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 |
|---|---|---|---|---|---|---|---|---|---|
4,499 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 5 | 4 | 3 | 6 | Vector operations and matrix calculations |
4,579 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 4 | 6 | 5 | 3 | Vector operations and matrix calculations |
831 | algebra | hard | Solve: x² + -10x + 16 = 0 | x = 8 or x = 2 | x = 7 or x = 3 | x = 8 or x = 2 | x = -8 or x = -2 | x = 9 or x = 1 | Algebraic manipulation and solving |
4,934 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 60 | 120 | 48 | 24 | Permutations and combinations |
121 | arithmetic | easy | Find 12 × 5 | 60 | 65 | 57 | 62 | 60 | Standard arithmetic calculation |
2,085 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 0/2 | 1/3 | 1/2 | 2/2 | Fraction arithmetic and simplification |
1,877 | fractions | medium | Calculate 1/3 × 1 | 1/3 | 2/3 | 3/1 | 1/4 | 1/3 | Fraction arithmetic and simplification |
4,549 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 5 | 4 | 6 | 3 | Vector operations and matrix calculations |
756 | algebra | hard | Solve: x² + -14x + 48 = 0 | x = 8 or x = 6 | x = 7 or x = 7 | x = 8 or x = 6 | x = -8 or x = -6 | x = 9 or x = 5 | Algebraic manipulation and solving |
1,463 | statistics | medium | What is the mode of 13 2 13 2 20 16 13? | 13 | 13 | 14 | 11 | 16 | Statistical measure calculation |
4,205 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [2, 7] | [3, 6] | [3, 7] | [4, 7] | Vector operations and matrix calculations |
4,137 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | False | Depends on other variables | True | Cannot determine | Logical reasoning and boolean operations |
1,356 | statistics | easy | What is the mean of 11 16 13 16 9? | 13 | 11 | 14 | 13 | 15 | Statistical measure calculation |
3,345 | number_theory | easy | Is 29 a prime number? | Yes | Cannot determine | Yes | Only if x>0 | No | Number theory and modular arithmetic |
4,862 | 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 |
1,413 | statistics | medium | Calculate the range of 18 11 6 2 19 20 | 18 | 18 | 16 | 21 | 19 | Statistical measure calculation |
2,463 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(2x) | 2x cos(x²) | cos(x²) | 2x sin(x²) | Calculus differentiation and integration |
4,418 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 10 | 11 | 9 | 8 | Vector operations and matrix calculations |
2,319 | calculus | medium | What is d/dx(4x^4 - 2x + 1)? | 16x^3 - 2 | 16x^4 - 2 | 16x^3 - 1 | 16x^3 - 2 | 4x^3 - 2 | Calculus differentiation and integration |
804 | algebra | hard | Solve: x² + -10x + 24 = 0 | x = 6 or x = 4 | x = 5 or x = 5 | x = 6 or x = 4 | x = -6 or x = -4 | x = 7 or x = 3 | Algebraic manipulation and solving |
2,491 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x sin(x²) | cos(2x) | 2x cos(x²) | cos(x²) | Calculus differentiation and integration |
629 | algebra | medium | Solve: 3x - 15 = 12 | 9 | 7 | 12 | 9 | 10 | Algebraic manipulation and solving |
1,666 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.24 | 1.74 | 2.54 | 2.94 | Statistical measure calculation |
3,325 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4 | 4.5 | 3.5 | 3 | Probability calculation and expected value |
2,698 | trigonometry | medium | What is tan(45°)? | 1 | √2 | 1 | √3 | 0 | Trigonometric functions and identities |
2,115 | calculus | easy | Evaluate ∫x^2 dx | x^3/3 + C | x^4/4 + C | x^3/3 + C | 2x^1 + C | x^2 + C | Calculus differentiation and integration |
3,671 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 1 | 2 | 3 | Number theory and modular arithmetic |
4,907 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 120 | 60 | 24 | 48 | Permutations and combinations |
92 | arithmetic | easy | Calculate 54 - 16 | 38 | 38 | 40 | 37 | 39 | Standard arithmetic calculation |
3,046 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 2/3 | 1/3 | 1/2 | 1/4 | Probability calculation and expected value |
2,211 | calculus | easy | Evaluate ∫x^4 dx | x^5/5 + C | x^5/5 + C | x^4 + C | 4x^3 + C | x^6/6 + C | Calculus differentiation and integration |
4,144 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | True | Cannot determine | False | Depends on other variables | Logical reasoning and boolean operations |
