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 |
|---|---|---|---|---|---|---|---|---|---|
3,004 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
7
|
8
|
5
|
Probability calculation and expected value
|
2,248 |
calculus
|
medium
|
What is d/dx(3x^3 - 3x + 1)?
|
9x^2 - 3
|
9x^2 - 3
|
9x^2 - 1
|
9x^3 - 3
|
3x^2 - 3
|
Calculus differentiation and integration
|
363 |
arithmetic
|
hard
|
Calculate (3^4 × 4) ÷ 9
|
36
|
36
|
44
|
31
|
39
|
Standard arithmetic calculation
|
4,986 |
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
|
2,222 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^5
|
x^4
|
5x^5
|
5x^4
|
Calculus differentiation and integration
|
379 |
arithmetic
|
hard
|
Calculate (4^4 × 2) ÷ 9
|
56
|
64
|
56
|
51
|
59
|
Standard arithmetic calculation
|
3,684 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
2
|
1
|
4
|
Number theory and modular arithmetic
|
3,559 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
75
|
60
|
65
|
50
|
Number theory and modular arithmetic
|
339 |
arithmetic
|
hard
|
Calculate (6^4 × 3) ÷ 3
|
1296
|
1304
|
1299
|
1291
|
1296
|
Standard arithmetic calculation
|
2,415 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(x²)
|
2x cos(x²)
|
cos(2x)
|
Calculus differentiation and integration
|
932 |
geometry
|
easy
|
What is the area of a rectangle with length 9 and width 8?
|
72
|
80
|
75
|
72
|
67
|
Geometric calculation and spatial reasoning
|
3,331 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
4
|
3
|
3.5
|
Probability calculation and expected value
|
4,954 |
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
|
2,554 |
trigonometry
|
easy
|
What is tan(45°)?
|
1
|
√3
|
1
|
0
|
√2
|
Trigonometric functions and identities
|
3,771 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
True
|
Cannot determine
|
False
|
Logical reasoning and boolean operations
|
4,840 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
125
|
50
|
75
|
Permutations and combinations
|
3,548 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
6
|
8
|
7
|
9
|
Number theory and modular arithmetic
|
4,908 |
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
|
2,139 |
calculus
|
easy
|
Find ∫x dx
|
x²/2 + C
|
x²
|
x²/2 + C
|
x³/3 + C
|
x + C
|
Calculus differentiation and integration
|
3,156 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/13
|
1/14
|
1/15
|
1/12
|
Probability calculation and expected value
|
1,671 |
fractions
|
easy
|
Simplify 9/15
|
3/5
|
10/16
|
3/5
|
4/7
|
8/14
|
Fraction arithmetic and simplification
|
645 |
algebra
|
medium
|
Find x: x² = 36
|
6
|
7
|
4
|
9
|
6
|
Algebraic manipulation and solving
|
3,538 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
45
|
50
|
60
|
35
|
Number theory and modular arithmetic
|
4,691 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
4
|
5
|
8
|
6
|
Permutations and combinations
|
747 |
algebra
|
hard
|
Solve: x² + -12x + 32 = 0
|
x = 8 or x = 4
|
x = 7 or x = 5
|
x = 8 or x = 4
|
x = -8 or x = -4
|
x = 9 or x = 3
|
Algebraic manipulation and solving
|
459 |
algebra
|
easy
|
Solve for x: x + 9 = 18
|
9
|
7
|
9
|
12
|
10
|
Algebraic manipulation and solving
|
852 |
geometry
|
easy
|
What is the area of a rectangle with length 8 and width 7?
|
56
|
56
|
59
|
51
|
64
|
Geometric calculation and spatial reasoning
|
4,803 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
60
|
125
|
75
|
Permutations and combinations
|
962 |
geometry
|
easy
|
How many sides does a pentagon have?
|
5
|
5
|
4
|
6
|
7
|
Geometric calculation and spatial reasoning
|
863 |
geometry
|
easy
|
How many sides does a octagon have?
