question_id int64 2 5k | category stringclasses 12
values | difficulty stringclasses 3
values | question stringlengths 10 89 | correct_answer stringclasses 370
values | option_a stringclasses 545
values | option_b stringclasses 544
values | option_c stringclasses 546
values | option_d stringclasses 550
values | explanation stringclasses 12
values |
|---|---|---|---|---|---|---|---|---|---|
4,939 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 24 | 60 | 48 | 120 | Permutations and combinations |
786 | algebra | hard | Solve: x² + -14x + 49 = 0 | x = 7 or x = 7 | x = 6 or x = 8 | x = 7 or x = 7 | x = -7 or x = -7 | x = 8 or x = 6 | Algebraic manipulation and solving |
2,129 | calculus | easy | Find d/dx(x^5) | 5x^4 | x^4 | x^5 | 5x^5 | 5x^4 | Calculus differentiation and integration |
1,133 | geometry | hard | Find the hypotenuse of a right triangle with legs 5 and 12 | 13 | 11 | 14 | 13 | 12 | Geometric calculation and spatial reasoning |
2,026 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/2 | 2/2 | 1/3 | 0/2 | Fraction arithmetic and simplification |
719 | algebra | hard | Solve: x² + -10x + 24 = 0 | x = 4 or x = 6 | x = 3 or x = 7 | x = 4 or x = 6 | x = -4 or x = -6 | x = 5 or x = 5 | Algebraic manipulation and solving |
1,084 | geometry | medium | What is the volume of a cube with side length 7? | 343 | 343 | 378 | 323 | 358 | Geometric calculation and spatial reasoning |
3,102 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/14 | 1/13 | 1/15 | 1/12 | Probability calculation and expected value |
947 | geometry | easy | What is the area of a rectangle with length 5 and width 9? | 45 | 53 | 45 | 48 | 40 | Geometric calculation and spatial reasoning |
1,403 | statistics | medium | What is the mode of 6 4 6 6 5 4 6? | 6 | 6 | 7 | 4 | 9 | Statistical measure calculation |
3,511 | number_theory | medium | Find LCM of 12 and 16 | 48 | 48 | 53 | 38 | 63 | Number theory and modular arithmetic |
2,522 | trigonometry | easy | Calculate tan(0°) | 0 | 0 | -1 | undefined | 1 | Trigonometric functions and identities |
1,043 | geometry | medium | Find the area of a circle with radius 7 (use π ≈ 3.14) | 153.94 | 155.74 | 153.94 | 151.44 | 157.14 | Geometric calculation and spatial reasoning |
2,862 | trigonometry | hard | Solve sin(x) = 1/2 for 0° ≤ x ≤ 360° | x = 30° or 150° | x = 30° or 60° | x = 30° or 150° | x = 60° or 120° | x = 45° or 135° | Trigonometric functions and identities |
295 | arithmetic | hard | Calculate (6^3 × 2) ÷ 7 | 61 | 61 | 69 | 56 | 64 | Standard arithmetic calculation |
1,752 | fractions | easy | Simplify 35/40 | 7/8 | 34/39 | 17/20 | 36/41 | 7/8 | Fraction arithmetic and simplification |
2,833 | trigonometry | hard | Solve sin(x) = 1/2 for 0° ≤ x ≤ 360° | x = 30° or 150° | x = 30° or 60° | x = 30° or 150° | x = 60° or 120° | x = 45° or 135° | Trigonometric functions and identities |
4,433 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 11 | 8 | 10 | Vector operations and matrix calculations |
1,687 | fractions | easy | What is 1/2 + 1/4? | 3/4 | 2/4 | 3/4 | 4/4 | 3/5 | Fraction arithmetic and simplification |
4,903 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 48 | 24 | 120 | 60 | Permutations and combinations |
752 | algebra | hard | Solve: x² + -13x + 42 = 0 | x = 7 or x = 6 | x = 6 or x = 7 | x = 7 or x = 6 | x = -7 or x = -6 | x = 8 or x = 5 | Algebraic manipulation and solving |
4,645 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 8 | 5 | 6 | 4 | Permutations and combinations |
1,988 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/3 | 0/2 | 2/2 | 1/2 | Fraction arithmetic and simplification |
3,634 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 4 | 2 | 3 | Number theory and modular arithmetic |
1,948 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 0/2 | 1/2 | 2/2 | 1/3 | Fraction arithmetic and simplification |
1,191 | geometry | hard | Find the hypotenuse of a right triangle with legs 7 and 24 | 25 | 24 | 26 | 23 | 25 | Geometric calculation and spatial reasoning |
264 | arithmetic | medium | What is 10²? | 100 | 100 | 90 | 115 | 108 | Standard arithmetic calculation |
1,886 | fractions | medium | Divide 1 ÷ 5/7 | 7/5 | 7/5 | 5/7 | 7/6 | 8/5 | Fraction arithmetic and simplification |
716 | algebra | hard | Solve: x² + -15x + 56 = 0 | x = 7 or x = 8 | x = 6 or x = 9 | x = 7 or x = 8 | x = -7 or x = -8 | x = 8 or x = 7 | Algebraic manipulation and solving |
1,594 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.94 | 2.24 | 1.74 | 2.54 | Statistical measure calculation |
