ACT Math Practice Test 1

Name: ______________________   Date: __________

45 questions, 50 minutes. Calculator allowed. Circle one answer for each question. steplyclass.com/act-math/act-math-practice-test-1/

1. 1 Question 1

   If 3x − 7 = 20, what is the value of x?
   1. A) 133
   2. B) 9
   3. C) 27
   4. D) 81

2. 2 Question 2

   A jacket costs $60. The sales tax is 5%. What is the total cost?
   1. A) $3
   2. B) $57
   3. C) $63
   4. D) $65

3. 3 Question 3

   Which expression is equivalent to √50?
   1. A) 2√5
   2. B) 5√2
   3. C) 10√5
   4. D) 25√2

4. 4 Question 4

   A bag has 3 red, 5 blue and 4 green marbles. One marble is picked at random. What is the probability that it is blue?
   1. A) 112
   2. B) 512
   3. C) 57
   4. D) 712

5. 5 Question 5

   Two angles form a straight line. One of them measures 128°. What is the measure of the other angle?
   1. A) 52°
   2. B) 128°
   3. C) 232°
   4. D) 308°

6. 6 Question 6

   A car travels 195 miles in 3 hours at a steady speed. How many miles does it travel in 1 hour?
   1. A) 65
   2. B) 192
   3. C) 198
   4. D) 585

7. 7 Question 7

   If 6(x − 2) = 4x + 10, what is the value of x?
   1. A) −1
   2. B) 2.2
   3. C) 6
   4. D) 11

8. 8 Question 8

   The function f is defined by f(x) = 3x² − 2x + 4. What is the value of f(−1)?
   1. A) 3
   2. B) 5
   3. C) 9
   4. D) 15

9. 9 Question 9

   For i = √−1, what is (4 + 3i) − (1 − 2i)?
   1. A) 3 + i
   2. B) 3 + 5i
   3. C) 5 + i
   4. D) 5 + 5i

10. 10 Question 10

    Ravi's test scores are 78, 84, 81 and 85. What score on the next test makes his mean 83?
    1. A) 4
    2. B) 83
    3. C) 84
    4. D) 87

11. 11 Question 11

    A circle has a radius of 7 inches. Using 3.14 for π, what is its area, in square inches?
    1. A) 21.98
    2. B) 43.96
    3. C) 153.86
    4. D) 615.44

12. 12 Question 12

    What is the solution (x, y) of the system 2x + y = 11 and x − y = 1?
    1. A) (3, 4)
    2. B) (4, 3)
    3. C) (4, 5)
    4. D) (12, 11)

13. 13 Question 13

    How many inches are in 3.5 feet?
    1. A) 10.5
    2. B) 15.5
    3. C) 35
    4. D) 42

14. 14 Question 14

    What is the 20th term of the arithmetic sequence 5, 8, 11, 14, ...?
    1. A) 57
    2. B) 62
    3. C) 65
    4. D) 100

15. 15 Question 15

    A right triangle has legs of length 8 and 15. What is the length of the hypotenuse?
    1. A) 7
    2. B) 17
    3. C) 23
    4. D) 289

16. 16 Question 16

    What is (3 × 10⁴)(2.5 × 10³)?
    1. A) 7.5 × 10¹
    2. B) 5.5 × 10⁷
    3. C) 7.5 × 10⁷
    4. D) 7.5 × 10¹²

17. 17 Question 17

    A café offers 4 sandwiches, 3 soups and 2 drinks. A lunch is one sandwich, one soup and one drink. How many different lunches are there?
    1. A) 6
    2. B) 9
    3. C) 12
    4. D) 24

18. 18 Question 18

    If 5x = 1524, what is the value of x?
    1. A) 3
    2. B) 8
    3. C) 14
    4. D) 72

19. 19 Question 19

    What is the value of log_2(32)?
    1. A) 5
    2. B) 16
    3. C) 30
    4. D) 64

20. 20 Question 20

    What is the distance between the points (2, 1) and (8, 9) in the standard (x, y) coordinate plane?
    1. A) 10
    2. B) 10√2
    3. C) 14
    4. D) 100

21. 21 Question 21

    21 is 35% of what number?
    1. A) 7.35
    2. B) 56
    3. C) 60
    4. D) 735

22. 22 Question 22

    What are the solutions of x² + 3x − 28 = 0?
    1. A) −14 and 2
    2. B) −7 and 4
    3. C) −4 and 7
    4. D) 4 and 7

23. 23 Question 23

    In a survey, 12 juniors chose art and 18 chose music; 20 seniors chose art and 10 chose music. A student who chose art is picked at random. What is the probability that the student is a senior?
    1. A) 13
    2. B) 38
    3. C) 58
    4. D) 23

