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 |
|---|---|---|---|---|---|---|---|---|---|
1,330 |
statistics
|
easy
|
What is the mean of 12 11 2 10 8 18 4 12?
|
9.6
|
11.6
|
7.6
|
9.6
|
10.6
|
Statistical measure calculation
|
2,228 |
calculus
|
medium
|
What is d/dx(5x^4 - 4x + 1)?
|
20x^3 - 4
|
20x^4 - 4
|
5x^3 - 4
|
20x^3 - 4
|
20x^3 - 1
|
Calculus differentiation and integration
|
2,699 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
0
|
2
|
sin(2x)
|
Trigonometric functions and identities
|
840 |
geometry
|
easy
|
How many sides does a octagon have?
|
8
|
7
|
10
|
8
|
9
|
Geometric calculation and spatial reasoning
|
3,580 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
50
|
35
|
60
|
45
|
Number theory and modular arithmetic
|
562 |
algebra
|
medium
|
Find x: x² = 49
|
7
|
10
|
5
|
7
|
8
|
Algebraic manipulation and solving
|
626 |
algebra
|
medium
|
Solve: 6x - 10 = 15
|
4
|
5
|
7
|
2
|
4
|
Algebraic manipulation and solving
|
547 |
algebra
|
easy
|
Solve for x: x + 8 = 16
|
8
|
8
|
9
|
11
|
6
|
Algebraic manipulation and solving
|
1,625 |
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
|
3,107 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/36
|
1/30
|
1/35
|
1/32
|
Probability calculation and expected value
|
753 |
algebra
|
hard
|
Solve: x² + -10x + 21 = 0
|
x = 3 or x = 7
|
x = 2 or x = 8
|
x = 3 or x = 7
|
x = -3 or x = -7
|
x = 4 or x = 6
|
Algebraic manipulation and solving
|
2,723 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
1
|
0
|
√2
|
√3
|
Trigonometric functions and identities
|
1,905 |
fractions
|
medium
|
Calculate 3/5 × 3/4
|
9/20
|
9/20
|
9/21
|
20/9
|
10/20
|
Fraction arithmetic and simplification
|
1,379 |
statistics
|
easy
|
What is the mean of 11 6 7 20 20 12?
|
12.7
|
14.7
|
10.7
|
12.7
|
13.7
|
Statistical measure calculation
|
4,409 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
10
|
11
|
9
|
Vector operations and matrix calculations
|
313 |
arithmetic
|
hard
|
Calculate (5^3 × 4) ÷ 8
|
62
|
62
|
70
|
57
|
65
|
Standard arithmetic calculation
|
4,960 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
120
|
48
|
24
|
Permutations and combinations
|
4,040 |
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
|
4,364 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
11
|
9
|
10
|
Vector operations and matrix calculations
|
3,369 |
number_theory
|
easy
|
What is the GCD of 12 and 18?
|
6
|
7
|
5
|
6
|
4
|
Number theory and modular arithmetic
|
3,893 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Cannot determine
|
True
|
False
|
Depends on values
|
Logical reasoning and boolean operations
|
1,468 |
statistics
|
medium
|
What is the mode of 5 12 5 13 19 12 12?
|
12
|
10
|
15
|
13
|
12
|
Statistical measure calculation
|
3,146 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/15
|
1/13
|
1/12
|
1/14
|
Probability calculation and expected value
|
844 |
geometry
|
easy
|
How many sides does a pentagon have?
|
5
|
7
|
6
|
5
|
4
|
Geometric calculation and spatial reasoning
|
3,373 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
7
|
5
|
6
|
8
|
Number theory and modular arithmetic
|
976 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
31.47
|
30.07
|
28.27
|
25.77
|
Geometric calculation and spatial reasoning
|
309 |
arithmetic
|
hard
|
Calculate (5^4 × 3) ÷ 6
|
312
|
312
|
315
|
320
|
307
|
Standard arithmetic calculation
|
1,492 |
statistics
|
medium
|
What is the mode of 16 12 11 11 7 12 12?
