).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "x³ + 11x² + 15x − 27 ÷ (x + 3) = x² + 8x − 9 (remainder 0).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q11b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": 5, "marks_confidence": "high", "question_text": "Tá sé beartaithe ag Tanya cabáiste a chur sa cheapach glasraí. Tá sé léite aici go dteastaíonn spás cearnach 0·3 m faoi 0·3 m ó gach cabáiste. De réir an eolais sin, cad é an líon is mó cabáistí ba cheart do Tanya a chur sa cheapach glasraí sin? Ná déan dearmad go mbeidh an cheapach glasraí 3 m ar fad agus 1·5 m ar leithead.", "has_images": true, "image_notes": "Íomhá de chabáiste in aice na ceiste, le toisí 0·3 m faoi 0·3 m don spás a theastaíonn ó gach cabáiste.", "topic": "Geometry", "marking_scheme_answer": "3 ÷ 0·3 = 10; 1·5 ÷ 0·3 = 5; 10 × 5 = 50 cabáiste", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q12a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Cheannaigh Jael píotsa. Is ar 19:50 a d'ordaigh Jael a phíotsa. Seachadadh air é 45 nóiméad ina dhiaidh sin. Cén t-am a tháinig a phíotsa?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "19:50 + 0:45 = 19:95 = 20:35", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q12ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)(i)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Is é seo an fheidhm f(x): f(x) = 2/(x + 2) le haghaidh x > −2. (i) Comhlánaigh an tábla thíos agus taispeáin luachanna f(x) le haghaidh na luachanna de x a thugtar. Bíodh na luachanna ceart go dtí 2 ionad dheachúlacha, nuair is cuí. (x: −1, 0, 1, 2, 3, 4; f(x): __, 1, __, 0·5, 0·4, __)", "has_images": true, "image_notes": "A function table. Row x: −1, 0, 1, 2, 3, 4. Row f(x): blank, 1, blank, 0·5, 0·4, blank (values given for x = 0, 2, 3). Function f(x) = 2/(x+2).", "topic": "Functions", "marking_scheme_answer": "f(−1) = 2/1 = 2; f(1) = 2/3 ≈ 0·67; f(4) = 2/6 ≈ 0·33. (Full table: x=−1→2, 0→1, 1→0·67, 2→0·5, 3→0·4, 4→0·33.) Graded together with part (a)(ii) on a single 10D scale.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q12aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)(ii)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "(ii) Bain úsáid as na luachanna sa tábla chun graf na feidhme y = f(x) a tharraingt ar na haiseanna thíos, le haghaidh −1 ≤ x ≤ 4, x ∈ ℝ.", "has_images": true, "image_notes": "Blank coordinate axes: y from 0·5 to 2·5 (marked 0·5, 1·0, 1·5, 2·0, 2·5), x from −1 to 4. The student plots the 6 table points and joins them with a smooth decreasing curve.", "topic": "Functions", "marking_scheme_answer": "Plot the 6 points from the table ((−1,2), (0,1), (1,0·67), (2,0·5), (3,0·4), (4,0·33)) and join with a smooth curve (a decreasing reciprocal-type curve). Graded together with (a)(i) on a 10D scale.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q12b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Réitigh na cothromóidí comhuaineacha seo a leanas chun luach x agus luach y a fháil: 3x + 4y = 29; 2x + y = 9.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "From 2x + y = 9, y = 9 − 2x. Substitute: 3x + 4(9 − 2x) = 29 → 3x + 36 − 8x = 29 → −5x = −7 → x = 7/5 = 1·4; y = 9 − 2(7/5) = 31/5 = 6·2. So x = 1·4, y = 6·2.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q12bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(i)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Tá an píotsa i mbosca dronuilleogach dúnta ina bhfuil na toisí seo: Fad = 28 cm; Leithead = 25 cm; Airde = 4 cm.\nOibrigh amach toirt an bhosca píotsa.", "has_images": true, "image_notes": "Íomhá de chruach boscaí píotsa in aice na ceiste (maisíoch). Toisí an bhosca: 28 cm fad, 25 cm leithead, 4 cm airde.", "topic": "Geometry", "marking_scheme_answer": "V = 28 × 25 × 4 = 2800 cm^3", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q12bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)(ii)", "parent_question": "12", "marks": 5, "marks_confidence": "derived", "question_text": "Oibrigh amach achar dromchla an bhosca píotsa. Bíodh do fhreagra ina cm^2.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "A = 2 × [(25 × 28) + (25 × 4) + (28 × 4)] = 2 × [700 + 100 + 112] = 2 × 912 = 1824 [cm^2]", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q12c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": 5, "marks_confidence": "high", "question_text": "Tá costas €14 ar phíotsa i Luimneach. Tá costas £12 ar an bpíotsa céanna i Londain. Is é an ráta malairte ná €1 = £0·93.\nOibrigh amach cé acu píotsa is saoire. Úsáid an ríomh chun tacú le do fhreagra.\nIs saoire an píotsa i: Luimneach / Londain (Ná cuir tic (✓) ach i mbosca amháin)\nRíomh: ____", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "Londain. Áireamh, mar shampla: 14 × 0·93 = 13·02 (NÓ 12/0·93 = 12·9… NÓ 12/14 = 0·85…), mar sin tá an píotsa i Londain níos saoire.", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q13a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 2, "marks_confidence": "derived", "question_text": "Tá gach fad ina cm sa cheist seo. Taispeántar sa léaráid thíos fráma dronuilleogach le haghaidh grianghraif, agus l, f, x ∈ ℝ. Is é l leithead an fhráma agus is é f fad an fhráma. Tá poll dronuilleogach sa lár le haghaidh an ghrianghraif, ag a bhfuil na toisí 12 faoi 18. Is é x leithead inmheánach an fhráma, mar a thaispeántar. (a) Is é fad an fhráma f = 18 + 2x. Scríobh leithead an fhráma, l, i dtéarmaí x.", "has_images": true, "image_notes": "A rectangular picture frame with a rectangular hole in the centre measuring 12 by 18. The frame border has uniform width x on all four sides. Outer dimensions: length f (= 18 + 2x) and width l. The inner hole is 18 wide × 12 tall.", "topic": "Algebra", "marking_scheme_answer": "l = 12 + 2x (inner height 12 plus a border x on each side). (Grouped Scála 5D shared with part (b).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q13a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "Is gnách go rothaíonn Tadhg 3 km chuig traenáil pheile. Tógann sé 10 nóiméad ar Thadhg rothaíocht chuig an traenáil.\nOibrigh amach a mheánluas, ina km/uair.", "has_images": true, "image_notes": "Íomhá de pháirc pheile / imreoirí in aice na ceiste (maisíoch).", "topic": "Number", "marking_scheme_answer": "10 nóim → 3 km; 60 nóim → 18 km, mar sin de 18 [km/uair]. NÓ S = D ÷ T = 3 ÷ (1/6) = 18 [km/uair]. NÓ 60 × (3/10) = 18", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q13b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)", "parent_question": "13", "marks": 3, "marks_confidence": "derived", "question_text": "Uaidh sin, taispeáin go bhfuil: f × l = 4x² + 60x + 216.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "f × l = (18 + 2x)(12 + 2x) = 216 + 36x + 24x + 4x² = 4x² + 60x + 216. (Grouped Scála 5D shared with part (a).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q13bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)(i)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Seo thíos graf faid is ama ina dtaispeántar a fhad ón mbaile a bhí rothar Thaidhg, feadh an bhealaigh a chuaigh sé, do cheann amháin de na laethanta a chuaigh sé ag traenáil. Bain úsáid as an ngraf chun codanna (b)(i), (b)(ii), agus (b)(iii) a fhreagairt.\nCá fhad, san iomlán, a bhí Tadhg as baile? Bíodh do fhreagra ina nóiméad.", "has_images": true, "image_notes": "Graf faid-ama. Ais x = 'Am (nóiméid)' marcáilte 20, 40, 60, 80, 100, 120. Ais y = 'Fad ón mbaile (km)' marcáilte 0·5, 1·0, 1·5, 2·0, 2·5, 3·0, le 'Baile' ag 0 agus 'Traenáil' ag 3·0. Léaráid: ardú ó 0 go 3 km (timpeall 0–30 nóim), ardchlár ag 3 km idir tuairim 30 agus 90 nóim, ansin íslíonn ar ais go baile (timpeall 90–110 nóim).", "topic": "Functions", "marking_scheme_answer": "110 [nóiméad]", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q13bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)(ii)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Cá fhad a bhí Tadhg ag an traenáil? Bíodh do fhreagra ina uaireanta agus ina nóiméid.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "90 − 30 = 60 nóiméad = 1 uair 0 nóiméad", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q13biii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(b)(iii)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Cé acu ag rothaíocht chuig an traenáil nó ag rothaíocht abhaile ón traenáil a bhí Tadhg níos tapúla? Agus úsáid a bhaint as an ngraf, tabhair cúis le do fhreagra.\nBhí Tadhg níos tapúla ag rothaíocht: chuig an traenáil / abhaile ón traenáil (Ná cuir tic (✓) ach i mbosca amháin)\nCúis: ____", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "Chuig an traenáil. Cúis: Tá an fhána níos géire (thóg sé níos lú ama), nó aon chúis bhailí ar bith eile a léiríonn go raibh an leataobh den ghraf níos géire ag fágáil an bhaile.", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q13c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)", "parent_question": "13", "marks": 5, "marks_confidence": "high", "question_text": "f × l = 648 cm². Bain úsáid as sin, agus as an eolas i gcuid (b), chun luach x a fháil. Bíodh do fhreagra, ina cm, ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "4x² + 60x + 216 = 648 → 4x² + 60x − 432 = 0; x = [−60 ± √(60² − 4(4)(−432))]/(2·4) = [−60 ± √(3600 + 6912)]/8 = [−60 ± √10512]/8; x = 5·31… (taking the positive root) ≈ 5·3 cm (1 d.p.).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q13ci", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)(i)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Bíonn scoláirí na chéad bhliana agus an dara bliain ag traenáil i dteannta a chéile. Roinntear gach bliain ina dhá fhoireann, an fhoireann dhearg agus an fhoireann ghorm. Taispeántar sa tábla thíos an líon scoláirí i ngach foireann.\nTábla: An chéad bhliain — Dearg 18, Gorm 17; An dara bliain — Dearg 10, Gorm 15.\n60 scoláire san iomlán atá ann. Roghnaítear scoláire amháin go randamach.\nCad é an dóchúlacht go bhfuil an scoláire sa chéad bhliain agus ar an bhfoireann dhearg?", "has_images": true, "image_notes": "Tábla 2×2 le sraitheanna Dearg agus Gorm, agus colúin 'An chéad bhliain' agus 'An dara bliain'. Luachanna: Dearg 18 (chéad), 10 (dara); Gorm 17 (chéad), 15 (dara). Iomlán = 60.", "topic": "Probability", "marking_scheme_answer": "18/60 nó 3/10 nó 0·3", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q13cii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13(c)(ii)", "parent_question": "13", "marks": 5, "marks_confidence": "derived", "question_text": "Cad é an dóchúlacht go bhfuil an scoláire ar an bhfoireann ghorm?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "(17 + 15)/60 = 32/60 = 8/15 nó 0·5333…", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q14ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)(i)", "parent_question": "14", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeántar na pointí A agus B ar an léaráid chomhordanáideach thíos.\nScríobh síos comhordanáidí an phointe A agus comhordanáidí an phointe B.\nA = ( , ) B = ( , )", "has_images": true, "image_notes": "Léaráid chomhordanáideach (greille) le haiseanna x (−4 go 5) agus y (−2 go 4). Pointe A marcáilte ag (3, 2). Pointe B marcáilte ag (3, −1).", "topic": "Coordinate Geometry", "marking_scheme_answer": "A = (3, 2); B = (3, −1)", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q14aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)(ii)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Scríobh síos fad |AB|.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q14aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)(iii)", "parent_question": "14", "marks": 1, "marks_confidence": "derived", "question_text": "Is é (−4 , 2) an pointe C. Breac agus lipéadaigh an pointe C ar an léaráid chomhordanáideach thuas.", "has_images": true, "image_notes": "Le breacadh ar an léaráid chomhordanáideach chéanna: pointe C ag (−4, 2).", "topic": "Coordinate Geometry", "marking_scheme_answer": "Tá pointe C breactha agus lipéadaithe ag (−4, 2) ar an léaráid.", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q14aiv", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(a)(iv)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Oibrigh amach fána BC. Bíodh do fhreagra ina chodán.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "Fána = Δrise/Δrun = (2 − (−1))/(−4 − 3) = 3/(−7) = −3/7 (B = (3, −1), C = (−4, 2))", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q14bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)(i)", "parent_question": "14", "marks": 2, "marks_confidence": "derived", "question_text": "Taispeántar an triantán PQR sa léaráid thíos. |PQ| = 24 m, |QR| = 12 m, agus |∠PQR| = 90°. Tá an uillinn ag P marcáilte le X.\nCé acu ceann díobh seo a leanas atá ceart? Ná cuir tic (✓) ach i mbosca amháin.\nsin X = 12/24 cos X = 12/24 tan X = 12/24", "has_images": true, "image_notes": "Triantán dronuilleach PQR. P ag bun ar chlé (uillinn X marcáilte ann), Q ag bun ar dheis (uillinn dhronuilleach 90°), R ag barr ar dheis. |PQ| = 24 m (an bonn), |QR| = 12 m (an taobh ingearach ar dheis).", "topic": "Trigonometry", "marking_scheme_answer": "tan X = 12/24", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q14bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "14(b)(ii)", "parent_question": "14", "marks": 3, "marks_confidence": "derived", "question_text": "Uaidh sin, bain úsáid as d'áireamhán chun méid na huillinne X a fháil, ceart go dtí an chéim is gaire.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "X = tan⁻¹(12/24) = 26·5… = 27[°]", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q2a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)", "parent_question": "2", "marks": 10, "marks_confidence": "high", "question_text": "Cheannaigh Noah 3 bharra seacláide ón siopa áitiúil. Bhí an costas céanna ar gach barra. D'íoc sé €20 agus fuair sé €13·40 mar shóinseáil. Oibrigh amach an costas a bhí ar 1 bharra seacláide amháin.", "has_images": true, "image_notes": "Íomhá de bharra seacláide Cadbury Dairy Milk Oreo in aice na ceiste (maisíoch; gan sonraí riachtanacha).", "topic": "Number", "marking_scheme_answer": "20 − 13·40 = 6·60; 6·60 ÷ 3 = [€] 2·20", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q2ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": 2, "marks_confidence": "derived", "question_text": "Scríobh síos an chéad dá théarma eile i ngach ceann de na seichimh seo a leanas. Tugtar an cineál seichimh i ngach cás. (i) Líneach: 1, 5, 9, ___, ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "13, 17 (common difference 4).