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 |
|---|---|---|---|---|---|---|---|---|---|
2,242 |
calculus
|
medium
|
What is d/dx(2x^4 - 4x + 1)?
|
8x^3 - 4
|
8x^3 - 4
|
8x^4 - 4
|
2x^3 - 4
|
8x^3 - 1
|
Calculus differentiation and integration
|
2,029 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
2/2
|
0/2
|
Fraction arithmetic and simplification
|
4,994 |
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
|
2,998 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
2/3
|
1/2
|
1/3
|
1/4
|
Probability calculation and expected value
|
4,889 |
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
|
2,243 |
calculus
|
medium
|
What is d/dx(3x^3 - 2x + 1)?
|
9x^2 - 2
|
9x^2 - 2
|
9x^2 - 1
|
9x^3 - 2
|
3x^2 - 2
|
Calculus differentiation and integration
|
1,280 |
statistics
|
easy
|
Find the median of 7 16 7 15 19 16 5
|
15
|
15
|
13
|
17
|
16
|
Statistical measure calculation
|
4,087 |
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
|
False
|
True
|
Logical reasoning and boolean operations
|
591 |
algebra
|
medium
|
Find x: x² = 49
|
7
|
8
|
10
|
7
|
5
|
Algebraic manipulation and solving
|
1,219 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
18
|
16
|
17
|
15
|
Geometric calculation and spatial reasoning
|
4,661 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
12
|
120
|
720
|
36
|
Permutations and combinations
|
1,585 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.54
|
2.94
|
2.24
|
1.74
|
Statistical measure calculation
|
1,086 |
geometry
|
medium
|
Find the area of a circle with radius 8 (use π ≈ 3.14)
|
201.06
|
202.86
|
201.06
|
204.26
|
198.56
|
Geometric calculation and spatial reasoning
|
233 |
arithmetic
|
medium
|
What is 30% of 308?
|
92
|
97
|
102
|
87
|
92
|
Standard arithmetic calculation
|
4,654 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
8
|
6
|
5
|
4
|
Permutations and combinations
|
3,259 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
4
|
3
|
3.5
|
Probability calculation and expected value
|
1,754 |
fractions
|
easy
|
Simplify 9/9
|
1/1
|
1/1
|
10/10
|
8/8
|
4/4
|
Fraction arithmetic and simplification
|
3,853 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
1,156 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
13
|
16
|
14
|
15
|
Geometric calculation and spatial reasoning
|
2,636 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
-1
|
0
|
1
|
undefined
|
Trigonometric functions and identities
|
841 |
geometry
|
easy
|
What is the area of a rectangle with length 9 and width 7?
|
63
|
58
|
71
|
63
|
66
|
Geometric calculation and spatial reasoning
|
740 |
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
|
4,269 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[4, 7]
|
[3, 6]
|
[2, 7]
|
Vector operations and matrix calculations
|
4,287 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[3, 7]
|
[2, 7]
|
Vector operations and matrix calculations
|
3,350 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
4
|
3
|
5
|
6
|
Number theory and modular arithmetic
|
2,780 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
0
|
1
|
2
|
Trigonometric functions and identities
|
3,947 |
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
|
1,977 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/2
|
1/3
|
2/2
|
Fraction arithmetic and simplification
|
3,885 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
pet
|
cat
|
mammal
|
animal
|
Logical reasoning and boolean operations
|
2,155 |
calculus
|
easy
|
Find d/dx(x^4)
|
4x^3
|
x^4
|
4x^3
|
4x^4
|
x^3
|
Calculus differentiation and integration
|
3,065 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/14
|
1/12
|
1/13
|
1/15
|
Probability calculation and expected value
|
3,716 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
3
|
4
|
Number theory and modular arithmetic
|
3,336 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4
|
4.5
|
3.5
|
Probability calculation and expected value
|
1,475 |
statistics
|
medium
|
Calculate the range of 15 10 5 15 18
|
13
|
14
|
16
|
13
|
11
|
Statistical measure calculation
|
3,927 |
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
|
842 |
geometry
|
easy
|
What is the area of a rectangle with length 5 and width 4?
|
20
|
28
|
23
|
20
|
15
|
Geometric calculation and spatial reasoning
|
1,397 |
statistics
|
medium
|
What is the mode of 4 9 9 15 9 16 3?