24. 24 Question 24

    In a right triangle, one angle measures 35° and the hypotenuse is 20 cm. What is the length of the side opposite the 35° angle, to the nearest tenth of a centimeter?
    1. A) 11.5
    2. B) 14.0
    3. C) 16.4
    4. D) 34.9

25. 25 Question 25

    If f(x) = x² − 2 and g(x) = 3x + 1, what is f(g(1))?
    1. A) −4
    2. B) −2
    3. C) 14
    4. D) 16

26. 26 Question 26

    What is the determinant of the matrix [3 2; 5 4]?
    1. A) −2
    2. B) 2
    3. C) 7
    4. D) 22

27. 27 Question 27

    A can is a cylinder with radius 3 cm and height 8 cm. Using 3.14 for π, what is its volume, in cubic centimeters?
    1. A) 75.36
    2. B) 150.72
    3. C) 226.08
    4. D) 602.88

28. 28 Question 28

    What are all the solutions of
    1. A) 5 only
    2. B) −2 and 5
    3. C) −5 and 2
    4. D) 2 and 5

29. 29 Question 29

    The function f is defined by f(x) = 2x − 1 for x < 3 and f(x) = x² for x ≥ 3. What is f(3)?
    1. A) 5
    2. B) 6
    3. C) 9
    4. D) 14

30. 30 Question 30

    A bag has 5 red and 7 blue marbles. Two marbles are picked at random, without replacement. What is the probability that both are red?
    1. A) 533
    2. B) 25144
    3. C) 512
    4. D) 103132

31. 31 Question 31

    What is the midpoint of the segment with endpoints (−3, 4) and (5, 10)?
    1. A) (1, 7)
    2. B) (2, 14)
    3. C) (4, 3)
    4. D) (8, 6)

32. 32 Question 32

    What is the slope of the line through (1, −2) and (4, 7)?
    1. A) 13
    2. B) 53
    3. C) 3
    4. D) 9

33. 33 Question 33

    A rectangular garden is 10 m by 7 m. A 3 m by 2 m rectangle inside it is a pond. What is the area of the garden without the pond, in square meters?
    1. A) 6
    2. B) 64
    3. C) 70
    4. D) 76

34. 34 Question 34

    $1,500 is invested at 2% interest compounded yearly. To the nearest cent, how much is in the account after 3 years?
    1. A) $1530.00
    2. B) $1590.00
    3. C) $1591.81
    4. D) $2592.00

35. 35 Question 35

    In a game, you win $10 with probability 14 and lose $2 otherwise. What is the expected value of one game?
    1. A) $1
    2. B) $2
    3. C) $2.50
    4. D) $8

36. 36 Question 36

    In triangle ABC, side a = 5, side b = 8 and angle C = 60°. What is the length of side c?
    1. A) 7
    2. B) √89
    3. C) √129
    4. D) 13

37. 37 Question 37

    Two cars start 420 km apart and drive toward each other, one at 65 km/h and the other at 75 km/h. After how many hours do they meet?
    1. A) 3
    2. B) 6
    3. C) 6.5
    4. D) 42

38. 38 Question 38

    If 3^{x − 1} = 81, what is the value of x?
    1. A) 3
    2. B) 4
    3. C) 5
    4. D) 28

39. 39 Question 39

    For i = √−1, which of the following equals (3 + 2i)(1 − i)?
    1. A) 1 − i
    2. B) 5 − i
    3. C) 5 − 5i
    4. D) 5 + 5i

40. 40 Question 40

    What is the measure of each interior angle of a regular octagon?
    1. A) 45°
    2. B) 135°
    3. C) 157.5°
    4. D) 1080°

41. 41 Question 41

    What is the median of 12, 7, 15, 9, 20, 11?
    1. A) 11.5
    2. B) 12
    3. C) 12.33
    4. D) 13.5

42. 42 Question 42

    What is the ones digit of 3⁴⁷?
    1. A) 1
    2. B) 3
    3. C) 7
    4. D) 9

43. 43 Question 43

    What is the 7th term of the geometric sequence 2, 6, 18, 54, ...?
    1. A) 26
    2. B) 486
    3. C) 1458
    4. D) 4374

44. 44 Question 44

    In triangle ABC, angle A = 40°, angle B = 65° and side a = 12. What is the length of side b, to the nearest tenth?
    1. A) 8.5
    2. B) 10.9
    3. C) 16.9
    4. D) 19.5

45. 45 Question 45

    A class of 18 students has a mean score of 75. A class of 12 students has a mean score of 85. What is the mean score of all 30 students?
    1. A) 79
    2. B) 80
    3. C) 81
    4. D) 2370