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 |
|---|---|---|---|---|---|---|---|---|---|
2,659 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
0
|
√3
|
√2
|
1
|
Trigonometric functions and identities
|
581 |
algebra
|
medium
|
Find x: x² = 36
|
6
|
9
|
7
|
6
|
4
|
Algebraic manipulation and solving
|
780 |
algebra
|
hard
|
Solve: x² + -7x + 10 = 0
|
x = 5 or x = 2
|
x = 4 or x = 3
|
x = 5 or x = 2
|
x = -5 or x = -2
|
x = 6 or x = 1
|
Algebraic manipulation and solving
|
4,233 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[2, 7]
|
[3, 7]
|
[3, 6]
|
Vector operations and matrix calculations
|
4,123 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
2,997 |
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
|
4,989 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
24
|
120
|
60
|
Permutations and combinations
|
1,029 |
geometry
|
medium
|
What is the volume of a cube with side length 6?
|
216
|
216
|
251
|
196
|
231
|
Geometric calculation and spatial reasoning
|
3,072 |
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
|
489 |
algebra
|
easy
|
What is 3x when x = 9?
|
27
|
32
|
27
|
24
|
29
|
Algebraic manipulation and solving
|
1,487 |
statistics
|
medium
|
Calculate the range of 15 11 20 19 5
|
15
|
18
|
13
|
15
|
16
|
Statistical measure calculation
|
4,716 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
8
|
4
|
5
|
Permutations and combinations
|
327 |
arithmetic
|
hard
|
Calculate (4^4 × 4) ÷ 3
|
341
|
336
|
349
|
341
|
344
|
Standard arithmetic calculation
|
3,392 |
number_theory
|
easy
|
Is 31 a prime number?
|
Yes
|
Only if x>0
|
No
|
Yes
|
Cannot determine
|
Number theory and modular arithmetic
|
2,273 |
calculus
|
medium
|
What is d/dx(3x^4 - 4x + 1)?
|
12x^3 - 4
|
12x^4 - 4
|
12x^3 - 1
|
12x^3 - 4
|
3x^3 - 4
|
Calculus differentiation and integration
|
364 |
arithmetic
|
hard
|
Calculate (6^4 × 4) ÷ 5
|
1036
|
1039
|
1036
|
1031
|
1044
|
Standard arithmetic calculation
|
1,573 |
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
|
4,394 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
8
|
10
|
9
|
Vector operations and matrix calculations
|
4,408 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
8
|
9
|
11
|
Vector operations and matrix calculations
|
3,192 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/13
|
1/15
|
1/14
|
1/12
|
Probability calculation and expected value
|
2,640 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
undefined
|
1
|
0
|
-1
|
Trigonometric functions and identities
|
4,729 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
60
|
50
|
75
|
Permutations and combinations
|
4,222 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[6, 8]
|
[5, 9]
|
[6, 9]
|
[7, 9]
|
Vector operations and matrix calculations
|
1,045 |
geometry
|
medium
|
Find the area of a circle with radius 6 (use π ≈ 3.14)
|
113.1
|
114.9
|
113.1
|
110.6
|
116.3
|
Geometric calculation and spatial reasoning
|
1,927 |
fractions
|
medium
|
Divide 5/3 ÷ 2/5
|
25/6
|
26/6
|
25/7
|
6/25
|
25/6
|
Fraction arithmetic and simplification
|
4,548 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
4
|
6
|
5
|
Vector operations and matrix calculations
|
1,139 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
23
|
26
|
25
|
24
|
Geometric calculation and spatial reasoning
|
4,626 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
4
|
5
|
6
|
8
|
Permutations and combinations
|
3,709 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
4
|
3
|
Number theory and modular arithmetic
|
2,572 |
trigonometry
|
easy
|
What is sin(90°)?
|
1
|
1/2
|
0
|
1
|
-1
|
Trigonometric functions and identities
|
1,584 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
1.74
|
2.54
|
2.94
|
Statistical measure calculation
|
4,464 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
3
|
5
|
4
|
Vector operations and matrix calculations
|
644 |
algebra
|
medium
|
Solve: 3x - 6 = 24
|
10
|
13
|
8
|
10
|
11
|
Algebraic manipulation and solving
|
4,712 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
36
|
12
|
120
|
720
|
Permutations and combinations
|
265 |
arithmetic
|
medium
|
Calculate 130 ÷ 13
|
10
|
11
|
10
|
8
|
13
|
Standard arithmetic calculation
|
2,434 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(x²)
|
2x cos(x²)
|
cos(2x)
|
2x sin(x²)
|
Calculus differentiation and integration
|
1,026 |
geometry
|
medium
|
What is the volume of a cube with side length 9?
