Module

Math
27 QUESTIONS

DIRECTIONS
The questions in this section address a number of important math skills.
Use of a calculator is permitted for all questions.

,a-nH
NOTES

Unless otherwise indicated:

• All variables and expressions represent real numbers.
• Figures provided are drawn to scale.
• All figures lie in a plane.
• The domain of a given function f is the set of all real numbers x for which f(x)
is a real number.

li04ii1Ut31
REFERENCE

G
£
x
CJw b~ ~ 0 '~
45°
b a x--../3 s
A =nr 2 A= Rw A =_!bh c2 = a2 + b2 Special Right Triangles
2
C=2nr

62h E} £

V= Rwh V= nr 2h
@
V = i,.r3
3
4
V=½nr 2h
£
1
V = 3 £wh

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2n.
The sum of the measures in degrees of the angles of a triangle is 180.

Unauthorized copying or reuse of any part of this page is illegal. 30 CO NTI N U E

 Module
1

For multiple-choice questions, solve each problem, choose the correct

answer from the choices provided, and then circle your answer in this book.
Circle only one answer for each question. If you change your mind, completely
erase the circle. You will not get credit for questions with more than one
answer circled, or for questions with no answers circled.

For student-produced response questions, solve each problem and write

your answer next to or under the question in the test book as described below.

• Once you've written your answer, circle it clearly. You will not receive credit
for anything written outside the circle, or for any questions with more than
one circled answer.
• If you find more than one correct answer, write and circle only one answer.
• Your answer can be up to 5 characters for a positive answer and up to
6 characters (including the negative sign) for a negative answer, but no more.
• If your answer is a fraction that is too long (over 5 characters for positive,
6 characters for negative), write the decimal equivalent.
• If your answer is a decimal that is too long (over 5 characters for positive,
6 characters for negative), truncate it or round at the fourth digit.
• If your answer is a mixed number (such as 3.!. ), write it as an improper
fraction (7/2) or its decimal equivalent (3.5). 2
• Don't include symbols such as a percent sign, comma, or dollar sign in
your circled answer.

Unauthorized copying or reuse of any part of this page is illegal. 31 CO NTI N U E

 Module
1

1 4

...............................................................................................................................................................................................................................................................................................................
The lengths of two sides of a triangle are The function g is defined by g (x) = x 2 + 9. For
4 centimeters and 6 centimeters. If the perimeter of
the triangle is 18 centimeters, what is the length, in which value of x is g (x) = 25 ?
centimeters, of the third side of this triangle? A) 4
A) 2 B) 5
B) 8 C) 9
C) 10 D) 13
D) 24

5
2
Which expression is equivalent to 9x 2 + 5x ?
16x + 30 = 190
A) x(9x + 5)
Which equation has the same solution as the given
equation? B) 5x(9x + 1)
A) 16x = 30 C) 9x(x + 5)
B) 16x = 130
D) x 2(9x + 5)
C) 16x = 160
D) 16x = 190

6
Each value in the data set shown represents the
. 3 ,_ _ ____, height, in centimeters, of a plant.
Ty set a goal to walk at least 24 kilometers every day 6, 10, 13, 2, 15, 22, 10, 4, 4, 4
to prepare for a multiday hike. On a certain day, Ty
plans to walk at an average speed of 4 kilometers per What is the mean height, in centimeters, of these
hour. What is the minimum number of hours Ty plants?
must walk on that day to fulfill the daily goal?
A) 4
B) 6
C) 20
D) 24

Unauthorized copying or reuse of any part of this page is illegal. 32 CO NTI N U E

 Module
1

7 9

...............................................................................................................................................................................................................................................................................................................
A student council group is selling school posters for a John paid a total of $165 for a microscope by making
fundraiser. They use the function p(x) = 5x − 220 to a down payment of $37 plus p monthly payments of
determine their profit p(x), in dollars, for selling $16 each. Which of the following equations
represents this situation?
x school posters. In order to earn a profit of $900 ,
how many school posters must they sell? A) 16p − 37 = 165
B) 37p − 16 = 165
C) 16p + 37 = 165
D) 37p + 16 = 165

