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
2,406
calculus
hard
Find the derivative of sin(x²)
2x cos(x²)
2x sin(x²)
cos(2x)
2x cos(x²)
cos(x²)
Calculus differentiation and integration
373
arithmetic
hard
Calculate (4^3 × 3) ÷ 7
27
30
22
35
27
Standard arithmetic calculation
4,214
linear_algebra
easy
Calculate 4 × [2, 3]
[8, 12]
[8, 11]
[8, 12]
[9, 12]
[7, 12]
Vector operations and matrix calculations
3,224
probability
hard
Expected value of rolling a fair six-sided die
3.5
3
3.5
4.5
4
Probability calculation and expected value
720
algebra
hard
Solve: x² + -10x + 21 = 0
x = 7 or x = 3
x = 6 or x = 4
x = 7 or x = 3
x = -7 or x = -3
x = 8 or x = 2
Algebraic manipulation and solving
3,459
number_theory
easy
What is the GCD of 14 and 21?
7
7
5
8
6
Number theory and modular arithmetic
1,972
fractions
hard
Simplify (2/3 + 1/6) × 3/5
1/2
1/3
2/2
1/2
0/2
Fraction arithmetic and simplification
2,035
fractions
hard
Simplify (2/3 + 1/6) × 3/5
1/2
1/2
2/2
0/2
1/3
Fraction arithmetic and simplification
4,253
linear_algebra
easy
Calculate 2 × [2, 3]
[4, 6]
[4, 6]
[5, 6]
[3, 6]
[4, 5]
Vector operations and matrix calculations
4,706
combinatorics
easy
How many ways can 5 people stand in a line?
120
10
25
120
24
Permutations and combinations
4,957
combinatorics
hard
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
48
24
120
60
48
Permutations and combinations
2,792
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
4,068
logic
hard
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
True
False
Depends on other variables
True
Cannot determine
Logical reasoning and boolean operations
3,979
logic
medium
What is NOT(True AND False)?
True
True
Cannot determine
False
Depends on values
Logical reasoning and boolean operations
2,384
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
2,623
trigonometry
easy
What is sin(60°)?
0.87
0.87
0
1
-1
Trigonometric functions and identities
4,881
combinatorics
hard
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
48
24
120
60
48
Permutations and combinations
1,640
statistics
hard
Find the standard deviation of 2 4 6 8 (population)
2.24
1.74
2.54
2.94
2.24
Statistical measure calculation
1,439
statistics
medium
Calculate the range of 2 4 20 4 12 19
18
18
16
21
19
Statistical measure calculation
18
arithmetic
easy
What is 72 + 82?
154
155
152
157
154
Standard arithmetic calculation
141
arithmetic
medium
Calculate 135 ÷ 9
15
16
13
18
15
Standard arithmetic calculation
2,352
calculus
medium
What is d/dx(3x^4 - 6x + 1)?
12x^3 - 6
12x^4 - 6
12x^3 - 1
3x^3 - 6
12x^3 - 6
Calculus differentiation and integration
1,486
statistics
medium
Calculate the range of 17 12 4 11 14 7 13
13
16
13
14
11
Statistical measure calculation
1,275
statistics
easy
What is the mean of 9 6 6 14 3?
7.6
5.6
7.6
9.6
8.6
Statistical measure calculation
4,247
linear_algebra
easy
Calculate 5 × [2, 3]
[10, 15]
[9, 15]
[11, 15]
[10, 15]
[10, 14]
Vector operations and matrix calculations
2,951
probability
easy
What is the probability of getting heads on a fair coin flip?
1/2
2/3
1/4
1/2
1/3
Probability calculation and expected value
4,006
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
2,448
calculus
hard
Find the derivative of sin(x²)
2x cos(x²)
2x cos(x²)
2x sin(x²)
cos(x²)
cos(2x)
Calculus differentiation and integration
4,792
combinatorics
medium
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
60
50
75
60
125
Permutations and combinations
3,382
number_theory
easy
What is the GCD of 15 and 25?
5
6
4
3
5
Number theory and modular arithmetic
140
arithmetic
medium
What is 15% of 123?
18
18
23
28
13
Standard arithmetic calculation
3,218
probability
hard
Expected value of rolling a fair six-sided die
3.5
3
4.5
3.5
4
Probability calculation and expected value
1,567
statistics
hard
Find the standard deviation of 2 4 6 8 (population)
2.24
2.94
1.74
2.24
2.54
Statistical measure calculation
1,306
statistics
easy
What is the mean of 3 17 13 16 9 12 5?
