Algebra
1. Solve for x): 5x + 3 = 18
2. If 2x + 4 = 12 , what is the value of x?
3. Solve for y : 3y - 7 = 2y + 5
4. What is the slope of the line represented by the equation 4x - 2y = 8 ?
Quadratics
5. Solve the quadratic equation: x^2 + 6x + 8 = 0
6. What are the roots of the equation x^2- 9 = 0?
7. Factor the expression:x^2 - 5x + 6
Geometry
8. What is the area of a triangle with a base of 10 units and a height of 5 units?
9. A circle has a radius of 4 units. What is the circumference of the circle? (Use approx 3.14)
10. If the perimeter of a rectangle is 36 units and its length is 10 units, what is its width?
Ratios and Proportions
11. If the ratio of boys to girls in a class is 2:3 and there are 12 boys, how many girls are there?
12. A recipe calls for a ratio of 1 part sugar to 4 parts flour. If you have 2 cups of sugar, how many cups of flour do you need?
Word Problems
13. If a train travels 150 miles in 3 hours, what is its average speed in miles per hour?
14. A book originally priced at $20 is on sale for 25% off. What is the sale price?
15. If 5 workers can complete a task in 10 hours, how long will it take 10 workers to complete the same task?
Functions
16. If f(x) = 2x + 3, what is f(4)?
17. What is the value of g(x) = x^2 - 3x + 2
when x = 1?
Statistics
18. What is the mean of the following numbers: 4, 8, 6, 5, 9?
19. In a data set, the numbers are 2, 4, 4, 4, 5, 6, 7. What is the mode of this set?
Systems of Equations
20. Solve the system of equations:
2x + 3y = 12
x - y = 2
Exponents and Radicals
21. Simplify: (3^2)(3^3)
22. What is the square root of 144?
Miscellaneous
23. What is the value of 3+2(8-5)?
24. If x = 2 and y = 3, what is 2x^2-3y+4?
25. If 5x + 3y = 12 and y = 2, what is the value of x?
26. What is the value of | -7 | + | 3 |?
Probability
27. What is the probability of flipping a coin and it landing on heads?
28. If you draw one card from a standard deck of 52 cards, what is the probability that it is a heart?
Sequences
29. What is the 5th term in the arithmetic sequence where the first term is 2 and the common difference is 3?
30. If the sequence is defined as an=3n+1, what is a4?
Algebra
1. Solve for x :
4x - 7 = 9
A) 2
B) 3
C) 4
D) 5
2. What is the value of x in the equation:
5(x - 2) = 3x + 6
A) 4
B) 5
C) 6
D) 7
3. If 3x + 4 = 19 , what is x ?
A) 2
B) 3
C) 5
D) 7
4. Which of the following represents a linear equation?
A) y =x2 + 3x
B) y = 2x + 5
C) y = x
D) y = 1^x
5. If 2(x + 3) = 16 , what is x ?
A) 4
B) 5
C) 6
D) 7
6. What is the solution to the equation:
x^2-6x+9=0
A) 3
B) 6
C) 9
D) No solution
7. If 4x + 2y = 12 and y = 3 , what is x ?
A) 1
B) 2
C) 3
D) 4
8. Which of the following is a solution to the equation: x^2-5x+6=0
A) 2
B) 3
C) Both A and B
D) None of the above
9. What is the value of x in:
2(x + 1) = 3(x - 2)
