The ACT Mathematics

Mock Test 3
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The ACT
Form MT3
Mathematics
Directions
This booklet contains a mathematics test. The test row of ovals with the same number as the question.
measures skills and abilities highly related to high Only responses marked on your answer document
school course work and success in college. will be scored. Your score on each test will be based
Calculators may be used on the mathematics test. only on the number of questions you answer correctly
The questions in the test are numbered, and the during the time allowed for the test. You will not be
suggested answers for each question are lettered. On penalized for guessing. It is to your advantage to
the answer document, the rows of ovals are numbered answer every question even if you must guess.
to match the questions, and the ovals in each row are You may work on the test only when the testing
lettered to correspond to the suggested answers. staff tells you to do so. If you finish the test before
For each question, first decide which answer is best. time is called for the test, you should use the time
Next, locate on the answer document the row of ovals remaining to reconsider questions you are uncertain
numbered the same as the question. Then, locate the about in the test.
oval in that row lettered the same as your answer. Lay your pencil down immediately when time is
called at the end of the test. You may not for any
Finally, fill in the oval completely. Use a soft lead
reason fill in or alter ovals for the test after time is
pencil and make your marks heavy and black. Do not
called for the test. To do so will disqualify you from
use ink or a mechanical pencil.
the examination.
Mark only one answer to each question. If you
Do not fold or tear the pages of your test booklet.
change your mind about an answer, erase your first
DO NOT OPEN THIS BOOKLET
mark thoroughly before marking your new answer.
UNTIL TOLD TO DO SO.
For each question, make certain that you mark in the

37
 You may wish to remove this answer document from the booklet to use in the mathematics mock test.

The ACT Mathematics

Mock Test 3
Answer Sheet

NAME: _______________________________________

DATE: ________________________________________

FORM CDOE: __________________________________

Cut Here

USE A SOFT LEAD NO. 2 PENCIL ONLY.

(Do NOT use a mechanical pencil, ink, ballpoint, correction fluid, or felt-tip pen.)

The ACT
Mathematics
38
2 2
MATHEMATICS MOCK TEST 3
60 Minutes – 60 Questions

DIRECTIONS: Solve each problem, choose the correct but some of the problems may best be done without using a
answer, and then in fill in the corresponding oval on your calculator.
answer document. Note: Unless otherwise stated, all of the following should be
Do not linger over problems that take too much time. assumed.
Solve as many as you can; then return to the others in the 1. Illustrative figures are NOT necessarily drawn to scale.
time you have left for this test. 2. Geometric figures lie in a plane.
You are permitted to use a calculator on this test. You may 3.The word line indicates a straight line.
use your calculator for any problems you choose, 4. The word average indicates arithmetic mean.

0.6 DO YOUR FIGURING HERE.

1. If x = 2, then x = ?

A. 0.06
B. 0.03
C. 0.1
D. 0.2
E. 0.3

2. The printing cost of a book is 15% higher this year than

they had been when the book was sold at $45. If the
selling price of the book had increased by the same
percent as the printing cost, what would the selling
price of the book be this year?

F. $47.25
G. $49.50
H. $50.25
J. $50.75
K. $51.75

3. Andrew earns his salary of $9 per hour for up to 35

hours of work each week. Over 35 hours of work in a
week, the salary for each hour will be paid 1 23 times
the original salary. How much does he earn in a week
for 42 hours of work?

A. $300.00
B. $352.80
C. $420.00
D. $525.80
E. $630.00

4. 4p6 × (–2p4) is equivalent to:

F. 2p10
G. 2p24
H. –8p6
J. –8p10
K. –8p24

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2 2
5. The total surface area, A, of a right circular cone with DO YOUR FIGURING HERE.
base radius r and slant height can be determined by
using the formula A =  r   r . Find the total surface
2

area, in square centimeters, of the figure below.