|
729
|
764
|
709
|
729
|
744
|
Geometric calculation and spatial reasoning
|
2,226 |
calculus
|
medium
|
What is d/dx(5x^3 - 2x + 1)?
|
15x^2 - 2
|
15x^2 - 1
|
15x^3 - 2
|
5x^2 - 2
|
15x^2 - 2
|
Calculus differentiation and integration
|
4,660 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
10
|
25
|
120
|
24
|
Permutations and combinations
|
4,455 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
3
|
4
|
6
|
Vector operations and matrix calculations
|
2,588 |
trigonometry
|
easy
|
Find cos(0°)
|
1
|
-1
|
1
|
1/2
|
0
|
Trigonometric functions and identities
|
1,851 |
fractions
|
medium
|
Divide 1/2 ÷ 1/3
|
3/2
|
2/3
|
4/2
|
3/2
|
3/3
|
Fraction arithmetic and simplification
|
2,020 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/3
|
2/2
|
1/2
|
Fraction arithmetic and simplification
|
1,893 |
fractions
|
medium
|
Calculate 2/3 × 3/2
|
1/1
|
2/1
|
1/2
|
1/1
|
1/1
|
Fraction arithmetic and simplification
|
3,176 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/36
|
1/32
|
1/30
|
1/35
|
Probability calculation and expected value
|
2,825 |
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
|
454 |
algebra
|
easy
|
What is 8x when x = 7?
|
56
|
56
|
61
|
53
|
58
|
Algebraic manipulation and solving
|
2,399 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
2x cos(x²)
|
cos(2x)
|
cos(x²)
|
Calculus differentiation and integration
|
487 |
algebra
|
easy
|
What is 8x when x = 8?
|
64
|
66
|
69
|
61
|
64
|
Algebraic manipulation and solving
|
2,354 |
calculus
|
medium
|
What is d/dx(3x^3 - 3x + 1)?
|
9x^2 - 3
|
9x^2 - 3
|
9x^3 - 3
|
3x^2 - 3
|
9x^2 - 1
|
Calculus differentiation and integration
|
2,395 |
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
|
2,523 |
trigonometry
|
easy
|
Find cos(60°)
|
1/2
|
1/2
|
1
|
0
|
-1
|
Trigonometric functions and identities
|
3,427 |
number_theory
|
easy
|
Is 13 a prime number?
|
Yes
|
Only if x>0
|
Yes
|
No
|
Cannot determine
|
Number theory and modular arithmetic
|
383 |
arithmetic
|
hard
|
Calculate (6^3 × 4) ÷ 8
|
108
|
103
|
108
|
111
|
116
|
Standard arithmetic calculation
|
3,532 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
38
|
63
|
48
|
53
|
Number theory and modular arithmetic
|
156 |
arithmetic
|
medium
|
What is 15²?
|
225
|
233
|
225
|
240
|
215
|
Standard arithmetic calculation
|
2,867 |
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
|
4,262 |
linear_algebra
|
easy
|
Calculate 4 × [2, 3]
|
[8, 12]
|
[7, 12]
|
[8, 11]
|
[9, 12]
|
[8, 12]
|
Vector operations and matrix calculations
|
2,436 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
2x cos(x²)
|
cos(x²)
|
cos(2x)
|
Calculus differentiation and integration
|
1,077 |
geometry
|
medium
|
Find the area of a circle with radius 6 (use π ≈ 3.14)
|
113.1
|
110.6
|
114.9
|
116.3
|
113.1
|
Geometric calculation and spatial reasoning
|
2,734 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
0
|
1
|
Trigonometric functions and identities
|
258 |
arithmetic
|
medium
|
What is 15% of 123?
|
18
|
18
|
28
|
13
|
23
|
Standard arithmetic calculation
|
2,301 |
calculus
|
medium
|
What is d/dx(4x^2 - 6x + 1)?
