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 |
|---|---|---|---|---|---|---|---|---|---|
4,503 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 6 | 3 | 4 | 5 | Vector operations and matrix calculations |
4,440 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 11 | 9 | 8 | 10 | Vector operations and matrix calculations |
2,624 | trigonometry | easy | Find cos(180°) | -1 | -1 | -1 | 0 | 1 | Trigonometric functions and identities |
3,228 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 4 | 4.5 | 3 | Probability calculation and expected value |
348 | arithmetic | hard | Calculate (6^4 × 4) ÷ 6 | 864 | 872 | 867 | 859 | 864 | Standard arithmetic calculation |
902 | geometry | easy | What is the area of a rectangle with length 8 and width 6? | 48 | 51 | 48 | 56 | 43 | Geometric calculation and spatial reasoning |
1,565 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.94 | 2.54 | 2.24 | 1.74 | Statistical measure calculation |
2,290 | calculus | medium | What is d/dx(3x^2 - 2x + 1)? | 6x^1 - 2 | 3x^1 - 2 | 6x^1 - 1 | 6x^1 - 2 | 6x^2 - 2 | Calculus differentiation and integration |
4,325 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 10 | 8 | 11 | 9 | Vector operations and matrix calculations |
4,199 | linear_algebra | easy | Calculate 2 × [2, 3] | [4, 6] | [5, 6] | [3, 6] | [4, 6] | [4, 5] | Vector operations and matrix calculations |
91 | arithmetic | easy | What is 12 + 48? | 60 | 60 | 58 | 63 | 61 | Standard arithmetic calculation |
1,044 | geometry | medium | Find the area of a circle with radius 5 (use π ≈ 3.14) | 78.54 | 81.74 | 78.54 | 80.34 | 76.04 | Geometric calculation and spatial reasoning |
79 | arithmetic | easy | Find 10 × 6 | 60 | 65 | 57 | 60 | 62 | Standard arithmetic calculation |
940 | geometry | easy | How many sides does a pentagon have? | 5 | 6 | 4 | 5 | 7 | Geometric calculation and spatial reasoning |
633 | algebra | medium | Solve: 6x - 13 = 22 | 5 | 6 | 5 | 3 | 8 | Algebraic manipulation and solving |
1,508 | statistics | medium | Calculate the range of 16 20 9 12 10 | 11 | 14 | 9 | 11 | 12 | Statistical measure calculation |
4,362 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 8 | 11 | 10 | Vector operations and matrix calculations |
1,152 | geometry | hard | Find the hypotenuse of a right triangle with legs 7 and 24 | 25 | 26 | 24 | 23 | 25 | Geometric calculation and spatial reasoning |
3,731 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 2 | 4 | 3 | Number theory and modular arithmetic |
3,269 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 3 | 4.5 | 4 | Probability calculation and expected value |
1,035 | geometry | medium | Find the area of a circle with radius 4 (use π ≈ 3.14) | 50.27 | 50.27 | 53.47 | 47.77 | 52.07 | Geometric calculation and spatial reasoning |
1,910 | fractions | medium | Divide 1 ÷ 5/6 | 6/5 | 5/6 | 6/6 | 6/5 | 7/5 | Fraction arithmetic and simplification |
2,056 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/2 | 1/3 | 0/2 | 2/2 | Fraction arithmetic and simplification |
3,598 | number_theory | medium | How many factors does 24 have? | 8 | 7 | 9 | 6 | 8 | Number theory and modular arithmetic |
2,849 | 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 |
2,255 | calculus | medium | What is d/dx(5x^3 - 1x + 1)? | 15x^2 - 1 | 15x^2 - 1 | 15x^3 - 1 | 5x^2 - 1 | 15x^2 - 1 | Calculus differentiation and integration |
2,449 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(x²) | 2x cos(x²) | 2x sin(x²) | cos(2x) | Calculus differentiation and integration |
718 | algebra | hard | Solve: x² + -9x + 14 = 0 | x = 7 or x = 2 | x = 6 or x = 3 | x = 7 or x = 2 | x = -7 or x = -2 | x = 8 or x = 1 | Algebraic manipulation and solving |
612 | algebra | medium | Solve: 3x - 6 = 21 | 9 | 7 | 9 | 10 | 12 | Algebraic manipulation and solving |
2,268 | calculus | medium | What is d/dx(5x^3 - 1x + 1)? | 15x^2 - 1 | 15x^2 - 1 | 5x^2 - 1 | 15x^3 - 1 | 15x^2 - 1 | Calculus differentiation and integration |
274 | arithmetic | medium | Calculate 169 ÷ 13 | 13 | 16 | 14 | 11 | 13 | Standard arithmetic calculation |
