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 |
|---|---|---|---|---|---|---|---|---|---|
4,355 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 8 | 10 | 11 | Vector operations and matrix calculations |
1,623 | 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 |
3,143 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/32 | 1/35 | 1/36 | 1/30 | Probability calculation and expected value |
3,650 | number_theory | hard | What is 7³ mod 11? | 2 | 2 | 1 | 4 | 3 | Number theory and modular arithmetic |
4,871 | 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 |
4,527 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 4 | 5 | 3 | 6 | Vector operations and matrix calculations |
3,940 | logic | medium | If P implies Q and P is true, what can we conclude about Q? | Q is true | Cannot determine | P is false | Q is true | Q is false | Logical reasoning and boolean operations |
49 | arithmetic | easy | Find 7 × 11 | 77 | 79 | 74 | 77 | 82 | Standard arithmetic calculation |
999 | 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 |
81 | arithmetic | easy | What is 69 + 65? | 134 | 132 | 134 | 137 | 135 | Standard arithmetic calculation |
937 | geometry | easy | How many sides does a heptagon have? | 7 | 7 | 9 | 8 | 6 | Geometric calculation and spatial reasoning |
3,619 | number_theory | hard | What is 7³ mod 11? | 2 | 2 | 3 | 4 | 1 | Number theory and modular arithmetic |
3,540 | number_theory | medium | How many factors does 30 have? | 8 | 7 | 9 | 6 | 8 | Number theory and modular arithmetic |
4,745 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 60 | 75 | 50 | 125 | Permutations and combinations |
4,601 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 6 | 8 | 5 | 4 | Permutations and combinations |
14 | arithmetic | easy | Calculate 57 - 45 | 12 | 13 | 11 | 14 | 12 | Standard arithmetic calculation |
1,066 | geometry | medium | What is the volume of a cube with side length 9? | 729 | 744 | 764 | 709 | 729 | Geometric calculation and spatial reasoning |
3,849 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Depends on context | False | True | Cannot determine | Logical reasoning and boolean operations |
1,384 | statistics | easy | Find the median of 3 2 17 17 | 10 | 10 | 12 | 11 | 8 | Statistical measure calculation |
4,624 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 8 | 5 | 4 | 6 | Permutations and combinations |
1,712 | fractions | easy | What is 1/2 + 1/6? | 2/3 | 1/3 | 3/3 | 2/4 | 2/3 | Fraction arithmetic and simplification |
1,477 | statistics | medium | Calculate the range of 3 8 8 9 13 9 13 | 10 | 8 | 10 | 11 | 13 | Statistical measure calculation |
2,762 | trigonometry | medium | What is tan(45°)? | 1 | √2 | 0 | 1 | √3 | Trigonometric functions and identities |
639 | algebra | medium | Find x: x² = 25 | 5 | 8 | 3 | 6 | 5 | Algebraic manipulation and solving |
516 | algebra | easy | What is 8x when x = 4? | 32 | 34 | 37 | 32 | 29 | Algebraic manipulation and solving |
2,550 | trigonometry | easy | What is sin(0°)? | 0 | 0 | -1 | 0 | 1 | Trigonometric functions and identities |
312 | arithmetic | hard | Calculate (6^4 × 2) ÷ 3 | 864 | 859 | 867 | 872 | 864 | Standard arithmetic calculation |
1,032 | geometry | medium | Find the area of a circle with radius 7 (use π ≈ 3.14) | 153.94 | 151.44 | 157.14 | 153.94 | 155.74 | Geometric calculation and spatial reasoning |
63 | arithmetic | easy | Calculate 54 - 46 | 8 | 10 | 8 | 7 | 9 | Standard arithmetic calculation |
3,776 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Depends on context | Cannot determine | True | False | Logical reasoning and boolean operations |
1,756 | fractions | easy | Simplify 4/8 | 1/2 | 5/9 | 3/7 | 2/4 | 1/2 | Fraction arithmetic and simplification |
1,586 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 1.74 | 2.94 | 2.24 | 2.54 | Statistical measure calculation |
3,163 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/35 | 1/32 | 1/36 | 1/30 | Probability calculation and expected value |
895 | geometry | easy | What is the area of a rectangle with length 11 and width 8? | 88 | 83 | 88 | 91 | 96 | Geometric calculation and spatial reasoning |
