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 |
|---|---|---|---|---|---|---|---|---|---|
4,926 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 120 | 60 | 48 | 24 | Permutations and combinations |
427 | algebra | easy | What is 8x when x = 8? | 64 | 61 | 66 | 69 | 64 | Algebraic manipulation and solving |
3,679 | number_theory | hard | What is 7³ mod 11? | 2 | 2 | 4 | 3 | 1 | Number theory and modular arithmetic |
4,868 | 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 |
2,000 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 2/2 | 1/2 | 0/2 | 1/3 | Fraction arithmetic and simplification |
3,210 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 4.5 | 4 | 3 | Probability calculation and expected value |
686 | algebra | medium | Solve: 4x - 13 = 12 | 6 | 6 | 9 | 4 | 7 | Algebraic manipulation and solving |
2,161 | calculus | easy | Evaluate ∫x^3 dx | x^4/4 + C | 3x^2 + C | x^4/4 + C | x^5/5 + C | x^3 + C | Calculus differentiation and integration |
3,901 | logic | medium | If P implies Q and P is true, what can we conclude about Q? | Q is true | Q is false | P is false | Cannot determine | Q is true | Logical reasoning and boolean operations |
3,160 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/30 | 1/36 | 1/32 | 1/35 | Probability calculation and expected value |
763 | algebra | hard | Solve: x² + -11x + 24 = 0 | x = 3 or x = 8 | x = 2 or x = 9 | x = 3 or x = 8 | x = -3 or x = -8 | x = 4 or x = 7 | Algebraic manipulation and solving |
3,284 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 4 | 3 | 4.5 | Probability calculation and expected value |
2,147 | calculus | easy | Find d/dx(x^5) | 5x^4 | 5x^4 | x^5 | 5x^5 | x^4 | Calculus differentiation and integration |
2,621 | trigonometry | easy | What is sin(60°)? | 0.87 | -1 | 0 | 0.87 | 1 | Trigonometric functions and identities |
3,363 | number_theory | easy | Is 23 a prime number? | Yes | Yes | Only if x>0 | Cannot determine | No | Number theory and modular arithmetic |
3,063 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/12 | 1/14 | 1/13 | 1/15 | Probability calculation and expected value |
2,107 | calculus | easy | Find d/dx(x^5) | 5x^4 | 5x^5 | x^5 | x^4 | 5x^4 | Calculus differentiation and integration |
2,755 | trigonometry | medium | What is tan(45°)? | 1 | 0 | 1 | √2 | √3 | Trigonometric functions and identities |
4,332 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 11 | 10 | 8 | Vector operations and matrix calculations |
3,320 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 4.5 | 4 | 3 | Probability calculation and expected value |
4,242 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 6] | [2, 7] | [3, 7] | [4, 7] | Vector operations and matrix calculations |
3,781 | 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 |
3,494 | number_theory | medium | Find LCM of 15 and 20 | 60 | 75 | 50 | 65 | 60 | Number theory and modular arithmetic |
1,662 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.54 | 1.74 | 2.94 | 2.24 | Statistical measure calculation |
2,126 | calculus | easy | Find d/dx(x^4) | 4x^3 | 4x^3 | 4x^4 | x^4 | x^3 | Calculus differentiation and integration |
1,435 | statistics | medium | What is the mode of 12 12 12 2 2 16 11? | 12 | 15 | 13 | 10 | 12 | Statistical measure calculation |
1,703 | fractions | easy | What is 1/2 + 1/6? | 2/3 | 3/3 | 1/3 | 2/3 | 2/4 | Fraction arithmetic and simplification |
1,264 | statistics | easy | What is the mean of 15 4 14 3? | 9 | 9 | 10 | 7 | 11 | Statistical measure calculation |
1,499 | statistics | medium | Calculate the range of 2 18 2 12 18 6 12 | 16 | 17 | 14 | 19 | 16 | Statistical measure calculation |
1,924 | fractions | medium | Calculate 5/4 × 2/3 | 5/6 | 6/5 | 5/7 | 5/6 | 6/6 | Fraction arithmetic and simplification |
2,389 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(x²) | cos(2x) | 2x sin(x²) | 2x cos(x²) | Calculus differentiation and integration |
2,731 | trigonometry | medium | What is tan(45°)? | 1 | √2 | 0 | 1 | √3 | Trigonometric functions and identities |
2,894 | 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 |