1,349 | statistics | easy | What is the mean of 20 8 15 8 18 16 3? | 12.6 | 13.6 | 10.6 | 12.6 | 14.6 | Statistical measure calculation |
680 | algebra | medium | Find x: x² = 36 | 6 | 4 | 6 | 9 | 7 | Algebraic manipulation and solving |
2,892 | 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 |
2,865 | 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 |
2,571 | trigonometry | easy | Find cos(30°) | √3/2 | √3/2 | 1 | -1 | 0 | Trigonometric functions and identities |
3,676 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 2 | 3 | 1 | Number theory and modular arithmetic |
3,616 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 1 | 3 | 2 | Number theory and modular arithmetic |
615 | algebra | medium | Solve: 2x - 7 = 24 | 15 | 15 | 18 | 16 | 13 | Algebraic manipulation and solving |
1,568 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.54 | 1.74 | 2.24 | 2.94 | Statistical measure calculation |
3,578 | number_theory | medium | Find LCM of 15 and 20 | 60 | 60 | 65 | 75 | 50 | Number theory and modular arithmetic |
4,419 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 11 | 10 | 9 | 8 | Vector operations and matrix calculations |
4,915 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 60 | 48 | 120 | 24 | Permutations and combinations |
2,608 | trigonometry | easy | Calculate tan(0°) | 0 | 1 | undefined | 0 | -1 | Trigonometric functions and identities |
3,994 | logic | medium | What is NOT(True AND False)? | True | Depends on values | Cannot determine | True | False | Logical reasoning and boolean operations |
4,338 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 10 | 11 | 9 | 8 | Vector operations and matrix calculations |
556 | algebra | easy | What is 3x when x = 8? | 24 | 24 | 29 | 26 | 21 | Algebraic manipulation and solving |
1,920 | fractions | medium | Calculate 2/5 × 4/7 | 8/35 | 9/35 | 8/36 | 35/8 | 8/35 | Fraction arithmetic and simplification |
3,246 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3 | 3.5 | 4 | Probability calculation and expected value |
4,551 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 6 | 4 | 3 | 5 | Vector operations and matrix calculations |
2,704 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 1 | sin(2x) | 2 | 0 | Trigonometric functions and identities |
638 | algebra | medium | Solve: 5x - 13 = 21 | 6 | 7 | 9 | 4 | 6 | Algebraic manipulation and solving |
2,845 | 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 |
3,087 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/12 | 1/14 | 1/15 | 1/13 | Probability calculation and expected value |
358 | arithmetic | hard | Calculate (6^3 × 3) ÷ 7 | 92 | 95 | 87 | 92 | 100 | Standard arithmetic calculation |
1,265 | statistics | easy | Find the median of 8 7 4 5 7 5 | 6 | 8 | 4 | 6 | 7 | Statistical measure calculation |
1,117 | geometry | hard | Find the hypotenuse of a right triangle with legs 9 and 12 | 15 | 14 | 15 | 13 | 16 | Geometric calculation and spatial reasoning |
2,180 | calculus | easy | Find ∫x dx | x²/2 + C | x²/2 + C | x + C | x² | x³/3 + C | Calculus differentiation and integration |
727 | algebra | hard | Solve: x² + -12x + 36 = 0 | x = 6 or x = 6 | x = 5 or x = 7 | x = 6 or x = 6 | x = -6 or x = -6 | x = 7 or x = 5 | Algebraic manipulation and solving |
2,611 | trigonometry | easy | Find cos(60°) | 1/2 | 0 | 1 | -1 | 1/2 | Trigonometric functions and identities |
1,826 | fractions | medium | Divide 2/7 ÷ 4/7 | 1/2 | 2/2 | 2/1 | 1/3 | 1/2 | Fraction arithmetic and simplification |
3,536 | number_theory | medium | Find LCM of 15 and 20 | 60 | 65 | 75 | 60 | 50 | Number theory and modular arithmetic |
670 | algebra | medium | Solve: 6x - 7 = 24 | 5 | 3 | 5 | 8 | 6 | Algebraic manipulation and solving |
1,518 | statistics | medium | Calculate the range of 18 18 12 14 3 | 15 | 13 | 15 | 18 | 16 | Statistical measure calculation |
3,035 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 1/2 | 1/3 | 2/3 | 1/4 | Probability calculation and expected value |
2,688 | trigonometry | medium | What is tan(45°)? | 1 | √2 | 0 | √3 | 1 | Trigonometric functions and identities |
