ACT MATHEMATICS TEST 1

60 Minutes—60 Questions
DIRECTIONS: Solve each problem, choose the correct but some of the problems may be best done without using
answer, and then fill in the corresponding oval on your a calculator.
answer sheet. Note: Unless otherwise stated, all of the following should
Do not linger over problems that take too much time. be 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 3. The word line indicates a straight line.
may use your calculator for any problems you choose, 4. The word average indicates arithmetic mean.
b

1. Linda purchased 1½ pounds of potatoes on Friday and DO FIGURING HERE

2⅓ pounds of potatoes on Saturday. What was the total
weight, in pounds, of potatoes purchased by Linda in the
two-day period?

A. 3⅙
B. 3⅖
C. 3⅓
D. 3⅔
E. 3⅚

2. 2x2 · 2x3y · 3x2y is equivalent to:

F. 7x7y2
G. 7x12y2
H. 12x7y2
J. 12x12y
K. 12x12y2

3. There are a total 12,715 seats in an arena. Of the total,

7,512 seats are currently occupied by spectators. How
many seats, to the nearest percent, are currently oc-
cupied?

A. 12
B. 52
C. 59
D. 61
E. 75

4. A gardener wants to use rope to section off a rectangular

plot of land to grow vegetables. The plot measures 11
feet by 15 feet. Assuming no waste and that no extra
rope is required to tie the ends, what is the minimum
number of feet of rope the gardener will need to section
off the plot of land?

F. 26
G. 52
H. 104
J. 139
K. 165

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1
ACT
 5. In the first 4 of 5 consecutive days, Martha delivered DO FIGURING HERE
144, 152, 139, and 171 newspapers. How many
newspapers did Martha deliver on the fifth day, if the
average number of newspapers she delivered per day
during the five-day period was 155?

A. 154
B. 162
C. 169
D. 171
E. Given the number of newspapers delivered by
Martha on the first four days, she cannot average
155 per day for the five-day period.

6. Mr. Lee regularly spends a total $145 commuting to

work by train Monday through Friday. On Wednesday
of a given five-day week, however, Mr. Lee decides to
commute to work by car, instead of by train. If the cost
of commuting by car is $7, how much money does Mr.
Lee save commuting to work that week? (Assume the
regular train fare is the same each day of the week.)

F. $ 7
G. $ 12
H. $ 22
J. $138
K. $143

7. If x is a real number such that x3 = 125, then

x2 – √5𝑥 = ?

A. 0
B. 5
C. 10
D. 20
E. 25

8. The expression a[(b – c) + d] is equivalent to:

F. ab – ac + ad
G. ab – ac – ad
H. b – c + ad
J. ab + ac + ad
K. ab + ac – ad

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2
ACT
 9. If 5x + 7 = 8x – 3, then x = ? DO FIGURING HERE
10
A. –
3
10
B. –
13
3
C.
10
10
D.
13
10
E.
3

10. If a coin is randomly chosen from a bag that contains

exactly 4 pennies, 3 nickels, and 8 dimes, what is the
probability that the coin will NOT be a nickel?

1
F.
5
1
G.
4
3
H.
4
4
J.
5
5
K.
4

11. If the difference between the consecutive numbers in the

sequence below is the same, which two numbers should
be placed in the blanks?

19, ___, ___, 37

A. 25, 31
B. 22, 25
C. 24, 32
D. 26, 33
E. 28, 36

12. A spherical rubber ball has a diameter of 2⅓ inches. If

the formula for the volume of a sphere with radius r is
4
V = πr3, what is the volume of the ball to the nearest
3
cubic inch?

F. 3
G. 7
H. 9
J. 10
K. 21
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3
ACT
 13. In the table below, the sums of the integers in each row, DO FIGURING HERE
column, and diagonal are equal. Which of the following
integers accurately expresses the value of x?

2 9 x
–1 3 7
8 –3 4

A. 2
B. 1
C. 0
D. – 1
E. – 2

14. The matrix below summarizes the number of students

that tried out for various sports teams Central High
School.

soccer lacrosse track tennis

[ 60 40 46 30 ]

The following matrix represents the percentage of

students that were ultimately chosen to participate in
each of the four sports.

soccer 30
lacrosse 40
track 50
tennis 40

Given the two matrices, what is the total number of

students accepted to participate on the four sports teams
at Central High School?

