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 |
|---|---|---|---|---|---|---|---|---|---|
4,072 |
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
|
2,340 |
calculus
|
medium
|
What is d/dx(5x^4 - 7x + 1)?
|
20x^3 - 7
|
5x^3 - 7
|
20x^3 - 1
|
20x^3 - 7
|
20x^4 - 7
|
Calculus differentiation and integration
|
3,697 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
3
|
4
|
2
|
Number theory and modular arithmetic
|
1,534 |
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
|
1,096 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
25.77
|
28.27
|
31.47
|
30.07
|
Geometric calculation and spatial reasoning
|
4,354 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
9
|
8
|
Vector operations and matrix calculations
|
386 |
arithmetic
|
hard
|
Calculate (3^3 × 4) ÷ 5
|
21
|
16
|
29
|
24
|
21
|
Standard arithmetic calculation
|
871 |
geometry
|
easy
|
What is the area of a rectangle with length 5 and width 7?
|
35
|
38
|
30
|
35
|
43
|
Geometric calculation and spatial reasoning
|
2,639 |
trigonometry
|
easy
|
What is sin(45°)?
|
0.71
|
1
|
-1
|
0
|
0.71
|
Trigonometric functions and identities
|
2,543 |
trigonometry
|
easy
|
What is sin(60°)?
|
0.87
|
0
|
-1
|
1
|
0.87
|
Trigonometric functions and identities
|
1,436 |
statistics
|
medium
|
What is the mode of 9 14 9 20 9 5 9?
|
9
|
10
|
7
|
12
|
9
|
Statistical measure calculation
|
1,823 |
fractions
|
medium
|
Divide 1/2 ÷ 4/5
|
5/8
|
5/9
|
6/8
|
8/5
|
5/8
|
Fraction arithmetic and simplification
|
2,084 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
2/2
|
1/2
|
0/2
|
Fraction arithmetic and simplification
|
243 |
arithmetic
|
medium
|
Calculate 120 ÷ 8
|
15
|
15
|
16
|
13
|
18
|
Standard arithmetic calculation
|
2,727 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√3
|
√2
|
0
|
1
|
Trigonometric functions and identities
|
3,850 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
True
|
Cannot determine
|
Depends on context
|
Logical reasoning and boolean operations
|
631 |
algebra
|
medium
|
Find x: x² = 64
|
8
|
9
|
11
|
8
|
6
|
Algebraic manipulation and solving
|
1,024 |
geometry
|
medium
|
What is the volume of a cube with side length 7?
|
343
|
323
|
358
|
343
|
378
|
Geometric calculation and spatial reasoning
|
1,250 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
6
|
4
|
3
|
5
|
Geometric calculation and spatial reasoning
|
4,007 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is false
|
P is false
|
Q is true
|
Cannot determine
|
Logical reasoning and boolean operations
|
1,825 |
fractions
|
medium
|
Calculate 1/2 × 1/2
|
1/4
|
4/1
|
1/5
|
1/4
|
2/4
|
Fraction arithmetic and simplification
|
151 |
arithmetic
|
medium
|
What is 25% of 369?
|
92
|
92
|
102
|
97
|
87
|
Standard arithmetic calculation
|
25 |
arithmetic
|
easy
|
What is 89 + 60?
|
149
|
147
|
149
|
150
|
152
|
Standard arithmetic calculation
|
3,262 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
3.5
|
4.5
|
4
|
Probability calculation and expected value
|
3,154 |
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
|
3,472 |
number_theory
|
easy
|
Is 29 a prime number?
