MATHEMATICS TEST - Lesson 3 - ACT Practice Test 3

1,296 ACT Practice Questions, 3rd Edition (2013)

ACT Practice Test 3

2. MATHEMATICS TEST

60 Minutes—60 Questions

DIRECTIONS: Solve each problem, choose the correct answer, and then darken the corresponding oval on your answer document.

Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.

Note: Unless otherwise stated, all of the following should be assumed:

1. Illustrative figures are NOT necessarily drawn to scale.

2. Geometric figures lie in a plane.

3. The word line indicates a straight line.

4. The word average indicates arithmetic mean.

1. |8 − 5| − |5 − 8| =?

A. −6

B. −5

C. −3

D. 0

E. 6

2. A science tutor charges $60 an hour to help students with biology homework. She also charges a flat fee of $40 to cover her transportation costs. How many hours of tutoring are included in a session that costs $220?

F. 2

G. 3

H. 3

J. 4

3. Train A averages 16 miles per hour, and Train B averages 24 miles per hour. At these rates, how many more hours does it take Train A than Train B to go 1,152 miles?

A. 20

B. 24

C. 40

D. 48

E. 72

4. 33r² − 24r + 75 − 41r² + r is equivalent to:

F. 44r²

G. 44r⁶

H. −8r² − 24r + 75

J. −8r⁴ − 23r² + 75

K. −8r² − 23r + 75

5. Six equilateral triangles form the figure below. If the perimeter of each individual triangle is 15 inches, what is the perimeter of ABCDEF, in inches?

A. 18

B. 30

C. 60

D. 54

E. 90

6. The expression (5x + 2)(x−− 3) is equivalent to:

F. 5x² + 13x − 6

G. 5x² − 13x − 6

H. 5x² − 4x + 5

J. 5x² − 6

K. 5x² − 5

7. If 35% of a given number is 14, then what is 20% of the given number?

A. 2.8

B. 4.9

C. 7.0

D. 7.7

E. 8.0

8. The 7 consecutive integers below add up to 511, x − 2, x − 1, x, x + 1, x + 2, x + 3, and x + 4.
What is the value of x?

F. 71

G. 72

H. 73

J. 74

K. 75

9. In the standard (x,y) coordinate plane, point B with coordinates of (5,6) is the midpoint of line and point A has coordinates at (9,4). What are the coordinates of C?

A. (13, 2)

B. (7, 5)

C. (1, 8)

D. (14,10)

E. (−1,−8)

10. Isosceles trapezoid ABCD, with equal sides and , has vertices A (3,0), B (6,6), and D (15,0). These vertices are graphed below in the standard (x,y) coordinate plane below. What are the coordinates of one possible vertex C?

F. (11,7)

G. (13,6)

H. (12,6)

J. (13,5)

K. (12,7)

11. The town of Ashville has three bus stations (A, B, and C) that offer round-trip fares to its business district at both peak and off-peak rates. The matrices below show the average weekly sales for each station at each rate and the costs for both rates. In an average week, what are the combined peak and off-peak sales for Ashville’s three bus stations?

A. $ 780

B. $1,590

C. $1,950

D. $2,090

E. $2,340

12. The triangle shown below has exterior angles a, b, and c. What is the sum of those angles?

F. 360°

G. 315°

H. 225°

J. 180°

K. Cannot be determined from the information given

Use the following information to answer questions 13−15.

A sample of 300 jellybeans was removed from a barrel of jellybeans. All of the jellybeans in the barrel are one of four colors: red, orange, green, and purple. For the sample, the number of jellybeans of each color is shown in the table below.

Color	Number of jellybeans
red	75
orange	120
green	60
purple	45

13. What percent of the jellybeans in the sample are green?

A. 15%

B. 20%

C. 25%

D. 40%

E. 60%

14. The sample of jellybeans was removed from a barrel containing 25,000 jellybeans. If the sample is indicative of the color distribution in the barrel, which of the following is the best estimate of the number of red jellybeans in the barrel?