8
Jay walks at a speed of 3 miles per hour and runs at a
speed of 5 miles per hour. He walks for w hours and
runs for r hours for a combined total of 14 miles.
Which equation represents this situation? 10
y − 57 = px
A) 3w + 5r = 14 The given equation relates the positive numbers p, x,
and y. Which equation correctly expresses y in terms
1 1 of p and x ?
B) w + r = 14
3 5
1 1 A) y = 57x + p
C) w + r = 112
3 5
B) y = px + 57
D) 3w + 5r = 112
C) y = 57px

px
D) y =
57

Unauthorized copying or reuse of any part of this page is illegal. 33 CO NTI N U E

 Module
1

11 13

...............................................................................................................................................................................................................................................................................................................
A company opens an account with an initial balance y = −2x
of $36,100.00. The account earns interest, and no 3x + y = 40
additional deposits or withdrawals are made. The
The solution to the given system of equations is
account balance is given by an exponential
(x, y). What is the value of x ?
function A, where A(t) is the account balance, in
dollars, t years after the account is opened. The
account balance after 13 years is $68,071.93. Which
equation could define A ?

A) A(t ) = 36,100.00(1.05)t
B) A(t ) = 31,971.93(1.05)t
14
t
C) A(t ) = 31,971.93(0.05)
Data value Frequency
D) A(t ) = 36,100.00(0.05)t 6 3
7 3
8 8
9 8
10 9
11 11
12 9
13 0
12 14 6

The frequency table summarizes the 57 data values in

a data set. What is the maximum data value in the
data set?

Note: Figure not drawn to scale.

The circle shown has center O, circumference 144π , 15

and diameters PR and QS. The length of arc PS is One leg of a right triangle has a length of
twice the length of arc PQ . What is the length of 43.2 millimeters. The hypotenuse of the triangle has a
arc QR ? length of 196.8 millimeters. What is the length of the
other leg of the triangle, in millimeters?
A) 24π
A) 43.2
B) 48π
B) 120
C) 72π
C) 192
D) 96π D) 201.5

Unauthorized copying or reuse of any part of this page is illegal. 34 CO NTI N U E

 16 18

...............................................................................................................................................................................................................................................................................................................
A wire with a length of 106 inches is cut into A landscaper uses a hose that puts 88x ounces of
two parts. One part has a length of x inches, and the water in a bucket in 5y minutes. Which expression
other part has a length of y inches. The value of x is represents the number of ounces of water the hose
6 more than 4 times the value of y. What is the value
puts in the bucket in 9y minutes at this rate?
of x ?
A) 25 9x
A)
440
B) 28
C) 56 440x
B)
D) 86 9
5x
C)
792
792x
D)
5

17
f (x ) = (x + 6)(x + 5)(x − 4)
The function f is given. Which table of values
represents y = f (x) − 3 ? 19

A) 4x − 9 y = 9 y + 5
x y
hy = 2 + 4x
−6 −9
−8 In the given system of equations, h is a constant. If
−5
the system has no solution, what is the value of h ?
4 1
A) −9
B) x y B) 0
−6 −3 C) 9
−5 −3 D) 18
4 −3

C) x y
−6 −3
−5 −2
4 7
20
D) x y 13 is p% of 25. What is the value of p ?
−6 3
−5 3
4 3

Unauthorized copying or reuse of any part of this page is illegal. 35 CO NTI N U E

 Module
1

21 24

...............................................................................................................................................................................................................................................................................................................
(x − 2)2 = 3x + 34 f (x ) = 4x 2 + 64x + 262
What is the smallest solution to the given equation? The function g is defined by g (x) = f (x + 5). For
what value of x does g (x) reach its minimum?
A) −13
B) −8
C) −5
D) −3
22
Function f is defined by
f (x ) = (x + 6)(x + 5)(x + 1). Function g is defined
by g (x) = f (x − 1). The graph of y = g (x) in the
xy-plane has x-intercepts at (a, 0), (b, 0), and (c, 0),
where a, b, and c are distinct constants. What is the 25
value of a + b + c ?
One gallon of stain will cover 170 square feet of a
A) −15 surface. A yard has a total fence area of w square feet.
B) −9 Which equation represents the total amount of
stain S, in gallons, needed to stain the fence in this
C) 11 yard twice?
D) 15 w
A) S =
170

