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 |
|---|---|---|---|---|---|---|---|---|---|
4,832 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
50
|
125
|
60
|
Permutations and combinations
|
2,801 |
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
|
3,230 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4.5
|
3
|
4
|
Probability calculation and expected value
|
3,052 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
6
|
7
|
8
|
Probability calculation and expected value
|
342 |
arithmetic
|
hard
|
Calculate (5^4 × 3) ÷ 4
|
468
|
468
|
471
|
476
|
463
|
Standard arithmetic calculation
|
1,025 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
153.94
|
157.14
|
151.44
|
155.74
|
Geometric calculation and spatial reasoning
|
177 |
arithmetic
|
medium
|
What is 12²?
|
144
|
159
|
152
|
134
|
144
|
Standard arithmetic calculation
|
1,677 |
fractions
|
easy
|
Simplify 28/24
|
7/6
|
14/12
|
7/6
|
29/25
|
27/23
|
Fraction arithmetic and simplification
|
791 |
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
|
857 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
7
|
6
|
9
|
8
|
Geometric calculation and spatial reasoning
|
1,337 |
statistics
|
easy
|
What is the mean of 19 5 11 9 11 16 8?
|
11.3
|
9.3
|
11.3
|
12.3
|
13.3
|
Statistical measure calculation
|
3,123 |
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
|
4,434 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
8
|
9
|
Vector operations and matrix calculations
|
1,757 |
fractions
|
easy
|
What is 1/3 + 1/4?
|
7/12
|
7/13
|
8/12
|
6/12
|
7/12
|
Fraction arithmetic and simplification
|
3,702 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
2
|
3
|
1
|
Number theory and modular arithmetic
|
3,703 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
2
|
3
|
4
|
Number theory and modular arithmetic
|
4,208 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[2, 7]
|
Vector operations and matrix calculations
|
149 |
arithmetic
|
medium
|
What is 40% of 163?
|
65
|
65
|
70
|
60
|
75
|
Standard arithmetic calculation
|
3,721 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
3
|
2
|
1
|
Number theory and modular arithmetic
|
2,240 |
calculus
|
medium
|
What is d/dx(5x^4 - 3x + 1)?
|
20x^3 - 3
|
20x^3 - 3
|
20x^4 - 3
|
20x^3 - 1
|
5x^3 - 3
|
Calculus differentiation and integration
|
4,594 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
120
|
10
|
25
|
24
|
Permutations and combinations
|
2,467 |
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
|
4,590 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
8
|
6
|
24
|
16
|
Permutations and combinations
|
1,091 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
30.07
|
28.27
|
31.47
|
25.77
|
Geometric calculation and spatial reasoning
|
876 |
geometry
|
easy
|
What is the area of a rectangle with length 9 and width 6?
|
54
|
49
|
54
|
57
|
62
|
Geometric calculation and spatial reasoning
|
2,984 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/3
|
1/2
|
2/3
|
1/4
|
Probability calculation and expected value
|
935 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
8
|
7
|
6
|
9
|
Geometric calculation and spatial reasoning
|
2,293 |
calculus
|
medium
|
What is d/dx(3x^2 - 7x + 1)?
|
6x^1 - 7
|
6x^1 - 7
|
3x^1 - 7
|
6x^2 - 7
|
6x^1 - 1
|
Calculus differentiation and integration
|
1,291 |
statistics
|
easy
|
Find the median of 3 15 10 4 10 16 20
|
10
|
10
|
12
|
11
|
8
|
Statistical measure calculation
|
2,746 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
1
|
√2
|
0
|
√3
|
Trigonometric functions and identities
|
1,378 |
statistics
|
easy
|
Find the median of 14 10 14 17 5 5
|
12
|
12
|
14
|
13
|
10
|
Statistical measure calculation
|
117 |
arithmetic
|
easy
|
What is 56 + 54?
