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 |
|---|---|---|---|---|---|---|---|---|---|
4,503 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
3
|
4
|
5
|
Vector operations and matrix calculations
|
4,440 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
9
|
8
|
10
|
Vector operations and matrix calculations
|
2,624 |
trigonometry
|
easy
|
Find cos(180°)
|
-1
|
-1
|
-1
|
0
|
1
|
Trigonometric functions and identities
|
3,228 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4
|
4.5
|
3
|
Probability calculation and expected value
|
348 |
arithmetic
|
hard
|
Calculate (6^4 × 4) ÷ 6
|
864
|
872
|
867
|
859
|
864
|
Standard arithmetic calculation
|
902 |
geometry
|
easy
|
What is the area of a rectangle with length 8 and width 6?
|
48
|
51
|
48
|
56
|
43
|
Geometric calculation and spatial reasoning
|
1,565 |
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
|
2,290 |
calculus
|
medium
|
What is d/dx(3x^2 - 2x + 1)?
|
6x^1 - 2
|
3x^1 - 2
|
6x^1 - 1
|
6x^1 - 2
|
6x^2 - 2
|
Calculus differentiation and integration
|
4,325 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
8
|
11
|
9
|
Vector operations and matrix calculations
|
4,199 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[5, 6]
|
[3, 6]
|
[4, 6]
|
[4, 5]
|
Vector operations and matrix calculations
|
91 |
arithmetic
|
easy
|
What is 12 + 48?
|
60
|
60
|
58
|
63
|
61
|
Standard arithmetic calculation
|
1,044 |
geometry
|
medium
|
Find the area of a circle with radius 5 (use π ≈ 3.14)
|
78.54
|
81.74
|
78.54
|
80.34
|
76.04
|
Geometric calculation and spatial reasoning
|
79 |
arithmetic
|
easy
|
Find 10 × 6
|
60
|
65
|
57
|
60
|
62
|
Standard arithmetic calculation
|
940 |
geometry
|
easy
|
How many sides does a pentagon have?
|
5
|
6
|
4
|
5
|
7
|
Geometric calculation and spatial reasoning
|
633 |
algebra
|
medium
|
Solve: 6x - 13 = 22
|
5
|
6
|
5
|
3
|
8
|
Algebraic manipulation and solving
|
1,508 |
statistics
|
medium
|
Calculate the range of 16 20 9 12 10
|
11
|
14
|
9
|
11
|
12
|
Statistical measure calculation
|
4,362 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
8
|
11
|
10
|
Vector operations and matrix calculations
|
1,152 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
26
|
24
|
23
|
25
|
Geometric calculation and spatial reasoning
|
3,731 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
2
|
4
|
3
|
Number theory and modular arithmetic
|
3,269 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
3
|
4.5
|
4
|
Probability calculation and expected value
|
1,035 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
50.27
|
53.47
|
47.77
|
52.07
|
Geometric calculation and spatial reasoning
|
1,910 |
fractions
|
medium
|
Divide 1 ÷ 5/6
|
6/5
|
5/6
|
6/6
|
6/5
|
7/5
|
Fraction arithmetic and simplification
|
2,056 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
3,598 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
7
|
9
|
6
|
8
|
Number theory and modular arithmetic
|
2,849 |
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
|
2,255 |
calculus
|
medium
|
What is d/dx(5x^3 - 1x + 1)?
|
15x^2 - 1
|
15x^2 - 1
|
15x^3 - 1
|
5x^2 - 1
|
15x^2 - 1
|
Calculus differentiation and integration
|
2,449 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
Calculus differentiation and integration
|
718 |
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
|
612 |
algebra
|
medium
|
Solve: 3x - 6 = 21
|
9
|
7
|
9
|
10
|
12
|
Algebraic manipulation and solving
|
2,268 |
calculus
|
medium
|
What is d/dx(5x^3 - 1x + 1)?
