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 |
|---|---|---|---|---|---|---|---|---|---|
4,832 | 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 |
2,801 | 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 |
3,230 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 4.5 | 3 | 4 | Probability calculation and expected value |
3,052 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 5 | 6 | 7 | 8 | Probability calculation and expected value |
342 | arithmetic | hard | Calculate (5^4 × 3) ÷ 4 | 468 | 468 | 471 | 476 | 463 | Standard arithmetic calculation |
1,025 | geometry | medium | Find the area of a circle with radius 7 (use π ≈ 3.14) | 153.94 | 153.94 | 157.14 | 151.44 | 155.74 | Geometric calculation and spatial reasoning |
177 | arithmetic | medium | What is 12²? | 144 | 159 | 152 | 134 | 144 | Standard arithmetic calculation |
1,677 | fractions | easy | Simplify 28/24 | 7/6 | 14/12 | 7/6 | 29/25 | 27/23 | Fraction arithmetic and simplification |
791 | 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 |
857 | geometry | easy | How many sides does a heptagon have? | 7 | 7 | 6 | 9 | 8 | Geometric calculation and spatial reasoning |
1,337 | statistics | easy | What is the mean of 19 5 11 9 11 16 8? | 11.3 | 9.3 | 11.3 | 12.3 | 13.3 | Statistical measure calculation |
3,123 | 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 |
4,434 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 10 | 11 | 8 | 9 | Vector operations and matrix calculations |
1,757 | fractions | easy | What is 1/3 + 1/4? | 7/12 | 7/13 | 8/12 | 6/12 | 7/12 | Fraction arithmetic and simplification |
3,702 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 2 | 3 | 1 | Number theory and modular arithmetic |
3,703 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 2 | 3 | 4 | Number theory and modular arithmetic |
4,208 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 7] | [3, 6] | [4, 7] | [2, 7] | Vector operations and matrix calculations |
149 | arithmetic | medium | What is 40% of 163? | 65 | 65 | 70 | 60 | 75 | Standard arithmetic calculation |
3,721 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 3 | 2 | 1 | Number theory and modular arithmetic |
2,240 | calculus | medium | What is d/dx(5x^4 - 3x + 1)? | 20x^3 - 3 | 20x^3 - 3 | 20x^4 - 3 | 20x^3 - 1 | 5x^3 - 3 | Calculus differentiation and integration |
4,594 | combinatorics | easy | How many ways can 5 people stand in a line? | 120 | 120 | 10 | 25 | 24 | Permutations and combinations |
2,467 | 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 |
4,590 | combinatorics | easy | How many ways can 4 people stand in a line? | 24 | 8 | 6 | 24 | 16 | Permutations and combinations |
1,091 | geometry | medium | Find the area of a circle with radius 3 (use π ≈ 3.14) | 28.27 | 30.07 | 28.27 | 31.47 | 25.77 | Geometric calculation and spatial reasoning |
876 | geometry | easy | What is the area of a rectangle with length 9 and width 6? | 54 | 49 | 54 | 57 | 62 | Geometric calculation and spatial reasoning |
2,984 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 1/3 | 1/2 | 2/3 | 1/4 | Probability calculation and expected value |
935 | geometry | easy | How many sides does a heptagon have? | 7 | 8 | 7 | 6 | 9 | Geometric calculation and spatial reasoning |
2,293 | calculus | medium | What is d/dx(3x^2 - 7x + 1)? | 6x^1 - 7 | 6x^1 - 7 | 3x^1 - 7 | 6x^2 - 7 | 6x^1 - 1 | Calculus differentiation and integration |
1,291 | statistics | easy | Find the median of 3 15 10 4 10 16 20 | 10 | 10 | 12 | 11 | 8 | Statistical measure calculation |
2,746 | trigonometry | medium | What is tan(45°)? | 1 | 1 | √2 | 0 | √3 | Trigonometric functions and identities |
1,378 | statistics | easy | Find the median of 14 10 14 17 5 5 | 12 | 12 | 14 | 13 | 10 | Statistical measure calculation |
117 | arithmetic | easy | What is 56 + 54? | 110 | 108 | 111 | 110 | 113 | Standard arithmetic calculation |
782 | algebra | hard | Solve: x² + -11x + 30 = 0 | x = 5 or x = 6 | x = 4 or x = 7 | x = 5 or x = 6 | x = -5 or x = -6 | x = 6 or x = 5 | Algebraic manipulation and solving |