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q2aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": 2, "marks_confidence": "derived", "question_text": "(ii) Triarach: 4, 12, 36, ___, ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "108, 324 (geometric, common ratio 3).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q2aiii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(iii)", "parent_question": "2", "marks": 1, "marks_confidence": "derived", "question_text": "(iii) Cearnach: 12, 19, 23, ___, ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "24, 22 (quadratic sequence; second differences constant, first differences 7, 4, 1, −2 → terms 24, 22).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q2b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": 5, "marks_confidence": "high", "question_text": "Bhí €13·40 ag Noah. Roinn sé an t-airgead idir é féin agus cara leis, Amy, sa chóimheas 3 : 2, faoi seach. Oibrigh amach an méid airgid a fuair an bheirt acu.\nNoah = ____\nAmy = ____", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "3 + 2 = 5; 1/5 de 13·40 = 2·68; Noah = 3/5 → [€] 8·04; Amy = 2/5 → [€] 5·36", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q2bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)(i)", "parent_question": "2", "marks": 4, "marks_confidence": "derived", "question_text": "Baineann Amy úsáid as bloic dhaite chun seicheamh a chruthú. Taispeántar na chéad 7 mbloc sa seicheamh thíos. Athfhilleann an patrún gach 4ú bloc. (Dearg, Dearg, Gorm, Uaine, Dearg, Dearg, Gorm.) (i) Cén dath atá ar an 10ú bloc sa seicheamh?", "has_images": true, "image_notes": "A row of 7 coloured cubes labelled below: Dearg (red), Dearg (red), Gorm (blue), Uaine (green), Dearg (red), Dearg (red), Gorm (blue). The repeating unit of 4 is Dearg, Dearg, Gorm, Uaine.", "topic": "Algebra", "marking_scheme_answer": "Rua/Dearg (Red). The pattern repeats every 4 blocks (Dearg, Dearg, Gorm, Uaine); the 10th block corresponds to position 2 in the cycle, which is Dearg (red).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q2bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)(ii)", "parent_question": "2", "marks": 6, "marks_confidence": "derived", "question_text": "(ii) Roghnaíonn Amy bloc amháin go randamach as na chéad 25 bhloc sa seicheamh. Cad é an dóchúlacht gur bloc dearg é an bloc sin?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "P(Dearg) = 13/25 = 52% (in the first 25 blocks there are 13 red blocks, since each group of 4 has 2 red and the partial group adds extra).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q3a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Beartaíonn Mae a seomra suí a phéinteáil. Taispeánann an tábla na luachanna atá in easnamh A, B, C, agus D orthu. Oibrigh amach na luachanna atá in easnamh agus a bhfuil na lipéid A, B, C, agus D orthu. Cuir na freagraí isteach sa tábla. (Earra | Praghas Aonaid | × | Líon na nAonad | = | Costas Iomlán: Canna péinte | €42·50 | × | 3 | = | A. Scuab phéinteála | €6·99 | × | B | = | €13·98. Braillín deannaigh agus paca téipe | €33·80 | × | 1 | = | C. Saothar | €120 in aghaidh an lae | × | 3·5 | = | D. Fo-iomlán = €595·28. CBL @ 13·5% = E. Costas Iomlán = F.)", "has_images": true, "image_notes": "A costing table. Columns: Cur síos ar an earra | Praghas Aonaid | × | Líon na nAonad | = | Costas Iomlán. Rows: Canna péinte €42·50 × 3 = A; Scuab phéinteála €6·99 × B = €13·98; Braillín deannaigh agus paca téipe €33·80 × 1 = C; Saothar €120 in aghaidh an lae × 3·5 = D. Fo-iomlán = €595·28; CBL @ 13·5% = E; Costas Iomlán = F.", "topic": "Number", "marking_scheme_answer": "A = €42·50 × 3 = €127·50; B = €13·98 / €6·99 = 2; C = €33·80 × 1 = €33·80; D = €120 × 3·5 = €420.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q3a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)", "parent_question": "3", "marks": 10, "marks_confidence": "high", "question_text": "Taispeántar sa tábla thíos an méid ama a chaith custaiméirí i gcaifé ar lá áirithe.\nAm (nóiméid): 0–10, 10–20, 20–30, 30–40, 40–50. Líon na gCustaiméirí: 12, 18, 16, 24, 8.\n(Nóta: Ciallaíonn '10 − 20' 10 nóiméad nó níos mó, ach níos lú ná 20 nóiméad, agus mar sin de.)\nCríochnaigh an hiseagram thíos chun an t-eolas sa tábla a thaispeáint.", "has_images": true, "image_notes": "Histeagram le líonadh isteach. Ais x = 'Am (nóiméid)' marcáilte 0, 10, 20, 30, 40, 50. Ais y = 'Líon na gCustaiméirí' marcáilte 0 go 28 i gcéimeanna de 4 (4, 8, 12, 16, 20, 24, 28). Aon bharra amháin tarraingthe cheana (an raon 30–40 le airde 24). Barraí le tarraingt: 0–10:12, 10–20:18, 20–30:16, 40–50:8.", "topic": "Statistics", "marking_scheme_answer": "Don bharra 10 − 20, glac le hairde ó i gcás gurb ionann an spás 16 < h < 20.", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q3b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 3, "marks_confidence": "derived", "question_text": "Oibrigh amach an luach atá in easnamh agus an lipéad E air, an CBL. Is 13·5% den Fho-iomlán é sin. Bíodh do fhreagra ceart go dtí 2 ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "E = 595·28 × (13·5/100) = 80·3628 = €80·36 (2 d.p.). (Grouped Scála 5C shared with part (c).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q3b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Faigh líon iomlán na gcustaiméirí a thug cuairt ar an gcaifé ar lá sin.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "12 + 18 + 16 + 24 + 8 = 78", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q3c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 2, "marks_confidence": "derived", "question_text": "Oibrigh amach an luach atá in easnamh agus an lipéad F air, an Costas Iomlán agus an CBL san áireamh. Bíodh do fhreagra ceart go dtí 2 ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "F = 80·36 + 595·28 = €675·64. (Grouped Scála 5C shared with part (b).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q3c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(c)", "parent_question": "3", "marks": 5, "marks_confidence": "derived", "question_text": "Cad é an líon is mó custaiméirí a bhféadfadh níos lú ná 15 nóiméad a bheith caite acu sa chaifé an lá sin?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "12 + 18 = 30", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q4a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Rinne 12 scoláire triail ranga san Ealaín agus sa Ghnó Dé Luain. Is iad seo a leanas na marcanna na scoláirí sa dá ábhar. (Ealaín: 54, 49, 47, 71, 52, 50, 51, 34, 62, 47, 46, 37. Gnó: 59, 64, 52, 67, 68, 67, 59, 65, 54, 53, 66, 69.) Comhlánaigh an léaráid ghais is duillí cúl le cúl thíos chun marcanna na scoláirí a léiriú. (Eochair Ealaín: 4|5| = 54 marc; Eochair Gnó: |5|3 = 53 marc.)", "has_images": true, "image_notes": "Two data tables (Ealaín marks: 54,49,47,71,52,50,51,34,62,47,46,37; Gnó marks: 59,64,52,67,68,67,59,65,54,53,66,69) and a blank back-to-back stem-and-leaf diagram with stems 3,4,5,6,7 and headings Ealaín (left) and Gnó (right). Keys: Ealaín 4|5| = 54 marc; Gnó |5|3 = 53 marc.", "topic": "Statistics", "marking_scheme_answer": "Back-to-back stem-and-leaf plot. Ealaín (leaves read right-to-left): stem 3 | 7 4; stem 4 | 9 7 7 6; stem 5 | 4 2 1 0; stem 6 | 2; stem 7 | 1. Gnó: stem 3 | (none); stem 4 | (none); stem 5 | 2 3 4 9 9; stem 6 | 4 5 6 7 7 8 9; stem 7 | (none). (23 leaf entries correct across the diagram.)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q4a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Tá bratach dhronuilleogach 100 cm ar fad agus 60 cm ar leithead, mar a thaispeántar sa léaráid thíos.\nOibrigh amach achar na brataí dronuilleogaí, ina cm^2.", "has_images": true, "image_notes": "Léaráid de bhratach dhronuilleogach (bratach na Beilíse). Fad an bharr marcáilte 100 cm, airde ar dheis marcáilte 60 cm.", "topic": "Geometry", "marking_scheme_answer": "100 × 60 = 6000 [cm^2]", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q4b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 10, "marks_confidence": "high", "question_text": "Ón ghrath atá ar an léaráid ghais is duillí, scríobh abairt chun comparáid a dhéanamh idir torthaí na scoláirí san Ealaín agus sa Ghnó. Ba cheart duit tagairt do cé chomh maith is a d'éirigh leis na scoláirí, ar an meán, agus cé chomh scaipthe amach is atá na marcanna.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "A valid comparison, for example: the Gnó marks are generally higher (on average/centre) than the Ealaín marks, and the Ealaín marks are more spread out than the Gnó marks. (Any answer referring to both a measure of centre and spread.)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q4b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Tá ciorcal laistigh den dronuilleog ar an mbratach. 21 cm is ea an ga don chiorcal. Oibrigh amach achar an chiorcail. Bíodh do fhreagra ceart go dtí an cm^2 is gaire.\nA = πr^2", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "A = πr^2 = π·21^2 = 441π = 1385·4… = 1385 [cm^2] (an cm^2 is gaire)", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q4c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": 5, "marks_confidence": "high", "question_text": "Oibrigh amach raon na marcanna don Ghnó.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Raon = 69 − 52 = 17 marc.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q4d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": 2, "marks_confidence": "derived", "question_text": "Tá Mícheál ar dhuine den 12 scoláire. Rinne sé an triail Ghnó arís, agus fuair sé marc níos airde ná mar a fuair sé an chéad uair a rinne sé an triail. Nuair a d'úsáid an múinteoir an marc nua a bhí faighte ag Mícheál agus nuair a d'oibrigh sí amach raon na marcanna, níor tháinig athrú ar bith ar an raon. Minigh an chaoi a bhféadfadh sé sin tarlú.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Any valid explanation, e.g.: Michael could have scored 53 the first time and a slightly higher mark such as 54 the second time — this does not change the range. OR if both his old and new marks lie between the minimum and maximum marks, the range is unchanged. OR if Michael went from 52 to 70, the range would still be the same. (Grouped Scála 5C shared with part (e).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q4e", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(e)", "parent_question": "4", "marks": 3, "marks_confidence": "derived", "question_text": "Bhí an 13ú scoláire, Ajani, as láthair don dá thriail Dé Luain. Rinne sé na trialacha an lá dár gcionn. Nuair a cuireadh a mharc san áireamh, tháinig ardú ar an meánmharc san Ealaín ó 50 go 51. Oibrigh amach an marc a fuair Ajani san Ealaín.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "Iomlán roimh Ajani = 12 × 50 = 600; Iomlán tar éis Ajani = 13 × 51 = 663; Marc Ajani = 663 − 600 = 63. (Grouped Scála 5C shared with part (d).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q5a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 4, "marks_confidence": "derived", "question_text": "Taispeántar na pointí A agus C ar an léaráid chomhordanáideach thíos. Scríobh comhordanáidí na bpointí A agus C sna spásanna thíos. A = ( , ) C = ( , )", "has_images": true, "image_notes": "Coordinate grid with x- and y-axes from −5 to 5. Point C is plotted at (0, 1) and labelled C; point A is plotted at (3, −2) and labelled A.", "topic": "Coordinate Geometry", "marking_scheme_answer": "A = (3, −2); C = (0, 1). (Grouped Scála 10C shared with part (b).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q5a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": 8, "marks_confidence": "derived", "question_text": "I suirbhé ar 120 scoláire i Scoil Thearmann an tSuaimhnis: imríonn 30 scoláire spórt (S) agus cluichí ríomhaire (C) araon; imríonn 48 scoláire cluichí ríomhaire.\nBain úsáid as an eolas thuas chun an léaráid Venn thíos a chríochnú. U [120]", "has_images": true, "image_notes": "Léaráid Venn le tacar uilíoch U [120]. Dhá chiorcal forluiteacha lipéadaithe S (spórt) agus C [48] (cluichí ríomhaire). An trasnú (S ∩ C) marcáilte 35. An réigiún lasmuigh den dá chiorcal marcáilte 37. Ciorcal C le líon iomlán 48.", "topic": "Probability", "marking_scheme_answer": "#(C ∩ S) = 35; #(C) = 48 → 48 − 35 = 13 sa chuid de C amháin", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q5b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 6, "marks_confidence": "derived", "question_text": "Is trí phointe eile iad B, D, agus E. Breac agus lipéadaigh an pointe B (4, 3) ar an léaráid ar an leathanach roimhe seo.", "has_images": true, "image_notes": "Same coordinate grid as part (a). The student must plot and label the point B at (4, 3).", "topic": "Coordinate Geometry", "marking_scheme_answer": "B (4, 3) plotted and labelled correctly on the grid. (Grouped Scála 10C shared with part (a).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q5b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": 7, "marks_confidence": "derived", "question_text": "Cé mhéad scoláire nach n-imríonn spórt ná cluichí ríomhaire?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q5c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Is comhthreomharán é ABCD. Bain úsáid as an eolas sin chun an pointe D a bhreacadh agus a lipéadú ar an léaráid ar an leathanach roimhe seo.", "has_images": true, "image_notes": "Same coordinate grid. ABCD is a parallelogram with A(3,−2), B(4,3), C(0,1) already known; the student must plot point D.", "topic": "Coordinate Geometry", "marking_scheme_answer": "D = (−1, −4) plotted and labelled correctly (so that ABCD is a parallelogram). (Grouped Scála 10D shared with part (d).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q5c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": 2, "marks_confidence": "derived", "question_text": "#(S∪C) = 35. Mínigh an bhrí atá leis an ráiteas sin, ó thaobh na rudaí a imríonn na scoláirí sa scoil (spórt agus cluichí ríomhaire).", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "Imríonn 35 scoláire spórt nó cluichí ríomhaire (nó a chéile/an dá rud).", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q5d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 5, "marks_confidence": "derived", "question_text": "Is é an pointe C lárphointe na mírlíne [AE]. Scríobh síos comhordanáidí an phointe E. E = ( , )", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": "C is midpoint of [AE]: E = (2(0)−3, 2(1)−(−2)) = (−3, 4). E = (−3, 4). (Grouped Scála 10D shared with part (c).