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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