926 | geometry | easy | What is the area of a rectangle with length 8 and width 5? | 40 | 40 | 35 | 43 | 48 | Geometric calculation and spatial reasoning |
3,488 | number_theory | medium | How many factors does 36 have? | 9 | 8 | 10 | 9 | 7 | Number theory and modular arithmetic |
2,214 | calculus | easy | Find d/dx(x^5) | 5x^4 | x^4 | 5x^5 | 5x^4 | x^5 | Calculus differentiation and integration |
2,802 | 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 |
921 | geometry | easy | What is the area of a rectangle with length 8 and width 7? | 56 | 51 | 59 | 64 | 56 | Geometric calculation and spatial reasoning |
2,843 | 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 |
3,235 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3.5 | 3 | 4 | Probability calculation and expected value |
524 | algebra | easy | What is 5x when x = 3? | 15 | 15 | 17 | 20 | 12 | Algebraic manipulation and solving |
1,731 | fractions | easy | Simplify 28/28 | 1/1 | 14/14 | 29/29 | 27/27 | 1/1 | Fraction arithmetic and simplification |
1,062 | geometry | medium | Find the area of a circle with radius 8 (use π ≈ 3.14) | 201.06 | 198.56 | 201.06 | 202.86 | 204.26 | Geometric calculation and spatial reasoning |
77 | arithmetic | easy | What is 10 + 96? | 106 | 106 | 109 | 104 | 107 | Standard arithmetic calculation |
1,380 | statistics | easy | What is the mean of 10 5 4 9 18 8? | 9 | 9 | 11 | 7 | 10 | Statistical measure calculation |
2,577 | trigonometry | easy | Calculate tan(0°) | 0 | undefined | -1 | 1 | 0 | Trigonometric functions and identities |
2,959 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 2/3 | 1/4 | 1/3 | 1/2 | Probability calculation and expected value |
3,088 | 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 |
1,228 | geometry | hard | Find the hypotenuse of a right triangle with legs 8 and 15 | 17 | 17 | 15 | 16 | 18 | Geometric calculation and spatial reasoning |
4,684 | combinatorics | easy | How many ways can 4 people stand in a line? | 24 | 16 | 24 | 6 | 8 | Permutations and combinations |
3,641 | number_theory | hard | What is 7³ mod 11? | 2 | 2 | 3 | 4 | 1 | Number theory and modular arithmetic |
3,386 | number_theory | easy | What is the GCD of 8 and 12? | 4 | 5 | 2 | 3 | 4 | Number theory and modular arithmetic |
2,327 | calculus | medium | What is d/dx(4x^4 - 2x + 1)? | 16x^3 - 2 | 4x^3 - 2 | 16x^4 - 2 | 16x^3 - 1 | 16x^3 - 2 | Calculus differentiation and integration |
4,251 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [2, 7] | [3, 6] | [4, 7] | [3, 7] | Vector operations and matrix calculations |
4,090 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Depends on other variables | Cannot determine | True | False | Logical reasoning and boolean operations |
4,237 | linear_algebra | easy | Calculate 3 × [2, 3] | [6, 9] | [5, 9] | [6, 8] | [7, 9] | [6, 9] | Vector operations and matrix calculations |
4,050 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | True | Depends on other variables | Cannot determine | False | Logical reasoning and boolean operations |
2,905 | 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 |
2,530 | trigonometry | easy | Find cos(60°) | 1/2 | -1 | 1 | 1/2 | 0 | Trigonometric functions and identities |
1,223 | geometry | hard | Find the hypotenuse of a right triangle with legs 9 and 12 | 15 | 15 | 16 | 14 | 13 | Geometric calculation and spatial reasoning |
3,867 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | True | Depends on context | False | Cannot determine | Logical reasoning and boolean operations |
3,647 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 3 | 4 | 2 | Number theory and modular arithmetic |
806 | algebra | hard | Solve: x² + -9x + 20 = 0 | x = 5 or x = 4 | x = 4 or x = 5 | x = 5 or x = 4 | x = -5 or x = -4 | x = 6 or x = 3 | Algebraic manipulation and solving |
1,462 | statistics | medium | Calculate the range of 16 20 5 20 20 6 15 12 | 15 | 15 | 13 | 18 | 16 | Statistical measure calculation |
537 | algebra | easy | Solve for x: x + 14 = 25 | 11 | 14 | 12 | 11 | 9 | Algebraic manipulation and solving |
4,092 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | False | True | Depends on other variables | Cannot determine | Logical reasoning and boolean operations |