|
12
|
10
|
15
|
13
|
12
|
Statistical measure calculation
|
766 |
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
|
3,249 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4.5
|
3
|
4
|
Probability calculation and expected value
|
3,969 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
P is false
|
Q is false
|
Q is true
|
Cannot determine
|
Logical reasoning and boolean operations
|
3,905 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
Q is true
|
Q is false
|
P is false
|
Logical reasoning and boolean operations
|
1,669 |
fractions
|
easy
|
Simplify 10/35
|
2/7
|
9/34
|
11/36
|
5/17
|
2/7
|
Fraction arithmetic and simplification
|
995 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
157.14
|
153.94
|
151.44
|
155.74
|
Geometric calculation and spatial reasoning
|
1,410 |
statistics
|
medium
|
What is the mode of 14 12 16 14 12 12 5?
|
12
|
10
|
15
|
13
|
12
|
Statistical measure calculation
|
758 |
algebra
|
hard
|
Solve: x² + -9x + 14 = 0
|
x = 2 or x = 7
|
x = 1 or x = 8
|
x = 2 or x = 7
|
x = -2 or x = -7
|
x = 3 or x = 6
|
Algebraic manipulation and solving
|
4,402 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
8
|
9
|
Vector operations and matrix calculations
|
1,284 |
statistics
|
easy
|
What is the mean of 5 17 9 8 13?
|
10.4
|
10.4
|
12.4
|
8.4
|
11.4
|
Statistical measure calculation
|
2,123 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
x^3/3 + C
|
2x^1 + C
|
x^2 + C
|
x^4/4 + C
|
Calculus differentiation and integration
|
155 |
arithmetic
|
medium
|
Calculate 108 ÷ 12
|
9
|
9
|
10
|
7
|
12
|
Standard arithmetic calculation
|
3,655 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
3,899 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is false
|
Q is true
|
Cannot determine
|
P is false
|
Logical reasoning and boolean operations
|
2,143 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^4
|
5x^5
|
5x^4
|
x^5
|
Calculus differentiation and integration
|
2,370 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
cos(x²)
|
2x cos(x²)
|
Calculus differentiation and integration
|
614 |
algebra
|
medium
|
Solve: 2x - 10 = 22
|
16
|
16
|
17
|
19
|
14
|
Algebraic manipulation and solving
|
2,368 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
cos(x²)
|
2x sin(x²)
|
2x cos(x²)
|
Calculus differentiation and integration
|
3,117 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/36
|
1/35
|
1/32
|
1/30
|
Probability calculation and expected value
|
1,340 |
statistics
|
easy
|
Find the median of 11 11 19 5 9 20 4
|
11
|
11
|
12
|
9
|
13
|
Statistical measure calculation
|
3,012 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/3
|
1/4
|
1/2
|
2/3
|
Probability calculation and expected value
|
2,169 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
3x^3
|
x^2
|
3x^2
|
x^3
|
Calculus differentiation and integration
|
319 |
arithmetic
|
hard
|
Calculate (4^3 × 4) ÷ 3
|
85
|
80
|
93
|
85
|
88
|
Standard arithmetic calculation
|
416 |
arithmetic
|
hard
|
Calculate (3^4 × 4) ÷ 5
|
64
|
67
|
72
|
59
|
64
|
Standard arithmetic calculation
|
2,127 |
calculus
|
easy
|
Find d/dx(x^4)
|
4x^3
|
4x^3
|
x^3
|
x^4
|
4x^4
|
Calculus differentiation and integration
|
1,490 |
statistics
|
medium
|
Calculate the range of 10 4 6 4 5 3
|
7
|
7
|
5
|
10
|
8
|
Statistical measure calculation
|
4,778 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
75
|
60
|
50
|
Permutations and combinations
|
4,516 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
6
|
3
|
5
|
Vector operations and matrix calculations
|
1,126 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
18
|
16
|
15
|
Geometric calculation and spatial reasoning
|
2,748 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
0
|
√2
|
√3
|
1
|
Trigonometric functions and identities
|
3,057 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/3
|
1/4
|
2/3
|
1/2
|
Probability calculation and expected value
|
2,976 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
5
|
6
|
8
|
Probability calculation and expected value
|
1,105 |
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
|
2,028 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
0/2
|
2/2
|
1/3
|
Fraction arithmetic and simplification
|
3,654 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
4
|
3
|
Number theory and modular arithmetic
|
2,514 |
trigonometry
|
easy
|