|
9
|
12
|
9
|
10
|
7
|
Statistical measure calculation
|
2,690 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
sin(2x)
|
2
|
0
|
Trigonometric functions and identities
|
4,914 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
24
|
120
|
48
|
Permutations and combinations
|
3,140 |
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
|
57 |
arithmetic
|
easy
|
What is 62 + 22?
|
84
|
85
|
82
|
87
|
84
|
Standard arithmetic calculation
|
1,644 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
2.94
|
1.74
|
2.54
|
Statistical measure calculation
|
4,062 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
True
|
Cannot determine
|
False
|
Depends on other variables
|
Logical reasoning and boolean operations
|
4,635 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
24
|
120
|
25
|
10
|
Permutations and combinations
|
628 |
algebra
|
medium
|
Find x: x² = 81
|
9
|
10
|
9
|
12
|
7
|
Algebraic manipulation and solving
|
444 |
algebra
|
easy
|
What is 5x when x = 3?
|
15
|
17
|
12
|
15
|
20
|
Algebraic manipulation and solving
|
4,229 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[2, 7]
|
[3, 6]
|
[3, 7]
|
[4, 7]
|
Vector operations and matrix calculations
|
1,473 |
statistics
|
medium
|
What is the mode of 10 10 11 4 10 7 19?
|
10
|
11
|
13
|
10
|
8
|
Statistical measure calculation
|
4,054 |
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
|
1,372 |
statistics
|
easy
|
What is the mean of 2 6 6 12 14 7 9?
|
8
|
9
|
8
|
10
|
6
|
Statistical measure calculation
|
4,807 |
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
|
1,683 |
fractions
|
easy
|
What is 1/2 + 1/3?
|
5/6
|
4/6
|
5/7
|
6/6
|
5/6
|
Fraction arithmetic and simplification
|
776 |
algebra
|
hard
|
Solve: x² + -11x + 30 = 0
|
x = 6 or x = 5
|
x = 5 or x = 6
|
x = 6 or x = 5
|
x = -6 or x = -5
|
x = 7 or x = 4
|
Algebraic manipulation and solving
|
4,842 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
75
|
50
|
60
|
Permutations and combinations
|
2,419 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
cos(x²)
|
2x sin(x²)
|
2x cos(x²)
|
Calculus differentiation and integration
|
2,953 |
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
|
2,362 |
calculus
|
medium
|
What is d/dx(2x^3 - 3x + 1)?
|
6x^2 - 3
|
6x^2 - 1
|
6x^2 - 3
|
6x^3 - 3
|
2x^2 - 3
|
Calculus differentiation and integration
|
3,965 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
False
|
True
|
Cannot determine
|
Logical reasoning and boolean operations
|
3,205 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
3
|
4
|
4.5
|
Probability calculation and expected value
|
2,707 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
sin(2x)
|
0
|
Trigonometric functions and identities
|
1,209 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
16
|
17
|
15
|
18
|
Geometric calculation and spatial reasoning
|
657 |
algebra
|
medium
|
Find x: x² = 100
|
10
|
11
|
13
|
10
|
8
|
Algebraic manipulation and solving
|
1,464 |
statistics
|
medium
|
What is the mode of 7 7 7 19 12 13 7?
|
7
|
5
|
7
|
10
|
8
|
Statistical measure calculation
|
2,104 |
calculus
|
easy
|
Find d/dx(x^4)
|
4x^3
|
4x^4
|
4x^3
|
x^4
|
x^3
|
Calculus differentiation and integration
|
445 |
algebra
|
easy
|
Solve for x: x + 5 = 13
|
8
|
11
|
6
|
9
|
8
|
Algebraic manipulation and solving
|
1,979 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
2/2
|
0/2
|
1/3
|
1/2
|
Fraction arithmetic and simplification
|
1,930 |
fractions
|
medium
|
Calculate 1/2 × 3/8
|
3/16
|
16/3
|
4/16
|
3/17
|
3/16
|
Fraction arithmetic and simplification
|
2,683 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
1
|
0
|
2
|
Trigonometric functions and identities
|
1,287 |
statistics
|
easy
|
What is the mean of 11 20 16 5?
|
13
|
13
|
15
|
11
|
14
|
Statistical measure calculation
|
1,269 |
statistics
|
easy
|
Find the median of 18 3 7 18 17 14 15
|
15
|
17
|
16
|
15
|
13
|
Statistical measure calculation
|
4,998 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
60
|
120
|
48
|
Permutations and combinations
|
2,269 |
calculus
|
medium
|
What is d/dx(3x^4 - 1x + 1)?