4,235 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 7] | [3, 6] | [4, 7] | [2, 7] | Vector operations and matrix calculations |
4,311 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 10 | 8 | 11 | Vector operations and matrix calculations |
1,985 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/3 | 0/2 | 2/2 | 1/2 | Fraction arithmetic and simplification |
4,365 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 11 | 9 | 8 | 10 | Vector operations and matrix calculations |
4,710 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 4 | 8 | 6 | 5 | Permutations and combinations |
2,556 | trigonometry | easy | Find cos(180°) | -1 | -1 | -1 | 1 | 0 | Trigonometric functions and identities |
4,323 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 8 | 9 | 11 | 10 | Vector operations and matrix calculations |
107 | arithmetic | easy | Find 11 × 9 | 99 | 99 | 104 | 101 | 96 | Standard arithmetic calculation |
565 | algebra | medium | Find x: x² = 16 | 4 | 2 | 5 | 7 | 4 | Algebraic manipulation and solving |
1,412 | statistics | medium | What is the mode of 16 7 7 13 7 14 6? | 7 | 10 | 5 | 7 | 8 | Statistical measure calculation |
3,524 | number_theory | medium | Find LCM of 15 and 20 | 60 | 75 | 50 | 65 | 60 | Number theory and modular arithmetic |
3,091 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/35 | 1/36 | 1/30 | 1/32 | Probability calculation and expected value |
2,365 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x cos(x²) | cos(2x) | 2x sin(x²) | cos(x²) | Calculus differentiation and integration |
2,424 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(x²) | 2x sin(x²) | 2x cos(x²) | cos(2x) | Calculus differentiation and integration |
3,337 | number_theory | easy | What is the GCD of 8 and 12? | 4 | 4 | 3 | 5 | 2 | Number theory and modular arithmetic |
2,781 | 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 |
4,852 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 125 | 50 | 60 | 75 | Permutations and combinations |
30 | arithmetic | easy | Calculate 64 - 40 | 24 | 25 | 23 | 24 | 26 | Standard arithmetic calculation |
2,070 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/3 | 2/2 | 1/2 | 0/2 | Fraction arithmetic and simplification |
2,705 | trigonometry | medium | What is tan(45°)? | 1 | √2 | √3 | 1 | 0 | Trigonometric functions and identities |
2,619 | trigonometry | easy | Calculate tan(0°) | 0 | -1 | 0 | undefined | 1 | Trigonometric functions and identities |
2,305 | calculus | medium | What is d/dx(4x^2 - 3x + 1)? | 8x^1 - 3 | 8x^2 - 3 | 8x^1 - 1 | 8x^1 - 3 | 4x^1 - 3 | Calculus differentiation and integration |
3,081 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/30 | 1/35 | 1/32 | 1/36 | Probability calculation and expected value |
2,447 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x cos(x²) | 2x sin(x²) | cos(2x) | cos(x²) | Calculus differentiation and integration |
4,193 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 6] | [2, 7] | [3, 7] | [4, 7] | Vector operations and matrix calculations |
75 | arithmetic | easy | What is 20 + 59? | 79 | 80 | 82 | 79 | 77 | Standard arithmetic calculation |
2,551 | trigonometry | easy | Find cos(90°) | 0 | 1 | 0 | -1 | 0 | Trigonometric functions and identities |
1,732 | fractions | easy | What is 1/2 + 1/4? | 3/4 | 3/5 | 3/4 | 2/4 | 4/4 | Fraction arithmetic and simplification |
3,860 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Cannot determine | Depends on context | False | True | Logical reasoning and boolean operations |
3,304 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3 | 3.5 | 4 | Probability calculation and expected value |
2,922 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 6 | 7 | 5 | 8 | Probability calculation and expected value |
479 | algebra | easy | What is 6x when x = 7? | 42 | 44 | 39 | 47 | 42 | Algebraic manipulation and solving |
3,183 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/30 | 1/32 | 1/35 | 1/36 | Probability calculation and expected value |
3,523 | number_theory | medium | Find LCM of 15 and 20 | 60 | 65 | 60 | 75 | 50 | Number theory and modular arithmetic |
2,502 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(2x) | 2x sin(x²) | cos(x²) | 2x cos(x²) | Calculus differentiation and integration |
