pid string | question string | image string | decoded_image image | choices list | unit string | precision int64 | answer string | question_type string | answer_type string | query string | metadata string |
|---|---|---|---|---|---|---|---|---|---|---|---|
001 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/1.JPG | [] | 0 | **Roll No: 40, Page: 01**
**Question 1.a:** Given that triangle is equilateral with side $= a$
**Heron's Formula:**
$$\text{Area} = \sqrt{S(S-a)(S-b)(S-c)}$$
where $S$ = Semi-perimeter of the triangle, and $a, b, c$ are side lengths.
In this case, this is an equilateral triangle, so $a = b = c$
$$\text{Area} = \sq... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - Heron's formula", "visual_context_type": "handwritten notes", "grade": "9", "reasoning_skills": ["geometry", "Heron's formula", "equilateral triangle", "area calculation"]} | ||
002 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/2.JPG | [] | 0 | **Roll No: 40, Page: 02-03**
**Question 2.a:** Given
$a = 18$, $b = 10$ and perimeter $= 42$
$a + b + c = 18 + 10 + c = 42$
$18 + c = 42$
$c = 42 - 18 = 24$
$c = 24$ cm
By Heron's Formula
---
**Question 3.a:** Given that side lengths are
$a = 11$ m, $b = 6$ cm, $c = 15$ cm
Perimeter $= 11 + 6 + 15 = 32$ cm
Se... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - Heron's formula", "visual_context_type": "handwritten notes", "grade": "9", "reasoning_skills": ["geometry", "Heron's formula", "triangle", "area calculation"]} | ||
003 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/3.JPG | [] | 0 | **Roll No: 2, Page: 04**
$$= \sqrt{21 \times 3 \times 11 \times 7}$$
$$= \sqrt{21 \times 231}$$
$$= \sqrt{4851}$$
$$= 95$$
$$\text{Area} = 95 \text{ cm}^2$$
---
**Question 4b:** Given the ratios $= 12:17:25$
Perimeter $= 540$ cm
Let the common multiplier be $k$
Then actual sides are: $12k$, $17k$ and $25k$
$... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - triangle sides from ratio", "visual_context_type": "handwritten notes", "grade": "9", "reasoning_skills": ["geometry", "ratios", "perimeter", "algebraic manipulation"]} | ||
004 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/4.JPG | [] | 0 | **Roll No: 10, Page: 01**
**Question 6:** Given $a + b + c = 5$ and $ab + bc + ca = 16$
$$a^3 + b^3 + c^3 - 3abc = (a+b+c)((a+b+c)^2 - 3(ab+bc+ca))$$
$$= 5((5)^2 - 3(10))$$
$$= 5(-4)$$
$$= -20$$
---
**Question 7:** Given $\angle ABC = 69°$, $\angle ACB = 31°$
i) $\angle BAC$
In Triangle ABC (inside the circle)
... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "algebra and circle geometry", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["algebra", "cubic expressions", "circle theorems", "inscribed angles"]} | ||
005 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/5.JPG | [] | 0 | **Roll No: 06, Page: 01**
**Question 6:** Given $a+b+c = 5$ and $ab+bc+ca = 16$
$$a^3+b^3+c^3-3abc = (a+b+c)((a+b+c)^2-3(ab+bc+ca))$$
$$= 5((5)^2 - 3(16))$$
$$= 5(-4)$$
$$= -20$$
---
**Question 7:** Given $\angle ABC = 60°$, $\angle ACB = 30°$
i) $\angle BAC$
In Triangle ABC (inside the circle)
$$\angle BAC = 1... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "algebra and circle geometry", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["algebra", "cubic expressions", "circle theorems", "inscribed angles"]} | ||
006 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/6.JPG | [] | 0 | **Roll No: 04, Page: 02**
**Question 8:** Given $\angle A = 90°$ and $AB = AC$
$\triangle ABC$ is a right angled at A and $AB = AC$ (isosceles right triangle)
Thus $\angle B = \angle C$ and
$\angle B + \angle C = 90°$
$2\angle B = 90°$
$\angle B = \angle C = 45°$ | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - isosceles right triangle", "visual_context_type": "handwritten notes", "grade": "9", "reasoning_skills": ["geometry", "triangles", "angle properties", "isosceles triangle"]} | ||
007 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/7.JPG | [] | 0 | **Roll No: 06, Page: 05**
**Question 9:** Given $4x^3 + ax^2 + 6x - 5$
When divided by $(x-2)$
$P(x) = 4x^3 + 6x - 5$
$Q(x) = x^2 + 2x + 4$
Then remainder $= 2$
$P(2) = \frac{4(2)^3 + a(2)^2 + 6(2) \cdot 5}{4(2)^3 + 4a + 12 \cdot 5}$