1,155 | geometry | hard | Find the hypotenuse of a right triangle with legs 5 and 12 | 13 | 14 | 13 | 11 | 12 | Geometric calculation and spatial reasoning |
2,162 | calculus | easy | Evaluate ∫x^2 dx | x^3/3 + C | x^4/4 + C | 2x^1 + C | x^2 + C | x^3/3 + C | Calculus differentiation and integration |
2,812 | 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 |
4,859 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 50 | 125 | 60 | 75 | Permutations and combinations |
3,310 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3 | 4 | 3.5 | Probability calculation and expected value |
3,594 | number_theory | medium | Find LCM of 12 and 16 | 48 | 63 | 48 | 53 | 38 | Number theory and modular arithmetic |
2,391 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x sin(x²) | cos(2x) | cos(x²) | 2x cos(x²) | Calculus differentiation and integration |
396 | arithmetic | hard | Calculate (5^3 × 2) ÷ 8 | 31 | 26 | 34 | 39 | 31 | Standard arithmetic calculation |
736 | algebra | hard | Solve: x² + -10x + 16 = 0 | x = 2 or x = 8 | x = 1 or x = 9 | x = 2 or x = 8 | x = -2 or x = -8 | x = 3 or x = 7 | Algebraic manipulation and solving |
647 | algebra | medium | Solve: 3x - 12 = 25 | 12 | 13 | 15 | 12 | 10 | Algebraic manipulation and solving |
3,469 | number_theory | easy | Is 19 a prime number? | Yes | No | Cannot determine | Only if x>0 | Yes | Number theory and modular arithmetic |
2,506 | trigonometry | easy | What is sin(180°)? | 0 | 0 | 1 | -1 | 0 | Trigonometric functions and identities |
4,446 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 8 | 10 | 9 | 11 | Vector operations and matrix calculations |
2,294 | calculus | medium | What is d/dx(4x^4 - 5x + 1)? | 16x^3 - 5 | 4x^3 - 5 | 16x^3 - 1 | 16x^4 - 5 | 16x^3 - 5 | Calculus differentiation and integration |
4,192 | linear_algebra | easy | Calculate 3 × [2, 3] | [6, 9] | [6, 8] | [6, 9] | [5, 9] | [7, 9] | Vector operations and matrix calculations |
3,749 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 1 | 3 | 2 | Number theory and modular arithmetic |
1,673 | fractions | easy | Simplify 20/20 | 1/1 | 21/21 | 1/1 | 10/10 | 19/19 | Fraction arithmetic and simplification |
4,931 | 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 |
1,181 | geometry | hard | Find the hypotenuse of a right triangle with legs 8 and 15 | 17 | 16 | 15 | 17 | 18 | Geometric calculation and spatial reasoning |
4,649 | combinatorics | easy | How many ways can 4 people stand in a line? | 24 | 16 | 8 | 24 | 6 | Permutations and combinations |
699 | algebra | hard | Solve: x² + -11x + 30 = 0 | x = 6 or x = 5 | x = 5 or x = 6 | x = 6 or x = 5 | x = -6 or x = -5 | x = 7 or x = 4 | Algebraic manipulation and solving |
4,441 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 11 | 8 | 10 | Vector operations and matrix calculations |
3,161 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/15 | 1/14 | 1/13 | 1/12 | Probability calculation and expected value |
3,852 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | False | True | Cannot determine | Depends on context | Logical reasoning and boolean operations |
656 | algebra | medium | Find x: x² = 36 | 6 | 6 | 9 | 4 | 7 | Algebraic manipulation and solving |
3,244 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4 | 4.5 | 3 | 3.5 | Probability calculation and expected value |
2,634 | trigonometry | easy | What is tan(45°)? | 1 | √3 | √2 | 1 | 0 | Trigonometric functions and identities |
3,806 | logic | easy | If all cats are mammals and Fluffy is a cat, then Fluffy is a: | mammal | pet | mammal | animal | cat | Logical reasoning and boolean operations |
3,291 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 4.5 | 3 | 4 | Probability calculation and expected value |
1,386 | statistics | easy | Find the median of 12 15 2 19 10 5 | 11 | 12 | 13 | 9 | 11 | Statistical measure calculation |
2,158 | calculus | easy | Find d/dx(x^4) | 4x^3 | x^3 | 4x^4 | 4x^3 | x^4 | Calculus differentiation and integration |
2,296 | calculus | medium | What is d/dx(2x^3 - 5x + 1)? | 6x^2 - 5 | 6x^2 - 5 | 6x^3 - 5 | 6x^2 - 1 | 2x^2 - 5 | Calculus differentiation and integration |
3,053 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 1/3 | 2/3 | 1/2 | 1/4 | Probability calculation and expected value |