|
8
|
7
|
8
|
10
|
9
|
Geometric calculation and spatial reasoning
|
4,299 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[2, 7]
|
[3, 6]
|
[3, 7]
|
Vector operations and matrix calculations
|
2,817 |
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
|
4,558 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
5
|
3
|
4
|
Vector operations and matrix calculations
|
4,923 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
120
|
48
|
60
|
Permutations and combinations
|
4,738 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
50
|
60
|
125
|
Permutations and combinations
|
632 |
algebra
|
medium
|
Solve: 3x - 10 = 10
|
6
|
9
|
4
|
7
|
6
|
Algebraic manipulation and solving
|
2,733 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
sin(2x)
|
0
|
2
|
Trigonometric functions and identities
|
3,400 |
number_theory
|
easy
|
Is 13 a prime number?
|
Yes
|
Only if x>0
|
Yes
|
No
|
Cannot determine
|
Number theory and modular arithmetic
|
2,873 |
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
|
1,792 |
fractions
|
easy
|
What is 1/2 + 1/4?
|
3/4
|
2/4
|
3/4
|
4/4
|
3/5
|
Fraction arithmetic and simplification
|
4,573 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
4
|
5
|
3
|
Vector operations and matrix calculations
|
886 |
geometry
|
easy
|
How many sides does a pentagon have?
|
5
|
4
|
7
|
6
|
5
|
Geometric calculation and spatial reasoning
|
3,531 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
7
|
6
|
8
|
9
|
Number theory and modular arithmetic
|
802 |
algebra
|
hard
|
Solve: x² + -6x + 8 = 0
|
x = 4 or x = 2
|
x = 3 or x = 3
|
x = 4 or x = 2
|
x = -4 or x = -2
|
x = 5 or x = 1
|
Algebraic manipulation and solving
|
790 |
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
|
2,830 |
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
|
3,564 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
8
|
7
|
6
|
9
|
Number theory and modular arithmetic
|
494 |
algebra
|
easy
|
What is 3x when x = 8?
|
24
|
26
|
21
|
29
|
24
|
Algebraic manipulation and solving
|
2,719 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
sin(2x)
|
0
|
2
|
Trigonometric functions and identities
|
2,889 |
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
|
4,043 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
False
|
True
|
Depends on other variables
|
Logical reasoning and boolean operations
|
2,474 |
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
|
1,621 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.54
|
2.24
|
1.74
|
Statistical measure calculation
|
3,925 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
False
|
True
|
Cannot determine
|
Depends on values
|
Logical reasoning and boolean operations
|
862 |
geometry
|
easy
|
How many sides does a octagon have?
|
8
|
8
|
9
|
10
|
7
|
Geometric calculation and spatial reasoning
|
512 |
algebra
|
easy
|
Solve for x: x + 7 = 15
|
8
|
6
|
9
|
11
|
8
|
Algebraic manipulation and solving
|
2,718 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
2
|
1
|
0
|
Trigonometric functions and identities
|
1,251 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
26
|
24
|
25
|
23
|
Geometric calculation and spatial reasoning
|
2,140 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^5/5 + C
|
x^6/6 + C
|
x^4 + C
|
4x^3 + C
|
Calculus differentiation and integration
|
168 |
arithmetic
|
medium
|
Calculate 180 ÷ 12
|
15
|
13
|
15
|
16
|
18
|
Standard arithmetic calculation
|
3,239 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
4
|
3
|
3.5
|
Probability calculation and expected value
|
1,868 |
fractions
|
medium
|
Calculate 2/3 × 4/7
|
8/21
|
21/8
|
8/21
|
9/21
|
8/22
|
Fraction arithmetic and simplification
|
266 |
arithmetic
|
medium
|
What is 8²?
|
64
|
79
|
72
|
54
|
64
|
Standard arithmetic calculation
|
4,154 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
False
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
2,824 |
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
|
2,095 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^5/5 + C
|
4x^3 + C
|
x^4 + C
|
x^6/6 + C
|
Calculus differentiation and integration
|
4,104 |
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
|
2,793 |
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
|
2,388 |
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
|
3,503 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
7
|
9
|
8
|
6
|
Number theory and modular arithmetic
|
2,342 |
calculus
|
medium
|
What is d/dx(5x^3 - 5x + 1)?