Remainder with $a = -11$
$Q(2) = 8(-1) = -\frac{3}{4}$
So $a = -11$, Remainder... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "polynomial division and remainder theorem", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["algebra", "polynomials", "remainder theorem", "division"]} | ||
008 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/8.JPG | [] | 0 | **Roll No: 06, Page: 08**
**Question 10:** Given:
Line $l$ is the bisector of $\angle A$
$BP \perp l$ and on $l$
$BQ$ is any other arm of $\angle A$
To prove: $\triangle APB \cong \triangle AQB$
In $\triangle APB$ and $\triangle AQB$:
- $AB = AB$ (common side)
- $\angle PAB = \angle QAB$ (given, since $l$ is angle b... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - triangle congruence", "visual_context_type": "handwritten notes", "grade": "9", "reasoning_skills": ["geometry", "congruent triangles", "SAS congruency", "CPCT"]} | ||
009 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/9.JPG | [] | 0 | **Roll No: 06, Page: 02**
Divide polynomial by $(x-1)$
$f(x) = (x+1)(x+1)(x+1)$
$n = 2$, $n = -2+1$
---
**Question 12:** Given: Circle with centre O, chord $AB = CD$
To prove $\angle AOB = \angle COD$
In $\triangle AOB$ and $\triangle COD$:
- $OA = OC$ (radii)
- $OB = OD$ (radii)
- $AB = CD$ (given)
$\therefore... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "polynomial division and circle theorems", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["algebra", "polynomials", "circle geometry", "congruent triangles", "SSS congrue... | ||
010 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/10.JPG | [] | 0 | **Roll No: 06, Page: 03**
**Question 10.1:** Given $\triangle CBD$
$AB = AB$ (bisects) $\angle CD$
In $\triangle ABR$ and $\triangle ABD$:
- $AB = AB$ (common side)
- $\angle ABR = \angle ABD$ (given)
- $\angle CAB = \angle DAB$ (as AB is angle bisector)
$\triangle ABR \cong \triangle ABD$
$BC = BD$ (by CPCT)
---
... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry and polynomial evaluation", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["geometry", "congruent triangles", "polynomials", "function evaluation"]} | ||
011 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/11.JPG | [] | 0 | **Finding Rational Numbers Between Two Fractions**
Given rational numbers $\frac{3}{5}$ and $\frac{4}{5}$
Since we need to find five rational numbers,
Let's multiply the numerator and denominator of both by 6
First fraction: $\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$
Second fraction: $\frac{4}{5... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "number system - rational numbers", "visual_context_type": "handwritten notes", "grade": "8", "reasoning_skills": ["rational numbers", "fractions", "number line", "ordering"]} | ||
012 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/12.JPG | [] | 0 | **Roll No: 02, Page: 00**
**Multiple Choice Answers:**
1) (a)
2) (d)
3) (a)
4) (c)
5) (c)
---
**Question 6:**
**Diagram Description:** A circle with center O. Points A, B, C, D on the circle.
$\angle DAC = 180° - (\angle ABC + \angle ACB)$
$= 180° - (61° + 31°)$
$= 180° - 100°$
$= 80°$
$\angle DOC = 80°$ (angles ... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry and triangle angles", "visual_context_type": "handwritten notes with circle diagram", "grade": "10", "reasoning_skills": ["circle theorems", "inscribed angles", "triangle angle sum"]} | ||
013 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/13.JPG | [] | 0 | **Roll No: 04, Page: 04-05**
**Diagram Description:** A circle with center O. Points A, B on the circle with chords and radii marked.
Given: $AB = CD$
In $\triangle AOB$ and $\triangle COD$:
- $AO = CO$ (radii) ... (i)
- $OB = OD$ (radii) ... (ii)
- $AB = CD$ (given) ... (iii)
$\therefore \triangle AOB \cong \trian... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry - equal chords theorem", "visual_context_type": "handwritten notes with circle diagram", "grade": "9", "reasoning_skills": ["circle theorems", "congruent triangles", "SSS congruency", "C... | ||
014 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/14.JPG | [] | 0 | **Roll No: 12, Page: 05**
