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 |
|---|---|---|---|---|---|---|---|---|---|
1,203 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
16
|
15
|
14
|
13
|
Geometric calculation and spatial reasoning
|
2,266 |
calculus
|
medium
|
What is d/dx(3x^2 - 3x + 1)?
|
6x^1 - 3
|
3x^1 - 3
|
6x^2 - 3
|
6x^1 - 3
|
6x^1 - 1
|
Calculus differentiation and integration
|
2,526 |
trigonometry
|
easy
|
What is sin(180°)?
|
0
|
1
|
0
|
0
|
-1
|
Trigonometric functions and identities
|
3,791 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
Depends on context
|
True
|
False
|
Logical reasoning and boolean operations
|
3,973 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
P is false
|
Q is true
|
Q is false
|
Cannot determine
|
Logical reasoning and boolean operations
|
1,526 |
statistics
|
medium
|
What is the mode of 5 5 6 5 18 14 5?
|
5
|
8
|
3
|
5
|
6
|
Statistical measure calculation
|
1,070 |
geometry
|
medium
|
What is the volume of a cube with side length 8?
|
512
|
527
|
512
|
492
|
547
|
Geometric calculation and spatial reasoning
|
3,274 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4.5
|
3.5
|
4
|
Probability calculation and expected value
|
1,171 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
3
|
6
|
4
|
5
|
Geometric calculation and spatial reasoning
|
1,888 |
fractions
|
medium
|
Divide 6/5 ÷ 3/5
|
2/1
|
2/1
|
1/2
|
2/2
|
3/1
|
Fraction arithmetic and simplification
|
1,929 |
fractions
|
medium
|
Divide 1 ÷ 1
|
1/1
|
1/1
|
1/2
|
2/1
|
1/1
|
Fraction arithmetic and simplification
|
249 |
arithmetic
|
medium
|
Calculate 165 ÷ 15
|
11
|
12
|
11
|
9
|
14
|
Standard arithmetic calculation
|
2,713 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
0
|
sin(2x)
|
2
|
Trigonometric functions and identities
|
1,937 |
fractions
|
medium
|
Divide 3/7 ÷ 1
|
3/7
|
4/7
|
7/3
|
3/7
|
3/8
|
Fraction arithmetic and simplification
|
1,467 |
statistics
|
medium
|
Calculate the range of 20 14 20 3 7 14 18
|
17
|
17
|
20
|
18
|
15
|
Statistical measure calculation
|
3,499 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
50
|
35
|
45
|
60
|
Number theory and modular arithmetic
|
2,207 |
calculus
|
easy
|
What is the derivative of x²?
|
2x
|
x²
|
2x
|
2x²
|
x
|
Calculus differentiation and integration
|
4,387 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
10
|
8
|
11
|
Vector operations and matrix calculations
|
4,810 |
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
|
1,134 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
13
|
16
|
14
|
15
|
Geometric calculation and spatial reasoning
|
1,229 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
16
|
13
|
14
|
15
|
Geometric calculation and spatial reasoning
|
1,143 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
13
|
14
|
16
|
15
|
Geometric calculation and spatial reasoning
|
3,078 |
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
|
191 |
arithmetic
|
medium
|
What is 12²?
|
144
|
134
|
144
|
159
|
152
|
Standard arithmetic calculation
|
1,643 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.24
|
2.54
|
1.74
|
Statistical measure calculation
|
1,637 |
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
|
2,627 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
1
|
0
|
-1
|
undefined
|
Trigonometric functions and identities
|
1,017 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
52.07
|
50.27
|
47.77
|
53.47
|
Geometric calculation and spatial reasoning
|
3,808 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
True
|
Depends on context
|
Cannot determine
|
Logical reasoning and boolean operations
|
4,238 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[3, 6]
|
[4, 5]
|
[4, 6]
|
[5, 6]
|
Vector operations and matrix calculations
|
3,567 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
7
|
6
|
8
|
9
|
Number theory and modular arithmetic
|
2,329 |
calculus
|
medium
|
What is d/dx(2x^4 - 4x + 1)?
|
8x^3 - 4
|
8x^4 - 4
|
8x^3 - 1
|
2x^3 - 4
|
8x^3 - 4
|
Calculus differentiation and integration
|
2,585 |
trigonometry
|
easy
|
What is sin(90°)?