|
110
|
108
|
111
|
110
|
113
|
Standard arithmetic calculation
|
782 |
algebra
|
hard
|
Solve: x² + -11x + 30 = 0
|
x = 5 or x = 6
|
x = 4 or x = 7
|
x = 5 or x = 6
|
x = -5 or x = -6
|
x = 6 or x = 5
|
Algebraic manipulation and solving
|
4,235 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[2, 7]
|
Vector operations and matrix calculations
|
4,311 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
10
|
8
|
11
|
Vector operations and matrix calculations
|
1,985 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
0/2
|
2/2
|
1/2
|
Fraction arithmetic and simplification
|
4,365 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
9
|
8
|
10
|
Vector operations and matrix calculations
|
4,710 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
4
|
8
|
6
|
5
|
Permutations and combinations
|
2,556 |
trigonometry
|
easy
|
Find cos(180°)
|
-1
|
-1
|
-1
|
1
|
0
|
Trigonometric functions and identities
|
4,323 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
9
|
11
|
10
|
Vector operations and matrix calculations
|
107 |
arithmetic
|
easy
|
Find 11 × 9
|
99
|
99
|
104
|
101
|
96
|
Standard arithmetic calculation
|
565 |
algebra
|
medium
|
Find x: x² = 16
|
4
|
2
|
5
|
7
|
4
|
Algebraic manipulation and solving
|
1,412 |
statistics
|
medium
|
What is the mode of 16 7 7 13 7 14 6?
|
7
|
10
|
5
|
7
|
8
|
Statistical measure calculation
|
3,524 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
75
|
50
|
65
|
60
|
Number theory and modular arithmetic
|
3,091 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/36
|
1/30
|
1/32
|
Probability calculation and expected value
|
2,365 |
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
|
2,424 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(x²)
|
2x sin(x²)
|
2x cos(x²)
|
cos(2x)
|
Calculus differentiation and integration
|
3,337 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
4
|
3
|
5
|
2
|
Number theory and modular arithmetic
|
2,781 |
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
|
4,852 |
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
|
30 |
arithmetic
|
easy
|
Calculate 64 - 40
|
24
|
25
|
23
|
24
|
26
|
Standard arithmetic calculation
|
2,070 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
2/2
|
1/2
|
0/2
|
Fraction arithmetic and simplification
|
2,705 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
1
|
0
|
Trigonometric functions and identities
|
2,619 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
-1
|
0
|
undefined
|
1
|
Trigonometric functions and identities
|
2,305 |
calculus
|
medium
|
What is d/dx(4x^2 - 3x + 1)?
|
8x^1 - 3
|
8x^2 - 3
|
8x^1 - 1
|
8x^1 - 3
|
4x^1 - 3
|
Calculus differentiation and integration
|
3,081 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/30
|
1/35
|
1/32
|
1/36
|
Probability calculation and expected value
|
2,447 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
cos(x²)
|
Calculus differentiation and integration
|
4,193 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
[3, 7]
|
[4, 7]
|
Vector operations and matrix calculations
|
75 |
arithmetic
|
easy
|
What is 20 + 59?
|
79
|
80
|
82
|
79
|
77
|
Standard arithmetic calculation
|
2,551 |
trigonometry
|
easy
|
Find cos(90°)
|
0
|
1
|
0
|
-1
|
0
|
Trigonometric functions and identities
|
1,732 |
fractions
|
easy
|
What is 1/2 + 1/4?
|
3/4
|
3/5
|
3/4
|
2/4
|
4/4
|
Fraction arithmetic and simplification
|
3,860 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
Depends on context
|
False
|
True
|
Logical reasoning and boolean operations
|
3,304 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3
|
3.5
|
4
|
Probability calculation and expected value
|
2,922 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
7
|
5
|
8
|
Probability calculation and expected value
|
479 |
algebra
|
easy
|
What is 6x when x = 7?