651 | algebra | medium | Solve: 6x - 12 = 18 | 5 | 6 | 5 | 8 | 3 | Algebraic manipulation and solving |
3,461 | number_theory | easy | What is the GCD of 8 and 12? | 4 | 2 | 3 | 4 | 5 | Number theory and modular arithmetic |
3,565 | number_theory | medium | How many factors does 30 have? | 8 | 7 | 8 | 6 | 9 | Number theory and modular arithmetic |
1,212 | geometry | hard | Find the hypotenuse of a right triangle with legs 7 and 24 | 25 | 25 | 26 | 23 | 24 | Geometric calculation and spatial reasoning |
1,128 | geometry | hard | Find the hypotenuse of a right triangle with legs 8 and 15 | 17 | 15 | 18 | 16 | 17 | Geometric calculation and spatial reasoning |
3,968 | logic | medium | What is NOT(True AND False)? | True | Cannot determine | Depends on values | True | False | Logical reasoning and boolean operations |
3,194 | 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 |
3,742 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 3 | 2 | 4 | Number theory and modular arithmetic |
3,922 | logic | medium | If P implies Q and P is true, what can we conclude about Q? | Q is true | Q is true | Cannot determine | P is false | Q is false | Logical reasoning and boolean operations |
2,815 | 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 |
2,106 | calculus | easy | Find d/dx(x^5) | 5x^4 | 5x^5 | 5x^4 | x^5 | x^4 | Calculus differentiation and integration |
3,208 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3 | 3.5 | 4 | 4.5 | Probability calculation and expected value |
2,764 | trigonometry | medium | What is tan(45°)? | 1 | √2 | 1 | √3 | 0 | Trigonometric functions and identities |
856 | geometry | easy | How many sides does a hexagon have? | 6 | 8 | 6 | 5 | 7 | Geometric calculation and spatial reasoning |
4,662 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 8 | 5 | 4 | 6 | Permutations and combinations |
2,848 | 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 |
2,631 | trigonometry | easy | What is sin(45°)? | 0.71 | 0 | 1 | 0.71 | -1 | Trigonometric functions and identities |
1,481 | statistics | medium | Calculate the range of 10 12 19 7 8 5 17 11 | 14 | 17 | 14 | 12 | 15 | Statistical measure calculation |
1,175 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 5 | 6 | 3 | 4 | Geometric calculation and spatial reasoning |
2,882 | 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 |
1,434 | statistics | medium | What is the mode of 12 12 12 8 12 16 18? | 12 | 15 | 13 | 10 | 12 | Statistical measure calculation |
4,276 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [2, 7] | [3, 7] | [4, 7] | [3, 6] | Vector operations and matrix calculations |
3,794 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Depends on context | True | False | Cannot determine | Logical reasoning and boolean operations |
1,067 | geometry | medium | Find the area of a circle with radius 8 (use π ≈ 3.14) | 201.06 | 202.86 | 204.26 | 201.06 | 198.56 | Geometric calculation and spatial reasoning |
3,621 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 3 | 1 | 2 | Number theory and modular arithmetic |
1,531 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 1.74 | 2.54 | 2.94 | 2.24 | Statistical measure calculation |
1,243 | geometry | hard | Find the hypotenuse of a right triangle with legs 7 and 24 | 25 | 26 | 25 | 23 | 24 | Geometric calculation and spatial reasoning |
2,157 | calculus | easy | Find d/dx(x^5) | 5x^4 | 5x^4 | x^5 | x^4 | 5x^5 | Calculus differentiation and integration |
1,278 | statistics | easy | Find the median of 4 8 3 14 12 3 | 6 | 7 | 4 | 8 | 6 | Statistical measure calculation |
3,438 | number_theory | easy | Is 23 a prime number? | Yes | Yes | No | Cannot determine | Only if x>0 | Number theory and modular arithmetic |
2,553 | trigonometry | easy | What is tan(45°)? | 1 | 0 | 1 | √2 | √3 | Trigonometric functions and identities |
3,193 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/13 | 1/12 | 1/14 | 1/15 | Probability calculation and expected value |
78 | arithmetic | easy | Calculate 83 - 82 | 1 | 2 | 1 | 0 | 3 | Standard arithmetic calculation |