10.7
12.7
8.7
11.7
10.7
Statistical measure calculation
913
geometry
easy
What is the area of a rectangle with length 9 and width 8?
72
80
67
72
75
Geometric calculation and spatial reasoning
38
arithmetic
easy
Find 7 × 12
84
84
86
81
89
Standard arithmetic calculation
3,998
logic
medium
What is NOT(True AND False)?
True
False
Cannot determine
Depends on values
True
Logical reasoning and boolean operations
4,565
linear_algebra
hard
Find the determinant of matrix [[2, 3], [1, 4]]
5
6
5
4
3
Vector operations and matrix calculations
1,814
fractions
medium
Divide 5/3 ÷ 4/5
25/12
12/25
25/13
25/12
26/12
Fraction arithmetic and simplification
3,711
number_theory
hard
What is 7³ mod 11?
2
1
3
2
4
Number theory and modular arithmetic
956
geometry
easy
What is the area of a rectangle with length 7 and width 9?
63
71
63
66
58
Geometric calculation and spatial reasoning
1,781
fractions
easy
Simplify 42/18
7/3
21/9
43/19
7/3
41/17
Fraction arithmetic and simplification
4,159
logic
hard
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
True
Cannot determine
False
Depends on other variables
True
Logical reasoning and boolean operations
550
algebra
easy
What is 8x when x = 3?
24
29
26
24
21
Algebraic manipulation and solving
4,522
linear_algebra
hard
Find the determinant of matrix [[2, 3], [1, 4]]
5
5
4
6
3
Vector operations and matrix calculations
2,515
trigonometry
easy
Find cos(90°)
0
0
1
0
-1
Trigonometric functions and identities
505
algebra
easy
Solve for x: x + 10 = 16
6
9
7
4
6
Algebraic manipulation and solving
4,230
linear_algebra
easy
Add vectors [2, 3] + [1, 4]
[3, 7]
[3, 7]
[4, 7]
[2, 7]
[3, 6]
Vector operations and matrix calculations
1,174
geometry
hard
Find the hypotenuse of a right triangle with legs 3 and 4
5
4
6
5
3
Geometric calculation and spatial reasoning
969
geometry
easy
How many sides does a pentagon have?
5
5
7
6
4
Geometric calculation and spatial reasoning
4,495
linear_algebra
hard
Find the determinant of matrix [[2, 3], [1, 4]]
5
5
3
6
4
Vector operations and matrix calculations
4,341
linear_algebra
medium
What is the dot product of [3, 4] and [2, 1]?
10
11
8
10
9
Vector operations and matrix calculations
3,782
logic
easy
True or False: 5 > 3 AND 2 < 4
True
Depends on context
Cannot determine
False
True
Logical reasoning and boolean operations
1,648
statistics
hard
Find the standard deviation of 2 4 6 8 (population)
2.24
2.94
1.74
2.24
2.54
Statistical measure calculation
1,206
geometry
hard
Find the hypotenuse of a right triangle with legs 3 and 4
5
5
4
3
6
Geometric calculation and spatial reasoning
300
arithmetic
hard
Calculate (6^4 × 2) ÷ 3
864
872
859
867
864
Standard arithmetic calculation
2,460
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
4,084
logic
hard
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
True
True
False
Cannot determine
Depends on other variables
Logical reasoning and boolean operations
3,326
probability
hard
Expected value of rolling a fair six-sided die
3.5
3
4
3.5
4.5
Probability calculation and expected value
2,064
fractions
hard
Simplify (2/3 + 1/6) × 3/5
1/2
2/2
1/2
0/2
1/3
Fraction arithmetic and simplification
1,620
statistics
hard
Find the standard deviation of 2 4 6 8 (population)
2.24
2.94
2.54
1.74
2.24
Statistical measure calculation
410
arithmetic
hard
Calculate (4^3 × 2) ÷ 7
18
13
18
21
26
Standard arithmetic calculation
3,775
logic
easy
True or False: 5 > 3 AND 2 < 4
True
Cannot determine
Depends on context
True
False
Logical reasoning and boolean operations
4,060
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
1,135
geometry
hard
Find the hypotenuse of a right triangle with legs 9 and 12
15
15
14
16
13
Geometric calculation and spatial reasoning
1,994
fractions
hard
Simplify (2/3 + 1/6) × 3/5
1/2
1/2
1/3
2/2
0/2
Fraction arithmetic and simplification
1,997
fractions
hard
Simplify (2/3 + 1/6) × 3/5
1/2
1/3
1/2
0/2
2/2
Fraction arithmetic and simplification
4,582
linear_algebra
hard
Find the determinant of matrix [[2, 3], [1, 4]]
5
6
3
5
4
Vector operations and matrix calculations
380
arithmetic
hard
Calculate (4^3 × 2) ÷ 3
42
42
45
50
37
Standard arithmetic calculation
4,572
linear_algebra
hard
Find the determinant of matrix [[2, 3], [1, 4]]
5
5
3
6
4
Vector operations and matrix calculations
3,055
probability
easy
What is the probability of getting heads on a fair coin flip?
