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 |
|---|---|---|---|---|---|---|---|---|---|
1,028 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
151.44
|
155.74
|
157.14
|
153.94
|
Geometric calculation and spatial reasoning
|
3,419 |
number_theory
|
easy
|
Is 13 a prime number?
|
Yes
|
Only if x>0
|
Cannot determine
|
Yes
|
No
|
Number theory and modular arithmetic
|
3,165 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/15
|
1/12
|
1/13
|
1/14
|
Probability calculation and expected value
|
905 |
geometry
|
easy
|
How many sides does a octagon have?
|
8
|
10
|
8
|
9
|
7
|
Geometric calculation and spatial reasoning
|
3,643 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
1
|
4
|
2
|
Number theory and modular arithmetic
|
4,768 |
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
|
2,879 |
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
|
1,166 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
14
|
13
|
11
|
12
|
Geometric calculation and spatial reasoning
|
388 |
arithmetic
|
hard
|
Calculate (5^3 × 2) ÷ 4
|
62
|
57
|
70
|
62
|
65
|
Standard arithmetic calculation
|
3,587 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
8
|
6
|
9
|
7
|
Number theory and modular arithmetic
|
1,307 |
statistics
|
easy
|
Find the median of 16 9 20 7 16
|
16
|
18
|
14
|
17
|
16
|
Statistical measure calculation
|
4,632 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
24
|
10
|
25
|
120
|
Permutations and combinations
|
2,808 |
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
|
2,499 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
2x cos(x²)
|
cos(x²)
|
2x sin(x²)
|
Calculus differentiation and integration
|
1,460 |
statistics
|
medium
|
Calculate the range of 4 14 9 18 17 4 9
|
14
|
14
|
12
|
15
|
17
|
Statistical measure calculation
|
4,122 |
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
|
1,999 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
4,406 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
10
|
9
|
11
|
Vector operations and matrix calculations
|
4,309 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
11
|
10
|
9
|
Vector operations and matrix calculations
|
749 |
algebra
|
hard
|
Solve: x² + -10x + 24 = 0
|
x = 6 or x = 4
|
x = 5 or x = 5
|
x = 6 or x = 4
|
x = -6 or x = -4
|
x = 7 or x = 3
|
Algebraic manipulation and solving
|
527 |
algebra
|
easy
|
Solve for x: x + 11 = 22
|
11
|
12
|
11
|
14
|
9
|
Algebraic manipulation and solving
|
4,517 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
5
|
4
|
6
|
Vector operations and matrix calculations
|
1,993 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
0/2
|
1/3
|
2/2
|
Fraction arithmetic and simplification
|
4,873 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
24
|
48
|
120
|
Permutations and combinations
|
1,846 |
fractions
|
medium
|
Calculate 3/5 × 1/2
|
3/10
|
4/10
|
3/11
|
3/10
|
10/3
|
Fraction arithmetic and simplification
|
2,673 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
0
|
2
|
1
|
Trigonometric functions and identities
|
1,456 |
statistics
|
medium
|
What is the mode of 12 19 12 4 12 11 12?
|
12
|
12
|
10
|
13
|
15
|
Statistical measure calculation
|
655 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
3
|
6
|
5
|
8
|
Algebraic manipulation and solving
|
154 |
arithmetic
|
medium
|
What is 8²?
|
64
|
79
|
54
|
72
|
64
|
Standard arithmetic calculation
|
2,178 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
x^2 + C
|
x^4/4 + C
|
x^3/3 + C
|
2x^1 + C
|
Calculus differentiation and integration
|
598 |
algebra
|
medium
|
Solve: 2x - 12 = 16
|
14
|
15
|
17
|
12
|
14
|
Algebraic manipulation and solving
|
2,927 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
6
|
5
|
8
|
Probability calculation and expected value
|
2,059 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
1/2
|
2/2
|
0/2
|
Fraction arithmetic and simplification
|
2,826 |
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
|
599 |
algebra
|
medium
|
Solve: 6x - 14 = 24
|
6
|
4
|
7
|
6
|
9
|
Algebraic manipulation and solving
|
2,256 |
calculus
|
medium
|
What is d/dx(5x^4 - 4x + 1)?