Find cos(45°)
|
√2/2
|
0
|
1
|
-1
|
√2/2
|
Trigonometric functions and identities
|
1,564 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.24
|
1.74
|
2.54
|
Statistical measure calculation
|
2,670 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
0
|
1
|
Trigonometric functions and identities
|
3,841 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
cat
|
pet
|
mammal
|
animal
|
Logical reasoning and boolean operations
|
3,630 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
1
|
2
|
4
|
Number theory and modular arithmetic
|
421 |
algebra
|
easy
|
Solve for x: x + 4 = 7
|
3
|
6
|
1
|
4
|
3
|
Algebraic manipulation and solving
|
3,907 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is false
|
Cannot determine
|
Q is true
|
P is false
|
Logical reasoning and boolean operations
|
2,989 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/3
|
1/2
|
1/4
|
2/3
|
Probability calculation and expected value
|
3,708 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
3
|
4
|
Number theory and modular arithmetic
|
1,559 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.54
|
2.24
|
2.94
|
1.74
|
Statistical measure calculation
|
3,595 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
38
|
63
|
53
|
48
|
Number theory and modular arithmetic
|
2,563 |
trigonometry
|
easy
|
What is sin(30°)?
|
0.5
|
0
|
0.5
|
-1
|
1
|
Trigonometric functions and identities
|
4,968 |
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
|
2,759 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
0
|
1
|
2
|
Trigonometric functions and identities
|
3,119 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/30
|
1/32
|
1/36
|
Probability calculation and expected value
|
1,760 |
fractions
|
easy
|
Simplify 30/25
|
6/5
|
29/24
|
15/12
|
6/5
|
31/26
|
Fraction arithmetic and simplification
|
4,157 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
True
|
Depends on other variables
|
False
|
Logical reasoning and boolean operations
|
3,142 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/32
|
1/35
|
1/30
|
1/36
|
Probability calculation and expected value
|
111 |
arithmetic
|
easy
|
Find 7 × 9
|
63
|
60
|
68
|
65
|
63
|
Standard arithmetic calculation
|
1,727 |
fractions
|
easy
|
What is 1/4 + 1/4?
|
1/2
|
2/2
|
1/3
|
1/2
|
0/2
|
Fraction arithmetic and simplification
|
4,324 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
8
|
9
|
Vector operations and matrix calculations
|
2,218 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
2x^1 + C
|
x^3/3 + C
|
x^4/4 + C
|
x^2 + C
|
Calculus differentiation and integration
|
1,124 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
16
|
15
|
18
|
Geometric calculation and spatial reasoning
|
242 |
arithmetic
|
medium
|
Calculate 88 ÷ 11
|
8
|
8
|
6
|
11
|
9
|
Standard arithmetic calculation
|
3,581 |
number_theory
|
medium
|
How many factors does 36 have?
|
9
|
7
|
9
|
10
|
8
|
Number theory and modular arithmetic
|
4,252 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
[4, 7]
|
Vector operations and matrix calculations
|
2,047 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
2/2
|
0/2
|
1/2
|
Fraction arithmetic and simplification
|
2,850 |
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
|
4,151 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
True
|
Depends on other variables
|
False
|
Logical reasoning and boolean operations
|
3,884 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
pet
|
mammal
|
cat
|
animal
|
Logical reasoning and boolean operations
|
2,799 |
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
|
1,346 |
statistics
|
easy
|
What is the mean of 14 15 8 4 20 8?
|
11.5
|
13.5
|
9.5
|
12.5
|
11.5
|
Statistical measure calculation
|
560 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
5
|
3
|
8
|
6
|
Algebraic manipulation and solving
|
978 |
geometry
|
medium
|
What is the volume of a cube with side length 5?
|
125
|
105
|
125
|
160
|
140
|
Geometric calculation and spatial reasoning
|
2,452 |
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
|
3,410 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
7
|
6
|
5
|
8
|
Number theory and modular arithmetic
|
1,420 |
statistics
|
medium
|
Calculate the range of 2 13 10 18 19 18 14 16
|
17
|
18
|
20
|
17
|
15
|
Statistical measure calculation
|
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