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q5d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(d)", "parent_question": "5", "marks": 3, "marks_confidence": "derived", "question_text": "Roghnaítear scoláire amháin go randamach as 120 scoláire a ndearnadh an suirbhé orthu. Cad é an dóchúlacht go n-imríonn an scoláire sin spórt nó cluichí ríomhaire ach nach n-imríonn sé an dá cheann?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": "Imríonn 35 spórt nó cluichí ríomhaire ach nach an dá rud: roinntear 35 + 18 nó uimhir ar bith ón Léaráid Venn ar 120; (35 + 18)/120 = 53/120", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q6a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 15, "marks_confidence": "high", "question_text": "Taispeántar an mhírlíne [PQ] thíos. Roinn an mhírlíne [PQ] ina trí chuid ar comhfhad, gan í a thomhas. Taispeáin go soiléir do línte tógála go léir.", "has_images": true, "image_notes": "A horizontal line segment [PQ] with endpoints labelled P (left) and Q (right). Student must construct, using construction lines only (no measuring), the division of [PQ] into three equal parts.", "topic": "Geometry", "marking_scheme_answer": "Construction dividing [PQ] into 3 equal parts: draw a ray from P (or Q) at an angle, mark off 3 equal lengths along it, join the last mark to Q, then draw parallels to that line through the other two marks back to PQ. Construction lines must be shown.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q6a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Tá 3 bhranda éagsúla de bhróga reatha ar díol i siopa spóirt. Tá gach branda ar fáil ina 4 dhath éagsúla a thaispeántar sa tábla thíos.\nBranda A: Dearg; Branda B: Gorm; Branda C: Dubh; Buí.\nCé mhéad rogha éagsúil bróige reatha atá ar díol sa siopa? Mar shampla, rogha amháin is ea branda B agus buí.", "has_images": true, "image_notes": "Íomhá de bhróga reatha in aice na ceiste (maisíoch). Tábla le colún 'Branda' (A, B, C) agus colún 'Dath' (Dearg, Gorm, Dubh, Buí).", "topic": "Probability", "marking_scheme_answer": "3 × 4 = 12 (NÓ liostaítear na roghanna difriúla / tarraingítear léaráid chrainn, agus luaitear 12)", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q6b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": 10, "marks_confidence": "high", "question_text": "Scríobhann Tomás liosta ina bhfuil cúig uimhir, ón gceann is lú go dtí an ceann is mó. Taispeánann dhá cheann de na huimhreacha sin thíos.\n2, ____, ____, 10, ____\nIs é 2 mód na gcúig uimhir sin.\nIs é 7 airmheán na n-uimhreacha sin.\nIs é 12 an raon.\nBain úsáid as an eolas sin chun na trí uimhir atá in easnamh ó liosta Thomáis a fháil, agus scríobh isteach sna spásanna thuas iad.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": "2, 2, 7, 10, 14 [2 + 12 = 14]", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q6bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)(i)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Taispeántar an triantán ABC sa léaráid thíos. Tá na pointí D agus E ar [AB] agus tá na pointí F agus G ar [AC]. Is chaoi go bhfuil DF, EG, agus BC comhthreomhar le chéile. Tugtar sa léaráid an mhéid atá i roinnt de na huillinneacha. (Uillinneacha taispeánta: 28° ag A; uillinn x ag D; uillinn z ag E; 72° ag B.) (i) Oibrigh amach an mhéid atá sna huillinneacha atá marcáilte le x, y, agus z sa léaráid. x = ___ y = ___ z = ___", "has_images": true, "image_notes": "Triangle ABC with vertex A at the left (angle 28°) and base AB along the bottom. Points D and E lie on AB, points F and G lie on AC. Line segments DF, EG and BC are parallel. Marked angles: at A = 28°; at D the marked angle x; at E the marked angle z; at B = 72°. (y is associated with point F/the parallel-line configuration.)", "topic": "Geometry", "marking_scheme_answer": "x = 72° (corresponding angle to angle ABC, lines parallel); y = 180 − (28 + 72) = 80°; z = 180 − x = 180 − 72 = 108° (so z = 28 + 80 = 108°).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q6bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)(ii)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Minigh an fáth a bhfuil an dá thriantán ABC agus ADF comhchosúil le chéile gan bheith iomchuí le chéile.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Any correct explanation, e.g.: The triangles are similar because the angles are equal in each (DF is parallel to BC so corresponding angles are equal / they share angle A). They are not congruent because corresponding sides are not equal in length, e.g. |DF| ≠ |BC|; the triangles are different sizes.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q6c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": 5, "marks_confidence": "high", "question_text": "Taispeántar arís na triantáin chéanna thíos. An uair seo, taispeántar fad roinnt de na sleasa. |AD| = |DE| = |EB| = 10 agus |BC| = 14·3. Bain úsáid as triantáin chomhchosúla chun fad [GE] a oibriú amach. (Sa léaráid: A — D — E — B ar an mbun le |AD| = 10, |DE| = 10, |EB| = 10; C ag an mbarr ar dheis le |BC| = 14·3; G ar [AC].)", "has_images": true, "image_notes": "Triangle ABC with base A-D-E-B (each of AD, DE, EB = 10, so AB = 30). C at top right with |BC| = 14·3. F and G lie on AC; G is above E, with EG parallel to BC. The student uses similar triangles to find |GE|.", "topic": "Geometry", "marking_scheme_answer": "|GE|/|CB| = |AE|/|AB|; |GE|/14·3 = 20/30; |GE| = (20 × 14·3)/30 = 143/15 = 9 8/15 ≈ 9·533 cm.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q7ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Tá cuid de ghalfchúrsa i gcruth dronuilleoige agus leathchiorcal ar thaobh amháin di, mar a thaispeántar sa léaráid thíos. Tá an cruth sin 50 m ar leithead agus 300 m ar fad san iomlán, mar a thaispeántar. (i) Oibrigh amach na faid atá marcáilte le x agus le y ar an léaráid. Is é x ga an leathchiorcail. x = ___ y = ___", "has_images": true, "image_notes": "A golf-course region: a rectangle with a semicircle on its right-hand end. Overall length (left to right) is 300 m, marked as y for the rectangle portion plus x. Width = 50 m. x is the radius of the semicircle (marked vertically/inside the semicircle near a flag). y is the length of the rectangular part.", "topic": "Geometry", "marking_scheme_answer": "x = 50/2 = 25 m (radius = half the width); y = 300 − x = 300 − 25 = 275 m.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q7ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Sa cheist seo, tá luach seasta ag gach cruth.\nBain úsáid as an gcothromóid a leanas chun luach ciorcail a oibriú amach:\n(ciorcal) + (ciorcal) + (ciorcal) = 21\n(ciorcal) = ____", "has_images": true, "image_notes": "Cothromóid amhairc: trí chiorcal ghlasa á suimiú = 21.", "topic": "Algebra", "marking_scheme_answer": "21/3 = 7 (ciorcal = 7)", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q7aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 10, "marks_confidence": "high", "question_text": "Uaidh sin, oibrigh amach achar iomlán na coda sin den ghalfchúrsa. Bíodh do fhreagra ceart go dtí an m² is gaire.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": "Area = (rectangle) + (semicircle) = (50 × 275) + ½π(25²) = 13 750 + ½(1963·495…) = 13 750 + 981·7… = 14 731·7… ≈ 14 732 m².", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q7aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": 5, "marks_confidence": "derived", "question_text": "Bain úsáid as an gcothromóid a leanas, agus as do fhreagra ar chuid (a)(i), chun luach triantáin a oibriú amach:\n(ciorcal) + (triantán) + (ciorcal) = 18\n(triantán) = ____", "has_images": true, "image_notes": "Cothromóid amhairc: ciorcal glas + triantán gorm + ciorcal glas = 18.", "topic": "Algebra", "marking_scheme_answer": "7 + triantán + 7 = 18 → triantán = 4", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q7b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Tá leasachán á leathadh ag Maciej ar an ngalfchúrsa iomlán. Tá na treoracha seo ar phaicéad an leasacháin: Úsáid 6 litear de leasachán le haghaidh gach 250 m² de thalamh atá le clúdach. Teastaíonn ó Maciej 809 371 m² de thalamh a chlúdach le leasachán. Cé mhéad litear de leasachán a chaithfidh Maciej a úsáid? Bíodh do fhreagra ceart go dtí an tslánuimhir is gaire.", "has_images": true, "image_notes": "A highlighted instruction box on the fertiliser packet: 'Úsáid 6 litear de leasachán le haghaidh gach 250 m² de thalamh atá le clúdach' (use 6 litres per 250 m²).", "topic": "Number", "marking_scheme_answer": "(809 371 × 6)/250 = 19 424·904 ≈ 19 425 litir (litre).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q7b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Taispeántar dhá chothromóid thíos. Oibrigh amach luach heicseagáin agus luach cearnóige.\n(heicseagán) + (heicseagán) + (cearnóg) = 24\n(cearnóg) + (heicseagán) = 13\n(heicseagán) = ____ (cearnóg) = ____", "has_images": true, "image_notes": "Dhá chothromóid amhairc le heicseagáin bhuí agus cearnóg dhearg: dhá heicseagán + cearnóg = 24; cearnóg + heicseagán = 13.", "topic": "Algebra", "marking_scheme_answer": "(heicseagán) + (heicseagán) + (cearnóg) = 24 agus (heicseagán) + 13 = 24 → heicseagán = 11; cearnóg + 11 = 13 → cearnóg = 2", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q7c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": 15, "marks_confidence": "high", "question_text": "Trí chomhábhar, A, B, agus C, atá sa leasachán agus iad sa chóimheas seo a leanas: A : B : C = 1 : 3/2 : 5/3. Oibrigh amach líon na millilítear de B in 1 litear amháin den leasachán.", "has_images": true, "image_notes": "A small ratio table: A : B : C with values 1 : 3/2 : 5/3.", "topic": "Number", "marking_scheme_answer": "Ratio A:B:C = 1 : 3/2 : 5/3 = 6 : 9 : 10 (multiplying by 6). Total parts = 6 + 9 + 10 = 25. B = 1000 × (9/25) = 360 ml.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q7d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(d)", "parent_question": "7", "marks": 5, "marks_confidence": "high", "question_text": "Is i gcruth sorcóra atá an tancaer a úsáidtear chun an leasachán a leathadh. 90 ceintiméadar is ga don tancaer agus tá an tancaer 4 mhéadar ar fad, mar a thaispeántar sa léaráid ar dheis. Oibrigh amach toirt an tancaera. Bíodh do fhreagra, ina m³, ceart go dtí 2 ionad dheachúlacha.", "has_images": true, "image_notes": "A horizontal cylinder (the tanker). Radius labelled 90 cm; length labelled 4 m.", "topic": "Geometry", "marking_scheme_answer": "r = 0·9 m; V = πr²h = π(0·9²)(4) = π(0·81)(4) = 10·178… = 10·18 m³ (2 d.p.).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q7e", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(e)", "parent_question": "7", "marks": 20, "marks_confidence": "high", "question_text": "Taispeántar sa léaráid seo ar dheis tancaer sorcóireach eile, agus is é 81π/125 m³ an toirt atá ann. Tá fad an tancaera trí oiread níos faide ná ga an tancaera, mar a thaispeántar. Oibrigh amach ga an tancaera sin, ina mhéadar.", "has_images": true, "image_notes": "A horizontal cylinder (second tanker). Radius labelled y; length labelled 'fad'. The text states the length is three times the radius (fad = 3 × ga). Volume = 81π/125 m³.", "topic": "Geometry", "marking_scheme_answer": "h = 3r; V = πr²h = πr²(3r) = 3πr³ = 81π/125; r³ = 27/125; r = (27/125)^(1/3) = 3/5 = 0·6 m.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q8a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Cos A = 0·27. Oibrigh amach méid na huillinne A, ceart go dtí an chéim is gaire.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": "A = cos⁻¹ 0·27 = 74·3… ≈ 74° (to the nearest degree).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q8ai", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Tugtar ocht n-uimhir sa tábla thíos.\nTábla: 1, 3, 8, 12 (sraith uachtair); 15, 24, 30, 60 (sraith íochtair).\nAs na huimhreacha sa tábla, scríobh síos: ré-uimhir.", "has_images": true, "image_notes": "Tábla 2×4 le hocht n-uimhir: sraith 1 = 1, 3, 8, 12; sraith 2 = 15, 24, 30, 60.", "topic": "Number", "marking_scheme_answer": "8, 12, 24, 30 nó 60", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q8aii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "an t-iolraí coiteann is lú (ICL) ar 12 agus 15.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "12 = 2 × 2 × 3; 15 = 3 × 5; ICL = 2 × 2 × 3 × 5 = 60", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q8b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 10, "marks_confidence": "high", "question_text": "Ba mhaith le Olga a fháil amach cad é airde cheartingearach, h, an dín ar fhoirgneamh. Glacann Olga na toisí seo a leanas agus taispeánann sí iad ar an léaráid thíos, agus h = |DC|: |∠CAB| = 22°, |∠DAB| = 29°, |AB| = 23 m, |∠ABC| = |∠ABD| = 90°. Bain úsáid as an triantánaíocht chun airde cheartingearach, h, an dín a oibriú amach. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": true, "image_notes": "Diagram of a building. A is on the ground to the left; B is at the base of the building (right). AB = 23 m horizontal. From A two lines of sight go up to D (top of roof) and C (eave), with angle CAB = 22° and angle DAB = 29°. Angles ABC = ABD = 90° (the building edge is vertical at B). h = |DC| is the vertical height of the roof (between C and D). A photo of a building with a clock tower is shown alongside.", "topic": "Trigonometry", "marking_scheme_answer": "tan 22° = |BC|/23 → |BC| = 23 tan 22° = 9·292…; tan 29° = |BD|/23 → |BD| = 23 tan 29° = 12·749…; h = |BD| − |BC| = 12·749… − 9·292… = 3·45… ≈ 3·5 m (1 d.p.).", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q8b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Tá naoi bhfachtóir dheimhneacha ag an uimhir 36. Tugtar ceithre cinn de na fachtóirí sin thíos. Líon isteach na cúig fhachtóir eile atá ag 36 sna boscaí a thugtar.\n1, 2, 3, ____, ____, ____, 12, ____, ____", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "1, 2, 3, 4, 6, 9, 12, 18, 36", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q8ci", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(i)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Taispeántar thíos na chéad trí phatrún i seicheamh. Is de chearnóga a dhéantar gach patrún.\nTarraing Patrún 4 sa seicheamh.", "has_images": true, "image_notes": "Seicheamh patrún déanta as cearnóga gorma. Patrún 1 = 1 chearnóg; Patrún 2 = 'T' iompaithe (3 chearnóg sa bhun-líne, 1 thuas) = 4 chearnóg; Patrún 3 = cruth níos mó (5 sa bhun-líne, 2 thuas) = 7 chearnóg. Le tarraingt: Patrún 4 (10 cearnóg).", "topic": "Algebra", "marking_scheme_answer": "Patrún 4 tarraingthe le 10 gcearnóg (an cruth 'T' iompaithe a leanúint).", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q8cii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(ii)", "parent_question": "8", "marks": 5, "marks_confidence": "derived", "question_text": "Líon isteach an tábla thíos chun an líon cearnóg i ngach ceann de na chéad 4 phatrún a thaispeáint.