|
1
|
0
|
1
|
-1
|
1/2
|
Trigonometric functions and identities
|
1,049 |
geometry
|
medium
|
What is the volume of a cube with side length 8?
|
512
|
512
|
527
|
547
|
492
|
Geometric calculation and spatial reasoning
|
1,080 |
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
|
4,316 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
9
|
11
|
8
|
Vector operations and matrix calculations
|
3,637 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
3
|
4
|
Number theory and modular arithmetic
|
3,572 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
9
|
6
|
7
|
8
|
Number theory and modular arithmetic
|
4,259 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[5, 9]
|
[6, 8]
|
[6, 9]
|
[7, 9]
|
Vector operations and matrix calculations
|
347 |
arithmetic
|
hard
|
Calculate (5^4 × 4) ÷ 7
|
357
|
357
|
365
|
352
|
360
|
Standard arithmetic calculation
|
1,917 |
fractions
|
medium
|
Calculate 2/3 × 1/2
|
1/3
|
3/1
|
1/3
|
2/3
|
1/4
|
Fraction arithmetic and simplification
|
2,576 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
undefined
|
0
|
-1
|
1
|
Trigonometric functions and identities
|
3,675 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
2
|
4
|
1
|
Number theory and modular arithmetic
|
290 |
arithmetic
|
hard
|
Calculate (5^4 × 4) ÷ 3
|
833
|
836
|
841
|
833
|
828
|
Standard arithmetic calculation
|
1,168 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
15
|
14
|
13
|
16
|
Geometric calculation and spatial reasoning
|
784 |
algebra
|
hard
|
Solve: x² + -14x + 48 = 0
|
x = 6 or x = 8
|
x = 5 or x = 9
|
x = 6 or x = 8
|
x = -6 or x = -8
|
x = 7 or x = 7
|
Algebraic manipulation and solving
|
221 |
arithmetic
|
medium
|
What is 20% of 224?
|
44
|
44
|
54
|
49
|
39
|
Standard arithmetic calculation
|
966 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
6
|
8
|
9
|
7
|
Geometric calculation and spatial reasoning
|
1,078 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
52.07
|
47.77
|
53.47
|
50.27
|
Geometric calculation and spatial reasoning
|
1,628 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
1.74
|
2.54
|
2.24
|
Statistical measure calculation
|
2,962 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
8
|
6
|
5
|
Probability calculation and expected value
|
1,590 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.54
|
2.24
|
1.74
|
2.94
|
Statistical measure calculation
|
715 |
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
|
4,317 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
8
|
11
|
10
|
Vector operations and matrix calculations
|
322 |
arithmetic
|
hard
|
Calculate (6^4 × 3) ÷ 4
|
972
|
972
|
975
|
967
|
980
|
Standard arithmetic calculation
|
4,194 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[2, 7]
|
[3, 7]
|
Vector operations and matrix calculations
|
640 |
algebra
|
medium
|
Solve: 6x - 5 = 25
|
5
|
3
|
5
|
8
|
6
|
Algebraic manipulation and solving
|
207 |
arithmetic
|
medium
|
What is 15% of 199?
|
29
|
34
|
39
|
24
|
29
|
Standard arithmetic calculation
|
2,651 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
0
|
2
|
sin(2x)
|
Trigonometric functions and identities
|
3,317 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4
|
4.5
|
3.5
|
Probability calculation and expected value
|
1,188 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
14
|
15
|
16
|
13
|
Geometric calculation and spatial reasoning
|
3,466 |
number_theory
|
easy
|
Is 23 a prime number?
|
Yes
|
Only if x>0
|
Cannot determine
|
No
|
Yes
|
Number theory and modular arithmetic
|
3,690 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
2
|
3
|
1
|
Number theory and modular arithmetic
|
170 |
arithmetic
|
medium
|
Calculate 99 ÷ 9
|
11
|
14
|
11
|
9
|
12
|
Standard arithmetic calculation
|
1,355 |
statistics
|
easy
|
Find the median of 11 6 14 6
|
8.5
|
6.5
|
9.5
|
8.5
|
10.5
|
Statistical measure calculation
|
4,458 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
5
|
3
|
4
|
Vector operations and matrix calculations
|
2,313 |
calculus
|
medium
|
What is d/dx(3x^2 - 4x + 1)?