F. 3,750

G. 5,000

H. 6,250

J. 10,000

K. 18,750

15. If the information in the table were converted into a circle graph (pie chart), then the central angle of the sector for orange jellybeans would measure how many degrees?

A. 54°

B. 72°

C. 90°

D. 120°

E. 144°

16. In rectangle ABCD shown below, E is the midpoint of , and F is the midpoint of . Which of the following is the ratio of the area of quadrilateral AECF to the area of the entire rectangle?

F. 1:1

G. 1:2

H. 1:3

J. 1:4

K. 2:5

17. In the standard (x,y) coordinate plane, what is the slope of the line parallel to the line y = x − 3?

A. −3

B. −2

C. −

E. 2

18. Aru watches a movie that is 120 minutes long in 2 sittings. The ratio of the 2 sitting times is 3:5. What is the length, in minutes, of the longer sitting?

F. 8

G. 15

H. 45

J. 60

K. 75

19. Which of the following could be a value of x if 11 < x < 12?

20. Susan is planning the layout of her garden. She wants to plant tomatoes in 3 plots, each 10 feet by 16 feet. Within the total area, she will leave a 4-foot-by-6-foot rectangular plot for beans, and a 2-foot-by-5-foot rectangular plot for lettuce. If each packet of tomato seeds will cover between 150 and 200 square feet of soil, which of the following is the minimum number of packets of seeds Susan needs to buy to plant tomatoes?

F. 5

G. 4

H. 3

J. 2

K. 1

21. What values of x are solutions in the equation x² + 4x = 12?

A. 8 and 12

B. 0 and 4

C. −2 and 6

D. −4 and 0

E. −6 and 2

22. For all xy ≠ 0, and when both x and y are greater than 1, the expression equals which of the following?

H. 1

23. If point A has a non-zero x-coordinate and a non-zero y-coordinate and at least one of these coordinate values is positive, then point A must be located in which of the 4 quadrants labeled below?

A. I only

B. I or II only

C. II or IV only

D. II, III, or IV only

E. I, II, or IV only

24. The variable cost to produce a box of paper is $4.75. The fixed cost for the paper production machinery is $1,600.00 each day. Which of the following expressions correctly models the cost of producing b boxes of paper each day?

F. 1,600b + 4.75

G. 1,600b − 4.75

H. 1,600 + 4.75b

J. 4.75b − 1600

K. 1,600b

25. In the figure below, where ABC ~ XYZ, lengths are given in inches and the perimeter of ABC is 576 inches. What is the length, in inches, of ?

(Note: The symbol ~ means “is similar to.”)

B. 144

D. 192

E. 240

26. Given that , what is the value of x?

F. 6

G. 11

H. 121

K. 2

27. Natalie starts at the finish line of a straight 1,300-foot track and runs to the left toward the starting line at a constant rate of 12 feet per second. Jonathon starts 150 feet to the right of the starting line and runs to the right toward the finish line at a constant rate of 9 feet per second. To the nearest tenth of a second, after how many seconds will Natalie and Jonathon be at the same point on the track?

A. 483.3

B. 383.3

C. 63.7

D. 54.8

E. 10.9

28. Steve is going to buy an ice-cream sundae. He first must choose 1 of 3 possible ice-cream flavors. Next, he must choose 1 of 2 types of syrup. Finally, he must choose 1 of 6 kinds of candy toppings. Given these conditions, how many different kinds of sundaes could Steve possibly order?

F. 162

G. 36

H. 18

J. 9

K. 6

29. The width of a rectangular cardboard box is half its length and twice its height. If the box is 12 cm long, what is the volume of the box in cubic centimeters?

A. 72

B. 216

C. 252

D. 1,296

E. 1,728

30. At the end of each month, a credit card company uses the formula D = B (1 + r) + 10m² to calculate debt owed, where D is the cardholder’s total debt; B is the amount charged to the card; r is the rate of interest; and m is the number of payments the cardholder has previously missed. If Daniel has charged $2,155 to his credit card with a 13% interest rate and has missed 2 payments, which value is closest to Daniel’s total credit card debt?