\nTábla: Patrún | An líon cearnóg. Patrún 1 = ?, Patrún 2 = ?, Patrún 3 = 7, Patrún 4 = ?", "has_images": true, "image_notes": "Tábla le colúin 'Patrún' agus 'An líon cearnóg'. Sraitheanna: 1, 2, 3 (=7 tugtha), 4. Le líonadh: Patrún 1 = 1, Patrún 2 = 4, Patrún 4 = 10.", "topic": "Algebra", "marking_scheme_answer": "Patrún 1 = 1; Patrún 2 = 4; Patrún 3 = 7; Patrún 4 = 10", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q8ciii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)(iii)", "parent_question": "8", "marks": 5, "marks_confidence": "high", "question_text": "Cén cineál seichimh a dhéantar leis an líon cearnóg i ngach patrún? Tabhair cúis le do fhreagra.\nFreagra: Líneach / Neamhlíneach (Ná cuir tic (✓) ach i mbosca amháin)\nCúis: ____", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": "Líneach. Cúis: méadaíonn sé faoi 3 gach uair nó aon chúis bhailí ar bith eile (an difríocht choiteann sa líon cearnóg, +3, is comhionann).", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q9a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Thaifead Fiadh an teocht ina cistin, ina céimeanna Celsius (°C), thar 10 n-uair an chloig. Is é T(x) an teocht a bhí ann x uair an chloig tar éis d'Fhiadh tosú á taifeadadh, le haghaidh 0 ≤ x ≤ 10. Taispeántar T(x) do na chéad 8 n-uair an chloig sa ghraf thíos. Tá an graf ina thrí mhír agus na lipéid P, Q, agus R orthu. Bain úsáid as an ghraf chun codanna (a) go (f) a fhreagairt. Ná húsáid aon litir níos mó ná uair amháin. (a) Déan meastachán ar an méid ama a thóg sé chun 20°C a bhaint amach den chéad uair. Bíodh do fhreagra, ina uaireanta an chloig, ceart go dtí ionad deachúlach amháin. Taispeáin do chuid oibre ar an ngraf.", "has_images": true, "image_notes": "Line graph of temperature T(x) °C (y-axis, marked 3,6,9,12,15,18,21,24) against time x in hours (x-axis 1–10). The plot has three segments labelled P, Q, R. Segment P rises steeply from about 12°C; segment Q is the upper near-flat/peak region around 21°C reaching point R; the graph shown covers x = 0 to 8.", "topic": "Functions", "marking_scheme_answer": "An estimate read from the graph, approximately 3 hours (a value between 2·5 and 3 is accepted). Work shown on the graph. (Grouped Scála 5C shared with part (b).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q9a", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": 4, "marks_confidence": "derived", "question_text": "Tá €100 faighte ag Alice dá breithlá, agus tá sé curtha isteach i gcuntas bainc aici. Cuirfidh sí €25 eile isteach sa chuntas bainc gach mí go ceann 6 mhí.\nOibrigh amach an méid iomlán a bheidh sa bhanc aici ag deireadh na 6 mhí.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "100 + 6 × 25 = 100 + 150 = [€] 250", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q9b", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Cé mhéad uair an chloig a bhí an teocht tairiseach, le haghaidh 0 ≤ x ≤ 8?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "4 (uair) — the temperature was constant for 4 hours (the flat section of the graph). (Grouped Scála 5C shared with part (a).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q9bi", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)(i)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Tá €130 curtha isteach i gcuntas coigiltis in oifig an phoist ag Alice. Is é 3% an ráta bliantúil úis.\nOibrigh amach an méid úis a gheobhaidh Alice in aon bhliain amháin.", "has_images": true, "image_notes": "Íomhá de phróca le boinn agus an lipéad 'Coigilteas' in aice na ceiste (maisíoch).", "topic": "Number", "marking_scheme_answer": "(3/100) × 130 = [€] 3·90", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q9bii", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)(ii)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Oibrigh amach an méid iomlán airgid a bheidh sa chuntas tar éis bliana.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "130 + 3·90 = [€] 133·90", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q9c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 2, "marks_confidence": "derived", "question_text": "Téann mír S den ghraf ó x = 8 go x = 10, agus T(8) = 15. Le linn mhír S den ghraf, is é 3°C san uair an chloig an ráta athraithe teochta. Bain úsáid as sin chun mír S den ghraf a tharraingt ar an léaráid thuas, le haghaidh 8 ≤ x ≤ 10, x ∈ ℝ.", "has_images": true, "image_notes": "Same temperature-time graph as part (a). Student must draw segment S from x = 8 to x = 10, starting at T(8) = 15 with a rate of change of +3°C per hour.", "topic": "Functions", "marking_scheme_answer": "Draw a line segment from (8, 15) to (10, 21) — rising 3°C per hour, so reaching 21°C at x = 10. (Grouped Scála 5D shared with part (d).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-ordinary-level-IV-q9c", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Chuir Alice €120 isteach i gcuntas Comhair Creidmheasa. Gnóthaíodh ús ar an gcuntas sin. Tar éis bliana, bhí €124·56 sa chuntas aici. Faigh an ráta céatadánach bliantúil úis don chuntas sin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": "(124·56 − 120)/120 × 100 = (4·56/120) × 100 = 3·8 [%]", "source_pdf": "2025 - Mathematics - Ordinary Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q9d", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(d)", "parent_question": "9", "marks": 3, "marks_confidence": "derived", "question_text": "Sa tábla thíos, tá feidhm don teocht i ngach ceann de na trí mhír, P, Q, agus R. Scríobh an litir cheart (P, Q, nó R) sa spás cuí sa tábla chun a thaispeáint cé acu feidhm a chomhfhreagraíonn do gach mír den ghraf. Ná húsáid aon litir níos mó ná uair amháin. (Mír: ___ → T(x) = 21; ___ → T(x) = x² + 12; ___ → T(x) = −6x + 63.)", "has_images": true, "image_notes": "A two-column table: 'Mír (P, Q, nó R)' and 'Le linn na míre seo, is é feidhm na teochta ná:'. Rows give the functions T(x) = 21, T(x) = x² + 12, and T(x) = −6x + 63, to be matched to graph segments P, Q, R.", "topic": "Functions", "marking_scheme_answer": "Q ↔ T(x) = 21 (the constant/flat segment); P ↔ T(x) = x² + 12 (the rising curved segment); R ↔ T(x) = −6x + 63 (the falling straight segment). (Grouped Scála 5D shared with part (c).)", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q9e", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(e)", "parent_question": "9", "marks": 10, "marks_confidence": "high", "question_text": "Cé acu ceann de na feidhmeanna seo a leanas a thugann an teocht i mír S den ghraf (an mhír a tharraing tú i gcuid (c))? Ná cuir tic (✓) ach in aice amháin. Cosain do fhreagra, mar shampla, trí phointí i mír S a sheiceáil. (T(x) = 3x − 9 T(x) = −3x − 12 T(x) = 3x + 12). Cosaint: ___", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": "T(x) = 3x − 9. Justification, e.g.: at x = 8, T(8) = 3(8) − 9 = 24 − 9 = 15 (matches the start point), and at x = 10, T(10) = 3(10) − 9 = 21 (matches the end point). Checking points on segment S confirms slope 3 and value 15 at x = 8.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2025-higher-level-IV-q9f", "subject_n": "Mathematics", "year": 2025, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(f)", "parent_question": "9", "marks": 5, "marks_confidence": "high", "question_text": "Ní féan dearmad go dtaispeántar sa ghraf an teocht i gcistin Fhiadh. Bíonn an teocht i seomra codlata Fhiadh 3°C faoi bhun na teochta i gcistin Fhiadh do na chéad 8 n-uair an chloig (0 ≤ x ≤ 8, x ∈ ℝ). Ar an léaráid ar an leathanach roimhe seo, tarraing graf a thaispeánann an teocht i seomra codlata Fhiadh do na chéad 8 n-uair an chloig. Bain úsáid as na haiseanna agus na scálaí céanna.", "has_images": true, "image_notes": "Same temperature-time graph axes (T(x) °C vs x hours, 0 ≤ x ≤ 8). Student draws a new graph that is the kitchen graph shifted down by 3°C everywhere (bedroom temperature = kitchen temperature − 3).", "topic": "Functions", "marking_scheme_answer": "Draw the kitchen graph translated down by 3 units (3°C lower at every point) over 0 ≤ x ≤ 8 — i.e. each plotted value reduced by 3.", "source_pdf": "2025 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q1a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "A game consists of spinning a fair spinner and rolling a fair six-sided die. The spinner has three equal coloured sectors: red (R), yellow (Y), and blue (B). Complete the table below to show all 18 possible outcomes of the game. Two have already been done for you. For example, R3 means red on the spinner and 3 on the die. (The table has the Die values 1–6 as columns and the Spinner values R, Y, B as rows; R3 is filled in the R-row under column 3, and B5 is filled in the B-row under column 5.)", "has_images": true, "image_notes": "A 3x6 outcome table. Columns are the die values 1, 2, 3, 4, 5, 6 (header 'Die'). Rows are the spinner colours R, Y, B (header 'Spinner'). Two cells are pre-filled: 'R3' in row R / column 3, and 'B5' in row B / column 5. Also a coloured spinner image (sectors R, Y, B) and a red die showing 5 pips.", "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q1ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(i)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Find the value of each of the following: 1851 + 175", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q1aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(ii)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Find the value of each of the following: 5·8 × 8", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q1aiii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(a)(iii)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Find the value of each of the following: 48 ÷ (7 − 5)", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q1b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "What number is halfway between 8 and 14?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q1bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Each outcome in the table is equally likely. The game is played once. Find the probability that the outcome is: red on the spinner.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q1bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Find the probability that the outcome is: blue on the spinner and an even number on the die.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q1c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "1(c)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Find the Lowest Common Multiple (LCM) of 5 and 6. LCM = ____", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q10a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "In a survey, 40 students were asked if they like playing football (F) or reading (R). Of these: 5 said they like both playing football (F) and reading (R); 12 said they like reading (R). Use the information above to fill in the three missing values in the Venn diagram below.", "has_images": true, "image_notes": "Venn diagram with universal set U (40). Two overlapping circles labelled F (football) and R (reading). The F-only region shows 11. The intersection region, the R-only region, and the region outside both circles are empty boxes to be filled in.", "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q10ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "In the two grids below, each of the small squares has sides of length 1 cm. On the grid below, draw a square that has a perimeter of 12 cm.", "has_images": true, "image_notes": "A blank square-grid (each cell 1 cm) on which the student draws a square of perimeter 12 cm (side 3 cm).", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q10aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "A rectangle has length l cm and width w cm, where l and w are whole numbers. The rectangle also has an area of 10 cm^2. Draw one such rectangle on the grid below.", "has_images": true, "image_notes": "A blank square-grid (each cell 1 cm) on which the student draws a rectangle with whole-number sides and area 10 cm^2 (e.g. 5 cm by 2 cm, or 10 cm by 1 cm).", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q10b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "How many students like reading only?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q10bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)(i)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "A triangle has base length of k cm and a perpendicular height of h cm. The area of the triangle is 4h cm^2. Find the value of k.", "has_images": true, "image_notes": "A triangle diagram with base labelled k, perpendicular height labelled h, and 'Area: 4h cm^2' marked inside the triangle.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q10bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(b)(ii)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "This triangle forms the ends of a triangular-based prism, as shown below. The length of the prism is (h + 4) cm. The volume of the prism is 240 cm^3. Work out the value of h, the perpendicular height of the triangle.", "has_images": true, "image_notes": "A triangular-based prism diagram. The triangular cross-section has 'Area: 4h cm^2' marked, and the length of the prism is labelled (h + 4) cm.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q10c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(c)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "Explain what the following statement means in the context of the survey: #(F\\R) = 11", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q10d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "10(d)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "One student is picked at random from the 40 students who were surveyed. What is the probability that this student does not like playing football nor reading?", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q11a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "A school designs a new wheelchair ramp for their entrance, as shown in the diagram below. The ramp has a perpendicular height of 40 cm and a horizontal length of 6 m. The slope of this ramp is |BC|/|AB|. The recommended maximum slope for this type of a wheelchair ramp is 1/12. Does this wheelchair ramp meet this recommendation? Use calculations to support your answer. Answer (Tick (✓) one box only): Yes / No. Calculations: ____.", "has_images": true, "image_notes": "A right-angled triangle ramp diagram: horizontal base AB = 6 m at the bottom, vertical side BC = 40 cm (height) on the right at B, with the incline AC rising from A to C. Angle θ is marked at A. The slope is |BC|/|AB|.