F. 47
G. 50
H. 62
J. 69
K. 72

15. A manufacturer needs 57 pounds of grapes to make 24

cartons of raisins. How many pounds of grapes would
the manufacturer need to make 16 cartons of raisins?

A. 28
B. 33
C. 38
D. 40
E. 41

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ACT
 16. y DO FIGURING HERE

II I

III IV

Point A, not shown, is in one of the four quadrants of the

xy-coordinate plane above. If the x and y coordinates of
point A are both negative, in which quadrant must A be
located?

F. Quadrant I
G. Quadrant II
H. Quadrant III
J. Quadrant IV
K. Quadrants II or IV

17. Which of the following is a solution of the equation

x2 – 16x = 0?

A. –4
B. 4
C. 12
D. 16
E. 20

18. A sandwich shop has 2 types of bread, 3 types of cheese,

and 5 types of meat. How many different sandwiches
can be made using one type of bread, one type of cheese,
and one type of meat?

F. 10
G. 16
H. 20
J. 26
K. 30
3
19. Given A = B + 0.23 and A = 0.65, what is the value
4
of B?

A. 0.30
B. 0.48
C. 0.56
D. 0.67
E. 0.76
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5
ACT
 Use the information that follows to answer questions 20-21. DO FIGURING HERE

The following chart represents the current enrollment in

three art classes at a community college.

Course Title Day Time Enrollment

Basic Drawing Mon 9 am 21
Wed 9 am 26
Fri 9 am 22
Watercolors Mon 11 am 28
Wed 9 am 24
Art History Fri 11 am 27

20. What is the average number of students enrolled per day

in the Basic Drawing class?

F. 23
G. 24
H. 25
J. 26
K. 69

21. Room 12 of the community college can be occupied by a

maximum 30 students. All but one of the art classes
meets in Room 12. Such class cannot meet in Room 12
due to a scheduling conflict. On which day and at what
time does the conflict occur?

A. Monday at 9 am
B. Friday at 9 am
C. Monday at 11 am
D. Wednesday at 9 am
E. Friday at 11 am

22. If a rectangular plot measures 36 feet by 15 feet, what is

the length, in feet, of the diagonal of the plot?

F. 39
G. 47
H. 51
J. 126
K. 540

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ACT
 23. For right triangle ABC below, what is the cos A? DO FIGURING HERE
𝑎
A.
𝑏
A
𝑎
B.
𝑐
b
𝑏
C. c
𝑐

𝑐
D.
𝑎
B a C
𝑐
E.
𝑏

24. Which of the following is the slope-intercept form of

9x + y – 3 = 0?

F. y = – 9x – 3
G. y = – 9x + 3
H. y = 9x – 3
J. y = 3x – 9
K. y = 3x + 9

25. For all positive integers a, b, and c, which of the

𝑎
following expressions equals ?
𝑐

𝑎 •𝑏
A.
𝑏 •𝑐
𝑎 •𝑎
B.
𝑐 •𝑐
𝑎 •𝑐
C.
𝑐 •𝑎

𝑎 –𝑏
D.
𝑐 –𝑏

𝑎+𝑏
E.
𝑐+𝑏

26. Right triangle XYZ below has a hypotenuse that is 12

3
inches long. If sin Z = , how long is ��
XY��, in inches?
4

F. 4 Y
G. 7
H. 8
J. 9
K. 16 X Z
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7
ACT
 27. Line AB intersects circle C at points A and B, as shown, DO FIGURING HERE
and is 12 cm long. If line AB is 2 cm from the center of
the circle C, what is the radius of circle C to the nearest
tenth of a centimeter?
A B
A. 7.5
r
B. 6.3
C. 5.2 C
D. 4.0
E. 3.4

28. Points Q, R, S, and T lie on QT ���� as shown below. Given

���� is 20 units long, ����
that QT ���� is 9
QS is 18 units long, and RT
units long, what is the unit length of RS?����

Q R S T

F. 7
G. 8
H. 10
J. 11
K. It cannot be determined based on the information
given.

29. Lines y = 3x + 5 and y = 4x + 2 intersect on a standard

(x, y) coordinate plane. What is the x-coordinate of the
point where the two lines intersect?

