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 |
|---|---|---|---|---|---|---|---|---|---|
3,558 |
number_theory
|
medium
|
How many factors does 36 have?
|
9
|
7
|
10
|
9
|
8
|
Number theory and modular arithmetic
|
1,353 |
statistics
|
easy
|
What is the mean of 8 18 10 3 12 20 17 7?
|
11.9
|
9.9
|
11.9
|
13.9
|
12.9
|
Statistical measure calculation
|
4,457 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
3
|
5
|
4
|
Vector operations and matrix calculations
|
4,478 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
3
|
6
|
Vector operations and matrix calculations
|
3,440 |
number_theory
|
easy
|
What is the GCD of 12 and 18?
|
6
|
5
|
6
|
4
|
7
|
Number theory and modular arithmetic
|
606 |
algebra
|
medium
|
Solve: 3x - 10 = 14
|
8
|
8
|
9
|
6
|
11
|
Algebraic manipulation and solving
|
4,769 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
60
|
75
|
125
|
Permutations and combinations
|
4,442 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
10
|
11
|
9
|
Vector operations and matrix calculations
|
4,751 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
75
|
125
|
60
|
Permutations and combinations
|
2,469 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
cos(x²)
|
cos(2x)
|
2x sin(x²)
|
Calculus differentiation and integration
|
3,356 |
number_theory
|
easy
|
Is 13 a prime number?
|
Yes
|
No
|
Cannot determine
|
Only if x>0
|
Yes
|
Number theory and modular arithmetic
|
943 |
geometry
|
easy
|
What is the area of a rectangle with length 10 and width 9?
|
90
|
98
|
85
|
90
|
93
|
Geometric calculation and spatial reasoning
|
2,133 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^4
|
5x^5
|
5x^4
|
x^5
|
Calculus differentiation and integration
|
3,473 |
number_theory
|
easy
|
Is 31 a prime number?
|
Yes
|
Yes
|
No
|
Only if x>0
|
Cannot determine
|
Number theory and modular arithmetic
|
3,586 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
6
|
8
|
7
|
9
|
Number theory and modular arithmetic
|
1,975 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/2
|
1/3
|
2/2
|
Fraction arithmetic and simplification
|
4,801 |
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
|
4,629 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
6
|
4
|
8
|
Permutations and combinations
|
4,146 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
True
|
Cannot determine
|
Depends on other variables
|
False
|
Logical reasoning and boolean operations
|
2,950 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/2
|
1/4
|
2/3
|
1/3
|
Probability calculation and expected value
|
2,507 |
trigonometry
|
easy
|
What is sin(45°)?
|
0.71
|
1
|
0
|
0.71
|
-1
|
Trigonometric functions and identities
|
835 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
9
|
6
|
7
|
8
|
Geometric calculation and spatial reasoning
|
1,596 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.54
|
1.74
|
2.24
|
Statistical measure calculation
|
3,591 |
number_theory
|
medium
|
How many factors does 36 have?
|
9
|
10
|
9
|
8
|
7
|
Number theory and modular arithmetic
|
3,774 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
2,813 |
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
|
1,512 |
statistics
|
medium
|
What is the mode of 11 11 16 11 7 20 6?
|
11
|
11
|
14
|
9
|
12
|
Statistical measure calculation
|
2,555 |
trigonometry
|
easy
|
What is sin(45°)?
|
0.71
|
1
|
0
|
-1
|
0.71
|
Trigonometric functions and identities
|
1,370 |
statistics
|
easy
|
What is the mean of 4 20 14 5?
|
10.8
|
10.8
|
8.8
|
11.8
|
12.8
|
Statistical measure calculation
|
456 |
algebra
|
easy
|
What is 4x when x = 4?