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q11ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(i)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "A candle is in the shape of a cylinder with a diameter of 4 cm and a height of 7 cm, as shown in the diagram on the right. Write down the radius of the candle. Radius = cm", "has_images": true, "image_notes": "Diagram of a cylindrical candle standing upright, with its height marked 7 cm and its diameter marked 4 cm.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q11aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(a)(ii)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Work out the volume of one candle. Give your answer correct to the nearest cm^3. V = π × r^2 × h", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q11b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Find |AC|, the length of the incline of the ramp. Give your answer in cm, correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q11bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)(i)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "18 of these candles fit exactly into a rectangular box, as shown below. The box has a width of 12 cm and a height of 7 cm. Write down the length of this rectangular box. Length = cm", "has_images": true, "image_notes": "Diagram of an open rectangular box packed with cylindrical candles standing upright (arranged in a grid, 18 candles total). The box width is marked 12 cm, the height is marked 7 cm, and the long dimension is labelled 'length'. With candle diameter 4 cm, the 12 cm width holds 3 candles across, so 18 candles imply 6 along the length.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q11bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(b)(ii)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Hence, work out the volume of this rectangular box.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q11c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Use trigonometry to work out the size of the angle marked θ in the diagram on the previous page. Give your answer in degrees, correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q11d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "11(d)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "A different ramp in the school has the following design: Work out the value of x, the perpendicular height of this ramp. Give your answer correct to the nearest cm.", "has_images": true, "image_notes": "A thin right-angled triangle ramp PQR: P at the left, the hypotenuse PR = 7·5 m along the top, with the angle at P marked 2·9°. The right angle is at Q (bottom right), and x is the vertical perpendicular height RQ on the right.", "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q12a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": null, "marks_confidence": "uncertain", "question_text": "The diagram below shows a circle with centre O. The three points R, S, and T are on the circle. The angles a and b are marked on the diagram. |∠TOS| = 96°. |∠OTR| = 20°. Work out the size of the angle a and the size of the angle b. a = ____; b = ____.", "has_images": true, "image_notes": "A circle with centre O and points R, S, T on the circumference. Chords/segments are drawn forming angles. At centre O, the angle ∠TOS = 96° is marked. Near T the angle ∠OTR = 20° is marked. Angle a is at/near O (in the triangle interior) and angle b is at R. Lines connect R, S, T and O.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q12a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": null, "marks_confidence": "uncertain", "question_text": "Simplify: 6a + a − 3b + 2a + b", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q12b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": null, "marks_confidence": "uncertain", "question_text": "In the triangle ABC: |AB| = 8 cm, |∠CAB| = 70°, |∠ABC| = 50°. Construct the triangle ABC in the box below. The point A is given. Label the points B and C on your diagram. Show all of your construction lines clearly.", "has_images": true, "image_notes": "Data table: |AB| = 8 cm, |∠CAB| = 70°, |∠ABC| = 50°. A construction box is provided with point A marked at the start of a horizontal ray (line) along which AB is to be drawn.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q12b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": null, "marks_confidence": "uncertain", "question_text": "Factorise the quadratic expression x^2 − 7x + 12. x^2 − 7x + 12 = (x − 3)( )", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q12c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "12(c)", "parent_question": "12", "marks": null, "marks_confidence": "uncertain", "question_text": "A mapping diagram of the function f(x) = 2x is shown below. Fill in the three missing entries into the diagram.", "has_images": true, "image_notes": "Mapping diagram for f(x) = 2x. Left oval (x values): 1, 3, 6, −2, and one blank box. Right oval (f(x) values): 2, 6, blank box, blank box, 10. Arrows map: 1→2, 3→6, 6→(blank), −2→(blank), (blank)→10. The three missing entries are: f(6) on the right, f(−2) on the right, and the x-value on the left mapping to 10.", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q13", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13", "parent_question": "13", "marks": null, "marks_confidence": "uncertain", "question_text": "A cylinder has a height of 24 cm and a radius of r cm, where r ∈ ℝ. The net of the curved surface of the cylinder is a rectangle, with a diagonal of length 37·6 cm. Use this to find the value of r, correct to 1 decimal place.", "has_images": true, "image_notes": "A cylinder of height 24 cm shown beside its net: a rectangle (the curved surface unrolled) of height 24 cm, with a diagonal of length 37·6 cm drawn across it. The rectangle's width equals the circumference 2πr; the diagonal forms a right triangle with the height (24 cm) and the width.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q13a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(a)", "parent_question": "13", "marks": null, "marks_confidence": "uncertain", "question_text": "A right-angled triangle is shown below. One of the sides is marked x. One of the angles is marked A. Use the Theorem of Pythagoras to work out the length x, in cm.", "has_images": true, "image_notes": "A right-angled triangle. The horizontal base is marked 8 cm, the vertical right-hand side is marked 6 cm, and the hypotenuse (the sloped top side) is marked x. The angle A is at the bottom-left vertex; the right angle is at the bottom-right vertex.", "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q13bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)(i)", "parent_question": "13", "marks": null, "marks_confidence": "uncertain", "question_text": "Use the right-angled triangle in the diagram above to write the value of tan A as a fraction. tan A = opposite / adjacent =", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q13bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "13(b)(ii)", "parent_question": "13", "marks": null, "marks_confidence": "uncertain", "question_text": "Hence, use your calculator to find the size of the angle A. Give your answer correct to the nearest degree.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q2ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "60 students were asked how much time they spent on their phone on a particular day. The results are shown in the frequency table below. [Note: 2 − 4 means 2 hours or more but less than 4 hours, and so on.] Use the information from the table to answer parts (a)(i), (a)(ii), and (a)(iii). Draw a histogram to show the information in the table. Use the axes and scales below.", "has_images": true, "image_notes": "Frequency table: Time (hours) intervals 0−2, 2−4, 4−6, 6−8, 8−10 with Number of students 21, 20, 14, 4, 1 respectively. A blank set of axes is provided: x-axis labelled 'Time (hours)' running 0 to 10, y-axis labelled 'Number of students' running 0 to 22 in steps of 2.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q2ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Parker goes to the shopping centre. The table shows some of the items he buys. Fill in the table to find the total cost of these items. Items: 1 t-shirt at €9·50; 1 schoolbag at €15·95; 2 sweatshirts at €23·95 each.", "has_images": true, "image_notes": "Two-column table headed 'Item' and 'Cost (€)'. Item rows: '1 t-shirt at €9·50', '1 schoolbag at €15·95', '2 sweatshirts at €23·95 each', and a final row labelled 'Total cost:'. The Cost column is blank for the student to fill in.", "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q2aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Find the maximum number of students who could have spent less than 3 hours on their phone.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q2aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Parker also buys a hat. In total he spends €83·35. Parker pays using one €50 note and two €20 notes. Work out how much change he gets.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q2aiii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(a)(iii)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Use mid-interval values to estimate the mean amount of time the 60 students spent on their phone. Give your answer in hours, correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q2b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "The 60 students were also asked what the most common use of their phone was. The results are shown in the table below. Complete the pie chart below to show the information in the table above. Label each sector and the size of each angle clearly. Show any workings out.", "has_images": true, "image_notes": "Table of 'Most common use' vs 'Number of students': Social Media = 30, Video Streaming = 10, Gaming = 6, Messaging = 14 (totals 60). A blank circle with a single radius drawn (centre marked) is provided for the pie chart.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q2bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)(i)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Parker has lunch while at the shopping centre. The menu offers a Main Course (Burger, Chicken, Salmon) and a Dessert (Apple Crumble, Brownie, Cheesecake, Ice-cream). Parker chooses one main course and one dessert from the menu. For example, one choice would be burger and apple crumble. Write down two more possible choices.", "has_images": true, "image_notes": "Two small menu tables. 'Main Course' table lists: Burger, Chicken, Salmon. 'Dessert' table lists: Apple Crumble, Brownie, Cheesecake, Ice-cream.", "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q2bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "2(b)(ii)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Find the total number of different choices of lunch that are possible if he chooses one main course and one dessert.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q3ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Martina buys a new car from the UK. The cost of the car is £21 250 sterling. The exchange rate is €1 = £0·85 sterling. Show that the cost of the car in euro is €25 000.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q3ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "In a survey, 30 students were asked to choose their favourite sport to watch on television. The results are shown in a grid of 30 responses. Complete the table below to show how many students chose each sport.", "has_images": true, "image_notes": "A 5-column by 6-row grid lists the 30 individual responses among: Darts, Gaelic Football, Hurling, Rugby, Soccer. Below it a frequency table headed 'Favourite Sport' / 'Number of students' with columns Darts, Gaelic Football, Hurling, Rugby, Soccer; the printed counts are Gaelic Football = 6 and Hurling = 5, the other cells are blank to be filled in.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q3aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Martina pays a customs charge of €3375. Write this charge as a percentage of €25 000.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q3aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "In the line plot below, each student is represented by a dot. Complete the line plot to show the information from the table above.", "has_images": true, "image_notes": "A line plot (dot plot) with horizontal axis labelled 'Favourite Sport' and categories Darts, Gaelic Football, Hurling, Rugby, Soccer. Some dots are already plotted in a partially completed column; the student completes the dots per category.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q3bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(i)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Martina has a gross annual income of €50 000. Martina pays income tax on her gross income at the rates given in the table below. (First €40 000 at 20%; Balance at 40%.) Work out Martina's annual income tax at each of these two rates (20% and 40%). Income tax at 20% = €____; Income tax at 40% = €____.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q3bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(i)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Which measure of centre – the mean, the median, or the mode – can you find for this data? (Tick one box only: Mean, Median, Mode.) In the box below, write the value of this measure of centre for the data. Value of measure of centre:", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q3bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(ii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Martina has annual tax credits of €3300. Work out Martina's net annual income.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q3bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(ii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "This survey was carried out during the World Darts Championship. Do you think this had an effect on the results? (Tick one box only: Yes / No.) Give a reason for your answer.