ACT Math Practice Test
Disclaimer: This practice test is designed to provide practice with the types of questions, passages, data displays, and time-management challenges often seen on the ACT. It is independently developed for educational purposes and is not affiliated with, endorsed by, or associated with ACT, Inc. The ACT name is used solely for reference. This test is intended as a study aid for students preparing for college admission assessments.
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