|
Yes
|
No
|
Only if x>0
|
Cannot determine
|
Yes
|
Number theory and modular arithmetic
|
4,179 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
Vector operations and matrix calculations
|
1,563 |
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
|
2,726 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
sin(2x)
|
2
|
1
|
Trigonometric functions and identities
|
2,498 |
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
|
4,294 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[2, 7]
|
[3, 6]
|
[3, 7]
|
Vector operations and matrix calculations
|
731 |
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
|
3,972 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is false
|
P is false
|
Q is true
|
Cannot determine
|
Logical reasoning and boolean operations
|
973 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
8
|
6
|
9
|
7
|
Geometric calculation and spatial reasoning
|
592 |
algebra
|
medium
|
Find x: x² = 49
|
7
|
7
|
8
|
5
|
10
|
Algebraic manipulation and solving
|
2,691 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
0
|
√3
|
√2
|
1
|
Trigonometric functions and identities
|
4,854 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
50
|
60
|
75
|
Permutations and combinations
|
2,546 |
trigonometry
|
easy
|
Find cos(90°)
|
0
|
-1
|
1
|
0
|
0
|
Trigonometric functions and identities
|
3,437 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
5
|
3
|
2
|
4
|
Number theory and modular arithmetic
|
1,494 |
statistics
|
medium
|
Calculate the range of 2 20 3 5 13 20
|
18
|
21
|
19
|
18
|
16
|
Statistical measure calculation
|
3,506 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
9
|
8
|
7
|
6
|
Number theory and modular arithmetic
|
960 |
geometry
|
easy
|
How many sides does a hexagon have?
|
6
|
8
|
7
|
5
|
6
|
Geometric calculation and spatial reasoning
|
3,990 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
P is false
|
Q is false
|
Q is true
|
Logical reasoning and boolean operations
|
2,453 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
cos(x²)
|
Calculus differentiation and integration
|
542 |
algebra
|
easy
|
What is 5x when x = 8?
|
40
|
40
|
45
|
37
|
42
|
Algebraic manipulation and solving
|
526 |
algebra
|
easy
|
Solve for x: x + 13 = 17
|
4
|
7
|
4
|
2
|
5
|
Algebraic manipulation and solving
|
2,001 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
2/2
|
1/2
|
0/2
|
1/3
|
Fraction arithmetic and simplification
|
1,557 |
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
|
1,401 |
statistics
|
medium
|
Calculate the range of 7 7 6 7 18 9 16
|
12
|
10
|
12
|
15
|
13
|
Statistical measure calculation
|
4,652 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
5
|
8
|
4
|
Permutations and combinations
|
4,132 |
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
|
True
|
False
|
Logical reasoning and boolean operations
|
1,504 |
statistics
|
medium
|
Calculate the range of 8 3 13 20 3 12
|
17
|
17
|
20
|
18
|
15
|
Statistical measure calculation
|
3,126 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/12
|
1/13
|
1/15
|
1/14
|
Probability calculation and expected value
|
4,415 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
9
|
8
|
Vector operations and matrix calculations
|
3,496 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
75
|
50
|
60
|
65
|
Number theory and modular arithmetic
|
189 |
arithmetic
|
medium
|
What is 40% of 333?
|
133
|
128
|
143
|
138
|
133
|
Standard arithmetic calculation
|
1,268 |
statistics
|
easy
|
What is the mean of 10 7 13 5 8 9 20?
|
10.3
|
12.3
|
8.3
|
10.3
|
11.3
|
Statistical measure calculation
|
2,832 |
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
|
702 |
algebra
|
hard
|
Solve: x² + -11x + 30 = 0
|
x = 5 or x = 6
|
x = 4 or x = 7
|
x = 5 or x = 6
|
x = -5 or x = -6
|
x = 6 or x = 5
|
Algebraic manipulation and solving
|
2,888 |
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
|
3,406 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
6
|
3
|
4
|
5
|
Number theory and modular arithmetic
|
4,972 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
60
|
48
|
24
|
Permutations and combinations
|
813 |
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
|
377 |
arithmetic
|
hard
|
Calculate (4^4 × 3) ÷ 5
|
153
|
148
|
161
|
156
|
153
|
Standard arithmetic calculation
|
206 |
arithmetic
|
medium
|
What is 13²?
|
169
|
159
|
169
|
184
|
177
|
Standard arithmetic calculation
|
1,773 |
fractions
|
easy
|
Simplify 21/24
|
7/8
|
20/23
|
7/8
|
22/25
|
10/12
|
Fraction arithmetic and simplification
|
2,146 |
calculus
|
easy
|
What is the derivative of x²?
