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 |
|---|---|---|---|---|---|---|---|---|---|
1,950 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
499 |
algebra
|
easy
|
What is 5x when x = 7?
|
35
|
37
|
32
|
40
|
35
|
Algebraic manipulation and solving
|
3,845 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
False
|
Depends on context
|
True
|
Logical reasoning and boolean operations
|
2,373 |
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
|
3,930 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
P is false
|
Cannot determine
|
Q is true
|
Q is false
|
Logical reasoning and boolean operations
|
4,781 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
125
|
50
|
75
|
Permutations and combinations
|
4,744 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
50
|
125
|
75
|
Permutations and combinations
|
1,575 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.54
|
1.74
|
2.94
|
2.24
|
Statistical measure calculation
|
4,484 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
6
|
5
|
3
|
Vector operations and matrix calculations
|
1,874 |
fractions
|
medium
|
Divide 4/5 ÷ 2/3
|
6/5
|
6/6
|
7/5
|
5/6
|
6/5
|
Fraction arithmetic and simplification
|
4,928 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
60
|
120
|
24
|
Permutations and combinations
|
3,448 |
number_theory
|
easy
|
Is 13 a prime number?
|
Yes
|
Only if x>0
|
Cannot determine
|
No
|
Yes
|
Number theory and modular arithmetic
|
1,238 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
13
|
11
|
14
|
12
|
Geometric calculation and spatial reasoning
|
2,529 |
trigonometry
|
easy
|
What is sin(180°)?
|
0
|
0
|
0
|
1
|
-1
|
Trigonometric functions and identities
|
3,455 |
number_theory
|
easy
|
Is 23 a prime number?
|
Yes
|
Cannot determine
|
No
|
Only if x>0
|
Yes
|
Number theory and modular arithmetic
|
2,217 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^4 + C
|
4x^3 + C
|
x^5/5 + C
|
x^6/6 + C
|
Calculus differentiation and integration
|
1,841 |
fractions
|
medium
|
Calculate 1 × 2/3
|
2/3
|
2/4
|
3/3
|
3/2
|
2/3
|
Fraction arithmetic and simplification
|
1,470 |
statistics
|
medium
|
What is the mode of 12 5 5 20 5 11 16?
|
5
|
6
|
3
|
5
|
8
|
Statistical measure calculation
|
1,848 |
fractions
|
medium
|
Calculate 5/6 × 3/4
|
5/8
|
5/9
|
5/8
|
8/5
|
6/8
|
Fraction arithmetic and simplification
|
3,756 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
True
|
Depends on context
|
Cannot determine
|
Logical reasoning and boolean operations
|
498 |
algebra
|
easy
|
Solve for x: x + 11 = 19
|
8
|
11
|
6
|
8
|
9
|
Algebraic manipulation and solving
|
3,250 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3.5
|
4
|
3
|
Probability calculation and expected value
|
1,539 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
1.74
|
2.94
|
2.24
|
2.54
|
Statistical measure calculation
|
402 |
arithmetic
|
hard
|
Calculate (5^3 × 3) ÷ 4
|
93
|
93
|
88
|
96
|
101
|
Standard arithmetic calculation
|
4,224 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[2, 7]
|
Vector operations and matrix calculations
|
2,560 |
trigonometry
|
easy
|
What is sin(60°)?
|
0.87
|
0
|
1
|
-1
|
0.87
|
Trigonometric functions and identities
|
2,430 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
cos(2x)
|
cos(x²)
|
2x sin(x²)
|
Calculus differentiation and integration
|
4,301 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[4, 6]
|
[4, 5]
|
[3, 6]
|
[5, 6]
|
Vector operations and matrix calculations
|
1,381 |
statistics
|
easy
|
Find the median of 3 17 7 20 8 13
|
10.5
|
11.5
|
8.5
|
10.5
|
12.5
|
Statistical measure calculation
|
1,519 |
statistics
|
medium
|
Calculate the range of 12 16 17 15 11 10
|
7
|
7
|
10
|
5
|
8
|
Statistical measure calculation
|
4,657 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
36
|
12
|
720
|
120
|
Permutations and combinations
|
1,402 |
statistics
|
medium
|
Calculate the range of 10 20 14 3 9 16 6 4
|
17
|
15
|
20
|
18
|
17
|
Statistical measure calculation
|
157 |
arithmetic
|
medium
|
What is 14²?