**Diagram Description:** A rhombus ABCD with diagonals AC and BD intersecting at point O.
$P(2) = 2(2)^3 + 3(2)^2 + 3(2) - 5 = 16 - 12 + 6 - 5 = 5$
$q = -3$, The remainder is 5
---
Given: $AC = BD$, $AB$ bisects $\angle A$
To prove: $\triangle ABC \cong \triangle ABD$
Proof:
- $AC = BD$... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - quadrilateral and triangle congruence", "visual_context_type": "handwritten notes with rhombus diagram", "grade": "9", "reasoning_skills": ["geometry", "congruent triangles", "SAS congruency"... | ||
015 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/15.JPG | [] | 0 | **Question 11:** $P(x) = 2x^3 + 5x^2 - 5x - 2$
$P(-1) = 2(-1)^3 + 5(-1)^2 - 5(-1) - 2 = -2 + 5 + 5 - 2 \neq 0$
$P(1) = 2(1)^3 + 5(1)^2 - 5(1) - 2 = 2 + 5 - 5 - 2 = 0$
$(x-1)$ is factor of $P(x)$
**Long Division:**
$= (x-1)(2x^2 + 7x + 2)$ | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "polynomial factorization", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["algebra", "polynomials", "factor theorem", "long division"]} | ||
016 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/16.JPG | [] | 0 | **Diagram Description:** A circle with center O, with points A, B, C, D on the circumference. Chords AB and CD are drawn.
Given: $AB = CD$
- $OA = OD$ (radii) ... (S)
- $OB = OC$ (radii) ... (S)
- $CD = AB$ (given) ... (S)
$\therefore \triangle AOB \cong \triangle COD$ by SSS congruency
By CPCT: $\angle AOB = \angl... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry - equal chords", "visual_context_type": "handwritten notes with circle diagram", "grade": "9", "reasoning_skills": ["circle theorems", "congruent triangles", "SSS congruency"]} | ||
017 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/17.JPG | [] | 0 | **Roll No: 02, Page: 06**
**Diagram 1:** Two triangles ABC and DBC sharing a common base BC.
**Question 10-a (i):** Given $AC = AB$
Proof: In $\triangle ABC$ and $\triangle ADB$:
- $AC = AB$ (given) ... (S)
- $\angle ABC = \angle ADB$ (given) ... (A)
- $AB = AB$ (common) ... (S)
$\therefore \triangle ABC \cong \tri... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "triangle congruence proofs", "visual_context_type": "handwritten notes with geometric diagrams", "grade": "9", "reasoning_skills": ["geometry", "congruent triangles", "SAS congruency", "SSS congruency",... | ||
018 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/18.JPG | [] | 0 | **Roll No: 04, Page: 02**
**Diagram Description:** A circle with inscribed angles. Points A, B, C marked on circumference.
**Question 7:** Given $\angle ABC = 69°$, $\angle ACB = 31°$
R.T.P: $\angle BDC$
In $\triangle ABC$:
$\angle ABC + \angle ACB + \angle BAC = 180°$ (angle sum property)
$\angle BAC = 180° - 90°... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry and triangle properties", "visual_context_type": "handwritten notes with circle diagram", "grade": "9", "reasoning_skills": ["circle theorems", "inscribed angles", "isosceles triangle", ... | ||
019 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/19.JPG | [] | 0 | **Roll No: 33, Page: 03**
**Diagram Description:** A circle with center O showing chords AB and CD.
**Question 11:** Trial and error method:
$g(1) = 2x^3 + 4x^2 - 5(1) + 8 = 2 + 4 - 5 - 8 = -2$
So, $(x-1)$ is a factor of $p(x)$
Synthetic division result: $q = -3$
---
**Question 12:** Given: $AB = CD$
R.T.P: $\a... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "polynomial factorization and circle geometry", "visual_context_type": "handwritten notes with circle diagram", "grade": "10", "reasoning_skills": ["polynomials", "factor theorem", "synthetic division", ... | ||
020 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/20.JPG | [] | 0 | **Roll No: 03, Page: 01**
