ACT Math Practice Test 2

Name: ______________________   Date: __________

45 questions, 50 minutes. Calculator allowed. Circle one answer for each question. steplyclass.com/act-math/act-math-practice-test-2/

1. 1 Question 1

   If 5x + 8 = 43, what is the value of x?
   1. A) 7
   2. B) 515
   3. C) 35
   4. D) 175

2. 2 Question 2

   A pair of shoes costs $80. It is on sale for 25% off. What is the sale price?
   1. A) $20
   2. B) $55
   3. C) $60
   4. D) $100

3. 3 Question 3

   Which expression is equivalent to √72?
   1. A) 2√6
   2. B) 6√2
   3. C) 6√12
   4. D) 36√2

4. 4 Question 4

   A bag has 6 red, 2 blue and 4 yellow marbles. One marble is picked at random. What is the probability that it is yellow?
   1. A) 112
   2. B) 13
   3. C) 12
   4. D) 23

5. 5 Question 5

   Three angles meet on a straight line. Two of them measure 40° and 65°. What is the measure of the third angle?
   1. A) 75°
   2. B) 105°
   3. C) 115°
   4. D) 255°

6. 6 Question 6

   Six pens cost $4.80. Each pen costs the same. What is the cost of one pen?
   1. A) $0.80
   2. B) $1.25
   3. C) $10.80
   4. D) $28.80

7. 7 Question 7

   If x4 + 3 = 7, what is the value of x?
   1. A) 1
   2. B) 16
   3. C) 25
   4. D) 40

8. 8 Question 8

   The function f is defined by f(x) = −2x² + 5x. What is the value of f(3)?
   1. A) −33
   2. B) −3
   3. C) 33
   4. D) 51

9. 9 Question 9

   For i = √−1, what is the value of i¹⁴?
   1. A) −1
   2. B) −i
   3. C) 1
   4. D) i

10. 10 Question 10

    The mean of 6 test scores is 80. What score on the next test makes the mean 82?
    1. A) 12
    2. B) 82
    3. C) 84
    4. D) 94

11. 11 Question 11

    A rectangle is 12 cm long and 7.5 cm wide. What is its area, in square centimeters?
    1. A) 19.5
    2. B) 39
    3. C) 90
    4. D) 180

12. 12 Question 12

    What is the solution (x, y) of the system x + 3y = 13 and 2x − 3y = 8?
    1. A) (2, 7)
    2. B) (7, 2)
    3. C) (7, 6)
    4. D) (7, 203)

13. 13 Question 13

    How many meters are in 2.5 kilometers?
    1. A) 0.0025
    2. B) 25
    3. C) 250
    4. D) 2500

14. 14 Question 14

    What is the 15th term of the arithmetic sequence 7, 4, 1, −2, ...?
    1. A) −42
    2. B) −38
    3. C) −35
    4. D) 49

15. 15 Question 15

    A right triangle has a hypotenuse of length 25 and one leg of length 7. What is the length of the other leg?
    1. A) 18
    2. B) 24
    3. C) √674
    4. D) 576

16. 16 Question 16

    What is 0.00072 written in scientific notation?
    1. A) 7.2 × 10⁻⁵
    2. B) 7.2 × 10⁻⁴
    3. C) 7.2 × 10⁻³
    4. D) 7.2 × 10⁴

17. 17 Question 17

    A club of 10 students chooses 3 of them to plan a trip. How many different groups of 3 are possible?
    1. A) 30
    2. B) 120
    3. C) 720
    4. D) 1000

18. 18 Question 18

    y varies inversely with x. y = 12 when x = 3. Find y when x = 9.
    1. A) 4
    2. B) 18
    3. C) 36
    4. D) 108

19. 19 Question 19

    What is the value of log_5(125)?
    1. A) 3
    2. B) 25
    3. C) 120
    4. D) 625

20. 20 Question 20

    Two parallel lines are cut by a transversal. Two alternate interior angles measure (5x − 15)° and (3x + 25)°. What is the value of x?
    1. A) 5
    2. B) 20
    3. C) 21.25
    4. D) 85

21. 21 Question 21

    A price goes from $80 to $92. What is the percent increase?
    1. A) 12%
    2. B) 13%
    3. C) 15%
    4. D) 115%

22. 22 Question 22

    What are the solutions of 2x² + 5x − 3 = 0?
    1. A) −3 and 12
    2. B) −3 and 1
    3. C) −32 and 1
    4. D) −12 and 3

23. 23 Question 23

    15 freshmen come to school by bus and 25 by car; 18 sophomores come by bus and 12 by car. A sophomore is picked at random. What is the probability that the sophomore comes by car?
    1. A) 635
    2. B) 1237
    3. C) 25
    4. D) 35