1/2
2/3
1/2
1/4
1/3
Probability calculation and expected value
4,689
combinatorics
easy
How many ways to choose 2 items from 4 items?
6
6
5
8
4
Permutations and combinations
3,724
number_theory
hard
What is 7³ mod 11?
2
1
3
2
4
Number theory and modular arithmetic
1,013
geometry
medium
What is the volume of a cube with side length 9?
729
709
729
764
744
Geometric calculation and spatial reasoning
2,320
calculus
medium
What is d/dx(4x^4 - 7x + 1)?
16x^3 - 7
4x^3 - 7
16x^4 - 7
16x^3 - 7
16x^3 - 1
Calculus differentiation and integration
1,875
fractions
medium
Calculate 2/3 × 5/8
5/12
5/12
5/13
12/5
6/12
Fraction arithmetic and simplification
167
arithmetic
medium
What is 20% of 360?
72
77
67
82
72
Standard arithmetic calculation
4,162
logic
hard
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
True
Cannot determine
True
False
Depends on other variables
Logical reasoning and boolean operations
3,945
logic
medium
What is NOT(True AND False)?
True
False
True
Depends on values
Cannot determine
Logical reasoning and boolean operations
4,599
combinatorics
easy
How many ways to choose 2 items from 4 items?
6
6
4
8
5
Permutations and combinations
3,530
number_theory
medium
Find LCM of 12 and 16
48
63
53
38
48
Number theory and modular arithmetic
1,455
statistics
medium
Calculate the range of 9 13 17 7 15 5 18
13
16
13
11
14
Statistical measure calculation
1,125
geometry
hard
Find the hypotenuse of a right triangle with legs 9 and 12
15
14
16
15
13
Geometric calculation and spatial reasoning
4,861
combinatorics
medium
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
60
75
60
50
125
Permutations and combinations
4,515
linear_algebra
hard
Find the determinant of matrix [[2, 3], [1, 4]]
5
5
3
4
6
Vector operations and matrix calculations
262
arithmetic
medium
What is 10²?
100
100
115
90
108
Standard arithmetic calculation
1,130
geometry
hard
Find the hypotenuse of a right triangle with legs 3 and 4
5
6
3
4
5
Geometric calculation and spatial reasoning
634
algebra
medium
Solve: 6x - 8 = 25
5
3
6
5
8
Algebraic manipulation and solving
1,634
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
2,653
trigonometry
medium
What is tan(45°)?
1
√3
√2
1
0
Trigonometric functions and identities
9
arithmetic
easy
What is 73 + 24?
97
97
98
95
100
Standard arithmetic calculation
1,295
statistics
easy
Find the median of 11 13 20 10 3 19 20 14
13.5
13.5
11.5
14.5
15.5
Statistical measure calculation
2,494
calculus
hard
Find the derivative of sin(x²)
2x cos(x²)
2x sin(x²)
cos(2x)
2x cos(x²)
cos(x²)
Calculus differentiation and integration
103
arithmetic
easy
Find 5 × 5
25
27
22
30
25
Standard arithmetic calculation
683
algebra
medium
Find x: x² = 100
10
10
8
13
11
Algebraic manipulation and solving
3,240
probability
hard
Expected value of rolling a fair six-sided die
3.5
4
3.5
3
4.5
Probability calculation and expected value
1,656
statistics
hard
Find the standard deviation of 2 4 6 8 (population)
2.24
2.54
2.94
1.74
2.24
Statistical measure calculation
2,739
trigonometry
medium
Calculate sin²(x) + cos²(x)
1
sin(2x)
1
0
2
Trigonometric functions and identities
4,747
combinatorics
medium
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
60
50
125
60
75
Permutations and combinations
2,706
trigonometry
medium
Calculate sin²(x) + cos²(x)
1
0
1
sin(2x)
2
Trigonometric functions and identities