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q3biii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(b)(iii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Martina gets a pay rise and her net annual income increases by €4800. Work out Martina's new gross annual income.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q3ci", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)(i)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "60 other students were asked to choose their favourite soccer team. The pie chart on the right shows the results of the survey. Use a protractor to find the sizes of the three missing pie chart angles. Write your answer in the appropriate space in the table below. (Teams: Alder F.C., Ballynore Town, Castlemore Celtic, Derryduff United; the Alder F.C. angle is given as 90°.)", "has_images": true, "image_notes": "A pie chart divided into four sectors for soccer teams: Ballynore Town, Alder F.C. (sector marked 90°), Derryduff United, and Castlemore Celtic. Below is a table 'Team' / 'Angle' with columns Alder F.C. (90°), Ballynore Town, Castlemore Celtic, Derryduff United; the three non-Alder angles are blank to be measured/filled in.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q3cii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "3(c)(ii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Work out how many students chose Alder F.C. as their favourite team. Remember that there were 60 students in total.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q4a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "The co-ordinate diagram below shows the triangle ABC. The point A has co-ordinates (2, −1). Write the co-ordinates of the point B and the point C in the spaces below. B = ( , ) C = ( , )", "has_images": true, "image_notes": "Coordinate diagram with x-axis from −6 to 6 and y-axis from −5 to 5. Triangle ABC is plotted: A at (2, −1), B at (5, 0) on the x-axis, and C at (4, 3). Sides AB, BC and CA are drawn.", "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q4ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(i)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Aileen took part in an adventure race. The race included a run, a cycle, and a mountain climb. The graph shows Aileen's distance from the start line, along the route travelled, during the race. Use the information in the graph to answer (a)(i) to (a)(iv). What was the total distance of the race?", "has_images": true, "image_notes": "Distance–time line graph. x-axis 'Time (minutes)' from 0 to 130 (marked every 10). y-axis 'Distance from start line (km)' marked 4, 8, 12, 16, 20, 24, 28, 32. The graph rises in three segments labelled 'run', 'cycle' (steeper), and 'climb', with a flat (horizontal) section between cycle and climb indicating a stopped break. The run reaches about 8 km by ~40 min, the cycle rises to about 24 km by ~80 min, a flat break, then the climb rises to about 32 km by ~130 min.", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q4aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(ii)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Aileen stopped for a break after the cycle. For how many minutes was she stopped?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q4aiii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(iii)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Aileen started the race at 9:00 a.m. At what time did she finish the race?", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q4aiv", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(a)(iv)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "In which part of the race was Aileen travelling the fastest? (Tick one box only: run, cycle, climb.) Give a reason for your answer based on the information in the graph.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q4b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "The equation of the line AC is y = 2x + k, where k ∈ ℤ. Find the value of k.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q4bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)(i)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Aileen completed the climb in 30 minutes. Write 30 minutes as a fraction of an hour. Answer:", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q4bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(b)(ii)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "The distance of the climb was 4 km. Work out Aileen's average speed for the climb, in km/hour.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q4c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Without measuring the diagram, investigate if the triangle ABC is an isosceles triangle. Use calculations to support your answer. Hint: It might be useful to find the distance |AB|. Triangle ABC is an isosceles triangle: True / False (Tick (✓) one box only).", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q4d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "The triangle A'B'C' is the image of the triangle ABC under central symmetry in the origin (0, 0). Draw and label the triangle A'B'C' on the co-ordinate diagram on the previous page.", "has_images": true, "image_notes": "Refers back to the coordinate diagram from part (a): triangle ABC with A(2, −1), B(5, 0), C(4, 3) on axes x: −6 to 6, y: −5 to 5. Student must plot the image under central symmetry in the origin.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q5a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "Viktoria is 9 years old and Senan is 11 years old. €120 is divided between them in the ratio of their ages. How much money does Viktoria get?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q5a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "Square A has sides of length of 5 cm. Work out the area of square A, in cm^2.", "has_images": true, "image_notes": "A small square labelled A with one side marked 5 cm.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q5b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "The distance from the Sun to Mars is approximately 250 million km. Light travels at a speed of approximately 300 000 km per second. Use this to work out the time it takes light to travel from the Sun to Mars. Give your answer in minutes, correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q5b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "Square B has a perimeter of 64 cm. Work out the length of one side of square B, in cm.", "has_images": true, "image_notes": "A square labelled B (no side lengths marked on the diagram).", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q5c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(c)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "Rectangle C has length (2x + 3) and width (x + 5). Multiply out and simplify the following expression for the area of rectangle C. Area = (2x + 3)(x + 5)", "has_images": true, "image_notes": "A rectangle labelled C with length marked (2x + 3) along the top and width marked (x + 5) along the left side.", "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q5di", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(d)(i)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "A triangle is shown on the diagram below. One of the sides has been extended. The sizes of two of the angles are given. Two other angles are marked X and Y. Find the size of the angle X and the size of the angle Y, without measuring. |∠X| = |∠Y| =", "has_images": true, "image_notes": "A triangle with one base side extended to the right past the bottom-right vertex. The bottom-left interior angle is marked 55°. The top vertex angle is marked Y. The bottom-right interior angle is marked X, and the exterior angle formed by the extended side at that vertex is marked 120°.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q5dii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "5(d)(ii)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "State whether the triangle in the diagram above is isosceles, scalene, or equilateral. (Tick one box only: Isosceles, Scalene, Equilateral.) Give a reason for your answer.", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q6a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "A mapping diagram of the function f(x) = 2x + 1 is shown below. Fill in the three missing entries into the diagram below.", "has_images": true, "image_notes": "A mapping (arrow) diagram for f(x) = 2x + 1. Left set (x) lists inputs 1, 3, −2 and one blank box. Right set lists outputs 3, 5, two blank boxes, and 11. Arrows map each input to its output; three entries (one input box and two output boxes) are missing and must be filled.", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q6a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "Alex uses sticks to make a sequence of patterns. The first three patterns in her sequence are shown. Draw Pattern 4 in the sequence.", "has_images": true, "image_notes": "Three stick patterns made of vertical and horizontal segments forming open-topped 'U' shapes joined side by side. Pattern 1 is a single U (3 sticks). Pattern 2 is two joined U-cells (5 sticks). Pattern 3 is three joined U-cells (7 sticks). Each new pattern adds one cell (2 more sticks).", "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q6b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "Which of the following diagrams does not represent a function from set A to set B? Give a reason for your answer. Which is not a function? Diagram 1 / Diagram 2 (Tick (✓) one box only). Reason: ____.", "has_images": true, "image_notes": "Two arrow/mapping diagrams labelled Diagram 1 and Diagram 2, each mapping elements of set A to set B. One of the diagrams has an element of A mapped to more than one element of B (or an element with no/multiple arrows) so it is not a function; the student must identify which and explain.", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q6b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "Complete the table below to show the number of sticks in each of the first five patterns. One is already done for you.", "has_images": true, "image_notes": "Table with row 'Pattern' (columns 1, 2, 3, 4, 5) and row 'Number of Sticks'. The Number of Sticks cell for Pattern 2 is already filled in as 5; the others (Patterns 1, 3, 4, 5) are blank.", "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q6c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(c)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "Pattern 150 has 301 sticks. How many sticks has Pattern 151?", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q6d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(d)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "What kind of sequence is made by the number of sticks in each pattern? Give a reason for your answer. (Tick one box only: linear / non-linear.)", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q6ei", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(e)(i)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "The number of sticks in Pattern n is: 2n + 1. Use this to work out the number of sticks in Pattern 38 (when n = 38).", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q6eii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "6(e)(ii)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "One of the patterns in the sequence, Pattern k, has exactly 27 sticks. Find the value of k.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q7ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "A group of students (U) were given three maths problems to solve: an algebra problem (A), a geometry problem (G), and a probability problem (P). The Venn diagram below shows the number of students who solved some of the different types of problem. For example, 4 students solved the algebra problem (A) only. Some of the values are given in terms of x and y, where x, y ∈ ℕ. Three values are missing. One of the regions of the Venn diagram has x students. Write a statement describing exactly which problems these students solved.", "has_images": true, "image_notes": "Three-circle Venn diagram (sets A, G, P) inside a universal set U. Labelled regions: A-only = 4; the region where A and P overlap (but not G) = y; the central region (A ∩ G ∩ P) = x; the region for G and P overlap = y (lower); P region also shows 3; the diagram has some regions blank. Region marked 'x' is the intersection of all three sets (A ∩ G ∩ P).", "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q7ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Passengers are waiting to board an aeroplane. Each passenger has one bag and their bag is weighed. The results are shown in the following frequency table. [Note: 7 − 8 means 7 kg or more, but less than 8 kg, and so on.] Work out the total number of passengers.", "has_images": true, "image_notes": "Frequency table. Row 'Weight of bag (kg)': intervals 7−8, 8−9, 9−10, 10−11, 11−12, 12−13. Row 'Number of passengers': 20, 47, 61, 30, 12, 10 respectively.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q7aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Use the following information to fill in the three missing values in the Venn diagram: 2 students solved all three problems; 2x students solved the geometry problem only; 7 students solved both the algebra problem and the geometry problem.", "has_images": true, "image_notes": "Refers to the same three-circle Venn diagram (A, G, P) from part (a)(i). Student fills in three missing region values using the given facts: A∩G∩P = 2, G-only = 2x, and the count solving both algebra and geometry = 7.", "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q7aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Passengers are charged an extra fee if their bag weighs more than 10·5 kg. What is the greatest number of passengers who could have been charged the extra fee?", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q7bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(i)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "#(A ∪ G) = 29 and #P = 13. Use this information to show that the following two equations are true: 3x + y = 18 and x + 2y = 11.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q7bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(i)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "A family of 5 are travelling together. The weights of their 5 bags (in kg) are: 9·9, 8·6, 7·2, 9·8, 9·0. Work out the mean weight of the 5 bags, in kg.