A. 765 
B. 810  39 cm
C. 1,836 
36 cm
D. 1,881 
E. 2,106 

6. In the figure below, AFB, CGD and EFG are lines.

AB and CD are parallel. The measure of
∠AFE is 128°. What is the measure of ∠AGC ?

?
F. 30° 128°
G. 32°
H. 38°
J. 52°
K. 60°

7. What is the least common numerator of the fractions

18 105 441
35 , 256 , and 125 ?

A. 21
B. 210
C. 2,205
D. 4,410
E. 833,490

8. Which of the following polynomial equations has roots

–7 and 2 ?

F. (x – 2)3(x + 7) = 0
G. (x + 2)3(x – 7) = 0
H. (x – 5)(x + 9)2 = 0
J. (x + 5)(x – 9)2 = 0
K. (x – 2)3(x – 7) = 0

ACT-Mathematics Mock Test 3 40 GO ON TO THE NEXT PAGE.

2 2
9. The combined length of 3 strips of ribbon is 100 cm. DO YOUR FIGURING HERE.
The lengths of the strips are in the ratio 4 : 7 : 9. What
is the length, in centimeters, of the shortest strip?

A. 10
B. 20
C. 35
D. 45
E. 65

10. Which of the following is a solution to the equation

x2 – 12x = 0 ?

F. 24
G. 12
H. 6
J. –6
K. –12

11. Points P(5,1) and Q(–1,3) lie in the standard (x,y)

coordinate plane. What is the midpoint of PQ ?

A. (2,2)
B. (3,2)
C. (2,3)
D. (3,3)
E. (4,3)

12. What is the volume, in cubic meters, of a rectangular

box that is 6 m deep, 4 m wide, and 9 m long?

F. 19
G. 33
H. 42
J. 58
K. 216

13. Which of the following expressions is equivalent to

(3x3 – 2x + 8) – (–2x2 + 4x – 3) for all real values of x ?

A. 3x3 + 2x2 + 2x + 5
B. 3x3 – 2x2 + 2x + 5
C. 3x3 + 2x2 – 6x + 11
D. 3x3 – 2x2 – 6x + 11
E. 3x3 + 2x2 + 6x – 11

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2 2
14. Let n be an integer. Let E be the statement that “n is DO YOUR FIGURING HERE.
positive” and let F be the statement that “n is odd”. If
n = 100, which of the following statements is true?

F. Both E and F are false.

G. E is true and F is false.
H. E is false and F is true.
J. Both E and F are true.
K. Cannot be determined from the given information

15. | –8(3) – 2(–6) | = ?

A. –36
B. –12
C. 12
D. 36
E. 109

16. In the standard (x,y) coordinate plane, what is the slope

of the line 8x – 3y = 24 ?

8
F. 3
3
G. 8

H. – 83
J. 8
K. –8

17. A function f is defined as f(x,y,z) = 3x2 + 2xy – yz3.

What is f(1,–2,3) ?

A. –55
B. –47
C. 25
D. 53
E. 61

Use the following information to answer

questions 18–21.

A class plans to organize a class journey. They have a

total budget of $800 to cover expenses in 5 categories.
Not all the budget has been assigned yet. The budget
amounts that have been assigned are shown in the table
below:

Expense category Budget amount

Transportation $80
Food $250
Rooms booking $300
Games ?
Others ?
Total budget $800

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2 2
18. In a circle graph illustrating the above 5 budget DO YOUR FIGURING HERE.
amounts, what should be the measure of the central
angle of the “Rooms booking” sector?

F. 36°
G. 76.5°
H. 112.5°
J. 125°
K. 135°

19. The amount budgeted for “Food” consists of 4 kinds

(pizzas, hotdogs, hamburgers and spaghettis). What is
the average price each kind of food?

A. $20
B. $62.5
C. $75
D. $100
E. $200

20. Suppose a bar graph will be used to illustrate the

amount of the expenses. The length of the bar for
“Transportation” should be what fraction of the length
of the bar for “Rooms booking”?