|
196
|
196
|
204
|
186
|
211
|
Standard arithmetic calculation
|
200 |
arithmetic
|
medium
|
Calculate 224 ÷ 14
|
16
|
19
|
14
|
16
|
17
|
Standard arithmetic calculation
|
3,318 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
3.5
|
4.5
|
3
|
Probability calculation and expected value
|
3,843 |
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
|
4,315 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
9
|
10
|
11
|
Vector operations and matrix calculations
|
1,428 |
statistics
|
medium
|
What is the mode of 6 2 2 18 6 6 13?
|
6
|
9
|
4
|
7
|
6
|
Statistical measure calculation
|
1,664 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
1.74
|
2.94
|
2.54
|
Statistical measure calculation
|
4,904 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
24
|
48
|
60
|
Permutations and combinations
|
3,694 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
1
|
4
|
Number theory and modular arithmetic
|
3,423 |
number_theory
|
easy
|
What is the GCD of 12 and 18?
|
6
|
4
|
6
|
7
|
5
|
Number theory and modular arithmetic
|
334 |
arithmetic
|
hard
|
Calculate (3^3 × 2) ÷ 8
|
6
|
14
|
1
|
6
|
9
|
Standard arithmetic calculation
|
2,667 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
0
|
1
|
√3
|
√2
|
Trigonometric functions and identities
|
3,648 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
3
|
2
|
1
|
Number theory and modular arithmetic
|
3,260 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4.5
|
4
|
3
|
Probability calculation and expected value
|
703 |
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
|
4,610 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
6
|
8
|
4
|
Permutations and combinations
|
1,842 |
fractions
|
medium
|
Calculate 2/5 × 2/5
|
4/25
|
5/25
|
4/25
|
25/4
|
4/26
|
Fraction arithmetic and simplification
|
4,953 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
60
|
48
|
120
|
Permutations and combinations
|
36 |
arithmetic
|
easy
|
Find 11 × 6
|
66
|
68
|
63
|
66
|
71
|
Standard arithmetic calculation
|
623 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
5
|
6
|
3
|
8
|
Algebraic manipulation and solving
|
4,295 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[3, 7]
|
[2, 7]
|
[3, 6]
|
Vector operations and matrix calculations
|
1,998 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
0/2
|
2/2
|
1/2
|
Fraction arithmetic and simplification
|
4,577 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
5
|
4
|
6
|
Vector operations and matrix calculations
|
2,742 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
0
|
√2
|
1
|
√3
|
Trigonometric functions and identities
|
3,668 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
3
|
2
|
1
|
Number theory and modular arithmetic
|
24 |
arithmetic
|
easy
|
Find 6 × 6
|
36
|
41
|
36
|
38
|
33
|
Standard arithmetic calculation
|
2,797 |
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
|
2,681 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
sin(2x)
|
0
|
Trigonometric functions and identities
|
2,181 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
x^3
|
x^2
|
3x^3
|
3x^2
|
Calculus differentiation and integration
|
2,402 |
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
|
4,498 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
5
|
4
|
6
|
Vector operations and matrix calculations
|
1,208 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
5
|
6
|
4
|
3
|
Geometric calculation and spatial reasoning
|
3,028 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
5
|
7
|
8
|
Probability calculation and expected value
|
2,165 |
calculus
|
easy
|
Find d/dx(x^4)
|
4x^3
|
4x^3
|
x^4
|
x^3
|
4x^4
|
Calculus differentiation and integration
|
1,101 |
geometry
|
medium
|
What is the volume of a cube with side length 4?