|
8x^1 - 6
|
8x^2 - 6
|
8x^1 - 1
|
4x^1 - 6
|
8x^1 - 6
|
Calculus differentiation and integration
|
3,265 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
4
|
3
|
3.5
|
Probability calculation and expected value
|
4,550 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
6
|
5
|
4
|
Vector operations and matrix calculations
|
1,469 |
statistics
|
medium
|
What is the mode of 9 9 14 11 3 9 9?
|
9
|
10
|
9
|
12
|
7
|
Statistical measure calculation
|
229 |
arithmetic
|
medium
|
Calculate 143 ÷ 13
|
11
|
9
|
11
|
14
|
12
|
Standard arithmetic calculation
|
2,508 |
trigonometry
|
easy
|
Find cos(30°)
|
√3/2
|
√3/2
|
0
|
-1
|
1
|
Trigonometric functions and identities
|
2,582 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
1
|
0
|
-1
|
undefined
|
Trigonometric functions and identities
|
478 |
algebra
|
easy
|
Solve for x: x + 4 = 10
|
6
|
6
|
4
|
7
|
9
|
Algebraic manipulation and solving
|
2,586 |
trigonometry
|
easy
|
What is sin(180°)?
|
0
|
1
|
-1
|
0
|
0
|
Trigonometric functions and identities
|
4,685 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
8
|
4
|
5
|
Permutations and combinations
|
4,648 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
4
|
5
|
6
|
8
|
Permutations and combinations
|
2,561 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
undefined
|
-1
|
0
|
1
|
Trigonometric functions and identities
|
2,919 |
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
|
3,099 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/14
|
1/13
|
1/15
|
1/12
|
Probability calculation and expected value
|
652 |
algebra
|
medium
|
Find x: x² = 16
|
4
|
5
|
7
|
2
|
4
|
Algebraic manipulation and solving
|
2,658 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
sin(2x)
|
0
|
2
|
Trigonometric functions and identities
|
2,926 |
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
|
66 |
arithmetic
|
easy
|
Find 11 × 8
|
88
|
88
|
85
|
93
|
90
|
Standard arithmetic calculation
|
2,721 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
2
|
0
|
1
|
sin(2x)
|
Trigonometric functions and identities
|
3,798 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
True
|
Depends on context
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
1,663 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
1.74
|
2.24
|
2.54
|
2.94
|
Statistical measure calculation
|
1,057 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
31.47
|
25.77
|
28.27
|
30.07
|
Geometric calculation and spatial reasoning
|
2,717 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
1
|
√2
|
0
|
√3
|
Trigonometric functions and identities
|
4,345 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
10
|
11
|
8
|
Vector operations and matrix calculations
|
126 |
arithmetic
|
easy
|
What is 72 + 31?
|
103
|
103
|
104
|
106
|
101
|
Standard arithmetic calculation
|
744 |
algebra
|
hard
|
Solve: x² + -10x + 25 = 0
|
x = 5 or x = 5
|
x = 4 or x = 6
|
x = 5 or x = 5
|
x = -5 or x = -5
|
x = 6 or x = 4
|
Algebraic manipulation and solving
|
3,900 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
True
|
Cannot determine
|
False
|
Logical reasoning and boolean operations
|
4,097 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
Cannot determine
|
True
|
Depends on other variables
|
Logical reasoning and boolean operations
|
893 |
geometry
|
easy
|
What is the area of a rectangle with length 9 and width 7?
|
63
|
71
|
58
|
63
|
66
|
Geometric calculation and spatial reasoning
|
1,138 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
14
|
13
|
12
|
11
|
Geometric calculation and spatial reasoning
|
84 |
arithmetic
|
easy
|
Calculate 90 - 78
|
12
|
14
|
13
|
12
|
11
|
Standard arithmetic calculation
|
4,395 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
4,616 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
4
|
8
|
5
|
6
|
Permutations and combinations
|
2,722 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
1
|
0
|
Trigonometric functions and identities
|
95 |
arithmetic
|
easy
|
What is 29 + 66?
|
95
|
95
|
98
|
93
|
96
|
Standard arithmetic calculation
|
2,393 |
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
|
4,865 |
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
|
3,086 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/30
|
1/36
|
1/32
|
Probability calculation and expected value
|
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