A. 0
B. 2
C. 3
D. 5
E. 8

30. An aquarium in the shape of a rectangular box can hold

180 gallons of water when completely filled. Given that
the width of the aquarium is 3 feet and its length is 7
feet, what is the minimum depth, in feet, of the
aquarium? (Assume that 1 cubic foot of water is equal
to 3 gallons of water.)

F. 2.54
G. 2.61
H. 2.72
J. 2.86
K. 3.12
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8
ACT
 31. The chart below displays information regarding the DO FIGURING HERE
number and type of pizza delivered on a given day by a
pizzeria.

Type of Pizza Number Delivered

Pepperoni

Cheese

Mushroom

Sausage

= 10 Pizzas

According to the chart, what fraction of the pizzas

delivered were mushroom?
1
A.
12
1
B.
10
1
C.
6
1
D.
3
1
E.
2

32. If 2a = 2b + 4, then (b – a)3 = ?

F. –8
G. –4
H. –2
J. 8
K. 16

33. For all real numbers R and S, if R = 2S + 10, then S = ?

R
A. – 10
2

R
B. + 10
2

R
C. – 20
2

R + 10
D.
2

R – 10
E.
2

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9
ACT
 34. A 12-foot ladder is leaning against the wall of a DO FIGURING HERE
building. If the bottom of the ladder touches the ground
5 feet from the base of the building, approximately how
far is the top of the ladder from the base of the building?

F. 9
G. 11
H. 12
J. 13
K. 15

35. Given the diagram as labeled below, what is the area, in

square units, of parallelogram ABCD?

B 18 C

10

A 6 D

A. 40
B. 72
C. 80
D. 110
E. 144

36. The ratio of the lengths of the sides of a triangle is 6:8:9.

The longest side of a second, similar triangle is 12 cm in
length. What is the length, in centimeters, of the shortest
side of the second triangle?

F. 6
G. 8
H. 9
J. 10
K. The length cannot be determined based on the
information given.

37. The larger of two numbers exceeds 3 times the smaller

number by 6. The sum of 3 times the larger number and
twice the smaller number is 62. Which equation
correctly identifies x as the smaller number?

A. 3(3x + 6) + 2x = 62
B. 3(3x – 6) + 2x = 62
C. 3(3x + 6) + 3x = 62
D. 2(3x + 6) + 2x = 62
E. (3x + 6) + 3x = 62
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10
ACT
 38. In the figure below, all angles shown are right angles DO FIGURING HERE
and the line segment lengths are given in centimeters.
What is the perimeter of the figure, in centimeters?

22
3
2
5 1
12

F. 42
G. 48
H. 52
J. 56
K. 58

39. The circle inscribed in the square below has a radius of 6

ft. What is the area of the square?

A. 24 ft2
B. 36 ft2
C. 98 ft2
D. 120 ft2
E. 144 ft2

40. Points R and S are located in a standard (x, y) coordinate

plane. If R has coordinates (7, 2) and S has coordinates
(5, 8), what are the coordinates of the midpoint between
R and S?

F. (2, 6)
G. (2, –6)
H. (6, 5)
J. (6, 6)
K. (12, 10)

41. For all positive integers a, b, and c, find the expression

that is equivalent to:

2a3b–2c
3–2a2c–3

A. (2ac3) ÷ (9b2)
B. (2ac4) ÷ (9b2)
C. (18ac) ÷ (b2)
D. (18ac4) ÷ (b2)
E. (18a5c2) ÷ (b2)

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11
ACT
 42. In the figure below, BCED is a trapezoid and points A, DO FIGURING HERE
B, and C are collinear. If the measure of angle ABD is
110° and the measure of angle DEB is 30°, what is the
measure of angle DBE?

F. 15° D E
G. 30°
H. 35°
J. 40°
K. 60° A B C

3
43. Of the total 365 cookies baked one day, were chocolate
5
1
chip. If of the chocolate chip cookies also had walnuts,
3
how many chocolate chip cookies with walnuts were
baked?

A. 65
B. 70
C. 73
D. 82
E. 90

44. A square has two diagonals and shown below.

How many diagonals does the hexagon below have?