|
20x^3 - 4
|
20x^3 - 1
|
20x^3 - 4
|
20x^4 - 4
|
5x^3 - 4
|
Calculus differentiation and integration
|
4,936 |
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
|
493 |
algebra
|
easy
|
Solve for x: x + 12 = 20
|
8
|
8
|
6
|
11
|
9
|
Algebraic manipulation and solving
|
3,809 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
Depends on context
|
False
|
True
|
Logical reasoning and boolean operations
|
2,933 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
8
|
5
|
7
|
Probability calculation and expected value
|
323 |
arithmetic
|
hard
|
Calculate (3^4 × 3) ÷ 5
|
48
|
43
|
48
|
51
|
56
|
Standard arithmetic calculation
|
2,970 |
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
|
4,969 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
24
|
60
|
48
|
Permutations and combinations
|
3,075 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/32
|
1/30
|
1/35
|
1/36
|
Probability calculation and expected value
|
4,935 |
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
|
2,601 |
trigonometry
|
easy
|
Find cos(0°)
|
1
|
1
|
1/2
|
0
|
-1
|
Trigonometric functions and identities
|
4,292 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[3, 6]
|
[2, 7]
|
[3, 7]
|
Vector operations and matrix calculations
|
4,508 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
6
|
5
|
4
|
Vector operations and matrix calculations
|
755 |
algebra
|
hard
|
Solve: x² + -10x + 16 = 0
|
x = 2 or x = 8
|
x = 1 or x = 9
|
x = 2 or x = 8
|
x = -2 or x = -8
|
x = 3 or x = 7
|
Algebraic manipulation and solving
|
2,377 |
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
|
3,409 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
4
|
6
|
3
|
5
|
Number theory and modular arithmetic
|
2,864 |
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
|
350 |
arithmetic
|
hard
|
Calculate (4^3 × 4) ÷ 9
|
28
|
31
|
28
|
36
|
23
|
Standard arithmetic calculation
|
4,347 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
8
|
11
|
10
|
Vector operations and matrix calculations
|
4,375 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
8
|
10
|
11
|
Vector operations and matrix calculations
|
4,131 |
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
|
708 |
algebra
|
hard
|
Solve: x² + -10x + 16 = 0
|
x = 2 or x = 8
|
x = 1 or x = 9
|
x = 2 or x = 8
|
x = -2 or x = -8
|
x = 3 or x = 7
|
Algebraic manipulation and solving
|
4,411 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
9
|
11
|
10
|
Vector operations and matrix calculations
|
2,238 |
calculus
|
medium
|
What is d/dx(4x^3 - 3x + 1)?
|
12x^2 - 3
|
4x^2 - 3
|
12x^2 - 1
|
12x^3 - 3
|
12x^2 - 3
|
Calculus differentiation and integration
|
193 |
arithmetic
|
medium
|
Calculate 126 ÷ 14
|
9
|
9
|
7
|
10
|
12
|
Standard arithmetic calculation
|
3,757 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
animal
|
pet
|
cat
|
mammal
|
Logical reasoning and boolean operations
|
918 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
9
|
6
|
7
|
8
|
Geometric calculation and spatial reasoning
|
3,150 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/12
|
1/13
|
1/14
|
1/15
|
Probability calculation and expected value
|
1,389 |
statistics
|
easy
|
What is the mean of 18 17 16 13?
|
16
|
16
|
17
|
14
|
18
|
Statistical measure calculation
|
4,477 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
4
|
3
|
5
|
Vector operations and matrix calculations
|
3,042 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
8
|
6
|
5
|
Probability calculation and expected value
|
2,604 |
trigonometry
|
easy
|
What is sin(180°)?
|
0
|
-1
|
0
|
1
|
0
|
Trigonometric functions and identities
|
2,510 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
0
|
undefined
|
1
|
-1
|
Trigonometric functions and identities
|
2 |
arithmetic
|
easy
|
What is 59 + 51?