|
6x^1 - 4
|
6x^1 - 1
|
6x^1 - 4
|
3x^1 - 4
|
6x^2 - 4
|
Calculus differentiation and integration
|
4,117 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
True
|
Cannot determine
|
Depends on other variables
|
False
|
Logical reasoning and boolean operations
|
934 |
geometry
|
easy
|
What is the area of a rectangle with length 10 and width 3?
|
30
|
25
|
30
|
38
|
33
|
Geometric calculation and spatial reasoning
|
3,575 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
8
|
6
|
9
|
7
|
Number theory and modular arithmetic
|
853 |
geometry
|
easy
|
How many sides does a pentagon have?
|
5
|
7
|
4
|
5
|
6
|
Geometric calculation and spatial reasoning
|
630 |
algebra
|
medium
|
Solve: 5x - 5 = 11
|
3
|
3
|
4
|
1
|
6
|
Algebraic manipulation and solving
|
1,658 |
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
|
2,426 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
2x sin(x²)
|
2x cos(x²)
|
cos(x²)
|
Calculus differentiation and integration
|
1,692 |
fractions
|
easy
|
Simplify 20/28
|
5/7
|
10/14
|
21/29
|
19/27
|
5/7
|
Fraction arithmetic and simplification
|
1,257 |
statistics
|
easy
|
What is the mean of 12 19 10 18 18 5?
|
13.7
|
13.7
|
14.7
|
11.7
|
15.7
|
Statistical measure calculation
|
4,524 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
3
|
6
|
5
|
Vector operations and matrix calculations
|
3,748 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
1
|
4
|
Number theory and modular arithmetic
|
4,553 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
5
|
6
|
3
|
Vector operations and matrix calculations
|
341 |
arithmetic
|
hard
|
Calculate (6^4 × 2) ÷ 8
|
324
|
327
|
319
|
332
|
324
|
Standard arithmetic calculation
|
3,525 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
63
|
38
|
53
|
48
|
Number theory and modular arithmetic
|
907 |
geometry
|
easy
|
How many sides does a hexagon have?
|
6
|
6
|
7
|
5
|
8
|
Geometric calculation and spatial reasoning
|
4,335 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
9
|
11
|
10
|
Vector operations and matrix calculations
|
3,501 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
50
|
65
|
75
|
60
|
Number theory and modular arithmetic
|
1,132 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
11
|
14
|
13
|
12
|
Geometric calculation and spatial reasoning
|
1,849 |
fractions
|
medium
|
Calculate 1 × 2/5
|
2/5
|
5/2
|
2/6
|
3/5
|
2/5
|
Fraction arithmetic and simplification
|
370 |
arithmetic
|
hard
|
Calculate (6^4 × 2) ÷ 5
|
518
|
518
|
521
|
513
|
526
|
Standard arithmetic calculation
|
1,019 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
30.07
|
31.47
|
25.77
|
28.27
|
Geometric calculation and spatial reasoning
|
4,731 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
125
|
75
|
60
|
Permutations and combinations
|
2,478 |
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
|
1,907 |
fractions
|
medium
|
Divide 2/5 ÷ 1/2
|
4/5
|
4/5
|
4/6
|
5/5
|
5/4
|
Fraction arithmetic and simplification
|
4,816 |
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
|
582 |
algebra
|
medium
|
Find x: x² = 100
|
10
|
8
|
11
|
10
|
13
|
Algebraic manipulation and solving
|
1,063 |
geometry
|
medium
|
Find the area of a circle with radius 8 (use π ≈ 3.14)
|
201.06
|
202.86
|
204.26
|
198.56
|
201.06
|
Geometric calculation and spatial reasoning
|
1,416 |
statistics
|
medium
|
What is the mode of 11 11 13 16 12 11 13?
|
11
|
12
|
14
|
11
|
9
|
Statistical measure calculation
|
2,497 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
cos(x²)
|
cos(2x)
|
2x sin(x²)
|
Calculus differentiation and integration
|
3,939 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
False
|
Cannot determine
|
True
|
Depends on values
|
Logical reasoning and boolean operations
|
4,164 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
False
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
3,041 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/4
|
2/3
|
1/3
|
1/2
|
Probability calculation and expected value
|
4,671 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
6
|
8
|
4
|
Permutations and combinations
|
Subsets and Splits
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