3,114 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/14 | 1/15 | 1/12 | 1/13 | Probability calculation and expected value |
3,006 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 1/4 | 1/3 | 1/2 | 2/3 | Probability calculation and expected value |
404 | arithmetic | hard | Calculate (4^4 × 3) ÷ 9 | 85 | 80 | 93 | 85 | 88 | Standard arithmetic calculation |
4,611 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 5 | 6 | 8 | 4 | Permutations and combinations |
611 | algebra | medium | Find x: x² = 81 | 9 | 12 | 7 | 9 | 10 | Algebraic manipulation and solving |
4,423 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 10 | 8 | 9 | 11 | Vector operations and matrix calculations |
4,672 | combinatorics | easy | How many ways can 4 people stand in a line? | 24 | 24 | 6 | 8 | 16 | Permutations and combinations |
2,249 | calculus | medium | What is d/dx(2x^4 - 6x + 1)? | 8x^3 - 6 | 8x^3 - 6 | 8x^4 - 6 | 2x^3 - 6 | 8x^3 - 1 | Calculus differentiation and integration |
3,566 | number_theory | medium | Find LCM of 12 and 16 | 48 | 53 | 63 | 48 | 38 | Number theory and modular arithmetic |
1,004 | geometry | medium | What is the volume of a cube with side length 4? | 64 | 44 | 79 | 64 | 99 | Geometric calculation and spatial reasoning |
4,303 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 6] | [2, 7] | [3, 7] | [4, 7] | Vector operations and matrix calculations |
1,822 | fractions | medium | Divide 4/7 ÷ 5/7 | 4/5 | 4/6 | 4/5 | 5/5 | 5/4 | Fraction arithmetic and simplification |
1,795 | fractions | easy | Simplify 20/20 | 1/1 | 21/21 | 19/19 | 10/10 | 1/1 | Fraction arithmetic and simplification |
3,795 | logic | easy | If all cats are mammals and Fluffy is a cat, then Fluffy is a: | mammal | pet | animal | mammal | cat | Logical reasoning and boolean operations |
942 | geometry | easy | What is the area of a rectangle with length 8 and width 5? | 40 | 43 | 40 | 48 | 35 | Geometric calculation and spatial reasoning |
2,646 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 1 | 2 | sin(2x) | 0 | Trigonometric functions and identities |
1,725 | fractions | easy | Simplify 20/24 | 5/6 | 21/25 | 19/23 | 5/6 | 10/12 | Fraction arithmetic and simplification |
2,516 | trigonometry | easy | Calculate tan(0°) | 0 | 1 | undefined | -1 | 0 | Trigonometric functions and identities |
1,345 | statistics | easy | Find the median of 4 9 10 8 6 12 12 | 9 | 10 | 11 | 9 | 7 | Statistical measure calculation |
3,248 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3.5 | 3 | 4 | Probability calculation and expected value |
3,847 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Cannot determine | Depends on context | True | False | Logical reasoning and boolean operations |
4,115 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Depends on other variables | True | False | Cannot determine | Logical reasoning and boolean operations |
104 | arithmetic | easy | Find 12 × 12 | 144 | 149 | 144 | 141 | 146 | Standard arithmetic calculation |
3,051 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 6 | 5 | 8 | 7 | Probability calculation and expected value |
4,905 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 24 | 120 | 48 | 60 | Permutations and combinations |
3,446 | number_theory | easy | What is the GCD of 12 and 18? | 6 | 4 | 7 | 6 | 5 | Number theory and modular arithmetic |
3,181 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/35 | 1/30 | 1/32 | 1/36 | Probability calculation and expected value |
668 | algebra | medium | Solve: 4x - 11 = 22 | 8 | 9 | 8 | 6 | 11 | Algebraic manipulation and solving |
3,780 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Depends on context | False | Cannot determine | True | Logical reasoning and boolean operations |
2,090 | calculus | easy | Find d/dx(x^5) | 5x^4 | 5x^5 | x^4 | 5x^4 | x^5 | Calculus differentiation and integration |
3,955 | logic | medium | If P implies Q and P is true, what can we conclude about Q? | Q is true | P is false | Cannot determine | Q is true | Q is false | Logical reasoning and boolean operations |
3,493 | number_theory | medium | Find LCM of 12 and 16 | 48 | 63 | 38 | 53 | 48 | Number theory and modular arithmetic |
3,033 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 1/3 | 1/4 | 1/2 | 2/3 | Probability calculation and expected value |
4,788 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 75 | 60 | 50 | 125 | Permutations and combinations |
1,510 | statistics | medium | Calculate the range of 5 17 4 19 13 | 15 | 18 | 16 | 15 | 13 | Statistical measure calculation |
3,266 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 3 | 4 | 4.5 | Probability calculation and expected value |
