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.

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.

REFERENCE

A =nr 2
C=2nr
A= l w ½
A = bh c2 = a2 + b2 Special Right Triangles

V= l wh V= nr 2 h V= 4/3πr3 V= ⅓πr h
2
1
V = 3 l 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.

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 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.

½
• 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.

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1 3
Tilly earns p dollars for every w hours of work. 3x = 12
Which expression represents the amount of money, −3x + y = −6
in dollars, Tilly earns for 39w hours of work?
The solution to the given system of equations
A) 39p is (x , y ). What is the value of y ?
p A) −3
B)
39 B) 6
C) 18
C) p + 39
D) 30

D) p - 39

4
s = 40 + 3t
2
The equation gives the speed s, in miles per hour, of
For a training program, Juan rides his bike at an a certain car t seconds after it began to accelerate.
average rate of 5.7 minutes per mile. Which What is the speed, in miles per hour, of the car
function m models the number of minutes it will take 5 seconds after it began to accelerate?
Juan to ride x miles at this rate?
A) 40
x
A) m(x ) = B) 43
5.7
C) 45
B) m(x ) = x + 5.7 D) 55

C) m(x ) = x - 5.7

D) m(x ) = 5.7x

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5 7

Note: Figure not drawn to scale.

For the right triangle shown, a = 4 and b = 5.

Which expression represents the value of c ?
The x-intercept of the graph shown is (x , 0). What is
A) 4 + 5 the value of x ?

B) (4)(5)

C) 4+5

D) 42 + 52

8
1
The function f is defined by f (x ) = x − 2. What
10
is the y-intercept of the graph of y = f (x) in the

6 xy-plane?
4x + 5 = 165
What is the solution to the given equation? A) (−2, 0)

B) (0, −2)

 1
C) 0, 
 10 

1 
D)  , 0
 10 

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9 11

The function f is defined by f (x ) = 7x 3. In the Which expression is equivalent

xy-plane, the graph of y = g (x ) is the result of to (7x 3 + 7x) − (6x 3 − 3x) ?
shifting the graph of y = f (x ) down 2 units. Which
A) x 3 + 10x
equation defines function g ?
B) −13x 3 + 10x
7 3
A) g (x ) = x C) −13x 3 + 4x
2
D) x 3 + 4x
3
2
B) g (x ) = 7x

C) g (x ) = 7x 3 + 2

D) g (x ) = 7x 3 − 2
12

The function p is defined by p(n) = 7n3. What is the

value of n when p(n) is equal to 56?

A) 2

10 8
B)
3
x + 7 = 10
(x + 7)2 = y C) 7

Which ordered pair (x, y) is a solution to the given D) 8

system of equations?

A) (3, 100)
B) (3, 3)
C) (3, 10)
D) (3, 70)

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13 15

The equation E(t ) = 5(1.8)t gives the estimated

number of employees at a restaurant, where t is the
number of years since the restaurant opened. Which
of the following is the best interpretation of the
number 5 in this context?
A) The estimated number of employees when the
restaurant opened
Note: Figure not drawn to scale.
B) The increase in the estimated number of
In the figure shown, line c intersects parallel lines s employees each year
and t. What is the value of x ?
C) The number of years the restaurant has been
open
D) The percent increase in the estimated number of
employees each year

14
A list of 10 data values is shown.
6, 8, 16, 4, 17, 26, 8, 5, 5, 5
16
What is the mean of these data?
g (x) = x 2 + 55
What is the minimum value of the given function?
A) 0
B) 55
C) 110
D) 3,025

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17 20
Each year, the value of an investment increases by An event planner is planning a party. It costs the
0.49% of its value the previous year. Which of the event planner a onetime fee of $35 to rent the venue
following functions best models how the value of the and $10.25 per attendee. The event planner has a
investment changes over time?
budget of $200 . What is the greatest number of
A) Decreasing exponential attendees possible without exceeding the budget?
B) Decreasing linear
C) Increasing exponential
D) Increasing linear

21
If 4x − 4 = 112, what is the positive value of x − 1 ?

18
The population of Greenville increased by 7%
from 2015 to 2016. If the 2016 population is k times
the 2015 population, what is the value of k ?
A) 0.07
B) 0.7 22
C) 1.07 A cube has an edge length of 68 inches. A solid
D) 1.7 sphere with a radius of 34 inches is inside the cube,
such that the sphere touches the center of each face
of the cube. To the nearest cubic inch, what is the
volume of the space in the cube not taken up by the
sphere?
A) 149,796
B) 164,500
19 C) 190,955
D) 310,800
11
12
Which expression is equivalent to a ,

where a > 0 ?

A) 12
a132

B) 144
a132

C) 121
a132

D) 11
a132

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23 25

What is the diameter of the circle in the xy -plane A model estimates that at the end of each year
from 2015 to 2020, the number of squirrels in a
with equation (x − 5)2 + (y − 3)2 = 16 ?
population was 150% more than the number of
A) 4 squirrels in the population at the end of the previous
B) 8 year. The model estimates that at the end of 2016,
there were 180 squirrels in the population. Which of
C) 16
the following equations represents this model, where
D) 32 n is the estimated number of squirrels in the
population t years after the end of 2015 and t ≤ 5 ?

A) n = 72(1.5)t
B) n = 72(2.5)t
C) n = 180(1.5)t

24 D) n = 180(2.5)t

For the exponential function f, the value of f (1) is k,

where k is a constant. Which of the following
equivalent forms of the function f shows the value of
k as the coefficient or the base?

A) f (x ) = 50(1.6)x+1
B) f (x ) = 80(1.6)x
C) f (x ) = 128(1.6)x−1
D) f (x ) = 204.8(1.6)x−2

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 26 27

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5x + 7y = 1 x 2 − 34x + c = 0
ax + by = 1 In the given equation, c is a constant. The equation
has no real solutions if c > n . What is the least
In the given pair of equations, a and b are constants. possible value of n?
The graph of this pair of equations in the xy-plane is
a pair of perpendicular lines. Which of the following
pairs of equations also represents a pair of
perpendicular lines?

A) 10x + 7y = 1
ax − 2by = 1

B) 10x + 7y = 1
ax + 2by = 1

C) 10x + 7y = 1
2ax + by = 1

D) 5x − 7y = 1
ax + by = 1

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.

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