F. $2,195

G. $2,435

H. $2,455

J. $2,475

K. $2,495

31. In the figure below, a cone is shown, with dimensions given in centimeters. What is the total surface area of this cone, in square centimeters? (Note: The total surface area of a cone is given by the expression πr² + πrs, where r is the radius and s is the slant height.)

A. 225π

B. 450π

C. 465π

D. 675π

E. 18,000π

32. Given the functions f and g are defined as f(a) = 3a − 4 and g(a) = 2a² + 1 what is the value of f(g(a))?

F. 6a² − 1

G. 6a² − 3

H. 2a² + 3a − 3

J. −2a² + 3a + 3

K. 18a² − 48a + 33

33. The table below shows the results of a recent poll in which 262 high school students were asked to rank a recent movie on a scale from 1 to 5 stars. To the nearest hundredth, what was the average star-rating given to this movie?

Stars given	Number of students who gave this rating
1	51
2	18
3	82
4	49
5	62

A. 0.31

B. 2.02

C. 3.06

D. 3.20

E. 18.8

34. Lines p, q, r, and s are shown in the figure below and the set of all angles that are supplementary to x is {1,3,8,11}. Which of the following is the set of all lines that must be parallel?

F. {q,r}

G. {q,s}

H. {r,s}

J. {p,q}

K. {q,r,s}

35. (4x⁴ y⁴)⁴ is equivalent to:

A. xy

B. 16x⁸ y⁸

C. 16x¹⁶ y¹⁶

D. 256x⁸ y⁸

E. 256x¹⁶ y¹⁶

36. Which of the following expressions is equivalent to the inequality 6x – 8 > 8x + 14?

F. x < −−11

G. x > −−11

H. x < −−3

J. x > −−3

K. x < 11

37. As shown in the standard (x,y) coordinate plane below, A (2,4) lies on the circle with center L (10,−2) and radius 10 coordinate units. What are the coordinates of the image of A after the circle is rotated 90° counterclockwise (Ó) about the center of the circle?

A. (10, 2)

B. (−2, 10)

C. (2, −8)

D. (0, −2)

E. (4,−10)

38. The length of the hypotenuse of the right triangle figured below is 16, and the length of one of its legs is 12. What is the cosine of angle θ?

39. In the figure shown below, bisects BAD, and bisects CAE What is the measure of CAD?

A. 30°

B. 45°

C. 60°

D. 90°

E. Cannot be determined from the given information

40. If the average number of carbon dioxide molecules per cubic inch in a container is 3 × 10⁴ and there are 6 × 10⁸ molecules of carbon dioxide in the container, what is the volume of the container in cubic inches?

F. 5 × 10⁵

G. 2 × 10²

H. 2 × 10⁴

J. 18 × 10¹²

K. 18 × 10³²

41. The figure below shows the screen of an automobile navigation map. Point A represents the car’s starting point, point B represents the driver’s intended destination, and point C, the center of the circle, is the car’s current position. Currently, point A is 15 miles from point C and 250° clockwise from due north, and point B is 20 miles from point C and 30° clockwise from due north. Which of the following represents the shortest distance (a straight line) between the car’s starting point and the driver’s desired destination?

(Note: For any ABC in which side a is opposite A, side b is opposite B, and side c is opposite C, the law of cosines applies: c² = a² + b² − 2ab cos C.)

42. What real number is halfway between and ?

43. In isosceles triangle ACE, shown below, B and D are the midpoints of congruent sides and respectively. ABE measures 95°, and DEA measures 35°. What is the measure of DEA?

A. 50°

B. 30°

C. 25°

D. 15°

E. 10°

44. A small square table and an L-shaped table fit together with no space between them to create a large square table. The area of the large square table is 108 square feet and is nine times the area of the small square. What is x, the edge of the L-shaped table labeled in the figure below in square feet?