|
12x^3 - 1
|
12x^3 - 1
|
12x^4 - 1
|
12x^3 - 1
|
3x^3 - 1
|
Calculus differentiation and integration
|
1,458 |
statistics
|
medium
|
What is the mode of 12 11 14 20 14 14 17?
|
14
|
17
|
12
|
15
|
14
|
Statistical measure calculation
|
2,567 |
trigonometry
|
easy
|
What is sin(30°)?
|
0.5
|
1
|
0
|
0.5
|
-1
|
Trigonometric functions and identities
|
807 |
algebra
|
hard
|
Solve: x² + -15x + 56 = 0
|
x = 7 or x = 8
|
x = 6 or x = 9
|
x = 7 or x = 8
|
x = -7 or x = -8
|
x = 8 or x = 7
|
Algebraic manipulation and solving
|
2,897 |
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
|
1,121 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
24
|
26
|
25
|
23
|
Geometric calculation and spatial reasoning
|
2,014 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/2
|
2/2
|
1/3
|
Fraction arithmetic and simplification
|
401 |
arithmetic
|
hard
|
Calculate (6^3 × 3) ÷ 5
|
129
|
124
|
129
|
137
|
132
|
Standard arithmetic calculation
|
3,796 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
Depends on context
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
1,498 |
statistics
|
medium
|
Calculate the range of 14 10 5 14 8
|
9
|
10
|
9
|
12
|
7
|
Statistical measure calculation
|
325 |
arithmetic
|
hard
|
Calculate (6^3 × 2) ÷ 8
|
54
|
57
|
54
|
62
|
49
|
Standard arithmetic calculation
|
1,446 |
statistics
|
medium
|
Calculate the range of 6 10 10 18 19
|
13
|
13
|
16
|
11
|
14
|
Statistical measure calculation
|
3,696 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
4
|
3
|
1
|
Number theory and modular arithmetic
|
2,308 |
calculus
|
medium
|
What is d/dx(2x^2 - 8x + 1)?
|
4x^1 - 8
|
4x^1 - 1
|
4x^2 - 8
|
4x^1 - 8
|
2x^1 - 8
|
Calculus differentiation and integration
|
3,778 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
Cannot determine
|
False
|
True
|
Logical reasoning and boolean operations
|
846 |
geometry
|
easy
|
What is the area of a rectangle with length 11 and width 9?
|
99
|
102
|
107
|
94
|
99
|
Geometric calculation and spatial reasoning
|
4,667 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
16
|
24
|
8
|
6
|
Permutations and combinations
|
3,858 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
pet
|
mammal
|
cat
|
animal
|
Logical reasoning and boolean operations
|
4,741 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
125
|
60
|
50
|
Permutations and combinations
|
3,184 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/32
|
1/35
|
1/30
|
1/36
|
Probability calculation and expected value
|
2,347 |
calculus
|
medium
|
What is d/dx(3x^2 - 3x + 1)?
|
6x^1 - 3
|
6x^2 - 3
|
3x^1 - 3
|
6x^1 - 1
|
6x^1 - 3
|
Calculus differentiation and integration
|
1,058 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
151.44
|
153.94
|
155.74
|
157.14
|
Geometric calculation and spatial reasoning
|
4,835 |
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
|
2,227 |
calculus
|
medium
|
What is d/dx(5x^4 - 8x + 1)?
|
20x^3 - 8
|
20x^4 - 8
|
5x^3 - 8
|
20x^3 - 8
|
20x^3 - 1
|
Calculus differentiation and integration
|
3,470 |
number_theory
|
easy
|
Is 31 a prime number?
|
Yes
|
No
|
Yes
|
Only if x>0
|
Cannot determine
|
Number theory and modular arithmetic
|
2,591 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
0
|
-1
|
undefined
|
1
|
Trigonometric functions and identities
|
58 |
arithmetic
|
easy
|
Find 11 × 12
|
132
|
137
|
132
|
129
|
134
|
Standard arithmetic calculation
|
2,110 |
calculus
|
easy
|
Find ∫x dx
|
x²/2 + C
|
x²/2 + C
|
x³/3 + C
|
x + C
|
x²
|
Calculus differentiation and integration
|
4,000 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
False
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
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