1,909 | fractions | medium | Divide 1/3 ÷ 2/3 | 1/2 | 1/2 | 2/2 | 2/1 | 1/3 | Fraction arithmetic and simplification |
514 | algebra | easy | Solve for x: x + 12 = 18 | 6 | 4 | 7 | 6 | 9 | Algebraic manipulation and solving |
4,719 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 6 | 8 | 4 | 5 | Permutations and combinations |
3,079 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/30 | 1/35 | 1/36 | 1/32 | Probability calculation and expected value |
4,150 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Cannot determine | Depends on other variables | True | False | Logical reasoning and boolean operations |
303 | arithmetic | hard | Calculate (6^3 × 3) ÷ 3 | 216 | 211 | 224 | 219 | 216 | Standard arithmetic calculation |
326 | arithmetic | hard | Calculate (6^3 × 2) ÷ 7 | 61 | 69 | 56 | 61 | 64 | Standard arithmetic calculation |
205 | arithmetic | medium | What is 14²? | 196 | 211 | 204 | 186 | 196 | Standard arithmetic calculation |
2,664 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 1 | 2 | sin(2x) | 0 | Trigonometric functions and identities |
3,439 | number_theory | easy | What is the GCD of 14 and 21? | 7 | 6 | 5 | 7 | 8 | Number theory and modular arithmetic |
4,430 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 8 | 10 | 9 | 11 | Vector operations and matrix calculations |
2,786 | 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 |
3,903 | logic | medium | What is NOT(True AND False)? | True | Depends on values | Cannot determine | True | False | Logical reasoning and boolean operations |
2,476 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x sin(x²) | cos(x²) | cos(2x) | 2x cos(x²) | Calculus differentiation and integration |
4,753 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 60 | 50 | 75 | 125 | Permutations and combinations |
3,720 | number_theory | hard | What is 7³ mod 11? | 2 | 3 | 2 | 4 | 1 | Number theory and modular arithmetic |
3,987 | logic | medium | What is NOT(True AND False)? | True | Depends on values | Cannot determine | False | True | Logical reasoning and boolean operations |
3,030 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 6 | 7 | 8 | 5 | Probability calculation and expected value |
4,101 | 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 |
2,166 | calculus | easy | Find d/dx(x^3) | 3x^2 | x^3 | x^2 | 3x^2 | 3x^3 | Calculus differentiation and integration |
4,644 | combinatorics | easy | How many ways can 4 people stand in a line? | 24 | 6 | 16 | 24 | 8 | Permutations and combinations |
3,128 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/30 | 1/32 | 1/36 | 1/35 | Probability calculation and expected value |
2,176 | calculus | easy | Find ∫x dx | x²/2 + C | x² | x³/3 + C | x²/2 + C | x + C | Calculus differentiation and integration |
2,790 | 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 |
2,490 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x cos(x²) | cos(x²) | 2x sin(x²) | cos(2x) | Calculus differentiation and integration |
1,116 | geometry | hard | Find the hypotenuse of a right triangle with legs 8 and 15 | 17 | 16 | 15 | 18 | 17 | Geometric calculation and spatial reasoning |
3,258 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3 | 4 | 3.5 | Probability calculation and expected value |
4,330 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 8 | 10 | 11 | 9 | Vector operations and matrix calculations |
4,190 | linear_algebra | easy | Calculate 2 × [2, 3] | [4, 6] | [4, 5] | [4, 6] | [5, 6] | [3, 6] | Vector operations and matrix calculations |
1,604 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 1.74 | 2.24 | 2.54 | 2.94 | Statistical measure calculation |
3,424 | number_theory | easy | Is 19 a prime number? | Yes | Cannot determine | Yes | Only if x>0 | No | Number theory and modular arithmetic |
2,819 | 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 |
1,889 | fractions | medium | Divide 2/3 ÷ 1 | 2/3 | 2/4 | 2/3 | 3/2 | 3/3 | Fraction arithmetic and simplification |
1,805 | fractions | easy | What is 1/2 + 1/6? | 2/3 | 2/3 | 2/4 | 1/3 | 3/3 | Fraction arithmetic and simplification |
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