|
2x
|
x
|
2x²
|
2x
|
x²
|
Calculus differentiation and integration
|
1,581 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.94
|
2.54
|
2.24
|
1.74
|
Statistical measure calculation
|
281 |
arithmetic
|
hard
|
Calculate (5^4 × 2) ÷ 3
|
416
|
411
|
419
|
416
|
424
|
Standard arithmetic calculation
|
5 |
arithmetic
|
easy
|
Find 7 × 8
|
56
|
56
|
58
|
61
|
53
|
Standard arithmetic calculation
|
3,583 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
7
|
8
|
9
|
6
|
Number theory and modular arithmetic
|
2,358 |
calculus
|
medium
|
What is d/dx(2x^3 - 2x + 1)?
|
6x^2 - 2
|
6x^3 - 2
|
6x^2 - 2
|
6x^2 - 1
|
2x^2 - 2
|
Calculus differentiation and integration
|
112 |
arithmetic
|
easy
|
What is 47 + 98?
|
145
|
146
|
145
|
143
|
148
|
Standard arithmetic calculation
|
2,728 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
0
|
1
|
2
|
Trigonometric functions and identities
|
1,540 |
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
|
866 |
geometry
|
easy
|
How many sides does a octagon have?
|
8
|
10
|
7
|
9
|
8
|
Geometric calculation and spatial reasoning
|
3,678 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
3
|
2
|
4
|
Number theory and modular arithmetic
|
399 |
arithmetic
|
hard
|
Calculate (5^4 × 2) ÷ 3
|
416
|
416
|
411
|
419
|
424
|
Standard arithmetic calculation
|
1,474 |
statistics
|
medium
|
Calculate the range of 18 17 16 6
|
12
|
15
|
13
|
10
|
12
|
Statistical measure calculation
|
1,514 |
statistics
|
medium
|
Calculate the range of 7 6 12 8
|
6
|
9
|
4
|
6
|
7
|
Statistical measure calculation
|
925 |
geometry
|
easy
|
What is the area of a rectangle with length 8 and width 6?
|
48
|
51
|
43
|
48
|
56
|
Geometric calculation and spatial reasoning
|
4,698 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
120
|
720
|
36
|
12
|
Permutations and combinations
|
3,255 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
3.5
|
3
|
4.5
|
Probability calculation and expected value
|
2,223 |
calculus
|
easy
|
What is the derivative of x²?
|
2x
|
2x²
|
2x
|
x²
|
x
|
Calculus differentiation and integration
|
865 |
geometry
|
easy
|
What is the area of a rectangle with length 6 and width 6?
|
36
|
44
|
31
|
36
|
39
|
Geometric calculation and spatial reasoning
|
4,533 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
6
|
5
|
4
|
Vector operations and matrix calculations
|
187 |
arithmetic
|
medium
|
Calculate 170 ÷ 10
|
17
|
17
|
20
|
15
|
18
|
Standard arithmetic calculation
|
4,975 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
48
|
24
|
60
|
Permutations and combinations
|
360 |
arithmetic
|
hard
|
Calculate (6^3 × 4) ÷ 7
|
123
|
123
|
131
|
118
|
126
|
Standard arithmetic calculation
|
3,981 |
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
|
965 |
geometry
|
easy
|
What is the area of a rectangle with length 10 and width 5?
|
50
|
45
|
53
|
50
|
58
|
Geometric calculation and spatial reasoning
|
3,997 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is true
|
Q is false
|
Cannot determine
|
P is false
|
Logical reasoning and boolean operations
|
3,463 |
number_theory
|
easy
|
Is 17 a prime number?
|
Yes
|
No
|
Cannot determine
|
Only if x>0
|
Yes
|
Number theory and modular arithmetic
|
1,704 |
fractions
|
easy
|
What is 1/2 + 1/4?
|
3/4
|
3/5
|
2/4
|
4/4
|
3/4
|
Fraction arithmetic and simplification
|
4,987 |
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
|
2,644 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
sin(2x)
|
2
|
1
|
Trigonometric functions and identities
|
4,646 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
10
|
24
|
120
|
25
|
Permutations and combinations
|
1,318 |
statistics
|
easy
|
What is the mean of 17 2 5 12 14?
|
10
|
11
|
10
|
12
|
8
|
Statistical measure calculation
|
3,311 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4
|
3.5
|
4.5
|
Probability calculation and expected value
|
4,578 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
6
|
3
|
Vector operations and matrix calculations
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