**Diagram Description:** A circle with center O, showing points A, B, C, D on the circumference.
**Question 7:** Given: $\angle ABC = 69°$, $\angle ACB = 31°$
$\angle ABC + \angle BCA + \angle CAB = 180°$
$69° + 31° + \angle BAC = 180°$
$100° + \angle BAC = 180°$
$\angle BAC = 80°$
$\angle... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry - inscribed angles", "visual_context_type": "handwritten notes with circle diagram", "grade": "9", "reasoning_skills": ["circle theorems", "inscribed angles", "angle sum property"]} | ||
021 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/21.JPG | [] | 0 | **Roll No: 25, Page: 01**
1. d
2. c
3. a
4. d
5. c
---
**Question 7.6:** Given $c = 5$, $a + b + c = 5$, $ab + bc + ca = 10$
$$a^3 + b^3 + c^3 - 3abc = -25$$
$$(a+b+c)^3 + c^3 + 3ab(c+a+b) - 3abc = -25$$
$$(5)^3 + 2(0) - 3abc - 25$$
$$4 \cdot 5 - 3abc = -25$$
$$3abc = -25 - 4 \cdot 5$$
$$abc = -\frac{70}{3}$$ | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "algebraic identities", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["algebra", "cubic identities", "algebraic manipulation"]} | ||
022 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/22.JPG | [] | 0 | **Roll No: 12, Page: 01**
**Diagram Description:** Two triangles sharing a common vertex.
**Question 10:** Here
$AB = AB$ (common side) ... S
$\angle PAB = \angle QAB$ (as $l$ is angle bisector) ... A
$\angle APB = \angle AQB$ (angle) ... A
By ASA congruency rule:
$\triangle ABP \cong \triangle ABQ$
By CPCT: $BC = ... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "triangle congruence - ASA", "visual_context_type": "handwritten notes with triangle diagram", "grade": "9", "reasoning_skills": ["geometry", "congruent triangles", "ASA congruency", "CPCT"]} | ||
023 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/23.JPG | [] | 0 | **Roll No: 12, Page: 08**
**Diagram Description:** A right triangle with vertices labeled.
**Question 9:** Given: $\angle A = 90°$, $AB = BC$
Find: $\angle B$ and $\angle C$
So, if $AB = BC$ then $\angle B = \angle C$
We know that angles in a triangle add up to $180°$
$90° + 2\angle B = 180°$
$2\angle B = 90°$
... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - isosceles right triangle", "visual_context_type": "handwritten notes with right triangle diagram", "grade": "9", "reasoning_skills": ["geometry", "triangles", "angle sum property", "isosceles... | ||
024 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/24.JPG | [] | 0 | **Roll No: 22, Page: 05**
**Diagram Description:** Two intersecting lines with angle markings.
**Question 10:** i) Given: $l$ is bisector of $\angle AOB$, $\angle A = 60°$
BP is perpendicular to $l$ and $\angle APB = \angle AQB$
Prove: $\triangle APB \cong \triangle AQB$
In $\triangle APB$ and $\triangle AQB$:
- $... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry and polynomial evaluation", "visual_context_type": "handwritten notes with geometric diagram", "grade": "10", "reasoning_skills": ["geometry", "congruent triangles", "polynomials", "function ev... | ||
025 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/25.JPG | [] | 0 | **Diagram Description:** A circle with center O, with points A, B marked on circumference.
**Question 12:** R.T.P: Equal chords of a circle subtend equal angles at the center.
Proof: In $\triangle AOB$ and $\triangle POC$:
- $OA = OP(c)$ (S)
- $OB = OC$ (S)
- $AB = DC$ (S)
$\triangle AOB \cong \triangle DOC$ by SSS ... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry - equal chords theorem", "visual_context_type": "handwritten notes with circle diagram", "grade": "9", "reasoning_skills": ["circle theorems", "congruent triangles", "SSS congruency", "e... | ||
026 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/26.JPG | [] | 0 | **Roll No: 05**