127 | arithmetic | easy | Find 11 × 12 | 132 | 134 | 132 | 129 | 137 | Standard arithmetic calculation |
3,735 | number_theory | hard | What is 7³ mod 11? | 2 | 3 | 1 | 2 | 4 | Number theory and modular arithmetic |
3,573 | number_theory | medium | Find LCM of 15 and 20 | 60 | 50 | 75 | 65 | 60 | Number theory and modular arithmetic |
2,738 | trigonometry | medium | What is tan(45°)? | 1 | √3 | 0 | √2 | 1 | Trigonometric functions and identities |
1,913 | fractions | medium | Calculate 3/5 × 1/3 | 1/5 | 1/5 | 2/5 | 5/1 | 1/6 | Fraction arithmetic and simplification |
280 | arithmetic | hard | Calculate (5^3 × 4) ÷ 5 | 100 | 108 | 100 | 103 | 95 | Standard arithmetic calculation |
3,434 | number_theory | easy | Is 13 a prime number? | Yes | No | Only if x>0 | Yes | Cannot determine | Number theory and modular arithmetic |
2,156 | calculus | easy | Find d/dx(x^5) | 5x^4 | x^5 | x^4 | 5x^5 | 5x^4 | Calculus differentiation and integration |
3,169 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/15 | 1/14 | 1/12 | 1/13 | Probability calculation and expected value |
3,629 | number_theory | hard | What is 7³ mod 11? | 2 | 3 | 1 | 2 | 4 | Number theory and modular arithmetic |
4,636 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 6 | 8 | 4 | 5 | Permutations and combinations |
4,569 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 4 | 5 | 6 | 3 | Vector operations and matrix calculations |
1,550 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.54 | 2.94 | 2.24 | 1.74 | Statistical measure calculation |
2,097 | calculus | easy | Evaluate ∫x^4 dx | x^5/5 + C | x^6/6 + C | x^4 + C | 4x^3 + C | x^5/5 + C | Calculus differentiation and integration |
3,526 | number_theory | medium | How many factors does 24 have? | 8 | 7 | 8 | 6 | 9 | Number theory and modular arithmetic |
503 | algebra | easy | What is 5x when x = 6? | 30 | 30 | 35 | 27 | 32 | Algebraic manipulation and solving |
3,918 | logic | medium | What is NOT(True AND False)? | True | True | Depends on values | Cannot determine | False | Logical reasoning and boolean operations |
1,104 | geometry | medium | Find the area of a circle with radius 7 (use π ≈ 3.14) | 153.94 | 157.14 | 153.94 | 151.44 | 155.74 | Geometric calculation and spatial reasoning |
964 | geometry | easy | How many sides does a octagon have? | 8 | 8 | 7 | 10 | 9 | Geometric calculation and spatial reasoning |
4,283 | linear_algebra | easy | Calculate 3 × [2, 3] | [6, 9] | [6, 8] | [5, 9] | [7, 9] | [6, 9] | Vector operations and matrix calculations |
1,302 | statistics | easy | What is the mean of 6 8 16 5 17 3? | 9.2 | 9.2 | 10.2 | 7.199999999999999 | 11.2 | Statistical measure calculation |
2,321 | calculus | medium | What is d/dx(3x^2 - 3x + 1)? | 6x^1 - 3 | 6x^1 - 3 | 6x^2 - 3 | 6x^1 - 1 | 3x^1 - 3 | Calculus differentiation and integration |
2,291 | calculus | medium | What is d/dx(3x^2 - 3x + 1)? | 6x^1 - 3 | 6x^2 - 3 | 3x^1 - 3 | 6x^1 - 1 | 6x^1 - 3 | Calculus differentiation and integration |
4,206 | linear_algebra | easy | Calculate 5 × [2, 3] | [10, 15] | [10, 15] | [10, 14] | [11, 15] | [9, 15] | Vector operations and matrix calculations |
4,930 | 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 |
3,662 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 2 | 3 | 4 | Number theory and modular arithmetic |
4,552 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 6 | 3 | 4 | 5 | Vector operations and matrix calculations |
646 | algebra | medium | Solve: 4x - 13 = 16 | 7 | 8 | 10 | 7 | 5 | Algebraic manipulation and solving |
2,079 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/3 | 1/2 | 2/2 | 0/2 | Fraction arithmetic and simplification |
2,134 | calculus | easy | Find d/dx(x^3) | 3x^2 | 3x^3 | 3x^2 | x^2 | x^3 | Calculus differentiation and integration |
3,537 | number_theory | medium | How many factors does 24 have? | 8 | 7 | 9 | 8 | 6 | Number theory and modular arithmetic |
449 | algebra | easy | What is 5x when x = 8? | 40 | 42 | 45 | 37 | 40 | Algebraic manipulation and solving |
1,716 | fractions | easy | Simplify 16/12 | 4/3 | 17/13 | 8/6 | 4/3 | 15/11 | Fraction arithmetic and simplification |
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