A) -1
B) 1
C) 2
D) 3
10. If 3x - 2 = 4x + 1 , what is x ?
A) -3
B) -1
C) 1
D) 3
Functions
11. What is f(3) if f(x) = 2x^2 + 3x - 5 ?
A) 10
B) 14
C) 18
D) 20
12. Which of the following represents a quadratic function?
A) f(x) = 3x + 4
B) f(x) =x^2 - 4
C) f(x) = 1/x
D) f(x) = 5
13. If g(x) = 3x - 7 , what is g(2) ?
A) -1
B) -3
C) 1
D) 3
14. Which function is represented by the equation y = 2(x-1)^2 + 3 ?
A) Linear
B) Quadratic
C) Exponential
D) Absolute value
15. If h(x) =x^2+ 4x + 4 , what is h(-2) ?
A) 0
B) 4
C) 8
D) 12
17. What is the y-intercept of the function y=-2x+5?
A) -2
B) 2
C) 5
D) -5
18. If f(x) = 2x - 4 , what is f(0) ?
A) -4
B) 0
C) 2
D) 4
19. If f(x) =x^2 - 3x + 2 , what are the roots of the function?
A) 1 and 2
B) 2 and 3
C) 1 and 3
D) None of the above
20. What is the output of the function f(x) = 5x^2 - 3 when x = -1 ?
A) -8
B) -2
C) 2
D) 8
Geometry
1. What is the area of a triangle with a base of 8 units and a height of 5 units?
A) 20
B) 30
C) 40
D) 50
2. What is the circumference of a circle with a radius of 3 units? (Use approx 3.14)
A) 6.28
B) 9.42
C) 12.56
D) 15.70
3. A rectangle has a length of 12 units and a width of 7 units. What is its area?
A) 42
B) 84
C) 96
D) 108
4. What is the volume of a cylinder with a radius of 2 units and a height of 5 units? (Use approx 3.14)
A) 20.88
B) 25.12
C) 31.4
D) 40.84
5. What is the measure of each interior angle of a regular hexagon?
A) 120°
B) 108°
C) 90°
D) 135°
6. What is the distance between the points (3, 4) and (7, 1)?
A) 3
B) 4
C) 5
D) 6
7. If the area of a circle is 36π square units, what is its radius?
A) 3
B) 6
C) 9
D) 12
8. What is the length of the diagonal of a rectangle with dimensions 6 units and 8 units?
A) 10 units
B) 12 units
C) 14 units
D) 16 units
9. What is the perimeter of a square with a side length of 5 units?
A) 10
B) 15
C) 20
D) 25
10. In a right triangle, if one leg is 6 units and the other leg is 8 units, what is the length of the hypotenuse?
A) 8
B) 10
C) 12
D) 14
Measurements
11. If a recipe calls for 2 cups of flour and you want to make half the recipe, how many cups of flour do you need?
A) 1
B) 1.5
C) 2
D) 3
12. A rectangular prism has a length of 4 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
A) 24 cm³
B) 12 cm³
C) 8 cm³
D) 6 cm³
13. What is the area of a trapezoid with bases of 6 units and 10 units, and a height of 5 units?
A) 30
B) 40
C) 50
D) 60
14. What is the surface area of a cube with a side length of 3 units?
A) 18
B) 27
C) 36
D) 54
15. If a wall is 10 feet high and 12 feet wide, what is its area?
A) 80 square feet
B) 100 square feet
C) 120 square feet
D) 140 square feet
16. A cone has a radius of 4 units and a height of 9 units. What is its volume? (Use approx 3.14)
A) 37.68
B) 50.24
C) 75.36
D) 113.04
17. What is the length of each side of an equilateral triangle with a perimeter of 30 units?
A) 5
B) 10
C) 15
D) 20
18. What is the area of a parallelogram with a base of 10 units and a height of 4 units?
A) 20
B) 30
C) 40
D) 50
19. If a triangle has sides measuring 7 units, 8 units, and 9 units, what is the perimeter?
A) 22
B) 24
C) 25
D) 26
20. What is the length of the radius of a sphere with a volume of 43r^2=36?
A) 2
B) 3
C) 4
D) 5
Advanced Topics
1. If 2x + 3y = 12 and y = 2 , what is the value of x ?
A) 3
B) 4
C) 5
D) 6
2. What is the value of x in the equation
x^2- 7x + 10 = 0 ?
A) 2 and 5
B) 1 and 10
C) 3 and 4
D) 5 and 7
3. If the expression 3(x + 2) - 2(2x - 1) = 1 , what is the value of x ?
A) -1
B) 0
C) 1
D) 2
4. What is the solution for x in the equation 2x+35=1?
A) -1
B) 1
C) 2
D) 3
5. If f(x) =x^2 - 4x + 3 , what are the zeros of the function?
A) 1 and 3
B) 2 and 4
C) 1 and 4
D) 3 and 4
6. If a = 2 and b = 3 , what is the value of 3a^2 - 4b + 5 ?
A) 1
B) 4
C) 10
D) 14
7. What is the vertex of the parabola given by the equation y = 2x^2 - 8x + 6 ?
A) (2, -2)
B) (4, -6)
C) (2, 6)
D) (4, 2)
8. What is the sum of the solutions to the equation x^2 - 6x + 8 = 0 ?
A) 4
B) 6
C) 8
D) 10
9. If the function g(x) =x^3- 3x + 2 has a root at x = 1 , what is the value of g(1) ?
A) 0
B) 1
C) 2
D) 3
12. In a geometric sequence, the first term is 3 and the common ratio is 2. What is the 5th term?
A) 12
B) 24
C) 48
D) 96
13. What is the area of a triangle with vertices at (0,0), (4,0), and (4,3)?
A) 6
B) 12
C) 8
D) 10
15. If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and 5, what is the value of a + b + c if a = 1 ?
A) 14
B) 20
C) 24
D) 30
16. In a coordinate plane, what is the distance between the points (3, 4) and (-1, -2)?
A) 5
B) 6
C) 7
D) 8
17. If 5x + 3y = 15 and 2y - x = 3 , what is the value of y ?
A) 1
B) 2
C) 3
D) 4
18. What is the value of (2^3)(x-2)?
A) 2
B) 3
C) 4
D) 5
20. If the sum of three consecutive integers is 48, what is the smallest integer?
A) 15
B) 16
C) 17
D) 18