B) S = 170w

C) S = 340w

23 w
D) S =
85
For x > 0, the function f is defined as follows:
f (x ) equals 201% of x
Which of the following could describe this function?
A) Decreasing exponential
B) Decreasing linear
C) Increasing exponential
D) Increasing linear

Unauthorized copying or reuse of any part of this page is illegal. 36 CO NTI N U E

 Module
1

26 27

..................................................................................................................................................................................................................................................
Poll Results Right rectangular prism X is similar to right
Angel Cruz 483
rectangular prism Y. The surface area of right
Terry Smith 320 I I rectangular prism X is 58 square centimeters (cm2),
The table shows the results of a poll. A total of and the surface area of right rectangular prism Y
803 voters selected at random were asked which
candidate they would vote for in the upcoming is 1,450 cm2. The volume of right rectangular
election. According to the poll, if 6,424 people vote in prism Y is 1,250 cubic centimeters (cm3). What is the
the election, by how many votes would Angel Cruz
be expected to win? sum of the volumes, in cm3, of right rectangular
prism X and right rectangular prism Y?
A) 163
B) 1,304
C) 3,864
D) 5,621

STOP
If you finish before time is called, you may check your work on this module only.
Do not turn to any other module in the test.

Unauthorized copying or reuse of any part of this page is illegal. 37

 Module
2

Math
27 QUESTIONS

DIRECTIONS
The questions in this section address a number of important math skills.
Use of a calculator is permitted for all questions.

,a-nH
NOTES
Unless otherwise indicated:
• All variables and expressions represent real numbers.
• Figures provided are drawn to scale.
• All figures lie in a plane.
• The domain of a given function f is the set of all real numbers x for which f(x)
is a real number.

li04ii1Ut31
REFERENCE

G
£
x
CJw b~ ~ 0 '~
45°
b a x--../3 s
A =nr 2 A= Rw A =_!bh c2 = a2 + b2 Special Right Triangles
2
C=2nr

62h E} £

V= Rwh V= nr 2h
@
V = i,.r3
3
4
V=½nr 2h
£
1
V = 3 £wh

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2n.
The sum of the measures in degrees of the angles of a triangle is 180.

Unauthorized copying or reuse of any part of this page is illegal. 38 CO NTI N U E

 Module
2

For multiple-choice questions, solve each problem, choose the correct

answer from the choices provided, and then circle your answer in this book.
Circle only one answer for each question. If you change your mind, completely
erase the circle. You will not get credit for questions with more than one
answer circled, or for questions with no answers circled.

For student-produced response questions, solve each problem and write

your answer next to or under the question in the test book as described below.

• Once you've written your answer, circle it clearly. You will not receive credit
for anything written outside the circle, or for any questions with more than
one circled answer.
• If you find more than one correct answer, write and circle only one answer.
• Your answer can be up to 5 characters for a positive answer and up to
6 characters (including the negative sign) for a negative answer, but no more.
• If your answer is a fraction that is too long (over 5 characters for positive,
6 characters for negative), write the decimal equivalent.
• If your answer is a decimal that is too long (over 5 characters for positive,
6 characters for negative), truncate it or round at the fourth digit.
• If your answer is a mixed number (such as 3.!. ), write it as an improper
fraction (7/2) or its decimal equivalent (3.5). 2
• Don't include symbols such as a percent sign, comma, or dollar sign in
your circled answer.

