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ACT Math Practice Exam

By — McGraw-Hill Professional
Updated on Sep 7, 2011

This practice exam contains 50 questions that review the 50 Skills that can be found at ACT Math Prep. Take the test. Then check your answers and review the skills for any questions that were difficult.

  1. A sack of sweet yams could be equally divided among 4, 5, or 6 families. What is the smallest number of yams that could be in the sack?
    1. 24
    2. 30
    3. 56
    4. 116
    5. 120
  2. If 4(x + 1) = 8x, then x = ?
    1. 1
    2. 2
    3. 4
    1. 8
    2. –7
  3. If D = RT, then which of the following is an expression for T in terms of D and R ?
    1. DR
    2. DR
    3. RD
  4. Sora earned $5 on Monday. On each following day, through Friday, she earned 1 more dollar than the preceding day. What was her mean earnings for the five-day period, Monday through Friday?
    1. 4
    2. 5
    3. 6
    1. 7
    2. 8
  5. The measure of BFE in the figure below is 138°. The measures of 3 angles are given in terms of m, in degrees. What is the measure of BFD
      Posttest
    1. 110
    2. 115
    3. 120
    4. 125
    5. 130
  6. In the figure below, if a || b and the measure of x = 25, what is the measure of y?
      Posttest
    1. 25
    2. 50
    3. 90
    1. 108
    2. 133
  7. In ΔQRX, and the measure of Q is 34°. What is the measure of X?
    1. 112°
    2. 56°
    3. 54°
    4. 34°
    5. 17°
  8. For all x, (5x – 2)2 =?
    1. 5x2 + 4
    2. 25x2 – 2
    3. 25x2 – 10x + 2
    1. 25x2 – 20x + 4
    2. x2 – 25x – 2
  9. Which of the following lists gives the 3 largest prime numbers that are less than 50 ?
    1. 5, 7, and 11
    2. 7, 11, and 13
    3. 41, 43, and 47
    4. 39, 43, and 47
    5. 43, 47, and 49
  10. Which of the following lists the factors of 36 ?
    1. 1, 36
    2. 2, 3
    3. 36, 72, 144
    1. 1, 2, 3, 4, 6, 9, 12, 18, 36
    2. The empty set
  11. What is the lowest common denominator of ?
    1. 3
    2. 24
    3. 36
    4. 96
    5. 288
  12. In the xy coordinate plane below, which of the following points has coordinates (x, y) such that x = y – 2 ?
      Posttest
    1. A
    2. B
    3. C
    1. D
    2. E
  13. If the line through the points (5, –3) and (–2, p) is parallel to the line y = –2x – 3, what is the value of p ?
    1. 11
    2. 4
    3. 0
    4. –10
    5. –17
  14. In the standard (x, y) coordinate plane, what is the slope of the line parallel to the line with equation 6x + 8y = –12 ?
    1. – 6
    1. –2
    2. 4
  15. The graph below shows the number of Texas Hold 'em tournaments won by each of four players. According to the graph, what fraction of the tournaments did Reisner win?
    1. 0.30
    2. 0.25
    3. 0.20
    4. 0.15
    5. 0.10
  16. The number of yoga postures that Ben knows after a series of yoga classes can be modeled by the function P(c) = 3c + 8, where c represents the number of classes that he has attended. Using this model, how many postures would you expect him to know after 10 classes?
    1. 3
    2. 8
    3. 10
    1. 30
    2. 38
  17. What is the distance, in coordinate units, between the points (–4, 3) and (7, –2) in the standard (x, y) coordinate plane?
    1. 15
    2. 21
  18. In the equation , x represents a positive integer. As x gets larger and larger without bound, the value of y
    1. approaches 5
    2. approaches 2
    3. approaches 1
    1. approaches 0
    2. remains unchanged
  19. If a completely fenced in square lot requires 80 feet of fence, what is the area, in square feet, of the lot?
    1. 6400
    2. 1600
    3. 400
    4. 200
    5. 20
  20. In the figure below, what is the area of the shaded region?
      Posttest
    1. 17
    2. 32
    3. 39
    1. 49
    2. 54
  21. If the numerator of a fraction is 4 more than the denominator and the fraction equals , what is the numerator of the fraction?
    1. 3
    2. 6
    3. 9
    4. 10
    5. 14
    1. undefined
  22. In a standard (x, y) coordinate plane, three points Q, R, and S have coordinates (5, 2), (–1, 5), and (5, b). If the three points determine a right triangle, what is the value of b ?
    1. 0
    2. 2
    3. 4
    4. 5
    5. 6
  23. The lengths of the sides of a right triangle are consecutive integers, and the length of the shortest side is x. Which of the following could be used to solve for x ?
    1. (x)2 + (x + 1)2 = (x + 2)2
    2. x + x – 3 = x
    3. (x)( x + 1) = (x + 2)2
    1. (x + 2) – (x + 1) = x
    2. (x)2 + (x + 2)2 = (x + 4)2
  24. Which of the following sets of 3 numbers could be the side lengths, in meters, of a 45°–45°–90° triangle?
    1. 2, 2, 2
    2. 2, 2, 2
    3. 2, 2 , 2
    4. 2, 2 , 2
    5. 2, 2 , 4
  25. Edward casts a shadow 3 meters long. At the same time, Bella casts a shadow 2.5 meters long. If Edward is 2 meters tall, which of the following is closest to Bella's height, in meters?
    1. 0.6
    2. 1.2
    3. 1.7
    1. 2.6
    2. 3.4
  26. 71 is what percent of 1420 ?
    1. 2%
    2. 5%
    3. 20%
    4. 50%
    5. 700%
  27. What is the total cost of 4.3 pounds of flour at $1.10 per pound and 0.5 pounds of baking soda at $0.82 per pound?
    1. $5.14
    2. $4.27
    3. $3.34
    1. $2.46
    2. $1.78
  28. If x2y2 = 72 and xy = 8, what is the value of x + y ?
    1. 8
    2. 9
    3. 36
    4. 72
    5. 80
  29. What is the product of 3m4 and 2b4 ?
    1. 5mb8
    2. 6mb8
    3. 6(mb)4
    1. 5(mb)8
    2. 6(mb)8
  30. What is the sum of 4x2 and 5x2 ?
    1. 9x4
    2. 9x2
    3. 4x2 + 5x2
    4. 20x4
    5. 20x2
  31. If Brian spends 7 minutes warming up and 3 minutes per yoga posture, which of the following equations expresses the number of minutes Brian spends on warm-ups and postures when he does p postures?
    1. y = 7
    2. y = 7p + 7
    3. y = 10p
    1. y = 3p – 7
    2. y = 4p + 4
  32. On the first day of Professor Gil's Reading Shakespeare class, six students will select a seat from the six seats at a table in the classroom. How many different sitting arrangements of the six students are possible?
    1. 6
    2. 72
    3. 144
    4. 720
    5. 1440
  33. In the right triangle shown below, which of the following statements is true about ?
      Posttest
    1. cos L =
    2. sin L =
    3. tan L =
    1. cos L =
    2. sin L =
  34. Which of the following expressions could be used to find the length of the side marked with the question mark in the triangle shown below, with measurements as marked?
  35. (Note: The law of cosines states that for any triangle with vertices A, B, and C and the sides opposite those vertices with lengths a, b, and c, respectively, c2 = a2 + b2 – 2ab cos C.)