F. 2

G. 4

H. 4

J. 4

K. 12

45. Which of the following is NOT an irrational number?

46. If x < 0 and y < 0, then |x + y| is equivalent to which of the following?

F. x + y

G. −(x + y)

H. x − y

J. |x − y|

47. Jane wants to bring her bowling average up to an 85 with her performance on her next game. So far she has bowled 5 out of 7 equally weighted games, and she has an average score of 83. What must her score on her next game be in order to reach her goal?

A. 83

B. 85

C. 90

D. 93

E. 95

48. In a complex plane, the vertical axis is the imaginary axis and the horizontal axis is the real axis. Within the complex plane, a complex number a + bi is comparable to the point (a, b) in the standard (x, y) coordinate plane. is the modulus of the complex point a + bi. Which of the complex numbers F, G, H, J, and K below has the smallest modulus?

F. F

G. G

H. H

J. J

K. K

49. In the real numbers, what is the solution of the equation 9^x−4 = 27^{3x + 2}?

B. −2

C. −3

E. −4

50. The graph of the trigonometric function f(x) = 2 sin x is represented below. Which of the following is true of this function?

F. f(x) is a 1:1 function (that is, x is unique for all f(x) and f(x) is unique for all x).

G. f(x) is undefined at x = 0.

H. f(x) is even (that is, f(x) = f(−x) for all x).

J. f(x) is odd (that is, f(−x) = −f(x) for all x).

K. f(x) falls entirely within the domain −6 ≤ x ≤ 6.

51. An integer from 299 through 1,000, inclusive, will be chosen randomly. What is the probability that the number chosen will have 1 as at least 1 of its digits?

52. In the figure below, side of isosceles triangle NLM lies on the line y + x = 2 in the standard (x,y) coordinate plane, and side is parallel to the x-axis. What is the slope of ?

53. In the figure below, 0 < y < x. One of the angle measures in the triangle is . What is ?

Use the following information to answer questions 54−56.

Melissa attaches her dog’s leash to a metal anchor in the grass so that the dog can roam only within a radius of 12 feet in any direction from the anchor. A map of the area accessible to the dog is shown below in the standard (x,y) coordinate plane, with the anchor at the origin and 1 coordinate unit representing 1 foot.

54. Which of the following is closest to the area, in square feet, the dog can roam?

F. 75

G. 144

H. 452

J. 904

K. 1,420

55. Which of the following is an equation of the circle shown on the map?

A. (x – y)² = 12

B. (x + y)² = 12

C. (x + y)² = 12²

D. x² + y² = 12

E. x² + y² = 12²

56. Joy brings her dog to the same park and anchors her dog 30 feet away from Melissa’s anchor along a walking trail. Joy’s dog can roam only within a radius of 20 feet in all directions from its anchor. For how many feet along the walking trail can both dogs roam?

(Note: Assume the leashes can’t stretch.)

F. 2

G. 8

H. 10

J. 18

K. 42

57. The graphs of the equations y = –(x) + 1 and y = −(x + 1)² + 4 are shown in the standard (x,y) coordinate plane below. What real values of x, if any, satisfy the following inequality: –(x + 1)² + 4 > –(x) + 1?

A. x < −3 and x > 1

B. x < −2 and x > 1

C. −3 < x < 1

D. −2 < x < 1

E. No real values

58. For any positive two-digit integer x with tens digit t, units digit u, and t ≠ u, y is the two-digit integer formed when the digits of x are reversed. What is the greatest possible value of (y − x) when t is less than u?

F. u − t

G. ut − tu

H. t² − 10tu + u²

J. 9|u − t|

K. Cannot be determined from the given information

59. In the figure below, the vertices of parallelogram ABCD are A (2,−4), B (8,−4), C (10,−2), and D (4,−2). What is the area of the parallelogram?

A. 6

B. 6

C. 12

D. 12

E. 16

60. The sum, S, of an arithmetic sequence with first term x₁ is given by , where n is the number of terms in the sequence. The sum of 5 consecutive terms in a given arithmetic sequence is 145, and x₅ is 48. What is the sixth term of this sequence?

F. 49

G. 57.5

H. 77

J. 154.5

K. 174

END OF TEST 2
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