|
16
|
13
|
18
|
21
|
16
|
Algebraic manipulation and solving
|
4,536 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
3
|
6
|
Vector operations and matrix calculations
|
3,396 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
5
|
2
|
4
|
3
|
Number theory and modular arithmetic
|
4,263 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[3, 7]
|
[4, 7]
|
[2, 7]
|
Vector operations and matrix calculations
|
2,175 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^5
|
x^4
|
5x^5
|
5x^4
|
Calculus differentiation and integration
|
2,908 |
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
|
4,322 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
248 |
arithmetic
|
medium
|
Calculate 120 ÷ 12
|
10
|
11
|
10
|
13
|
8
|
Standard arithmetic calculation
|
3,361 |
number_theory
|
easy
|
Is 31 a prime number?
|
Yes
|
Cannot determine
|
Only if x>0
|
Yes
|
No
|
Number theory and modular arithmetic
|
3,560 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
6
|
7
|
8
|
9
|
Number theory and modular arithmetic
|
3,468 |
number_theory
|
easy
|
Is 23 a prime number?
|
Yes
|
Yes
|
Only if x>0
|
Cannot determine
|
No
|
Number theory and modular arithmetic
|
418 |
algebra
|
easy
|
What is 6x when x = 9?
|
54
|
56
|
54
|
59
|
51
|
Algebraic manipulation and solving
|
2,730 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
0
|
1
|
Trigonometric functions and identities
|
4,037 |
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
|
2,405 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
2x cos(x²)
|
cos(x²)
|
cos(2x)
|
Calculus differentiation and integration
|
3,394 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
6
|
4
|
3
|
5
|
Number theory and modular arithmetic
|
4,562 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
4
|
5
|
6
|
Vector operations and matrix calculations
|
4,073 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
True
|
False
|
Depends on other variables
|
Logical reasoning and boolean operations
|
3,590 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
6
|
7
|
8
|
9
|
Number theory and modular arithmetic
|
3,487 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
9
|
7
|
8
|
6
|
Number theory and modular arithmetic
|
710 |
algebra
|
hard
|
Solve: x² + -14x + 48 = 0
|
x = 6 or x = 8
|
x = 5 or x = 9
|
x = 6 or x = 8
|
x = -6 or x = -8
|
x = 7 or x = 7
|
Algebraic manipulation and solving
|
1,311 |
statistics
|
easy
|
Find the median of 8 7 17 10 6 17 9 14
|
9.5
|
10.5
|
7.5
|
11.5
|
9.5
|
Statistical measure calculation
|
2,784 |
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
|
3,618 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
4
|
1
|
2
|
Number theory and modular arithmetic
|
2,937 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/3
|
1/4
|
2/3
|
1/2
|
Probability calculation and expected value
|
1,802 |
fractions
|
easy
|
What is 1/3 + 1/3?
|
2/3
|
2/3
|
2/4
|
1/3
|
3/3
|
Fraction arithmetic and simplification
|
3,874 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
True
|
Cannot determine
|
Depends on context
|
False
|
Logical reasoning and boolean operations
|
148 |
arithmetic
|
medium
|
What is 14²?
|
196
|
186
|
196
|
211
|
204
|
Standard arithmetic calculation
|
778 |
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
|
4,587 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
4
|
5
|
8
|
Permutations and combinations
|
298 |
arithmetic
|
hard
|
Calculate (5^4 × 4) ÷ 7
|
357
|
357
|
360
|
365
|
352
|
Standard arithmetic calculation
|
4,642 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
12
|
720
|
36
|
120
|
Permutations and combinations
|
1,442 |
statistics
|
medium
|
Calculate the range of 6 9 10 5 16 20
|
15
|
15
|
16
|
13
|
18
|
Statistical measure calculation
|
106 |
arithmetic
|
easy
|
Calculate 77 - 16
|
61
|
62
|
61
|
63
|
60
|
Standard arithmetic calculation
|
2,390 |
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
|
1,691 |
fractions
|
easy
|
Simplify 48/54
|
8/9
|
8/9
|
24/27
|
49/55
|
47/53
|
Fraction arithmetic and simplification
|
3,108 |
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
|
1,810 |
fractions
|
medium
|
Divide 3/4 ÷ 2/3
|
9/8
|
8/9
|
9/9
|
10/8
|
9/8
|
Fraction arithmetic and simplification
|
3,534 |
number_theory
|
medium
|
How many factors does 36 have?