|
15x^2 - 1
|
15x^2 - 1
|
5x^2 - 1
|
15x^3 - 1
|
15x^2 - 1
|
Calculus differentiation and integration
|
274 |
arithmetic
|
medium
|
Calculate 169 ÷ 13
|
13
|
16
|
14
|
11
|
13
|
Standard arithmetic calculation
|
1,349 |
statistics
|
easy
|
What is the mean of 20 8 15 8 18 16 3?
|
12.6
|
13.6
|
10.6
|
12.6
|
14.6
|
Statistical measure calculation
|
680 |
algebra
|
medium
|
Find x: x² = 36
|
6
|
4
|
6
|
9
|
7
|
Algebraic manipulation and solving
|
2,892 |
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
|
2,865 |
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
|
2,571 |
trigonometry
|
easy
|
Find cos(30°)
|
√3/2
|
√3/2
|
1
|
-1
|
0
|
Trigonometric functions and identities
|
3,676 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
2
|
3
|
1
|
Number theory and modular arithmetic
|
3,616 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
1
|
3
|
2
|
Number theory and modular arithmetic
|
615 |
algebra
|
medium
|
Solve: 2x - 7 = 24
|
15
|
15
|
18
|
16
|
13
|
Algebraic manipulation and solving
|
1,568 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.54
|
1.74
|
2.24
|
2.94
|
Statistical measure calculation
|
3,578 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
60
|
65
|
75
|
50
|
Number theory and modular arithmetic
|
4,419 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
9
|
8
|
Vector operations and matrix calculations
|
4,915 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
48
|
120
|
24
|
Permutations and combinations
|
2,608 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
1
|
undefined
|
0
|
-1
|
Trigonometric functions and identities
|
3,994 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
4,338 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
9
|
8
|
Vector operations and matrix calculations
|
556 |
algebra
|
easy
|
What is 3x when x = 8?
|
24
|
24
|
29
|
26
|
21
|
Algebraic manipulation and solving
|
1,920 |
fractions
|
medium
|
Calculate 2/5 × 4/7
|
8/35
|
9/35
|
8/36
|
35/8
|
8/35
|
Fraction arithmetic and simplification
|
3,246 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3
|
3.5
|
4
|
Probability calculation and expected value
|
4,551 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
4
|
3
|
5
|
Vector operations and matrix calculations
|
2,704 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
sin(2x)
|
2
|
0
|
Trigonometric functions and identities
|
638 |
algebra
|
medium
|
Solve: 5x - 13 = 21
|
6
|
7
|
9
|
4
|
6
|
Algebraic manipulation and solving
|
2,845 |
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
|
3,087 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/12
|
1/14
|
1/15
|
1/13
|
Probability calculation and expected value
|
358 |
arithmetic
|
hard
|
Calculate (6^3 × 3) ÷ 7
|
92
|
95
|
87
|
92
|
100
|
Standard arithmetic calculation
|
1,265 |
statistics
|
easy
|
Find the median of 8 7 4 5 7 5
|
6
|
8
|
4
|
6
|
7
|
Statistical measure calculation
|
1,117 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
14
|
15
|
13
|
16
|
Geometric calculation and spatial reasoning
|
2,180 |
calculus
|
easy
|
Find ∫x dx
|
x²/2 + C
|
x²/2 + C
|
x + C
|
x²
|
x³/3 + C
|
Calculus differentiation and integration
|
727 |
algebra
|
hard
|
Solve: x² + -12x + 36 = 0
|
x = 6 or x = 6
|
x = 5 or x = 7
|
x = 6 or x = 6
|
x = -6 or x = -6
|
x = 7 or x = 5
|
Algebraic manipulation and solving
|
2,611 |
trigonometry
|
easy
|
Find cos(60°)
|
1/2
|
0
|
1
|
-1
|
1/2
|
Trigonometric functions and identities
|
1,826 |
fractions
|
medium
|
Divide 2/7 ÷ 4/7
|
1/2
|
2/2
|
2/1
|
1/3
|
1/2
|
Fraction arithmetic and simplification
|
3,536 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
65
|
75
|
60
|
50
|
Number theory and modular arithmetic
|
670 |
algebra
|
medium
|
Solve: 6x - 7 = 24
|
5
|
3
|
5
|
8
|
6
|
Algebraic manipulation and solving
|
1,518 |
statistics
|
medium
|
Calculate the range of 18 18 12 14 3
|
15
|
13
|
15
|
18
|
16
|
Statistical measure calculation
|
3,035 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/2
