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 |
|---|---|---|---|---|---|---|---|---|---|
1,313 |
statistics
|
easy
|
Find the median of 20 7 7 18 19 9 11 10
|
10.5
|
11.5
|
10.5
|
8.5
|
12.5
|
Statistical measure calculation
|
4,714 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
24
|
8
|
16
|
6
|
Permutations and combinations
|
1,970 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/2
|
2/2
|
1/3
|
Fraction arithmetic and simplification
|
2,752 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
sin(2x)
|
0
|
Trigonometric functions and identities
|
4,955 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
24
|
48
|
60
|
Permutations and combinations
|
4,177 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[6, 8]
|
[7, 9]
|
[6, 9]
|
[5, 9]
|
Vector operations and matrix calculations
|
2,285 |
calculus
|
medium
|
What is d/dx(3x^2 - 8x + 1)?
|
6x^1 - 8
|
6x^1 - 1
|
6x^2 - 8
|
6x^1 - 8
|
3x^1 - 8
|
Calculus differentiation and integration
|
4,687 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
4
|
8
|
5
|
6
|
Permutations and combinations
|
3,307 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3.5
|
4
|
3
|
Probability calculation and expected value
|
3,639 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
2,208 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
x^3
|
x^2
|
3x^3
|
3x^2
|
Calculus differentiation and integration
|
3,011 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
8
|
7
|
5
|
Probability calculation and expected value
|
2,154 |
calculus
|
easy
|
Evaluate ∫x^3 dx
|
x^4/4 + C
|
3x^2 + C
|
x^5/5 + C
|
x^4/4 + C
|
x^3 + C
|
Calculus differentiation and integration
|
4,615 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
120
|
24
|
10
|
25
|
Permutations and combinations
|
40 |
arithmetic
|
easy
|
Calculate 99 - 29
|
70
|
71
|
69
|
72
|
70
|
Standard arithmetic calculation
|
4,949 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
48
|
24
|
120
|
Permutations and combinations
|
3,175 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/36
|
1/32
|
1/35
|
1/30
|
Probability calculation and expected value
|
1,217 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
14
|
11
|
12
|
13
|
Geometric calculation and spatial reasoning
|
3,623 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
4
|
1
|
3
|
Number theory and modular arithmetic
|
4,722 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
6
|
4
|
8
|
Permutations and combinations
|
2,234 |
calculus
|
medium
|
What is d/dx(2x^2 - 8x + 1)?
|
4x^1 - 8
|
2x^1 - 8
|
4x^2 - 8
|
4x^1 - 8
|
4x^1 - 1
|
Calculus differentiation and integration
|
4,539 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
4
|
5
|
3
|
Vector operations and matrix calculations
|
436 |
algebra
|
easy
|
What is 5x when x = 3?
|
15
|
17
|
15
|
12
|
20
|
Algebraic manipulation and solving
|
4,775 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
60
|
125
|
50
|
Permutations and combinations
|
486 |
algebra
|
easy
|
What is 7x when x = 3?
|
21
|
18
|
21
|
26
|
23
|
Algebraic manipulation and solving
|
1,533 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
1.74
|
2.94
|
2.54
|
2.24
|
Statistical measure calculation
|
3,257 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
4.5
|
3.5
|
3
|
Probability calculation and expected value
|
4,735 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
75
|
50
|
125
|
Permutations and combinations
|
2,034 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
2/2
|
1/2
|
1/3
|
Fraction arithmetic and simplification
|
2,345 |
calculus
|
medium
|
What is d/dx(2x^2 - 2x + 1)?
|
4x^1 - 2
|
4x^1 - 1
|
4x^2 - 2
|
2x^1 - 2
|
4x^1 - 2
|
Calculus differentiation and integration
|
641 |
algebra
|
medium
|
Solve: 4x - 12 = 19
|
7
|
8
|
10
|
7
|
5
|
Algebraic manipulation and solving
|
4,976 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
48
|
60
|
120
|
Permutations and combinations
|
1,447 |
statistics
|
medium
|
Calculate the range of 14 5 6 15 17
|
12
|
12
|
15
|
13
|
10
|
Statistical measure calculation
|
2,573 |
trigonometry
|
easy
|
Find cos(0°)
|
1
|
1/2
|
-1
|
0
|
1
|
Trigonometric functions and identities
|
393 |
arithmetic
|
hard
|
Calculate (3^4 × 3) ÷ 3
|
81
|
76
|
84
|
81
|
89
|
Standard arithmetic calculation
|
2,114 |
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
|
3,674 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
1
|
4
|
2
|
Number theory and modular arithmetic
|
3,211 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4.5
|
4
|
3.5
|
Probability calculation and expected value
|
4,306 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[2, 7]
|
[3, 6]
|
[3, 7]
|
Vector operations and matrix calculations
|
413 |
arithmetic
|
hard
|
Calculate (5^3 × 2) ÷ 4
|
62
|
62
|
57
|
65
|
70
|
Standard arithmetic calculation
|
2,938 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/4
|
2/3
|
1/2
|
1/3
|
Probability calculation and expected value
|
1,102 |
geometry
|
medium
|
What is the volume of a cube with side length 4?
|
64
|
44
|
79
|
64
|
99
|
Geometric calculation and spatial reasoning
|
1,479 |
statistics
|
medium
|
Calculate the range of 8 18 3 16
|
15
|
13
|
15
|
16
|
18
|
Statistical measure calculation
|
2,359 |
calculus
|
medium
|
What is d/dx(3x^4 - 6x + 1)?