|
42
|
44
|
39
|
47
|
42
|
Algebraic manipulation and solving
|
3,183 |
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
|
3,523 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
65
|
60
|
75
|
50
|
Number theory and modular arithmetic
|
2,502 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
2x sin(x²)
|
cos(x²)
|
2x cos(x²)
|
Calculus differentiation and integration
|
1,693 |
fractions
|
easy
|
Simplify 10/20
|
1/2
|
1/2
|
11/21
|
9/19
|
5/10
|
Fraction arithmetic and simplification
|
1,079 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
25.77
|
28.27
|
30.07
|
31.47
|
Geometric calculation and spatial reasoning
|
2,612 |
trigonometry
|
easy
|
Find cos(0°)
|
1
|
1
|
1/2
|
-1
|
0
|
Trigonometric functions and identities
|
4,172 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[2, 7]
|
Vector operations and matrix calculations
|
480 |
algebra
|
easy
|
Solve for x: x + 7 = 13
|
6
|
4
|
7
|
9
|
6
|
Algebraic manipulation and solving
|
2,955 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/4
|
1/2
|
1/3
|
2/3
|
Probability calculation and expected value
|
4,078 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
Depends on other variables
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
1,860 |
fractions
|
medium
|
Calculate 2/3 × 1/2
|
1/3
|
1/3
|
3/1
|
1/4
|
2/3
|
Fraction arithmetic and simplification
|
1,068 |
geometry
|
medium
|
What is the volume of a cube with side length 9?
|
729
|
764
|
729
|
709
|
744
|
Geometric calculation and spatial reasoning
|
4,849 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
50
|
125
|
75
|
Permutations and combinations
|
1,194 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
25
|
23
|
26
|
24
|
Geometric calculation and spatial reasoning
|
3,789 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
cat
|
animal
|
mammal
|
pet
|
Logical reasoning and boolean operations
|
2,574 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
undefined
|
-1
|
1
|
0
|
Trigonometric functions and identities
|
1,150 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
23
|
26
|
24
|
25
|
Geometric calculation and spatial reasoning
|
587 |
algebra
|
medium
|
Solve: 3x - 12 = 10
|
7
|
8
|
7
|
5
|
10
|
Algebraic manipulation and solving
|
4,460 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
3
|
6
|
4
|
Vector operations and matrix calculations
|
3,949 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
False
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
4,999 |
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
|
1,221 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
6
|
5
|
3
|
4
|
Geometric calculation and spatial reasoning
|
4,901 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
120
|
60
|
24
|
Permutations and combinations
|
2,751 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
0
|
√2
|
1
|
√3
|
Trigonometric functions and identities
|
1,775 |
fractions
|
easy
|
What is 1/2 + 1/3?
|
5/6
|
4/6
|
5/7
|
5/6
|
6/6
|
Fraction arithmetic and simplification
|
3,064 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/12
|
1/15
|
1/13
|
1/14
|
Probability calculation and expected value
|
2,326 |
calculus
|
medium
|
What is d/dx(5x^2 - 3x + 1)?
|
10x^1 - 3
|
10x^1 - 1
|
5x^1 - 3
|
10x^1 - 3
|
10x^2 - 3
|
Calculus differentiation and integration
|
2,598 |
trigonometry
|
easy
|
What is sin(90°)?
|
1
|
1/2
|
1
|
0
|
-1
|
Trigonometric functions and identities
|
3,909 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
False
|
True
|
Cannot determine
|
Depends on values
|
Logical reasoning and boolean operations
|
3,444 |
number_theory
|
easy
|
Is 19 a prime number?
|
Yes
|
Yes
|
Cannot determine
|
Only if x>0
|
No
|
Number theory and modular arithmetic
|
2,720 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
1
|
√2
|
0
|
√3
|
Trigonometric functions and identities
|
4,258 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[6, 8]
|
[7, 9]
|
[6, 9]
|
[5, 9]
|
Vector operations and matrix calculations
|
1,617 |
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
|
552 |
algebra
|
easy
|
What is 8x when x = 4?
|
32
|
29
|
34
|
32
|
37
|
Algebraic manipulation and solving
|
659 |
algebra
|
medium
|
Find x: x² = 49
|
7
|
10
|
5
|
8
|
7
|
Algebraic manipulation and solving
|
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