1
F. 10
8
G. 25
4
H. 15
3
J. 5
4
K. 5

21. Which of the following percents is closest to the

percent of the total budget that remains to be assigned?

A. 10%
B. 21%
C. 31%
D. 38%
E. 48%

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2 2
22. In the figure below, find the value of x ? DO YOUR FIGURING HERE.
2x°
x° + 46°

104° 78°

F. 32
G. 39
H. 41
J. 44
K. 46

23. What is the area, in square coordinate units, of

parallelogram PQRS shown in the standard (x,y)
coordinate plane below?

P(0,9) S(6,9)

A. 54
B. 72
C. 84
D. 96
E. 108

Q(2,0) R(8,0)

24. Right triangle △UVW is shown below. The side lengths

are given in inches. What is tan  ?
U

W
V 10

10
F. 3
3
G. 10
3
H.
109
109
J. 3
10
K.
109

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2 2
25. The system of equations below has 1 solution (p,q). DO YOUR FIGURING HERE.
What is the value of p ?

 6 p  5q  19

3 p  2q  13

A. –2
B. –1
C. 1
D. 2
E. 5

26. Stephen joined the local petrol station’s rewards

programme. He can earn points toward free petrol each
time he purchases petrol. Points are earned according to
the following table:

Rewards programme:
Join the programme, earn 1,000 points
Buy 1 litre regular petrol, earn 10 points
Buy 1 litre supreme petrol, earn 15 points

At the end of the first month, Stephen had 2,350 points

which included 1,000 points he received for joining the
programme and 115 litres of petrol. Let r and s be the
litres of regular petrol and supreme petrol he bought in
the first month. We know that r + s = 115. If he wanted
to find how much supreme petrol he had purchased, he
needed another equation. Which of the following could
be this equation?

F. 2r + 3s = 270
G. 2r + 3s = 470
H. 3r + 2s = 270
J. 3r + 2s = 400
K. 3r + 2s = 470

27. In the figure below, the first pattern consists of 10

square dots. The second pattern, and of each successive
nth pattern after the second, is determined by
continuing the following pattern: (2n + 3) square dots
are added to the (n – 1)th pattern. What is the number
of square dots in the 6th pattern?

A. 37
B. 50
C. 65
D. 82
E. 101

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28. Which of the following expressions below is a factor of DO YOUR FIGURING HERE.
the polynomial 4x3 – 7x2 – 2x ?

I. x
II. x+2
III. 4x – 1

F. I only
G. I and II only
H. I and III only
J. II and III only
K. I, II and III

29. Shown below is a circular dartboard with a square

shaded region. Alice will throw a dart at random and
hits the dartboard, what is the probability that the dart
hits the shaded region?

1
A. 16 3 cm

B. 16
1
C. 8

D. 4 12 cm
1
E. 4

30. The dimensions of equilateral triangle △PQR are given

in inches in the figure below. What is the value of b ?
P
F. 1
G. 2
H. 3 3a – 1 7a – 9
J. 4
K. 5
Q 2b – 3 R

8
31. For right triangle △UVW below, cos V = 17 . What is
tan V ?
U
8
A. 17
8
B. 15 17
15
C. 8
15
D. 17

E. 17 V 8 W
15

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2 2
32. When a sports store sets the price of a pair of sports
shoes at $100, it sells 150 pairs of sports shoes a day.
With each $5 increase in the $100 price, 10 pairs of
sports shoes are sold less. Let n be the number of $5
increases in the price. Which of the following
expressions best represents the amount of the store’s
sale of the sports shoes a day?

F. 50(35 + n)
G. 25(20 – n)(15 + n)
H. 25(20 – n)(15 – n)
J. 50(20 + n)(15 + n)
K. 50(20 + n)(15 – n)

33. The circumference of a circle is 40 inches. What is the

length, in inches, of the diameter of the circle?