      Posttest
    1. 412 + 322 – 2(41)(32) cos 67
    2. 352 + 782 – 2(41)(32) cos 67
    3. 352 + 782 – 67(41)(32) cos 2
    4. 412 + 322 – 67(35)(67) cos 41
    5. 352 + 782 – 2(41)(32) cos 32
  36. There are 16 buttons in a bag: 8 are red, 4 are blue, and 4 are white. What is the probability that a button selected at random from the bag is NOT white?
    1. 1
  37. What is the product of the 2 solutions of the equation x2 + 2x – 24 = 0 ?
    1. –24
    2. –10
    3. –2
    4. 8
    5. 14
  38. What are the coordinates for the minimum point in the graph of y – 5 = (x – 4)2 ?
    1. (4, 5)
    2. (–4, 5)
    3. (4, –5)
    1. (–4, –5)
    2. (0, 0)
  39. A circle in the standard (x, y) coordinate plane has center (4, 9) and radius of 9 coordinate units. Which of the following is an equation of the circle?
    1. (x – 4)2 – (y – 3)2 = 9
    2. (x + 4)2 + (y + 9)2 = 9
    3. (x – 4)2 – (y – 9)2 = 81
    4. (x – 4)2 + (y – 9)2 = 81
    5. (x + 4)2 – (y – 9)2 = 81
  40. The ratio of the radii of two circles is 2 : 3. What is the ratio of their areas?
    1. 2 :3
    2. 4:9
    3. 8:27
    1. 2:π
    2. π:3
  41. Which of the following are solutions to |q – 5| = 10 ?
    1. 15 only
    2. –5 only
    3. –15 only
    4. –5 and –15 only
    5. 15 and –5 only
  42. What is the next term after 12 in the geometric sequence – , 3, –6, 12, …?
    1. 24
    2. 0
    1. –24
    2. –48
  43. 137°F is the point at which ethanol will boil. Since Fahrenheit and Celsius temperatures are related by the formula F = C + 32, to the nearest degree, which of the following is the boiling point of ethanol in degrees Celsius? (Note: F = C + 32)
    1. 58°C
    2. 76°C
    3. 105°C
    4. 247°C
    5. 279°C
  44. (5x + 2) – (8x – 5) is equivalent to
    1. (–3x – 3)
    2. (–3x + 7)
    3. (3x – 3)
    1. (3x – 7)
    2. (x – 3)
  45. When x = –3, what is the value of the equation y = 2x2 + 4 ?
    1. –2
    2. –14
    3. 12
    4. 22
    5. 40
  46. If (x – 2)(x + 3) = 0, then x could equal
    1. –3
    2. 0
    3. 2
    1. II only
    2. I and II
    3. I and III
    1. II and III
    2. I, II, and III
  47. Which of the following is a value that satisfies log6 216 = x ?
    1. 0
    2. 1
    3. 2
    4. 3
    5. 4
  48. If the product of 3 and (2i2 + x) equals –9, then x = ?
    1. 0
    2. –1
    3. –2
    1. i
    2. 2i
  49. What is the slope of a line parallel to the line through (–6, 3) and (5, 8) in the standard (x, y) coordinate plane?
    1. –2
    2. 5
    3. 16
  50. If m = –2 and n > 0, which of the following is greatest?
    1. mn
    2. m2n
    3. m3n
    1. m4n
    2. m5n
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