|
1/3
|
2/3
|
1/4
|
Probability calculation and expected value
|
2,688 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
0
|
√3
|
1
|
Trigonometric functions and identities
|
1,909 |
fractions
|
medium
|
Divide 1/3 ÷ 2/3
|
1/2
|
1/2
|
2/2
|
2/1
|
1/3
|
Fraction arithmetic and simplification
|
514 |
algebra
|
easy
|
Solve for x: x + 12 = 18
|
6
|
4
|
7
|
6
|
9
|
Algebraic manipulation and solving
|
4,719 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
8
|
4
|
5
|
Permutations and combinations
|
3,079 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/30
|
1/35
|
1/36
|
1/32
|
Probability calculation and expected value
|
4,150 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
Depends on other variables
|
True
|
False
|
Logical reasoning and boolean operations
|
303 |
arithmetic
|
hard
|
Calculate (6^3 × 3) ÷ 3
|
216
|
211
|
224
|
219
|
216
|
Standard arithmetic calculation
|
326 |
arithmetic
|
hard
|
Calculate (6^3 × 2) ÷ 7
|
61
|
69
|
56
|
61
|
64
|
Standard arithmetic calculation
|
205 |
arithmetic
|
medium
|
What is 14²?
|
196
|
211
|
204
|
186
|
196
|
Standard arithmetic calculation
|
2,664 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
sin(2x)
|
0
|
Trigonometric functions and identities
|
3,439 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
6
|
5
|
7
|
8
|
Number theory and modular arithmetic
|
4,430 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
10
|
9
|
11
|
Vector operations and matrix calculations
|
2,786 |
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
|
3,903 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
2,476 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(x²)
|
cos(2x)
|
2x cos(x²)
|
Calculus differentiation and integration
|
4,753 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
50
|
75
|
125
|
Permutations and combinations
|
3,720 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
2
|
4
|
1
|
Number theory and modular arithmetic
|
3,987 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
Cannot determine
|
False
|
True
|
Logical reasoning and boolean operations
|
3,030 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
7
|
8
|
5
|
Probability calculation and expected value
|
4,101 |
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
|
2,166 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
x^3
|
x^2
|
3x^2
|
3x^3
|
Calculus differentiation and integration
|
4,644 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
6
|
16
|
24
|
8
|
Permutations and combinations
|
3,128 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/30
|
1/32
|
1/36
|
1/35
|
Probability calculation and expected value
|
2,176 |
calculus
|
easy
|
Find ∫x dx
|
x²/2 + C
|
x²
|
x³/3 + C
|
x²/2 + C
|
x + C
|
Calculus differentiation and integration
|
2,790 |
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
|
2,490 |
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
|
1,116 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
16
|
15
|
18
|
17
|
Geometric calculation and spatial reasoning
|
3,258 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3
|
4
|
3.5
|
Probability calculation and expected value
|
4,330 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
10
|
11
|
9
|
Vector operations and matrix calculations
|
4,190 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[4, 5]
|
[4, 6]
|
[5, 6]
|
[3, 6]
|
Vector operations and matrix calculations
|
1,604 |
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
|
3,424 |
number_theory
|
easy
|
Is 19 a prime number?
|
Yes
|
Cannot determine
|
Yes
|
Only if x>0
|
No
|
Number theory and modular arithmetic
|
2,819 |
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
|
1,889 |
fractions
|
medium
|
Divide 2/3 ÷ 1
|
2/3
|
2/4
|
2/3
|
3/2
|
3/3
|
Fraction arithmetic and simplification
|
1,805 |
fractions
|
easy
|
What is 1/2 + 1/6?
|
2/3
|
2/3
|
2/4
|
1/3
|
3/3
|
Fraction arithmetic and simplification
|
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