|
15x^2 - 5
|
5x^2 - 5
|
15x^2 - 1
|
15x^3 - 5
|
15x^2 - 5
|
Calculus differentiation and integration
|
1,624 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
1.74
|
2.54
|
2.24
|
2.94
|
Statistical measure calculation
|
3,710 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
52 |
arithmetic
|
easy
|
Calculate 89 - 56
|
33
|
33
|
32
|
34
|
35
|
Standard arithmetic calculation
|
3,902 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
Q is true
|
P is false
|
Q is false
|
Logical reasoning and boolean operations
|
567 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
6
|
8
|
3
|
5
|
Algebraic manipulation and solving
|
4,407 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
8
|
11
|
9
|
Vector operations and matrix calculations
|
1,633 |
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
|
3,760 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
True
|
Depends on context
|
Cannot determine
|
Logical reasoning and boolean operations
|
706 |
algebra
|
hard
|
Solve: x² + -11x + 28 = 0
|
x = 7 or x = 4
|
x = 6 or x = 5
|
x = 7 or x = 4
|
x = -7 or x = -4
|
x = 8 or x = 3
|
Algebraic manipulation and solving
|
4,848 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
60
|
50
|
75
|
Permutations and combinations
|
1,614 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
2.54
|
1.74
|
2.94
|
Statistical measure calculation
|
294 |
arithmetic
|
hard
|
Calculate (6^3 × 2) ÷ 4
|
108
|
103
|
116
|
111
|
108
|
Standard arithmetic calculation
|
2,237 |
calculus
|
medium
|
What is d/dx(4x^4 - 3x + 1)?
|
16x^3 - 3
|
4x^3 - 3
|
16x^4 - 3
|
16x^3 - 3
|
16x^3 - 1
|
Calculus differentiation and integration
|
4,447 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
6
|
5
|
4
|
Vector operations and matrix calculations
|
3,589 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
60
|
50
|
35
|
45
|
Number theory and modular arithmetic
|
3,271 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3
|
3.5
|
4
|
Probability calculation and expected value
|
2,355 |
calculus
|
medium
|
What is d/dx(5x^2 - 2x + 1)?
|
10x^1 - 2
|
10x^1 - 2
|
10x^1 - 1
|
5x^1 - 2
|
10x^2 - 2
|
Calculus differentiation and integration
|
1,561 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
2.54
|
2.94
|
1.74
|
Statistical measure calculation
|
2,257 |
calculus
|
medium
|
What is d/dx(3x^3 - 8x + 1)?
|
9x^2 - 8
|
9x^3 - 8
|
9x^2 - 8
|
9x^2 - 1
|
3x^2 - 8
|
Calculus differentiation and integration
|
1,173 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
16
|
18
|
15
|
Geometric calculation and spatial reasoning
|
2,455 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(x²)
|
2x cos(x²)
|
cos(2x)
|
Calculus differentiation and integration
|
3,522 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
50
|
60
|
35
|
45
|
Number theory and modular arithmetic
|
2,323 |
calculus
|
medium
|
What is d/dx(5x^4 - 2x + 1)?
|
20x^3 - 2
|
20x^3 - 2
|
5x^3 - 2
|
20x^3 - 1
|
20x^4 - 2
|
Calculus differentiation and integration
|
72 |
arithmetic
|
easy
|
What is 43 + 61?
|
104
|
107
|
104
|
105
|
102
|
Standard arithmetic calculation
|
3,340 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
4
|
6
|
5
|
3
|
Number theory and modular arithmetic
|
1,626 |
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
|
2,663 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
sin(2x)
|
2
|
1
|
Trigonometric functions and identities
|
3,769 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
cat
|
mammal
|
pet
|
animal
|
Logical reasoning and boolean operations
|
2,080 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
2/2
|
1/3
|
1/2
|
Fraction arithmetic and simplification
|
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