24. 24 Question 24

    In a right triangle, one angle measures 28° and the side adjacent to it is 15 m. What is the length of the side opposite the 28° angle, to the nearest tenth of a meter?
    1. A) 7.0
    2. B) 8.0
    3. C) 13.2
    4. D) 28.2

25. 25 Question 25

    If f(x) = 3x − 6, which of the following is the inverse function f⁻¹(x)?
    1. A) (x − 6)/3
    2. B) (x + 6)/3
    3. C) 3x + 6
    4. D) 1/(3x − 6)

26. 26 Question 26

    What is the dot product of the vectors <3, −1> and <2, 4>?
    1. A) 2
    2. B) 6
    3. C) 8
    4. D) 10

27. 27 Question 27

    A cone has radius 6 cm and height 10 cm. Using 3.14 for π, what is its volume, in cubic centimeters?
    1. A) 62.8
    2. B) 376.8
    3. C) 1130.4
    4. D) 1507.2

28. 28 Question 28

    What are all the solutions of
    1. A) −13 and 5
    2. B) −5 and 13
    3. C) 5 only
    4. D) −9 and 9

29. 29 Question 29

    What is the remainder when x³ − 2x² + 4x − 5 is divided by x − 2?
    1. A) −29
    2. B) 1
    3. C) 3
    4. D) 8

30. 30 Question 30

    A bag has 2 green and 8 yellow marbles. Two marbles are picked at random, without replacement. What is the probability that both are yellow?
    1. A) 145
    2. B) 2845
    3. C) 1625
    4. D) 45

31. 31 Question 31

    Triangle ABC is similar to triangle DEF, with AB = 4, BC = 6, CA = 8 and DE = 10, EF = x, FD = 20. What is the value of x?
    1. A) 2.4
    2. B) 12
    3. C) 15
    4. D) 60

32. 32 Question 32

    What is the slope of the line through (−2, 5) and (4, −1)?
    1. A) −6
    2. B) −1
    3. C) 1
    4. D) 2

33. 33 Question 33

    A floor is a 10 m by 6 m rectangle with a semicircle on one 6 m end. Using 3.14 for π, what is its area, in square meters?
    1. A) 60
    2. B) 74.13
    3. C) 88.26
    4. D) 116.52

34. 34 Question 34

    $2,000 is invested at 5% interest compounded yearly. How much is in the account after 2 years?
    1. A) $2100
    2. B) $2200
    3. C) $2205
    4. D) $4500

35. 35 Question 35

    In a game, you win $12 with probability 16 and lose $3 otherwise. What is the expected value of one game?
    1. A) -$0.50
    2. B) $0.50
    3. C) $2
    4. D) $9

36. 36 Question 36

    What is the exact value of sin 135°?
    1. A) −√22
    2. B) 12
    3. C) √22
    4. D) √32

37. 37 Question 37

    Ana can paint a fence in 12 hours. Ben can paint the same fence in 4 hours. Working together, how many hours will it take them?
    1. A) 13
    2. B) 3
    3. C) 8
    4. D) 16

38. 38 Question 38

    If 5^2x = 125, what is the value of x?
    1. A) 32
    2. B) 3
    3. C) 12.5
    4. D) 25

39. 39 Question 39

    For i = √−1, which of the following equals 3 + i1 − i?
    1. A) 1 + 2i
    2. B) 2 + 2i
    3. C) 2 + 4i
    4. D) 3 − i

40. 40 Question 40

    Each interior angle of a regular polygon measures 150°. How many sides does the polygon have?
    1. A) 6
    2. B) 12
    3. C) 15
    4. D) 30

41. 41 Question 41

    What is the mean of 14, 9, 22, 17, 13, 9?
    1. A) 9
    2. B) 13.5
    3. C) 14
    4. D) 16.8

42. 42 Question 42

    What is the 60th digit after the decimal point of 57?
    1. A) 1
    2. B) 5
    3. C) 7
    4. D) 10

43. 43 Question 43

    What is the sum of the first 6 terms of the geometric sequence 3, 6, 12, ...?
    1. A) 96
    2. B) 189
    3. C) 192
    4. D) 381

44. 44 Question 44

    In triangle ABC, side a = 8, side b = 11 and angle C = 50°. What is the area of the triangle, to the nearest tenth?
    1. A) 28.3
    2. B) 33.7
    3. C) 44
    4. D) 67.4

45. 45 Question 45

    A class of 24 students has a mean score of 70. A class of 16 students has a mean score of 80. What is the mean score of all 40 students?
    1. A) 74
    2. B) 75
    3. C) 76
    4. D) 2960