Unauthorized copying or reuse of any part of this page is illegal. 39 CO NTI N U E

 Module
2

1 3

...............................................................................................................................................................................................................................................................................................................
w + 7 = 357 Live east Live west
What value of w is the solution to the given of the river of the river Total
equation? Less than
17 11 28
40 years old
A) 51 At least
18 89 107
B) 350 40 years old
C) 364 Total 35 100 135
D) 3,577 The table summarizes members of a local
organization by age and whether they live east or
west of the river. If a member of the organization is
selected at random, what is the probability that the
selected member is at least 40 years old?
28
A)
135
2
35
B)
Which expression is equivalent to 16(x + 15) ? 135
A) 16x + 31 100
C)
B) 16x + 240 135
C) 16x + 1 107
D)
D) 16x + 15 135

3x = 12
−3x + y = −6

The solution to the given system of equations

is (x , y ). What is the value of y ?
A) −3
B) 6
C) 18
D) 30

Unauthorized copying or reuse of any part of this page is illegal. 40 CO NTI N U E

 Module
2

5 7

...............................................................................................................................................................................................................................................................................................................
1 8
A line in the xy-plane has a slope of and passes f (x ) = x +
9 11
through the point (0, 14). Which equation represents
The function f is defined by the given equation.
this line? 3
What is the value of f (x ) when x = ?
11
1
A) y = − x − 14
9
1
B) y = − x + 14
9
1
C) y = x − 14
9
8
1
D) y = x + 14 x y
9
0 18
1 13
2 8

The table shows three values of x and their

corresponding values of y. There is a linear
relationship between x and y. Which of the
6 following equations represents this relationship?
C A) y = 18x + 13
B) y = 18x + 18
C) y = −5x + 13
D) y = −5x + 18

Note: Figure not drawn to scale.

In the figure shown, line c intersects parallel lines s

and t. What is the value of x ?

Unauthorized copying or reuse of any part of this page is illegal. 41 CO NTI N U E

 Module
2

9 11

...............................................................................................................................................................................................................................................................................................................
x + 7 = 10 Time (years) Total amount (dollars)
(x + 7) = y2 0 604.00
1 606.42
Which ordered pair (x, y) is a solution to the given 2 608.84
system of equations? Rosa opened a savings account at a bank. The table
A) (3, 100) shows the exponential relationship between the
time t, in years, since Rosa opened the account and
B) (3, 3) the total amount n, in dollars, in the account. If Rosa
made no additional deposits or withdrawals, which
C) (3, 10)
of the following equations best represents the
D) (3, 70) relationship between t and n ?

A) n = (1 + 604)t
B) n = (1 + 0.004)t
C) n = 604(1 + 0.004)t
D) n = 0.004(1 + 604)t
10
The function f is defined by f (x ) = 7x − 84 . What is
the x-intercept of the graph of y = f (x) in the
xy-plane?
A) (−12, 0)
12
B) (−7, 0)
C) (7, 0) w(t) = 300 − 4t
D) (12, 0) The function w models the volume of liquid, in
milliliters, in a container t seconds after it begins
draining from a hole at the bottom. According to the
model, what is the predicted volume, in milliliters,
draining from the container each second?
A) 300
B) 296
C) 75
D) 4

Unauthorized copying or reuse of any part of this page is illegal. 42 CO NTI N U E

 Module
2

13 16

...............................................................................................................................................................................................................................................................................................................
h (x ) = x + b The population of Greenville increased by 7%
from 2015 to 2016. If the 2016 population is k times
For the linear function h, b is a constant and the 2015 population, what is the value of k ?
h(0) = 45. What is the value of b ?
A) 0.07
B) 0.7
C) 1.07
D) 1.7

14

z 2 + 10z − 24 = 0
What is one of the solutions to the given equation?
17
Class A Class B

•• ••• ••• •• •• •••

• •• •• •• •• ••
•
•I •I •I ••I ••• ••• •• •
•
• • • •• ••• •• ••
15 I I I
1 2 3 4 5 6 7 14 15 16 17 18 19 20
Triangle FGH is similar to triangle JKL , where Each of the dot plots shown represents the number of
glue sticks brought in by each student for two classes,
angle F corresponds to angle J and angles G and K class A and class B. Which statement best compares
the standard deviations of the numbers of glue sticks
308 brought in by each student for these two classes?
are right angles. If sin (F ) = , what is the value of
317
A) The standard deviation of the number of glue
sin (J ) ? sticks brought in by each student for class A is
less than the standard deviation of the number of
75 glue sticks brought in by each student for class B.
A)
317 B) The standard deviation of the number of glue
308 sticks brought in by each student for class A is
B) equal to the standard deviation of the number of
317 glue sticks brought in by each student for class B.
C)
317 C) The standard deviation of the number of glue
308 sticks brought in by each student for class A is
greater than the standard deviation of the
317 number of glue sticks brought in by each student
D)
75 for class B.
D) There is not enough information to compare
these standard deviations.

