ACT Math Practice Test
Directions: Solve each problem, choose the best answer, and fill in the corresponding answer choice.
Unless otherwise stated:
- Assume all figures are drawn to scale.
- Use your calculator as needed.
- All variables represent real numbers.
- An answer choice may be used more than once.
1. What is the value of 7 + 12 − 5?
A. 10
B. 12
C. 14
D. 16
2. If 3x = 6561, then x =
A. 6
B. 7
C. 8
D. 9
3. What is 25% of 80?
A. 15
B. 20
C. 25
D. 30
4. Simplify: 4(3) + 2
A. 10
B. 12
C. 14
D. 16
5. A shirt costs $40 and is discounted by $8. What is the sale price?
A. $30
B. $31
C. $32
D. $33
6. Solve: 2x + 5 = 17
A. 4
B. 5
C. 6
D. 7
7. What is the perimeter of a rectangle with length 8 and width 3?
A. 11
B. 16
C. 22
D. 24
8. Which fraction is equivalent to 0.75?
A. 1/4
B. 1/2
C. 3/4
D. 4/5
9. Evaluate: 5²
A. 10
B. 20
C. 25
D. 30
10. The average of 4, 8, and 12 is:
A. 6
B. 7
C. 8
D. 9
11. If y = 3x, what is y when x = 7?
A. 18
B. 20
C. 21
D. 24
12. What is 18 ÷ 3 + 2?
A. 4
B. 6
C. 8
D. 10
13. A bag contains 5 red and 7 blue marbles. How many marbles are there altogether?
A. 10
B. 11
C. 12
D. 13
14. Solve: x − 9 = 13
A. 20
B. 21
C. 22
D. 23
15. What is the area of a square with side length 6?
A. 12
B. 24
C. 30
D. 36
16. Which number is prime?
A. 15
B. 21
C. 27
D. 29
17. What is 60% of 50?
A. 25
B. 28
C. 30
D. 32
18. If a car travels 120 miles in 2 hours, its average speed is:
A. 40 mph
B. 50 mph
C. 60 mph
D. 70 mph
19. Simplify: 9 − 2(3)
A. 0
B. 2
C. 3
D. 6
20. Which value is greatest?
A. 0.30
B. 0.25
C. 0.32
D. 0.29
21. Solve: 3x − 4 = 20
A. 6
B. 7
C. 8
D. 9
22. Factor: x² − 9
A. (x − 9)(x + 1)
B. (x − 3)²
C. (x − 3)(x + 3)
D. (x + 9)(x − 1)
23. What is the slope of the line through (1, 2) and (5, 10)?
A. 1
B. 2
C. 3
D. 4
24. If 2a + b = 15 and a = 4, then b =
A. 5
B. 6
C. 7
D. 8
25. The probability of rolling a 4 on a fair six-sided die is:
A. 1/6
B. 1/5
C. 1/4
D. 1/3
26. Solve: x² = 49
A. 7 only
B. −7 only
C. ±7
D. 14
27. The area of a triangle with base 10 and height 8 is:
A. 20
B. 30
C. 40
D. 50
28. Which point lies on y = 2x + 1?
A. (1, 1)
B. (1, 2)
C. (1, 3)
D. (2, 2)
29. What is the median of: 2, 5, 7, 9, 12
A. 5
B. 6
C. 7
D. 8
30. Simplify: (3x²)(2x³)
A. 5x⁵
B. 6x⁵
C. 6x⁶
D. 5x⁶
31. A circle has radius 5. Its circumference is:
A. 5π
B. 10π
C. 15π
D. 20π
32. Solve: 4x + 3 = 2x + 11
A. 2
B. 3
C. 4
D. 5
33. What is the value of: √144
A. 10
B. 11
C. 12
D. 13
34. The sum of interior angles of a triangle is:
A. 90°
B. 120°
C. 180°
D. 270°
35. What is 2⁻³?
A. 8
B. 4
C. 1/4
D. 1/8
36. If f(x) = x² + 1, then f(3) =
A. 8
B. 9
C. 10
D. 11
37. The ratio 6:9 simplifies to:
A. 1:2
B. 2:3
C. 3:4
D. 4:5
38. A store increases a price from $50 to $60. The percent increase is:
A. 10%
B. 15%
C. 20%
D. 25%
39. Solve: |x| = 8
A. 8 only
B. −8 only
C. ±8
D. 16
40. What is the distance between 3 and −5 on a number line?
A. 2
B. 5
C. 6
D. 8
41. Solve: x² − 5x + 6 = 0
A. 1 and 6
B. 2 and 3
C. −2 and −3
D. 1 and 5
42. A right triangle has legs 5 and 12. Its hypotenuse is:
A. 11
B. 12
C. 13
D. 14
43. The vertex of y = (x − 4)² + 2 is:
A. (−4, 2)
B. (4, −2)
C. (2, 4)
D. (4, 2)
44. What is sin 30°?
A. 0
B. 1/2
C. √2/2
D. √3/2
45. The solution to 2x² = 18 is:
A. ±2
B. ±3
C. ±4
D. ±5
46. If g(x) = 3x − 2, find g⁻¹(10).
A. 2
B. 3
C. 4
D. 5
47. A sequence begins 4, 7, 10, 13, ... What is the 10th term?
A. 28
B. 29
C. 30
D. 31
48. The probability of getting exactly one head when flipping 2 fair coins is:
A. 1/4
B. 1/3
C. 1/2
D. 2/3
49. What is the equation of a line with slope 2 and y-intercept 5?
A. y = 2x − 5
B. y = 5x + 2
C. y = 2x + 5
D. y = x + 5
50. If log₁₀(1000) = x, then x =
A. 1
B. 2
C. 3
D. 10
51. The area of a circle with radius 4 is:
A. 8π
B. 12π
C. 16π
D. 20π
52. How many diagonals does a hexagon have?
A. 6
B. 7
C. 8
D. 9
53. Solve: (x − 2)/3 = 5
A. 13
B. 15
C. 17
D. 19
54. If x + y = 12 and xy = 35, then x and y are:
A. 1 and 11
B. 2 and 10
C. 5 and 7
D. 4 and 8
55. The domain of f(x) = 1/(x − 4) is all real numbers except:
A. 0
B. 1
C. 2
D. 4
56. What is cos 60°?
A. 0
B. 1/2
C. √2/2
D. √3/2
57. A box contains 3 red, 4 blue, and 5 green balls. Probability of selecting a green ball?
A. 1/4
B. 1/3
C. 5/12
D. 1/2
58. The equation x² + 4x + 4 = 0 has:
A. Two distinct real roots
B. One real root
C. No real roots
D. Three roots
59. What is (3 + i)/1 written in standard complex form?
A. 3 + i
B. 1 + 3i
C. i + 3
D. Both A and C
60. The remainder when x³ − 1 is divided by x − 1 is:
A. 0
B. 1
C. −1
D. 2