|
64
|
44
|
64
|
79
|
99
|
Geometric calculation and spatial reasoning
|
561 |
algebra
|
medium
|
Solve: 6x - 13 = 13
|
4
|
7
|
4
|
2
|
5
|
Algebraic manipulation and solving
|
2,429 |
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
|
4,860 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
60
|
125
|
50
|
Permutations and combinations
|
2,303 |
calculus
|
medium
|
What is d/dx(4x^2 - 3x + 1)?
|
8x^1 - 3
|
8x^1 - 3
|
8x^2 - 3
|
8x^1 - 1
|
4x^1 - 3
|
Calculus differentiation and integration
|
476 |
algebra
|
easy
|
Solve for x: x + 6 = 12
|
6
|
9
|
6
|
4
|
7
|
Algebraic manipulation and solving
|
2,475 |
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
|
2,030 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
2/2
|
0/2
|
Fraction arithmetic and simplification
|
1,110 |
geometry
|
medium
|
What is the volume of a cube with side length 7?
|
343
|
358
|
323
|
343
|
378
|
Geometric calculation and spatial reasoning
|
946 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
9
|
6
|
8
|
7
|
Geometric calculation and spatial reasoning
|
4,393 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
8
|
9
|
Vector operations and matrix calculations
|
571 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
5
|
8
|
6
|
3
|
Algebraic manipulation and solving
|
3,445 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
8
|
7
|
6
|
5
|
Number theory and modular arithmetic
|
1,654 |
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
|
276 |
arithmetic
|
medium
|
Calculate 247 ÷ 13
|
19
|
22
|
19
|
17
|
20
|
Standard arithmetic calculation
|
3,261 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3.5
|
4
|
3
|
Probability calculation and expected value
|
897 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
6
|
7
|
9
|
8
|
Geometric calculation and spatial reasoning
|
3,062 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/15
|
1/12
|
1/14
|
1/13
|
Probability calculation and expected value
|
1,398 |
statistics
|
medium
|
What is the mode of 17 12 15 5 15 15 13?
|
15
|
18
|
13
|
15
|
16
|
Statistical measure calculation
|
4,867 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
48
|
120
|
24
|
Permutations and combinations
|
2,513 |
trigonometry
|
easy
|
What is sin(30°)?
|
0.5
|
0.5
|
-1
|
0
|
1
|
Trigonometric functions and identities
|
3,926 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Cannot determine
|
Depends on values
|
True
|
False
|
Logical reasoning and boolean operations
|
2,836 |
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
|
439 |
algebra
|
easy
|
What is 2x when x = 9?
|
18
|
23
|
18
|
15
|
20
|
Algebraic manipulation and solving
|
4,898 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
48
|
60
|
120
|
Permutations and combinations
|
2,220 |
calculus
|
easy
|
Evaluate ∫x^3 dx
|
x^4/4 + C
|
x^4/4 + C
|
x^3 + C
|
3x^2 + C
|
x^5/5 + C
|
Calculus differentiation and integration
|
4,650 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
25
|
24
|
10
|
120
|
Permutations and combinations
|
2,381 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
Calculus differentiation and integration
|
3,393 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
5
|
3
|
4
|
6
|
Number theory and modular arithmetic
|
1,963 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
1/2
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
1,943 |
fractions
|
medium
|
Divide 1/4 ÷ 2/5
|
5/8
|
5/8
|
5/9
|
8/5
|
6/8
|
Fraction arithmetic and simplification
|
1,075 |
geometry
|
medium
|
Find the area of a circle with radius 8 (use π ≈ 3.14)
|
201.06
|
198.56
|
201.06
|
202.86
|
204.26
|
Geometric calculation and spatial reasoning
|
600 |
algebra
|
medium
|
Find x: x² = 64
|
8
|
8
|
9
|
11
|
6
|
Algebraic manipulation and solving
|
4,340 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
8
|
9
|
Vector operations and matrix calculations
|
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