Unauthorized copying or reuse of any part of this page is illegal. 43 CO NTI N U E

 Module
2

18 20

...............................................................................................................................................................................................................................................................................................................
t
 t 2 t 
m(t) = –0.0274  + 7.3873  + 75.032 The function f (t ) = 60,000(2) 410 gives the number
7   7 
The function m gives the predicted body mass m(t ), of bacteria in a population t minutes after an initial
in kilograms (kg), of a certain animal t days after it
was born in a wildlife reserve, where t ≤ 390. Which observation. How much time, in minutes, does it
of the following is the best interpretation of the
take for the number of bacteria in the population to
statement “m(330) is approximately equal to 362” in
this context?
double?
A) The predicted body mass of the animal was
approximately 330 kg 362 days after it was born.
B) The predicted body mass of the animal was
approximately 362 kg 330 days after it was born.
C) The predicted body mass of the animal was
330 21
approximately 362 kg days after it was born.
7 The function f is defined by f (x ) = a x + b , where a
D) The predicted body mass of the animal was and b are constants and a > 0. In the xy-plane, the
330 graph of y = f (x ) has a y-intercept at (0, −25) and
approximately kg 362 days after it was born. passes through the point (2, 23). What is the value of
7
a+b?

19
Triangle XYZ is similar to triangle RST such that X,
Y, and Z correspond to R, S, and T, respectively.
The measure of ∠ Z is 20° and 2XY = RS. What is
the measure of ∠ T ?
A) 2°
B) 10°
C) 20°
D) 40°

Unauthorized copying or reuse of any part of this page is illegal. 44 CO NTI N U E

 Module
2

22 24

...............................................................................................................................................................................................................................................................................................................
y > 13x − 18
A square is inscribed in a circle. The radius of the
For which of the following tables are all the values of
x and their corresponding values of y solutions to the 20 2
circle is inches. What is the side length, in
given inequality? 2
inches, of the square?
A) x y
3 21
5 47 A) 20
8 86
20 2
B) x y B)
2
3 26
5 42
C) 20 2
8 86

C) x y D) 40
3 16
5 42
8 81

D) x y
3 26
5 52
8 91 25

Which expression is equivalent

y + 12 y(x − 8)
to + 2 ?
x−8 x y − 8xy

xy + y + 4
23 A)
x y − 16x 2y + 64xy
3
A certain town has an area of 4.36 square miles.
What is the area, in square yards, of this town? xy + 9y + 12
B)
(1 mile = 1,760 yards) 2
x y − 8xy + x − 8
A) 404
xy 2 + 13xy − 8y
B) 7,674 C)
x 2y − 8xy
C) 710,459
D) 13,505,536 xy 2 + 13xy − 8y
D)
x 3y − 16x 2y + 64xy

Unauthorized copying or reuse of any part of this page is illegal. 45 CO NTI N U E

 Module
2

26 27

...............................................................................................................................................................................................................................................
The function f is defined by f (x ) = a(2.2x + 2.2b), x(kx − 56) = −16
where a and b are integer constants and 0 < a < b . In the given equation, k is an integer constant. If
the equation has no real solution, what is the least
The functions g and h are equivalent to function f,
possible value of k ?
where k and m are constants. Which of the
following equations displays the y-coordinate of the
y-intercept of the graph of y = f (x ) in the xy-plane
as a constant or coefficient?
I. g (x ) = a(2.2x + k)
II. h(x ) = a(2.2)x + m
A) I only
B) II only
C) I and II
D) Neither I nor II

STOP
If you finish before time is called, you may check your work on this module only.
Do not turn to any other module in the test.

Unauthorized copying or reuse of any part of this page is illegal. 46