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q7bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(ii)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Solve these simultaneous equations to find the value of x and the value of y. 3x + y = 18; x + 2y = 11. x = ____; y = ____.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q7bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(b)(ii)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Work out the median weight of the 5 bags, in kg. (Bag weights: 9·9, 8·6, 7·2, 9·8, 9·0.)", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q7c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(c)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Each flight costs the same. The total cost of the 5 flights is €756·40. This includes a single fee of €21·40 for travel insurance. Work out the cost of one flight (excluding the travel insurance).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q7d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "7(d)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "The family change €400 into sterling. The exchange rate is €1 = £0·89 sterling. Work out how much sterling they get.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q8a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "The triangle ABC is shown in the co-ordinate diagram below. Complete the table below to show the co-ordinates of the points A, B, and C.", "has_images": true, "image_notes": "Coordinate grid with x-axis and y-axis from -4 to 4. Triangle ABC drawn (shaded green): A at (1, 1), B at (3, 1), C at (2, 4). A and C are vertical (x = 2 for C, between A and B on the base). The answer table 'Point' / 'Co-ordinates' shows A = (1, 1) pre-filled; B and C are blank.", "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q8ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "During an experiment, the number of bacteria in a sample can be modelled by the function: b(t) = 10(2^t), where b(t) is the number of bacteria t hours after the start of the experiment, with 0 ≤ t ≤ 24, t ∈ ℝ. Complete the table below to show the number of bacteria for the first 4 hours of the experiment.", "has_images": true, "image_notes": "Table: Time, t (hours) = 0, 1, 2, 3, 4 across the top; Number of bacteria, b(t) row mostly blank with the value 80 already entered under t = 3. Student completes the remaining cells using b(t) = 10(2^t).", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q8aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Hence, draw the graph of the function b(t) in the domain 0 ≤ t ≤ 4, t ∈ ℝ.", "has_images": true, "image_notes": "Blank axes provided: x-axis labelled 'Time, t (hours)' from 0 to 4, y-axis labelled 'Number of bacteria, b(t)' from 0 to 180 in steps of 20.", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q8b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "How many axes of symmetry does the triangle ABC have? (Tick one box only: 0, 1, 2, 3.)", "has_images": false, "image_notes": null, "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q8bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)(i)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Use your graph to answer parts (b)(i) and (b)(ii). Estimate the number of bacteria 2·5 hours after the start of the experiment. Show your work on the graph.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q8bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(b)(ii)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Estimate how many hours it takes until there are 120 bacteria. Show your work on the graph. Give your answer correct to 1 decimal place.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q8c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "What kind of pattern is made by the number of bacteria in the table on the previous page? Give a reason for your answer. Answer (Tick (✓) one box only): Linear / Quadratic / Exponential / None of these. Reason: ____.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q8c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "On the diagram above, draw the image of ABC under axial symmetry in the x-axis.", "has_images": true, "image_notes": "Refers to the coordinate diagram from part (a) with triangle ABC (A(1,1), B(3,1), C(2,4)); student draws the reflection of the triangle in the x-axis.", "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q8d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "What is the number of bacteria 24 hours after the start of the experiment, according to the function b(t) = 10(2^t)? Give your answer in the form a × 10^n, where 1 ≤ a < 10 and n ∈ ℕ. Write a correct to 3 significant figures.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q8d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Work out the area of the triangle ABC.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q8e", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "8(e)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "The slope of the line AC is 3. Use this to find the equation of the line AC. Give your answer in the form y = mx + c.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q9a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Solve the equation 2x^2 + 7x − 3 = 0. Give each answer correct to 2 decimal places.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q9a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Sarah has a gross income of €550 per week. Sarah pays income tax at 20%. Work out Sarah's gross tax for one week.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q9b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Write the following expression as a single fraction in its simplest form: 3/(x + 1) − 4/x", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q9b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Sarah's weekly tax credit is €78. Work out Sarah's net tax for one week.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-EV-q9c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "g(x) is the function g(x) = ax^2 + bx + c, where a, b, and c are constants. The graph of y = g(x) cuts the x-axis at the points (−3, 0) and (−2, 0). It also cuts the y-axis at the point (0, 12). Use this to find the value of a, the value of b, and the value of c. a = ____; b = ____; c = ____.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level - Exam Paper.pdf" }, { "id": "2026-ordinary-level-EV-q9c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "EV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Work out Sarah's net income for one week.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Ordinary Level - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q1a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(a)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "I gcluiche, rothlaítear rothlóir cóir agus caitear disle cóir séshleasach. Tá trí theascóg dhaite chothroma ar an rothlóir: dearg (D), buí (B), agus gorm (G). Comhlánaigh an tábla thíos chun gach ceann de na 18 bhfothoradh a d'fhéadfadh a bheith ar an gcluiche a thaispeáint. Tá dhá cheann déanta duit cheana. Ciallaíonn D3 dearg ar an rothlóir agus 3 ar an disle, mar shampla.", "has_images": true, "image_notes": "A pie-chart spinner divided into three equal coloured sectors labelled D (dearg/red), B (buí/yellow), G (gorm/green), shown beside a red six-sided die. Below is an outcome table (sample space): rows labelled Rothlóir = D, B, G; columns of the Disle = 1, 2, 3, 4, 5, 6. Two cells are pre-filled: D3 (row D, column 3) and G5 (row G, column 5). Students complete the remaining 16 cells.", "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q1bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(i)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá gach ceann de na torthaí sa tábla chomh dóchúil lena chéile. Imrítear an cluiche uair amháin. Faigh an dóchúlacht gurb é an fothoradh ná: dearg ar an rothlóir.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q1bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "1(b)(ii)", "parent_question": "1", "marks": null, "marks_confidence": "uncertain", "question_text": "Faigh an dóchúlacht gurb é an fothoradh ná: gorm ar an rothlóir agus ré-uimhir ar an disle.", "has_images": false, "image_notes": null, "topic": "Probability", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q10ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(i)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "Sa dá ghreille thíos, tá sleasa 1 cm ar fad ar gach ceann de na cearnóga beaga. Ar an ngreille thíos, tarraing cearnóg a bhfuil imlíne 12 cm aici.", "has_images": true, "image_notes": "A blank centimetre grid (squares of side 1 cm). Student draws a square with perimeter 12 cm (i.e. side 3 cm).", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q10aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(a)(ii)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá dronuilleog ann atá l cm ar fad agus w cm ar leithead, áit ar slánuimhreacha l agus w. Tá achar 10 cm^2 ag an dronuilleog freisin. Tarraing dronuilleog amháin den sórt sin ar an ngreille thíos.", "has_images": true, "image_notes": "A blank centimetre grid (1 cm squares). Student draws a rectangle with integer length l and width w whose area is 10 cm^2 (e.g. 2 by 5 or 1 by 10).", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q10bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)(i)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá bonn triantáin k cm ar fad agus tá an triantán h cm ar airde ingearach. Is é 4h cm^2 achar an triantáin. Faigh luach k.", "has_images": true, "image_notes": "A triangle drawn with horizontal base labelled k (at the bottom), vertical height labelled h (a vertical arrow up the side), and the area written inside as 'Achar: 4h cm^2'.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q10bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "10(b)(ii)", "parent_question": "10", "marks": null, "marks_confidence": "uncertain", "question_text": "Is é an triantán sin a dhéanann tosach agus cúl priosma triantánaigh, mar a thaispeántar thíos. Tá an priosma (h + 4) cm ar fad. Is é 240 cm^3 toirt an phriosma. Oibrigh amach luach h, airde ingearach an triantáin.", "has_images": true, "image_notes": "A triangular prism whose triangular end-face is the triangle from part (i) (Achar: 4h cm^2), with the length of the prism labelled (h + 4) cm. The prism has volume 240 cm^3.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q11a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(a)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Dhear scoil rampa cathaoireacha rothaí nua don bhealach isteach sa scoil, mar a thaispeántar sa léaráid thíos. Tá an rampa 40 cm ar airde ingearach agus 6 m ar fad cothrománach. Is é |BC|/|AB| fána an rampa. Is é 1/12 an fhána uasta a mholtar don chineál seo rampa cathaoireacha rothaí. An bhfuil an rampa cathaoireacha rothaí seo de réir an mhola sin? Déan ríomh chun tacú le do fhreagra. Freagra (Cuir tic (✓) i mbosca amháin): Tá / Níl. Ríomh:", "has_images": true, "image_notes": "A right-angled triangle representing a wheelchair ramp: horizontal base A to B = 6 m, vertical rise at the right side BC = 40 cm (right angle at B), with the slope angle θ marked at A. C is at the top right, B at the bottom right. Slope = |BC|/|AB|.", "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q11b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(b)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Faigh |AC|, fad claonadh an rampa. Bíodh do fhreagra in cm, ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q11c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(c)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Bain úsáid as an triantánacht chun méid na huillinne a bhfuil θ marcáilte uirthi sa léaráid ar an leathanach roimhe seo a oibriú amach. Bíodh do fhreagra ina chéimeanna, ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q11d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "11(d)", "parent_question": "11", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá an dearadh seo a leanas ar rampa eile sa scoil. Oibrigh amach luach x, airde ingearach an rampa. Bíodh do fhreagra ceart go dtí an cm is gaire.", "has_images": true, "image_notes": "A right-angled triangle PQR (ramp): the long top side PR = 7·5 m, the angle at P = 2·9°, vertical rise x = |RQ| at the right with the right angle at Q. Student finds x (the vertical height).", "topic": "Trigonometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q12a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(a)", "parent_question": "12", "marks": null, "marks_confidence": "uncertain", "question_text": "Taispeántar sa léaráid thíos ciorcal a bhfuil an lárphointe O aige. Tá na trí phointe, R, S, agus T, ar an gciorcal. Tá uillinn a agus uillinn b marcáilte ar an léaráid. |∠TOS| = 96°. |∠OTR| = 20°. Oibrigh amach méid uillinn a agus méid uillinn b. a = ___ b = ___", "has_images": true, "image_notes": "A circle with centre O and three points R, S, T on the circumference. Chords/lines RT and SO (and OT, OS) are drawn. The central angle ∠TOS = 96°; the angle ∠OTR = 20° at T. Angle a is at O (between OS and OT region, near centre) and angle b is at R. Student finds a and b using circle angle theorems.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q12b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "12(b)", "parent_question": "12", "marks": null, "marks_confidence": "uncertain", "question_text": "Sa triantán ABC: |AB| = 8 cm, |∠CAB| = 70°, |∠ABC| = 50°. Tóg an triantán ABC sa bhosca thíos. Tá pointe A tugtha. Lipéadaigh pointe B agus pointe C ar do léaráid. Taispeáin do chuid línte tógála go léir go soiléir.", "has_images": true, "image_notes": "A construction box with point A pre-marked on a horizontal ray near the bottom left. Student constructs triangle ABC where |AB| = 8 cm, angle CAB = 70°, angle ABC = 50°, labelling B and C and showing construction lines.