20
A. 
40
B. 
C. 10
D. 40
E. 40

34. The height of Canada’s CN Tower is 553 m. What is

the closest angle of elevation of the top S of the tower
from a point T 300 m away?

553 m

T
R
300 m

F. 23.8°
G. 28.5°
H. 32.9°
J. 57.1°
K. 61.5°

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DO YOUR FIGURING HERE.
Use the following information to answer
questions 35–38.

Square PQRS, shown below, has side length 7 feet. The

square is divided into 49 non-overlapping congruent
squares. Point O is the center of the square PQRS.

Q P

O 7

R S

35. What is the length, in feet, of PR ?

A. 7
B. 7 2
C. 98
D. 2 98
E. 14

36. What is the perimeter, in feet, of 1 of the 49 congruent

squares?

F. 1
G. 4
H. 7
J. 14
K. 28

37. Point M starts at P and is rotated clockwise about O a

total of 540°. After the rotation, M is at the same
location as which of the following points?

A. O
B. P
C. Q
D. R
E. S

38. Suppose PQRS is in the standard (x,y) coordinate plane

such that RS lies on the x-axis, the midpoint of RS is
the origin, P has positive coordinates, and 1 coordinate
unit is equal to 1 foot. What are the coordinates of S?

F. (–3.5,7)
G. (2.5,0)
H. (–2.5,7)
J. (3.5,0)
K. (3.5,7)

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2 2
39. For what value of x is the equation 3
5x  2 + 8 = 11 DO YOUR FIGURING HERE.
true?

A. 1
B. 4
C. 5
D. 10
E. 256

40. Tina deposits $10,000 at 3% interest compounded

monthly. Which of the following expressions represents
the amount she will receive after 5 years?

$10,000 × 1  0.03
5
F.

G. $10,000 × 1  0.03
12

H. $10,000 × 1  300 
1 12

$10,000 × 1  400 
60
J. 1

K. $10,000 × 1  121 
60

41. Which of the following is the decimal equivalent to

3
13 ?
(Note: A bar indicates a digit pattern that is repeated.)

A. 0.230769
B. 0.23076923
C. 0.23072307
D. 0.230769
E. 0.23076923

42. The table below shows the distribution of the numbers

of questions in 32 sets of exercises in a mathematics
textbook. Which of the following statements about the
mean of the 32 sets of exercises is true?

No. of questions 10 11 12 13 14
No. of sets of
6 5 8 9 4
exercises

F. The mean is less than 10.

G. The mean is 10.
H. The mean is between 10 and 11.
J. The mean is 11.
K. The mean is greater than 11.

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2 2
43. The cost $C of printing a poster can be found by using DO YOUR FIGURING HERE.
A
the formula C = , where A cm2 is the area of the
9 n
poster and n is the number of copies printed. Which of
the following gives the number of posters printed for
cost $50 and the area of each poster is 4,500 cm2?

4,500
A. (9)(50)

 
2
4,500
B. (9)(50)
(9)(50)
C. 4,500

D.  (9)(50) 2
4,500 
E. (9)(50)(4,500)

44. Tommy has $1.78 in quarters ($0.25), dimes ($0.10),

nickels ($0.05), and pennies ($0.01). He notices that
there are 4 more dimes than quarters, 8 more nickels
than quarters, and 16 more pennies than quarters. How
many nickels does Tommy have?

F. 4
G. 6
H. 10
J. 14
K. 18

45. Consider the transformation of the standard (x,y)

coordinate plane that maps each point (a,b) to the point
(ka,kb) for a positive constant k. For example, this
transformation maps (4,7) to (16,28). This
transformation maps (7,2) to which of the following
points?

A. (28,8)
B. (21,8)
C. (28,6)
D. (21,6)
E. (49,14)

46. The length of a side of a square is 8 cm. Which of the

following values is closest to the sum of the diagonals
of the square, in centimeters?