4,082 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | False | Depends on other variables | Cannot determine | True | Logical reasoning and boolean operations |
1,855 | fractions | medium | Divide 1 ÷ 1/3 | 3/1 | 4/1 | 3/1 | 1/3 | 3/2 | Fraction arithmetic and simplification |
3,474 | number_theory | easy | What is the GCD of 14 and 21? | 7 | 6 | 8 | 7 | 5 | Number theory and modular arithmetic |
1,615 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.94 | 2.54 | 1.74 | 2.24 | Statistical measure calculation |
1,770 | fractions | easy | What is 1/2 + 1/6? | 2/3 | 2/4 | 1/3 | 3/3 | 2/3 | Fraction arithmetic and simplification |
1,081 | geometry | medium | What is the volume of a cube with side length 6? | 216 | 196 | 231 | 251 | 216 | Geometric calculation and spatial reasoning |
1,274 | statistics | easy | Find the median of 15 3 12 8 15 11 20 | 12 | 10 | 12 | 14 | 13 | Statistical measure calculation |
3,604 | number_theory | medium | Find LCM of 12 and 16 | 48 | 38 | 48 | 63 | 53 | Number theory and modular arithmetic |
3,746 | number_theory | hard | What is 7³ mod 11? | 2 | 3 | 1 | 4 | 2 | Number theory and modular arithmetic |
263 | arithmetic | medium | What is 40% of 236? | 94 | 99 | 104 | 94 | 89 | Standard arithmetic calculation |
2,098 | calculus | easy | Find d/dx(x^4) | 4x^3 | 4x^4 | 4x^3 | x^3 | x^4 | Calculus differentiation and integration |
3,251 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3 | 4 | 3.5 | 4.5 | Probability calculation and expected value |
2,798 | trigonometry | hard | Solve sin(x) = 1/2 for 0° ≤ x ≤ 360° | x = 30° or 150° | x = 30° or 60° | x = 30° or 150° | x = 60° or 120° | x = 45° or 135° | Trigonometric functions and identities |
1,373 | statistics | easy | What is the mean of 19 10 4 17 8 2 6 16? | 10.2 | 8.2 | 12.2 | 10.2 | 11.2 | Statistical measure calculation |
1,177 | geometry | hard | Find the hypotenuse of a right triangle with legs 8 and 15 | 17 | 15 | 17 | 18 | 16 | Geometric calculation and spatial reasoning |
329 | arithmetic | hard | Calculate (3^4 × 2) ÷ 3 | 54 | 54 | 49 | 62 | 57 | Standard arithmetic calculation |
4,215 | linear_algebra | easy | Calculate 5 × [2, 3] | [10, 15] | [9, 15] | [10, 14] | [11, 15] | [10, 15] | Vector operations and matrix calculations |
2,493 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(x²) | 2x sin(x²) | cos(2x) | 2x cos(x²) | Calculus differentiation and integration |
3,402 | number_theory | easy | Is 31 a prime number? | Yes | Cannot determine | Yes | No | Only if x>0 | Number theory and modular arithmetic |
3,280 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4 | 3 | 4.5 | 3.5 | Probability calculation and expected value |
2,545 | trigonometry | easy | What is sin(30°)? | 0.5 | 0 | -1 | 0.5 | 1 | Trigonometric functions and identities |
4,126 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Cannot determine | True | False | Depends on other variables | Logical reasoning and boolean operations |
2,027 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 0/2 | 1/2 | 1/3 | 2/2 | Fraction arithmetic and simplification |
1,971 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 0/2 | 1/3 | 2/2 | 1/2 | Fraction arithmetic and simplification |
1,090 | geometry | medium | Find the area of a circle with radius 4 (use π ≈ 3.14) | 50.27 | 50.27 | 52.07 | 53.47 | 47.77 | Geometric calculation and spatial reasoning |
3,024 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 8 | 6 | 7 | 5 | Probability calculation and expected value |
4,694 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 8 | 4 | 5 | 6 | Permutations and combinations |
1,507 | statistics | medium | What is the mode of 8 8 19 4 16 8 8? | 8 | 9 | 8 | 6 | 11 | Statistical measure calculation |
951 | geometry | easy | What is the area of a rectangle with length 10 and width 5? | 50 | 50 | 58 | 45 | 53 | Geometric calculation and spatial reasoning |
1,347 | statistics | easy | What is the mean of 6 12 7 18? | 10.8 | 8.8 | 12.8 | 11.8 | 10.8 | Statistical measure calculation |
4,220 | linear_algebra | easy | Calculate 3 × [2, 3] | [6, 9] | [7, 9] | [6, 8] | [6, 9] | [5, 9] | Vector operations and matrix calculations |
2,921 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 7 | 5 | 8 | 6 | Probability calculation and expected value |
4,763 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 75 | 50 | 125 | 60 | Permutations and combinations |
4,462 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 5 | 6 | 4 | 3 | Vector operations and matrix calculations |
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