**Diagram Description:** A right triangle ABC with angle markings.
**Question 8:** Given: $\triangle ABC$ is right angled at $\angle ABC = 90°$
Sum of all angles in a triangle $= 180°$
$\angle A + \angle B + \angle C = 180°$
Let $\angle B$ and $\angle C$ be $x$
$\angle A + x + x = 180°$
$= 2x + 18... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "triangle angles and polynomials", "visual_context_type": "handwritten notes with triangle diagram", "grade": "9", "reasoning_skills": ["geometry", "angle sum property", "polynomials"]} | ||
027 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/27.JPG | [] | 0 | **Roll No: 04, Page: 03**
$\Rightarrow x = \frac{q^2}{a} = 4k^2$
$\therefore l = l_1^2 = 2 + 4k^2$
$l = 3x^3 + 4a^2 + 3x - 5$
$\Rightarrow 8(3)^3 + 4a + 3(3) - 5$
$\Rightarrow 27 + 4a + 4 - 5$
$\Rightarrow 12 + 4a = 0$
$\frac{12}{3} = 4$
**(4)** $x = (8)^3 + (1)^2 - 8(1) + a$
$\Rightarrow 8 + 1 - 8 + a = 0$
$\Rig... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "polynomial problems", "visual_context_type": "handwritten notes with triangle diagram", "grade": "10", "reasoning_skills": ["algebra", "polynomials", "solving equations"]} | ||
028 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/28.JPG | [] | 0 | **Roll No: 05, Page: 02**
**Diagram 1:** A circle with center O showing inscribed angle theorem.
**Question 7.a:** Given: $\angle AOC = 60°$, $\angle AOB = 31°$, find $\angle DOC$
$\angle BOC = \angle BOC + \angle COD$
$180° = 60° + \angle COD$
$\angle DOC = 180° - 100° = 80°$
---
**Diagram 2:** A right triangle.
... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry and triangle angles", "visual_context_type": "handwritten notes with circle and triangle diagrams", "grade": "9", "reasoning_skills": ["circle theorems", "inscribed angles", "angle sum p... | ||
029 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/29.JPG | [] | 0 | **Roll No: 25, Page: 01**
**Question 11:** $P(x) = 2x^3 + 5x^2 - 5x - 2$
$P(1) = x - 1 = 0$, $x = 1$
$= 2(1)^3 + 5(1)^2 - 5(1) - 2 = 2 + 5 - 5 - 2 = 0$
$(x-1)$ is factor
$= (x-1)(2x^2 + 7x + 2)$
$a = 2, c = 2$
$\frac{-b + \sqrt{b^2 - 4ac}}{2a}$
$= \frac{-7 + \sqrt{(7)^2 - 4 \times 2 \times 2}}{2 \times 2}$
$= ... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "polynomial factorization and quadratic formula", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["algebra", "polynomials", "factor theorem", "quadratic formula"]} | ||
030 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/30.JPG | [] | 0 | **Roll No: 27, Page: 06**
**Diagram Description:** A circle with center O, showing equal chords AB and CD with radii drawn.
**Question 12:** R.T.P: $\angle AOB = \angle COD$
Proof: $AB = CD$ (given)
In $\triangle AOB$ and $\triangle DOC$:
- $OA = OC$ (radii of circle) ... (S)
- $OB = OD$ (radii of circle) ... (S)
... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry - equal chords theorem", "visual_context_type": "handwritten notes with circle diagram", "grade": "9", "reasoning_skills": ["circle theorems", "congruent triangles", "SSS congruency", "e... | ||
031 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/31.JPG | [] | 0 | **Roll No: 35, Page: 01**
1. a
2. d
3. a
4. c
5. c
**Question 6:**
$$a^3 + b^3 + c^3 - 3abc = (a+b+c)((a+b+c)^2 - (ab+bc+ac))$$
$$2 \cdot 5 - 20 = 5 \cdot a^2 + b^2 + c^2 + 2 \cdot 10$$
$$a^2 + b^2 + c^2 - 3ab = (-5)(-5) = -25$$
---
**Diagram Description:** A circle with center O showing inscribed angle theorem.
... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "algebraic identities and circle geometry", "visual_context_type": "handwritten notes with circle diagram", "grade": "10", "reasoning_skills": ["algebra", "cubic identities", "circle theorems", "inscribe... | ||
032 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/32.JPG | [] | 0 | **Roll No: 35, Page: 03**