F. 0
G. 3
H. 6
J. 7
K. 9

45. If 135% of a number is 540, what is 65% of the number?

A. 260
B. 280
C. 300
D. 320
E. 400
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12
ACT
 46. Which of the following complex numbers is equivalent DO FIGURING HERE
1 1+𝑖 2
to • , where i = – 1?
1–𝑖 1+𝑖

F. 2+i
G. 1+i
H. 1–i
J. (1+ i) ⁄ 2
K. (1– i) ⁄ 2

47. In a standard (x, y) coordinate plane, what is the distance

between the points (1, 0) and (0, 4)?

A. √19
B. √17
C. 16
D. 5
E. 4

48. If the ratio of the radii of two circles is 3:5, what is the
ratio of area of the smaller circle to the area of the larger
circle?

F. 3:5
G. 6:10
H. 9:25
J. 18:50
K. It cannot be determined based on the information
given.

49. A circle in the standard (x, y) coordinate plane is tangent

to the x-axis at the point (3, 0) and to the y-axis at the
point (0, 3). Which of the following is an equation of
the circle?

A. x2 – y2 = 9
B. x2 + y2 = 9
C. (x – 3)2 – (y – 3)2 = 9
D. (x + 3)2 + (y + 3)2 = 9
E. (x – 3)2 + (y – 3)2 = 9

3 3
50. If tan θ = and π < θ < π, then sin θ?
4 2

3
F. –
5

3
G. ̶
4

5
H. ̶
4

3
J.
5

5
K.
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13
ACT
 51. Mary drew a circle graph (not shown) that included all DO FIGURING HERE
of the various types of flowers in her garden. The
garden included the following:

20% tulips;
25% daisies;
15% roses; and
10% pansies.

The last sector of her graph included the remaining

flowers that were not tulips, daisies, roses, or pansies.
What is the degree measure of the last sector of the circle
graph?

A. 30°
B. 35°
C. 54°
D. 108°
E. 150°

52. The chart below shows the relationship between rows

and blocks. What is the total number of blocks in row n,
in terms of n?

Row Number 1 2 3 4 … n

Total Number 4 6 8 10 … ?
of Blocks in
Row

F. 2n – 2
G. 2n + 2
H. 2n
J. n2
K. n

53. Out of 30 girls, 16 participated in tennis and 12

participated in soccer during the academic year. Given
this information, what is the minimum number of girls
who play both tennis and soccer?

A. 0
B. 2
C. 4
D. 7
E. 12

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14
ACT
 54. Which of the following is the set of all real numbers x, DO FIGURING HERE
such that 2x + 2 > 2x + 4?

F. The set containing all real numbers.

G. The set containing all positive real numbers.
H. The set containing all negative real numbers.
J. The set containing only zero.
K. The empty set.

55. The figure below is an octagon with 8 equal interior

angles. What is the measurement of one of the interior
angles?

A. 60°
B. 85°
C. 110°
D. 135°
E. 145°

56. If x = t + 7 and y = 2 – 3t, which of the following

properly expresses y in terms of x?

F. y = 23 – 3x
G. y = 23 + 3x
H. y = –23 – 3x
J. y = –19 – 3x
K. y = 19 + 3x

57. Which system of inequalities is represented by the

shaded region below?

A. y ≤ 4x and y ≥ 2
B. y ≤ 4x and x ≤ 2
C. y ≤ 2x and y ≥ 2
D. y ≤ 2x and x ≤ 4
E. y ≤ 2x and x ≤ 2

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15
ACT
 58. In the standard (x, y) coordinate plane, which of the DO FIGURING HERE
following is the graph y = (x + 2)2 – 3?
F.

G.

H.

J.

K.

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16
ACT
 59. If the diagonal of a square is 6 inches long, what is the DO FIGURING HERE
area of square?

A. 6
B. 3√2
C. 18
D. 24
E. 36√2

60. If f(x) = 2x2 – 3, then f(x + a) = ?

F. 2x2 + 2ax + 2a2 – 3

G. 2x2 + 4ax + 2a2 – 3
H. 2x2 – 4ax + 2a2 – 3
J. 4x2 + 8ax + 4a2 – 3
K. 4x2 + 4ax + 4a2 – 3

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17
ACT