|
12x^3 - 6
|
12x^4 - 6
|
12x^3 - 1
|
12x^3 - 6
|
3x^3 - 6
|
Calculus differentiation and integration
|
3,294 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4
|
3.5
|
4.5
|
Probability calculation and expected value
|
4,612 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
8
|
4
|
6
|
5
|
Permutations and combinations
|
3,605 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
50
|
75
|
60
|
65
|
Number theory and modular arithmetic
|
3,485 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
45
|
60
|
35
|
50
|
Number theory and modular arithmetic
|
4,886 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
60
|
24
|
120
|
Permutations and combinations
|
252 |
arithmetic
|
medium
|
What is 20% of 223?
|
44
|
49
|
44
|
54
|
39
|
Standard arithmetic calculation
|
1,922 |
fractions
|
medium
|
Divide 1/2 ÷ 1/2
|
1/1
|
1/1
|
2/1
|
1/2
|
1/1
|
Fraction arithmetic and simplification
|
4,643 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
4
|
8
|
6
|
Permutations and combinations
|
3,985 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
P is false
|
Cannot determine
|
Q is false
|
Q is true
|
Logical reasoning and boolean operations
|
4,800 |
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
|
3,076 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/36
|
1/30
|
1/32
|
1/35
|
Probability calculation and expected value
|
1,037 |
geometry
|
medium
|
What is the volume of a cube with side length 4?
|
64
|
44
|
79
|
64
|
99
|
Geometric calculation and spatial reasoning
|
1,127 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
3
|
4
|
5
|
6
|
Geometric calculation and spatial reasoning
|
2,821 |
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
|
627 |
algebra
|
medium
|
Find x: x² = 64
|
8
|
6
|
8
|
9
|
11
|
Algebraic manipulation and solving
|
977 |
geometry
|
medium
|
What is the volume of a cube with side length 8?
|
512
|
512
|
492
|
547
|
527
|
Geometric calculation and spatial reasoning
|
4,876 |
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
|
4,390 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
1,258 |
statistics
|
easy
|
What is the mean of 6 11 19 12 20 17?
|
14.2
|
12.2
|
14.2
|
16.2
|
15.2
|
Statistical measure calculation
|
4,827 |
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
|
4,260 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
[3, 7]
|
[4, 7]
|
Vector operations and matrix calculations
|
1,393 |
statistics
|
medium
|
What is the mode of 15 13 7 13 7 13 15?
|
13
|
14
|
11
|
16
|
13
|
Statistical measure calculation
|
1,195 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
18
|
15
|
16
|
Geometric calculation and spatial reasoning
|
1,093 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
47.77
|
53.47
|
52.07
|
50.27
|
Geometric calculation and spatial reasoning
|
4,664 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
36
|
120
|
12
|
720
|
Permutations and combinations
|
2,011 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/3
|
1/2
|
2/2
|
Fraction arithmetic and simplification
|
2,895 |
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
|
1,122 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
3
|
4
|
5
|
6
|
Geometric calculation and spatial reasoning
|
2,785 |
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
|
4,403 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
8
|
9
|
11
|
Vector operations and matrix calculations
|
3,970 |
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
|
1,992 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
2/2
|
1/2
|
1/3
|
0/2
|
Fraction arithmetic and simplification
|
178 |
arithmetic
|
medium
|
Calculate 162 ÷ 9
|
18
|
18
|
16
|
21
|
19
|
Standard arithmetic calculation
|
2,765 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
1
|
0
|
Trigonometric functions and identities
|
3,180 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/14
|
1/13
|
1/12
|
1/15
|
Probability calculation and expected value
|
120 |
arithmetic
|
easy
|
Calculate 66 - 66
|
0
|
1
|
2
|
0
|
-1
|
Standard arithmetic calculation
|
1,120 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
18
|
16
|
15
|
Geometric calculation and spatial reasoning
|
1,227 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
3
|
6
|
5
|
4
|
Geometric calculation and spatial reasoning
|
519 |
algebra
|
easy
|
Solve for x: x + 4 = 10
|
6
|
7
|
4
|
9
|
6
|
Algebraic manipulation and solving
|
3,309 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
3.5
|
3
|
4.5
|
Probability calculation and expected value
|
4,067 |
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
|
2,856 |
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
|
1,676 |
fractions
|
easy
|
What is 1/2 + 1/4?
|
3/4
|
4/4
|
2/4
|
3/4
|
3/5
|
Fraction arithmetic and simplification
|
223 |
arithmetic
|
medium
|
What is 9²?
|
81
|
96
|
81
|
71
|
89
|
Standard arithmetic calculation
|
1,796 |
fractions
|
easy
|
What is 1/2 + 1/6?
|
2/3
|
1/3
|
3/3
|
2/4
|
2/3
|
Fraction arithmetic and simplification
|
3,897 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is true
|
P is false
|
Q is false
|
Cannot determine
|
Logical reasoning and boolean operations
|
4,377 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
4,940 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
60
|
120
|
24
|
Permutations and combinations
|
714 |
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
|
4,707 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
25
|
24
|
120
|
10
|
Permutations and combinations
|
3,640 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
3
|
4
|
Number theory and modular arithmetic
|
810 |
algebra
|
hard
|
Solve: x² + -8x + 16 = 0
|
x = 4 or x = 4
|
x = 3 or x = 5
|
x = 4 or x = 4
|
x = -4 or x = -4
|
x = 5 or x = 3
|
Algebraic manipulation and solving
|
3,477 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
9
|
8
|
7
|
6
|
Number theory and modular arithmetic
|
1,299 |
statistics
|
easy
|
Find the median of 19 12 9 5 17
|
12
|
10
|
14
|
13
|
12
|
Statistical measure calculation
|
175 |
arithmetic
|
medium
|
What is 8²?
|
64
|
72
|
79
|
64
|
54
|
Standard arithmetic calculation
|
3,890 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
animal
|
cat
|
mammal
|
pet
|
Logical reasoning and boolean operations
|
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