**Diagram Description:** A rhombus ABCD with diagonals intersecting.
$17 + 4a = 0$
$P(x) = x^3 - 3x^2 - 2x + a = 0$
$(2)^3 - 3(1)^2 - 2(1) - a = 0$
$8 - 4 + 4 - a = 0$
$(-) 7 + 4a = 0$
$3a = 0$
$a = 2b$
---
**Question 10:** Given: $ABCD$ as a quadrilateral
In $\triangle ABC$ and $\trian... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "polynomial equations and quadrilateral congruence", "visual_context_type": "handwritten notes with quadrilateral diagram", "grade": "10", "reasoning_skills": ["algebra", "polynomials", "geometry", "cong... | ||
033 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/33.JPG | [] | 0 | **Roll No: 39, Page: 01**
**Diagram Description:** A rhombus ABCD with diagonals AC and BD intersecting at point O.
**Question 10:** Given: $ABCD$ $\rightarrow$ Quadrilateral, $AC = AD$, $AB$ Bisects $\angle A$
To prove: $\triangle ABC \cong \triangle ABD$
Proof: In $\triangle ACB$ and $\triangle ADB$:
- $AC = AD$ ... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "quadrilateral congruence and polynomials", "visual_context_type": "handwritten notes with quadrilateral diagram", "grade": "10", "reasoning_skills": ["geometry", "congruent triangles", "SAS congruency",... | ||
034 | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | images/34.JPG | [] | 0 | **Roll No: 06, Page: 06**
**Diagram Description:** A circle with center O showing two equal chords AB and CD.
**Question 12:** Equal chords of a circle subtend equal angles at the center.
Given: $AB = CD$
To prove: $\angle AOB \cong \triangle COD$
Proof: In $\triangle AOB$ and $\triangle DOD$:
- (S) $AB = CD$ (giv... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet including any diagrams. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "circle geometry and polynomial factorization", "visual_context_type": "handwritten notes with circle diagram", "grade": "10", "reasoning_skills": ["circle theorems", "SSS congruency", "polynomials", "fa... | ||
035 | Extract and describe all the mathematical content from this handwritten page including the histogram. | images/35.jpg | [] | 0 | **Histogram Analysis - Frequency Distribution of Surnames by Number of Letters**
**Graph Description:** A histogram showing frequency distribution of surnames based on number of letters.
**Axes:**
- X-axis: Number of letters (1 to 20)
- Y-axis: Frequency Density (0 to 30)
**Bar Data:**
| Class Interval | Frequency |... | free_form | text | Extract and describe all the mathematical content from this handwritten page including the histogram. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "statistics - histogram analysis", "visual_context_type": "handwritten histogram/bar graph", "grade": "10", "reasoning_skills": ["statistics", "histogram", "frequency distribution", "data interpretation"... | ||
036 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/36.jpg | [] | 0 | **Roll No: 13, Page No: 3**
**Question 26:** Assumes $5 + 2\sqrt{2} = \frac{p}{q}$
Rearranges: $2\sqrt{2} = \frac{p}{q} - 5$
Student writes: $\sqrt{2}$ becomes rational so contradiction
**Question 27:** Let zeroes $= 2k, 3k$
Sum $= -b = 5k$
Product $= c = 6k^2$
Forms equation: $x^2 - 5kx + 6k^2 = 0$
**Question 28:**... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "mixed mathematics problems", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["irrational numbers", "quadratic equations", "arithmetic progression", "coordinate geometry",... | ||
037 | Extract and describe all the mathematical content from this handwritten page including the bar graph. | images/37.jpg | [] | 0 | **Roll No: 14, Page: 04**
**Bar Graph: Female Fatality Rate by Cause (Ages 15-44)**
**Axes:**
- X-axis: Causes of fatality
- Y-axis: Female Fatality Rate (%) - scale 0 to 30
**Data:**
| Cause | Fatality Rate (%) |
|-------|------------------|
| Reproductive health conditions | 33.1 |
| Other causes | 25.4 |
| Injuri... | free_form | text | Extract and describe all the mathematical content from this handwritten page including the bar graph. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "statistics - bar graph analysis", "visual_context_type": "handwritten bar graph", "grade": "10", "reasoning_skills": ["statistics", "bar graph", "data interpretation", "percentages"]} | ||
038 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/38.jpg | [] | 0 | **Roll No: 13, Page No: 4**
**Question 32:** $R(x) = dx + e$
For $x = \sqrt{3}$: $d\sqrt{3} + e = 7$