4,561 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 3 | 5 | 4 | 6 | Vector operations and matrix calculations |
3,273 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3 | 3.5 | 4 | Probability calculation and expected value |
760 | 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 |
2,975 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 7 | 8 | 6 | 5 | Probability calculation and expected value |
4,996 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 24 | 60 | 120 | 48 | Permutations and combinations |
3,097 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/32 | 1/30 | 1/36 | 1/35 | Probability calculation and expected value |
1,200 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 3 | 6 | 4 | 5 | Geometric calculation and spatial reasoning |
275 | arithmetic | medium | What is 15% of 86? | 12 | 22 | 17 | 12 | 7 | Standard arithmetic calculation |
4,380 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 11 | 8 | 10 | Vector operations and matrix calculations |
2,674 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 0 | 2 | sin(2x) | 1 | Trigonometric functions and identities |
3,738 | number_theory | hard | What is 7³ mod 11? | 2 | 2 | 3 | 4 | 1 | Number theory and modular arithmetic |
554 | algebra | easy | What is 5x when x = 7? | 35 | 35 | 37 | 40 | 32 | Algebraic manipulation and solving |
3,408 | number_theory | easy | What is the GCD of 8 and 12? | 4 | 3 | 2 | 4 | 5 | Number theory and modular arithmetic |
2,539 | trigonometry | easy | Find cos(30°) | √3/2 | 1 | 0 | √3/2 | -1 | Trigonometric functions and identities |
245 | arithmetic | medium | What is 8²? | 64 | 72 | 54 | 79 | 64 | Standard arithmetic calculation |
1,990 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 0/2 | 1/3 | 1/2 | 2/2 | Fraction arithmetic and simplification |
4,605 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 4 | 8 | 5 | 6 | Permutations and combinations |
3,680 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 3 | 4 | 2 | Number theory and modular arithmetic |
3,129 | 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 |
608 | algebra | medium | Solve: 4x - 8 = 17 | 6 | 4 | 7 | 9 | 6 | Algebraic manipulation and solving |
4,207 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 6] | [4, 7] | [2, 7] | [3, 7] | Vector operations and matrix calculations |
2,185 | calculus | easy | Find d/dx(x^3) | 3x^2 | 3x^3 | x^2 | 3x^2 | x^3 | Calculus differentiation and integration |
2,010 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/2 | 0/2 | 1/3 | 2/2 | Fraction arithmetic and simplification |
2,770 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 1 | sin(2x) | 0 | 2 | Trigonometric functions and identities |
4,085 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Cannot determine | False | Depends on other variables | True | Logical reasoning and boolean operations |
2,348 | calculus | medium | What is d/dx(2x^4 - 5x + 1)? | 8x^3 - 5 | 2x^3 - 5 | 8x^3 - 5 | 8x^3 - 1 | 8x^4 - 5 | Calculus differentiation and integration |
4,655 | combinatorics | easy | How many ways can 4 people stand in a line? | 24 | 16 | 8 | 6 | 24 | Permutations and combinations |
2,145 | calculus | easy | What is the derivative of x²? | 2x | x² | 2x² | x | 2x | Calculus differentiation and integration |
2,016 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/3 | 2/2 | 1/2 | 0/2 | Fraction arithmetic and simplification |
1,934 | fractions | medium | Calculate 2/5 × 1/3 | 2/15 | 15/2 | 3/15 | 2/16 | 2/15 | Fraction arithmetic and simplification |
4,076 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | False | True | Depends on other variables | Cannot determine | Logical reasoning and boolean operations |
4,428 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 11 | 10 | 9 | 8 | Vector operations and matrix calculations |
4,647 | combinatorics | easy | How many ways can 5 people stand in a line? | 120 | 24 | 25 | 120 | 10 | Permutations and combinations |
2,338 | calculus | medium | What is d/dx(2x^3 - 8x + 1)? | 6x^2 - 8 | 6x^2 - 8 | 6x^2 - 1 | 6x^3 - 8 | 2x^2 - 8 | Calculus differentiation and integration |
3,414 | number_theory | easy | What is the GCD of 8 and 12? | 4 | 2 | 4 | 3 | 5 | Number theory and modular arithmetic |
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