F. 23
G. 24
H. 26
J. 30
K. 32

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2 2
47. Miss Chen is a college mathematics teacher whose
salary is $38,915 for this school year which has 181
DO YOUR FIGURING HERE.
school days. In Miss Chen’s school district, substitute
teachers are paid $105 each day. Suppose that she takes
a no-paid day off and a substitute teacher is paid for
here classes, how much less does the school district pay
for salary by paying a substitute teacher instead of Miss
Chen for her day off?

A. $80
B. $105
C. $110
D. $175
E. $215

48. For a certain location in Yellowstone National Park, the

highest and the lowest temperatures on record are 85°F
and 60°F respectively. Which of the following
statements below is true about the temperatures on
record for this location?

I. The range of temperatures is 25°F.

II. The range of temperatures is 145°F.
III. The average temperature is 72.5°F.

F. I only
G. II only
H. III only
J. I and III only
K. II and III only

49. x 2 3
The graph of y = in the standard (x,y)
x 2 5 x  6
coordinate plane has a vertical asymptote with equation
x=?

A. –6
9
B. – 5
9
C. 5
D. 1
E. –1

50. What fraction of a 8-inch-diameter disk equals the

same amount of disk as 1 slice of a 16-inch-diameter
disk of the same thickness cut into 16 equal slices?

1
F. 4
1
G. 3
1
H. 2
2
J. 3
3
K. 4

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2 2
51. For what real value of x is
DO YOUR FIGURING HERE.
(5x )(52 ) 1
= 125
(57 )3
true?

A. 4
B. 6
C. 11
D. 14
E. 16

52. What are the real values of m such that any line passing
through the points (m,4) and (5,4) will be horizontal to
the x-axis when it is graphed in the standard (x,y)
coordinate plane?

F. –4
G. 4
H. All real numbers satisfy this condition.
J. All real numbers except 5 satisfy this condition.
K. No real numbers satisfy this condition.

53. What is the value of x in the figure below?

P

60°

700

70°
Q R
x
A. 700 tan 60°
700
B.
cos70
700
C.
sin 70
700sin 60
D.
sin 70
700sin 70
E.
sin 60

54. The graphs of the functions y = f(x) = (x – 2)2 + 1 and

y = g(x) = x – 1 are shown in the standard (x,y)
coordinate plane below. Which of the following is
false?

F. | f(x) | = f(x)
G. | g(x) | = g(x)
H. f(2) = g(2)
J. f(3) = g(3)
K. f(g(2)) = 2

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2 2
55. If 1 ≤ s ≤ 3 and 7 ≤ t ≤ 11, the largest possible value
2
DO YOUR FIGURING HERE.
for t s is?

1
A. 10
1
B. 5
1
C. 4
1
D. 2
E. 1

56. Given that P(3x,4) is rotated counterclockwise about

the origin through 270° to Q(4,9). What is the value of
x?

F. –3
G. –2
4
H. 3
J. 2
K. 3

57. Which of the following matrices is equivalent to the

matrix product

 3 7  2
 2 4  3  ?
  

6 7
A. 6
 4 
 3 14
B. 2
 12 
6 14 
C. 6 12 
 
 15
D.  16
 
 27 
E. 8
 

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2 2
58. In the figure, ABC , BGE , FGC and FED are
lines. The lengths marked are in feet. What is the length
of BE ?

10
A F

B E
G

C D
14

F. 11
1
G. 11 2
H. 12
J. 24
1
K. 24 2

59. Suppose that x will be randomly selected from the set

E = {–6, –3, –1,0,1,2} and that y will be randomly
selected from the set F = {–2, –1,0,1,3}. What is the
probability that xy < 0 ?

3
A. 11
1
B. 6
5
C. 6
1
D. 3
3
E. 5

60. If x = 2t – 5 and y = 4t + 3, which of the following

expresses y in terms of x ?

F. y=x+8
G. y = x + 13
H. y = 2x + 8
J. y = 2x + 13
K. y = 4x + 13

END OF MOCK TEST 3

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ACT-Mathematics Mock Test 3 54

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