|
110
|
111
|
110
|
108
|
113
|
Standard arithmetic calculation
|
2,995 |
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
|
2,317 |
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
|
4,018 |
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
|
Cannot determine
|
Q is false
|
Logical reasoning and boolean operations
|
1,014 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
157.14
|
155.74
|
153.94
|
151.44
|
Geometric calculation and spatial reasoning
|
1,689 |
fractions
|
easy
|
What is 1/2 + 1/4?
|
3/4
|
2/4
|
4/4
|
3/4
|
3/5
|
Fraction arithmetic and simplification
|
1,945 |
fractions
|
medium
|
Divide 5/3 ÷ 4/7
|
35/12
|
35/12
|
35/13
|
36/12
|
12/35
|
Fraction arithmetic and simplification
|
1,785 |
fractions
|
easy
|
Simplify 12/8
|
3/2
|
11/7
|
13/9
|
3/2
|
6/4
|
Fraction arithmetic and simplification
|
1,505 |
statistics
|
medium
|
Calculate the range of 3 12 10 15 11 12 6
|
12
|
13
|
12
|
15
|
10
|
Statistical measure calculation
|
1,525 |
statistics
|
medium
|
What is the mode of 14 7 7 6 18 14 7?
|
7
|
10
|
8
|
7
|
5
|
Statistical measure calculation
|
2,117 |
calculus
|
easy
|
Evaluate ∫x^3 dx
|
x^4/4 + C
|
x^5/5 + C
|
x^4/4 + C
|
x^3 + C
|
3x^2 + C
|
Calculus differentiation and integration
|
1,818 |
fractions
|
medium
|
Divide 5/8 ÷ 3/4
|
5/6
|
5/6
|
6/5
|
6/6
|
5/7
|
Fraction arithmetic and simplification
|
1,354 |
statistics
|
easy
|
Find the median of 16 5 2 8 3 16 8 6
|
7
|
8
|
9
|
7
|
5
|
Statistical measure calculation
|
2,935 |
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
|
428 |
algebra
|
easy
|
What is 3x when x = 6?
|
18
|
20
|
15
|
18
|
23
|
Algebraic manipulation and solving
|
2,924 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
8
|
6
|
5
|
Probability calculation and expected value
|
3,823 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
animal
|
mammal
|
pet
|
cat
|
Logical reasoning and boolean operations
|
119 |
arithmetic
|
easy
|
Calculate 32 - 17
|
15
|
17
|
14
|
16
|
15
|
Standard arithmetic calculation
|
2,615 |
trigonometry
|
easy
|
What is sin(30°)?
|
0.5
|
0
|
1
|
0.5
|
-1
|
Trigonometric functions and identities
|
4,019 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
389 |
arithmetic
|
hard
|
Calculate (6^3 × 3) ÷ 5
|
129
|
137
|
132
|
124
|
129
|
Standard arithmetic calculation
|
1,636 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
1.74
|
2.24
|
2.94
|
2.54
|
Statistical measure calculation
|
1,167 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
16
|
18
|
15
|
17
|
Geometric calculation and spatial reasoning
|
4,022 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
Q is false
|
Q is true
|
P is false
|
Logical reasoning and boolean operations
|
1,587 |
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
|
3,432 |
number_theory
|
easy
|
Is 13 a prime number?
|
Yes
|
No
|
Cannot determine
|
Yes
|
Only if x>0
|
Number theory and modular arithmetic
|
4,036 |
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
|
False
|
True
|
Logical reasoning and boolean operations
|
520 |
algebra
|
easy
|
What is 4x when x = 9?
|
36
|
36
|
33
|
38
|
41
|
Algebraic manipulation and solving
|
2,503 |
trigonometry
|
easy
|
Find cos(90°)
|
0
|
-1
|
0
|
0
|
1
|
Trigonometric functions and identities
|
4,863 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
120
|
48
|
60
|
Permutations and combinations
|
916 |
geometry
|
easy
|
What is the area of a rectangle with length 6 and width 8?
|
48
|
56
|
43
|
48
|
51
|
Geometric calculation and spatial reasoning
|
1,111 |
geometry
|
medium
|
What is the volume of a cube with side length 7?
|
343
|
343
|
323
|
358
|
378
|
Geometric calculation and spatial reasoning
|
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