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q13", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "13", "parent_question": "13", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá sorcóir 24 cm ar airde agus ga r cm aige, áit a bhfuil r ∈ ℝ. Is dronuilleog í eangach dhromchla cuartha an tsorcóra, agus fad trasnánach 37·6 cm aici. Bain úsáid as sin chun luach r a fháil, ceart go dtí ionad deachúlach amháin.", "has_images": true, "image_notes": "A cylinder of height 24 cm with radius r is shown, with an arrow to its unrolled curved surface (net) drawn as a rectangle. The rectangle has a diagonal labelled 37·6 cm. The rectangle's height equals the cylinder height 24 cm and its width equals the circumference 2πr; the diagonal of 37·6 cm links them via Pythagoras.", "topic": "Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q2ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(i)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Fiafraíodh de 60 scoláire cé mhéad ama a chaith siad ar an bhfón ar lá áirithe. Taispeántar na torthaí sa tábla minicíochta thíos. [Nóta: Is é is ciall le 2 – 4 ná 2 uair an chloig nó níos mó, ach níos lú ná 4 uair an chloig, agus mar sin de.] Úsáid an t-eolas sa tábla chun na codanna (a)(i), (a)(ii), agus (a)(iii) a fhreagairt. Tarraing histeagram chun an t-eolas sa tábla a thaispeáint. Úsáid na haiseanna agus na scálaí thíos.", "has_images": true, "image_notes": "Frequency table: top row 'Am (uaireanta an chloig)' with class intervals 0–2, 2–4, 4–6, 6–8, 8–10; bottom row 'An líon scoláirí' with frequencies 21, 20, 14, 4, 1. A blank histogram grid is provided: x-axis 'Am (uaireanta an chloig)' marked 0,2,4,6,8,10; y-axis 'An líon scoláirí' marked 0 to 22 in steps of 2. A small smartphone icon appears beside the table.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q2aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(ii)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Faigh an t-uasluach scoláirí a d'fhéadfadh níos lú ná 3 uair an chloig a chaitheamh ar an bhfón.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q2aiii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(a)(iii)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Bain úsáid as lárluachanna eatraimh chun meastachán a dhéanamh ar an meánmhéid ama a chaith an 60 scoláire ar an bhfón. Bíodh do fhreagra ina uaireanta an chloig, ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q2b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "2(b)", "parent_question": "2", "marks": null, "marks_confidence": "uncertain", "question_text": "Fiafraíodh freisin den 60 scoláire cad é an úsáid is coitianta a bhaineann siad as an bhfón. Taispeántar na torthaí sa tábla thíos. Críochnaigh an phíchairt thíos chun an t-eolas sa tábla thuas a thaispeáint. Lipéadaigh gach teascóg agus méid gach uillinne go soiléir. Taispeáin aon oibriú amach.", "has_images": true, "image_notes": "Table 'An úsáid is coitianta' with categories: Meáin Shóisialta = 30, Sruthú Físeán = 10, Cluichíocht = 6, Teachtaireacht = 14 (total 60 students). A blank circle with a marked centre and one radius drawn is provided for the pie chart.", "topic": "Statistics", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q3ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(i)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá Martina ag ceannach carr nua as an Ríocht Aontaithe. £21 250 steirling atá ar an gcarr. Is é an ráta malairte ná €1 = £0·85 steirling. Taispeáin gurb é €25 000 praghas an chairr ina euro.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q3aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(a)(ii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Íocann Martina táille custaim €3375. Scríobh an táille sin mar chéatadán de €25 000.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q3bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)(i)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá ioncam bliantúil comhlán €50 000 ag Martina. Íocann Martina cáin ioncaim ar a hioncam comhlán de réir na rátaí sa tábla thíos. [Ioncam Bliantúil: An chéad €40 000 ar Ráta Cánach 20%; Iarmhéid ar Ráta Cánach 40%.] Oibrigh amach cáin ioncaim bhliantúil Martina de réir gach ceann den dá ráta sin (20% agus 40%).", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q3bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)(ii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá creidmheasanna cánach bliantúla €3300 ag Martina. Oibrigh amach glanioncam bliantúil Martina.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q3biii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "3(b)(iii)", "parent_question": "3", "marks": null, "marks_confidence": "uncertain", "question_text": "Tugadh ardú pá do Martina agus tháinig méadú €4800 ar a glanioncam bliantúil. Oibrigh amach ioncam bliantúil comhlán nua Martina.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q4a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(a)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Taispeántar triantán ABC sa léaráid chomhordanáideach thíos. Tá na comhordanáidí (2, −1) ag pointe A. Scríobh comhordanáidí phointe B agus phointe C sna spásanna thíos. B = ( , ) C = ( , )", "has_images": true, "image_notes": "A coordinate diagram (x-axis −6 to 6, y-axis −5 to 5) showing triangle ABC. Vertices read from grid: A = (2, −1), B = (5, 0), C = (4, 3).", "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q4b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(b)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Is é cothromóid líne AC ná y = 2x + k, áit a bhfuil k ∈ ℤ. Faigh luach k.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q4c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(c)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Fiosraigh, gan an léaráid a thomhas, cé acu is triantán comhchosach é triantán ABC nó nach ea. Déan ríomh chun tacú le do fhreagra. Leid: B'fhéidir go mbeadh sé úsáideach fad |AB| a fháil. Is triantán comhchosach é triantán ABC: Fíor / Bréagach (Cuir tic (✓) i mbosca amháin).", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q4d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "4(d)", "parent_question": "4", "marks": null, "marks_confidence": "uncertain", "question_text": "Is é triantán A'B'C' íomhá thriantán ABC faoi shiméadracht lárnach sa bhunphointe (0, 0). Tarraing agus lipéadaigh triantán A'B'C' ar an léaráid chomhordanáideach ar an leathanach roimhe seo.", "has_images": false, "image_notes": null, "topic": "Coordinate Geometry", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q5a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(a)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "Tá Viktoria 9 mbliana d'aois agus tá Seanán 11 bhliain d'aois. Roinneadh €120 eatarthu i gcóimheas a n-aoise. Cé mhéad airgid a fuair Viktoria?", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q5b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "5(b)", "parent_question": "5", "marks": null, "marks_confidence": "uncertain", "question_text": "Is é an fad idir an Ghrian agus Mars ná thart ar 250 milliún km. Taistealaíonn solas ar luas thart ar 300 000 km sa soicind. Úsáid é sin chun an t-am a thógann sé ar sholas taisteal ón nGrian go Mars a oibriú amach. Bíodh do fhreagra in nóiméid, ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q6a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(a)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "Taispeántar thíos léaráid mhapála den fheidhm f(x) = 2x + 1. Líon isteach na léaráid thíos na trí iontráil atá in easnamh.", "has_images": true, "image_notes": "A mapping (arrow) diagram for f(x) = 2x + 1. Left oval (domain x) lists inputs 1, 2, 3, −2 (one input box blank/missing). Right oval lists outputs 3, 5, 11 with two output boxes blank. Arrows map inputs to outputs; three entries are missing for the student to fill in.", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q6b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "6(b)", "parent_question": "6", "marks": null, "marks_confidence": "uncertain", "question_text": "Cé acu ceann de na léaráidí seo a leanas nach léirítear feidhm ó thacar A go tacar B inti? Tabhair cúis le do fhreagra. Cé acu ceann nach feidhm é? (Cuir tic (✓) i mbosca amháin): Léaráid 1 / Léaráid 2. Cúis:", "has_images": true, "image_notes": "Two arrow/mapping diagrams, Léaráid 1 and Léaráid 2, each mapping elements of set A to set B with dots and arrows. In one diagram a single element of A maps to two elements of B (so it is not a function); in the other each element of A maps to exactly one element of B. Student identifies which is not a function and gives a reason.", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q7ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(i)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Tugadh trí fhadhb mhatamaitice do ghrúpa scoláirí (U) lena réiteach: fadhb ailgéabair (A), fadhb chéimseata (C), agus fadhb dhóchúlachta (D). Taispeántar sa léaráid Venn thíos an líon scoláirí a réitigh roinnt de na cineálacha éagsúla faidhbe. 4 scoláirí a réitigh an fhadhb ailgéabair (A) agus an fhadhb sin amháin, mar shampla. Tugtar roinnt de na luachanna i dtéarmaí x agus y, áit a bhfuil x, y ∈ ℕ. Tá trí luach in easnamh. Tá x scoláirí i gceann amháin de na réigiúin sa léaráid Venn. Scríobh ráiteas a chuireann in iúl go díreach cé acu de na fadhbanna a réitigh na scoláirí sin.", "has_images": true, "image_notes": "A three-set Venn diagram inside a universal set U with circles labelled A, C, D. Region values shown: 4 in A only; 'y' in the A∩C overlap region; 'x' in the C∩D overlap region; 'y' in the D-only region; 3 in C only (region near C/right). Three values are missing. The 'x' region asked about is the intersection region containing x.", "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q7aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(a)(ii)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Úsáid an t-eolas seo a leanas chun na trí luach atá in easnamh a líonadh isteach sa léaráid Venn thuas: 2 scoláirí a réitigh gach ceann de na trí fhadhb; 2x scoláirí a réitigh an fhadhb chéimseata, agus an fhadhb sin amháin; 7 scoláirí a réitigh an fhadhb ailgéabair agus an fhadhb chéimseata araon.", "has_images": false, "image_notes": null, "topic": "Number", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q7bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)(i)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "#(A ∪ C) = 29 agus #D = 13. Úsáid an t-eolas sin chun a thaispeáint go bhfuil an dá chothromóid seo a leanas fíor: 3x + y = 18 agus x + 2y = 11.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q7bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "7(b)(ii)", "parent_question": "7", "marks": null, "marks_confidence": "uncertain", "question_text": "Réitigh na cothromóidí comhuaineacha seo chun luach x agus luach y a fháil: 3x + y = 18; x + 2y = 11. x = ___ y = ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q8ai", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(i)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Le linn turgnaimh, is féidir líon na baictéar i sampla a shamhltú de réir na feidhme: b(t) = 10(2^t), áit arb é b(t) an líon baictéar t uair an chloig tar éis thús an turgnaimh, agus 0 ≤ t ≤ 24, t ∈ ℝ. Comhlánaigh an tábla thíos chun an líon baictéar a bheidh ann sa linn na chéad 4 uair an chloig den turgnamh a thaispeáint.", "has_images": true, "image_notes": "Table with top row 'Am, t (uaireanta an chloig)' values 0, 1, 2, 3, 4 and bottom row 'An líon baictéar, b(t)' partly filled: the value 80 is shown under t = 3; the cells for t = 0, 1, 2, 4 are blank for the student to complete using b(t) = 10(2^t).", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q8aii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(a)(ii)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Uaidh sin, tarraing an graf den fheidhm b(t) san fhearann 0 ≤ t ≤ 4, t ∈ ℝ.", "has_images": true, "image_notes": "A blank graph grid is provided: x-axis 'Am, t (uaireanta an chloig)' marked 0 to 4; y-axis 'An líon baictéar, b(t)' marked 0 to 180 in steps of 20. Student plots the exponential curve b(t) = 10(2^t).", "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q8bi", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)(i)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Bain úsáid as do ghraf chun na codanna (b)(i) agus (b)(ii) a fhreagairt. Déan meastachán ar an líon baictéar a bheidh ann 2·5 uair an chloig tar éis thús an turgnaimh. Taispeáin do chuid oibre ar an ngraf.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q8bii", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(b)(ii)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Déan meastachán ar an líon uaireanta an chloig a thógfaidh sé go dtí go mbeidh 120 baictéar ann. Taispeáin do chuid oibre ar an ngraf. Bíodh do fhreagra ceart go dtí ionad deachúlach amháin.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q8c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(c)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Cén cineál patrúin a dhéanann líon na mbaictéar sa tábla ar an leathanach roimhe seo? Tabhair cúis le do fhreagra. Freagra (Cuir tic (✓) i mbosca amháin): Líneach / Cearnach / Easpónantúil / Ní ceann ar bith díobh. Cúis:", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q8d", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "8(d)", "parent_question": "8", "marks": null, "marks_confidence": "uncertain", "question_text": "Cad é an líon baictéar a bheidh ann 24 uair an chloig tar éis thús an turgnaimh, de réir na feidhme b(t) = 10(2^24)? Bíodh do fhreagra san fhoirm a × 10^n, áit a mbeidh 1 ≤ a < 10 agus n ∈ ℕ. Scríobh a ceart go dtí 3 fhigiúr bhunúsacha.", "has_images": false, "image_notes": null, "topic": "Functions", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q9a", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(a)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Réitigh an chothromóid 2x^2 + 7x − 3 = 0. Bíodh gach freagra ceart go dtí 2 ionad dheachúlacha.", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q9b", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(b)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Scríobh an slonn seo a leanas mar chodán aonair san fhoirm is simplí: 3/(x + 1) − 4/x", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" }, { "id": "2026-higher-level-IV-q9c", "subject_n": "Mathematics", "year": 2026, "paper": 0, "version": "IV", "material_type": "exampapers", "question_number": "9(c)", "parent_question": "9", "marks": null, "marks_confidence": "uncertain", "question_text": "Is é g(x) an fheidhm g(x) = ax^2 + bx + c, áit ar tairisigh iad a, b, agus c. Trasnaíonn graf y = g(x) an x-ais ag na pointí (−3, 0) agus (−2, 0). Trasnaíonn sé an y-ais freisin ag an bpointe (0, 12). Bain úsáid as sin chun luach a, luach b agus luach c a fháil. a = ___ b = ___ c = ___", "has_images": false, "image_notes": null, "topic": "Algebra", "marking_scheme_answer": null, "source_pdf": "2026 - Mathematics - Higher Level (Irish) - Exam Paper.pdf" } ]