|
9
|
9
|
8
|
7
|
10
|
Number theory and modular arithmetic
|
2,910 |
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
|
3,395 |
number_theory
|
easy
|
Is 19 a prime number?
|
Yes
|
Cannot determine
|
No
|
Only if x>0
|
Yes
|
Number theory and modular arithmetic
|
1,239 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
18
|
16
|
17
|
15
|
Geometric calculation and spatial reasoning
|
174 |
arithmetic
|
medium
|
Calculate 182 ÷ 14
|
13
|
16
|
13
|
14
|
11
|
Standard arithmetic calculation
|
4,546 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
3
|
6
|
Vector operations and matrix calculations
|
2,996 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/4
|
1/3
|
2/3
|
1/2
|
Probability calculation and expected value
|
4,724 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
60
|
75
|
50
|
Permutations and combinations
|
2,925 |
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
|
3,803 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
Cannot determine
|
Depends on context
|
True
|
Logical reasoning and boolean operations
|
1,707 |
fractions
|
easy
|
Simplify 35/20
|
7/4
|
34/19
|
36/21
|
17/10
|
7/4
|
Fraction arithmetic and simplification
|
1,895 |
fractions
|
medium
|
Divide 2/5 ÷ 1/2
|
4/5
|
4/5
|
4/6
|
5/4
|
5/5
|
Fraction arithmetic and simplification
|
3,100 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/30
|
1/32
|
1/36
|
Probability calculation and expected value
|
4,389 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
8
|
9
|
Vector operations and matrix calculations
|
3,527 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
60
|
50
|
45
|
35
|
Number theory and modular arithmetic
|
4,169 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[4, 7]
|
[3, 6]
|
[2, 7]
|
Vector operations and matrix calculations
|
579 |
algebra
|
medium
|
Solve: 3x - 14 = 11
|
8
|
11
|
9
|
6
|
8
|
Algebraic manipulation and solving
|
2,652 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
1
|
2
|
sin(2x)
|
Trigonometric functions and identities
|
261 |
arithmetic
|
medium
|
Calculate 112 ÷ 14
|
8
|
11
|
9
|
8
|
6
|
Standard arithmetic calculation
|
4,285 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[2, 7]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
Vector operations and matrix calculations
|
761 |
algebra
|
hard
|
Solve: x² + -8x + 15 = 0
|
x = 5 or x = 3
|
x = 4 or x = 4
|
x = 5 or x = 3
|
x = -5 or x = -3
|
x = 6 or x = 2
|
Algebraic manipulation and solving
|
1,659 |
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
|
4,798 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
125
|
60
|
50
|
Permutations and combinations
|
1,598 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.24
|
2.54
|
1.74
|
Statistical measure calculation
|
1,335 |
statistics
|
easy
|
Find the median of 16 14 11 17
|
15
|
15
|
17
|
16
|
13
|
Statistical measure calculation
|
1,532 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
2.94
|
2.54
|
1.74
|
Statistical measure calculation
|
108 |
arithmetic
|
easy
|
Calculate 57 - 42
|
15
|
17
|
16
|
15
|
14
|
Standard arithmetic calculation
|
1,528 |
statistics
|
medium
|
Calculate the range of 15 12 13 8 12 7 7
|
8
|
8
|
6
|
11
|
9
|
Statistical measure calculation
|
1,983 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
2/2
|
0/2
|
Fraction arithmetic and simplification
|
457 |
algebra
|
easy
|
Solve for x: x + 5 = 9
|
4
|
7
|
2
|
5
|
4
|
Algebraic manipulation and solving
|
2,774 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
2
|
1
|
sin(2x)
|
Trigonometric functions and identities
|
2,332 |
calculus
|
medium
|
What is d/dx(2x^2 - 5x + 1)?
|
4x^1 - 5
|
4x^1 - 5
|
4x^1 - 1
|
4x^2 - 5
|
2x^1 - 5
|
Calculus differentiation and integration
|
3,036 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/4
|
1/3
|
2/3
|
1/2
|
Probability calculation and expected value
|
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