For $x = -\sqrt{3}$: $-d\sqrt{3} + e = -1$
Finds $d = 1$, $e = 6$
**Question 33:** "All altitudes create right angles so triangles share AA similarity"
**Question 34:** $TSA = 2\pi rh + 2\pi r^2$
Replaces $h = 2r$ $\... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "mixed mathematics - geometry, statistics, trigonometry", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["polynomials", "triangle similarity", "surface area", "statistics... | ||
039 | Extract and describe all the mathematical content from this handwritten page including the line graph. | images/39.jpg | [] | 0 | **Frequency Polygon - Runs Scored Comparison (Team A vs Team B)**
**Axes:**
- X-axis: Class Mark (No. of Balls) - 3.5, 9.5, 15.5, 21.5, 27.5, 33.5, 39.5, 45.5, 51.5, 57.5
- Y-axis: Runs Scored (Frequency) - scale 0 to 10
**Legend:**
- Solid line with circles: Team A
- Dashed line with squares: Team B
**Data Points:*... | free_form | text | Extract and describe all the mathematical content from this handwritten page including the line graph. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "statistics - frequency polygon", "visual_context_type": "handwritten frequency polygon/line graph", "grade": "10", "reasoning_skills": ["statistics", "frequency polygon", "data comparison", "graphical a... | ||
040 | Extract and describe all the mathematical content from this handwritten answer sheet showing partial fraction decomposition. | images/40.jpg | [] | 0 | **Partial Fraction Decomposition**
$\rightarrow$ Using Partial fraction decomposition:
$$\frac{n^2 + n + 1}{(n+2)(n^2+1)} = \frac{A}{n+2} + \frac{Bn+c}{n^2+1}$$
$\rightarrow n^2 + n + 1 = A(n^2+1) + (Bn+c)(n+2)$
$\rightarrow$ Substitute $n = -2$ to find $A$:
$4 - 2 + 1 = A(5)$
$3 = 5A \Rightarrow A = \frac{3}{5}$
... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet showing partial fraction decomposition. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "calculus - partial fractions and integration", "visual_context_type": "handwritten notes", "grade": "12", "reasoning_skills": ["calculus", "partial fractions", "integration", "algebraic manipulation", "... | ||
041 | Extract and describe all the mathematical content from this handwritten answer sheet about properties of squares. | images/41.jpg | [] | 0 | **Part (ii): Show that diagonal BD bisects $\angle B$ and $\angle D$**
**1. Diagonal of a Square:**
* In a square, the diagonals bisect each other at right angles and divide the angles into two equal parts.
**2. Angle $\angle B$ and $\angle D$ in the Square:**
* Since ABCD is a square, $\angle B = \angle D = 90°$
**... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet about properties of squares. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - properties of squares", "visual_context_type": "handwritten notes", "grade": "9", "reasoning_skills": ["geometry", "squares", "diagonals", "angle bisectors", "properties of quadrilaterals"]} | ||
042 | Extract and describe all the mathematical content from this handwritten answer sheet. | images/42.jpg | [] | 0 | **Roll No: 13, Page No: 2**
**Question 21:** $D = b^2 - 4ac$
Here $b = -(3+d)$, $a = 2$, $c = 1 + 2a$
"Equal roots" mean $D = a^2$, so $(3+a)^2 = 8(1+2a)$. Solved: $a = 1$
**Question 22:**
i) Squares look similar because all angles $= 90°$
ii) Rectangles $8 \times 12$ and $4 \times 6$ are similar since ratio $2:3$
ii... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "mixed mathematics", "visual_context_type": "handwritten notes", "grade": "10", "reasoning_skills": ["quadratic equations", "discriminant", "similarity", "arithmetic progression", "section formula", "tri... | ||
043 | Extract and describe all the mathematical content from this handwritten page including both graphs. | images/43.jpg | [] | 0 | **Page contains two graphs:**
---
**Graph 1: Bar Graph - Female Fatality Rate by Cause (Age 15-44)**
**Axes:**
- X-axis: Causes
- Y-axis: Fatality Rate (0-35)
**Data:**
- Reproductive conditions: ~33%
- Injuries: ~20%
- Neuropsychiatric conditions: ~15%
- Other causes: ~8%
- Cardiovascular conditions: ~5%
- Respira... | free_form | text | Extract and describe all the mathematical content from this handwritten page including both graphs. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "statistics and coordinate geometry", "visual_context_type": "handwritten bar graph and coordinate geometry diagram", "grade": "10", "reasoning_skills": ["statistics", "bar graph", "linear equations", "c... | ||