979 | geometry | medium | Find the area of a circle with radius 3 (use π ≈ 3.14) | 28.27 | 30.07 | 25.77 | 28.27 | 31.47 | Geometric calculation and spatial reasoning |
1,471 | statistics | medium | Calculate the range of 20 17 18 16 | 4 | 7 | 4 | 2 | 5 | Statistical measure calculation |
3,761 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | False | True | Cannot determine | Depends on context | Logical reasoning and boolean operations |
4,141 | 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 |
3,549 | number_theory | medium | How many factors does 36 have? | 9 | 8 | 9 | 10 | 7 | Number theory and modular arithmetic |
637 | algebra | medium | Find x: x² = 36 | 6 | 4 | 9 | 7 | 6 | Algebraic manipulation and solving |
4,896 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 120 | 48 | 24 | 60 | Permutations and combinations |
82 | arithmetic | easy | Find 5 × 8 | 40 | 45 | 37 | 42 | 40 | Standard arithmetic calculation |
4,404 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 8 | 9 | 10 | 11 | Vector operations and matrix calculations |
4,020 | logic | medium | What is NOT(True AND False)? | True | True | Cannot determine | False | Depends on values | Logical reasoning and boolean operations |
1,073 | geometry | medium | Find the area of a circle with radius 4 (use π ≈ 3.14) | 50.27 | 53.47 | 47.77 | 52.07 | 50.27 | Geometric calculation and spatial reasoning |
2,775 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 0 | 1 | 2 | sin(2x) | Trigonometric functions and identities |
2,489 | 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 |
2,847 | 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 |
3,389 | number_theory | easy | What is the GCD of 15 and 25? | 5 | 4 | 6 | 5 | 3 | Number theory and modular arithmetic |
549 | algebra | easy | Solve for x: x + 14 = 21 | 7 | 7 | 8 | 10 | 5 | Algebraic manipulation and solving |
2,788 | 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 |
299 | arithmetic | hard | Calculate (3^3 × 4) ÷ 3 | 36 | 31 | 39 | 36 | 44 | Standard arithmetic calculation |
2,015 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 0/2 | 2/2 | 1/2 | 1/3 | Fraction arithmetic and simplification |
1,388 | statistics | easy | What is the mean of 18 20 9 18 13? | 15.6 | 16.6 | 15.6 | 13.6 | 17.6 | Statistical measure calculation |
3,835 | logic | easy | If all cats are mammals and Fluffy is a cat, then Fluffy is a: | mammal | mammal | animal | pet | cat | Logical reasoning and boolean operations |
4,679 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 4 | 8 | 6 | 5 | Permutations and combinations |
4,963 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 60 | 24 | 120 | 48 | Permutations and combinations |
2,005 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 2/2 | 0/2 | 1/3 | 1/2 | Fraction arithmetic and simplification |
2,990 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 7 | 8 | 5 | 6 | Probability calculation and expected value |
4,675 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 8 | 4 | 5 | 6 | Permutations and combinations |
3,330 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 4 | 3.5 | 3 | Probability calculation and expected value |
3,313 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4 | 3 | 4.5 | 3.5 | Probability calculation and expected value |
4,693 | combinatorics | easy | How many ways can 5 people stand in a line? | 120 | 10 | 120 | 25 | 24 | Permutations and combinations |
3,805 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | True | Depends on context | Cannot determine | False | Logical reasoning and boolean operations |
836 | geometry | easy | How many sides does a heptagon have? | 7 | 7 | 8 | 6 | 9 | Geometric calculation and spatial reasoning |
3,705 | number_theory | hard | What is 7³ mod 11? | 2 | 3 | 1 | 2 | 4 | Number theory and modular arithmetic |
3,215 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3 | 4.5 | 3.5 | 4 | Probability calculation and expected value |
2,261 | calculus | medium | What is d/dx(4x^2 - 2x + 1)? | 8x^1 - 2 | 8x^2 - 2 | 8x^1 - 2 | 4x^1 - 2 | 8x^1 - 1 | Calculus differentiation and integration |
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