1,693 | fractions | easy | Simplify 10/20 | 1/2 | 1/2 | 11/21 | 9/19 | 5/10 | Fraction arithmetic and simplification |
1,079 | geometry | medium | Find the area of a circle with radius 3 (use π ≈ 3.14) | 28.27 | 25.77 | 28.27 | 30.07 | 31.47 | Geometric calculation and spatial reasoning |
2,612 | trigonometry | easy | Find cos(0°) | 1 | 1 | 1/2 | -1 | 0 | Trigonometric functions and identities |
4,172 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 7] | [3, 6] | [4, 7] | [2, 7] | Vector operations and matrix calculations |
480 | algebra | easy | Solve for x: x + 7 = 13 | 6 | 4 | 7 | 9 | 6 | Algebraic manipulation and solving |
2,955 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 1/4 | 1/2 | 1/3 | 2/3 | Probability calculation and expected value |
4,078 | 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 |
1,860 | fractions | medium | Calculate 2/3 × 1/2 | 1/3 | 1/3 | 3/1 | 1/4 | 2/3 | Fraction arithmetic and simplification |
1,068 | geometry | medium | What is the volume of a cube with side length 9? | 729 | 764 | 729 | 709 | 744 | Geometric calculation and spatial reasoning |
4,849 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 60 | 50 | 125 | 75 | Permutations and combinations |
1,194 | geometry | hard | Find the hypotenuse of a right triangle with legs 7 and 24 | 25 | 25 | 23 | 26 | 24 | Geometric calculation and spatial reasoning |
3,789 | logic | easy | If all cats are mammals and Fluffy is a cat, then Fluffy is a: | mammal | cat | animal | mammal | pet | Logical reasoning and boolean operations |
2,574 | trigonometry | easy | Calculate tan(0°) | 0 | undefined | -1 | 1 | 0 | Trigonometric functions and identities |
1,150 | geometry | hard | Find the hypotenuse of a right triangle with legs 7 and 24 | 25 | 23 | 26 | 24 | 25 | Geometric calculation and spatial reasoning |
587 | algebra | medium | Solve: 3x - 12 = 10 | 7 | 8 | 7 | 5 | 10 | Algebraic manipulation and solving |
4,460 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 5 | 3 | 6 | 4 | Vector operations and matrix calculations |
3,949 | logic | medium | What is NOT(True AND False)? | True | Depends on values | False | Cannot determine | True | Logical reasoning and boolean operations |
4,999 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 48 | 60 | 120 | 24 | Permutations and combinations |
1,221 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 6 | 5 | 3 | 4 | Geometric calculation and spatial reasoning |
4,901 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 48 | 120 | 60 | 24 | Permutations and combinations |
2,751 | trigonometry | medium | What is tan(45°)? | 1 | 0 | √2 | 1 | √3 | Trigonometric functions and identities |
1,775 | fractions | easy | What is 1/2 + 1/3? | 5/6 | 4/6 | 5/7 | 5/6 | 6/6 | Fraction arithmetic and simplification |
3,064 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/12 | 1/15 | 1/13 | 1/14 | Probability calculation and expected value |
2,326 | calculus | medium | What is d/dx(5x^2 - 3x + 1)? | 10x^1 - 3 | 10x^1 - 1 | 5x^1 - 3 | 10x^1 - 3 | 10x^2 - 3 | Calculus differentiation and integration |
2,598 | trigonometry | easy | What is sin(90°)? | 1 | 1/2 | 1 | 0 | -1 | Trigonometric functions and identities |
3,909 | logic | medium | What is NOT(True AND False)? | True | False | True | Cannot determine | Depends on values | Logical reasoning and boolean operations |
3,444 | number_theory | easy | Is 19 a prime number? | Yes | Yes | Cannot determine | Only if x>0 | No | Number theory and modular arithmetic |
2,720 | trigonometry | medium | What is tan(45°)? | 1 | 1 | √2 | 0 | √3 | Trigonometric functions and identities |
4,258 | linear_algebra | easy | Calculate 3 × [2, 3] | [6, 9] | [6, 8] | [7, 9] | [6, 9] | [5, 9] | Vector operations and matrix calculations |
1,617 | 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 |
552 | algebra | easy | What is 8x when x = 4? | 32 | 29 | 34 | 32 | 37 | Algebraic manipulation and solving |
659 | algebra | medium | Find x: x² = 49 | 7 | 10 | 5 | 8 | 7 | Algebraic manipulation and solving |
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