044 | Extract and describe all the mathematical content from this handwritten page showing graph of linear equations. | images/44.jpg | [] | 0 | **Roll No: 14, Page No: 05**
**Graph of Linear Equations and the X-axis**
**Key Points:**
- $(1, 0)$ - intersection with x-axis
- $(2, 4)$ - vertex/intersection point
- $(4, 0)$ - intersection with x-axis
**Shaded Region:** Triangular, bounded by:
1. Line through $(1, 0)$ and $(2, 4)$: Slope $= 4$, Equation: $y = 4x... | free_form | text | Extract and describe all the mathematical content from this handwritten page showing graph of linear equations. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "coordinate geometry - linear equations", "visual_context_type": "handwritten coordinate geometry graph", "grade": "10", "reasoning_skills": ["coordinate geometry", "linear equations", "graphing", "area ... | ||
045 | Extract and describe all the mathematical content from this handwritten page showing a histogram. | images/45.jpg | [] | 0 | **Histogram - Frequency Density vs Age in Years**
**Scale:**
- X-axis: 1 unit = 1 year
- Y-axis: 2 units = 1 unit of frequency density
**Data:**
| Age Interval | Class Width | Frequency Density | Frequency |
|--------------|-------------|-------------------|----------|
| 1-2 | 1 | 5 | 5 |
| 2-3 | 1 | 3 | 3 |
| 3-5 | ... | free_form | text | Extract and describe all the mathematical content from this handwritten page showing a histogram. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "statistics - histogram with unequal class widths", "visual_context_type": "handwritten histogram", "grade": "10", "reasoning_skills": ["statistics", "histogram", "frequency density", "unequal class inte... | ||
046 | Extract and describe all the mathematical content from this handwritten answer sheet showing integration. | images/46.jpg | [] | 0 | **Integration using Partial Fractions (Continued)**
$\rightarrow$ Split the integral into simpler parts:
$$I = \frac{3}{5} \int \frac{1}{n+2} dn + \frac{1}{5} \int \frac{2n+1}{n^2+1} dn$$
$$I = \frac{3}{5} \int \frac{1}{n+2} dn + \frac{1}{5} \int \frac{2n}{n^2+1} dn + \frac{1}{5} \int \frac{1}{n^2+1} dn$$
$\rightar... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet showing integration. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "calculus - integration", "visual_context_type": "handwritten notes", "grade": "12", "reasoning_skills": ["calculus", "integration", "partial fractions", "logarithmic integration", "inverse trigonometric... | ||
047 | Extract and describe all the mathematical content from this handwritten answer sheet about rectangle and square properties. | images/47.jpg | [] | 0 | **Part (i): Show that ABCD is a Square**
**1. Diagonals of a rectangle:**
* In a rectangle, diagonals bisect each other and are equal in length.
**2. AC bisects $\angle A$ and $\angle C$:**
* Since diagonal AC bisects both angles, each is divided into two equal parts.
* This implies $\angle A = 2 \times$ (angle forme... | free_form | text | Extract and describe all the mathematical content from this handwritten answer sheet about rectangle and square properties. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "geometry - proving square from rectangle", "visual_context_type": "handwritten notes", "grade": "9", "reasoning_skills": ["geometry", "rectangles", "squares", "diagonals", "angle bisectors", "properties... | ||
048 | Extract and describe all the mathematical content from this handwritten page including both graphs. | images/48.jpg | [] | 0 | **Roll No: 16**
**Page contains two graphs:**
---
**Graph 1: Bar Graph - Female Fatality Rate by Cause (Age 15-44)**
**Categories and Values:**
| Cause | Fatality Rate (%) |
|-------|------------------|
| Respiratory conditions | ~30 |
| Injuries | ~25 |
| Neuropsychiatric conditions | ~17 |
| Cardiovascular condit... | free_form | text | Extract and describe all the mathematical content from this handwritten page including both graphs. | {"split": "train", "language": "English", "source": "Handwritten Answer Sheet", "category": "math-ocr", "task_type": "statistics and coordinate geometry", "visual_context_type": "handwritten bar graph and coordinate geometry diagram", "grade": "10", "reasoning_skills": ["statistics", "bar graph", "linear equations", "c... |
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