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.

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 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.

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 Module
1

-1 - - - - - - - - ~ -3 - - - - - - - - ~

...............................................................................................................................................................................................................................................................................................................
The scatterplot shows the temperature, in degrees Ip I + 61 = 65
Fahrenheit (°F), and the distance above sea level, in Which value is a solution to the given equation?
feet, measured at 6 locations on Mount Jefferson. A
line of best fit is also shown. 65
A)
61
y
80 B) 4
70
60
C) 126

-- -- ---
50
Temperature
40
-'
(OF) ',
D) 130
30 c-.
,__
20
10
X
0 2,000 4,000 6,000 8,000
Distance above sea level (feet)

At a distance of 4,000 feet above sea level, what is the

temperature, in °F, predicted by the line of best fit? -4 --------~
A) 47 Lorenzo purchased a box of cereal and some
strawberries at the grocery store. Lorenzo paid $2 for
B) 35
the box of cereal and $1.90 per pound for the
C) 25 strawberries. If Lorenzo paid a total of $9.60 for the
D) 0 box of cereal and the strawberries, which of the
following equations can be used to find p, the
number of pounds of strawberries Lorenzo
purchased? (Assume there is no sales tax.)
A) 1.90p + 2 = 9.60
B) 1.90p − 2 = 9.60
C) 1.90 + 2p = 9.60
- --------~
2 D) 1.90 − 2p = 9.60
Rectangle P has an area of 72 square inches. If a
rectangle with an area of 20 square inches is removed
from rectangle P, what is the area, in square inches,
of the resulting figure?
A) 92
B) 84
C) 80
D) 52

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 Module
1

-5 - - - - - - - - - -7 - - - - - - - - -

...............................................................................................................................................................................................................................................................................................................
The bar graph summarizes the charge, in What is an x-coordinate of an x-intercept of the
kilowatt-hours (kWh), a battery received each day graph of y = 3(x − 14)(x + 5)(x + 4) in the xy-plane?
for 15 days.
7
6
!'o 5 -
4 -
~

~ 3 -
§ 2
-8 - - -
-
z
1 - y
I I I I I I
~

0
0 8 9 11 16 23 35 0
Charge (kWh) 30 0
25 0
For how many of these 15 days did the battery
receive a charge of 0 kWh? Value (dollars) 20 0 ' ~
i-..
15 0 I',,
A) 0
--
100 ,-...
B) 1 50
C) 4 X
0 4 8 12 16 20 24
D) 6
Number of months
after purchase

The graph shown gives the estimated value, in

dollars, of a tablet as a function of the number of
months since it was purchased. What is the best
interpretation of the y-intercept of the graph in this
context?
-
6 - - - - - - - - - A) The estimated value of the tablet was $225 when
A line in the xy-plane has a slope of 9 and passes it was purchased.
through the point (0, −5). The equation y = px + r B) The estimated value of the tablet 24 months after
defines the line, where p and r are constants. What it was purchased was $225.
is the value of p ? C) The estimated value of the tablet had decreased
by $225 in the 24 months after it was purchased.
D) The estimated value of the tablet decreased by
approximately 2.25% each year after it was
purchased.

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 Module
1

-9 - - - - - - - - ~ - 11 - - - - -

...............................................................................................................................................................................................................................................................................................................
Triangles EFG and JKL are congruent, where E, F, y
and G correspond to J, K, and L, respectively. The 9 " ,i

measure of angle E is 45° and the measure of i\ /V

angle F is 20° . What is the measure of angle J ?

'' ~/
/ ll6

'
A) 20°
B) 45° V/ 5
C) 135°
XV 4
D) 160°
/ 3
V 2
/ 1
V
-8 -7 -6 -5 -4 -3 -2 -1 u 1 2 3
X

The graph of a system of an absolute value function

and a linear function is shown. What is the solution
10 (x , y ) to this system of two equations?
- --------~
1
The function f is defined by f (x ) = (x + 6). What A) (0, 8)
2
is the value of f (4) ? 7 9
B)  , 
A) 20  2 2 
B) 12  7 9
C) − , 
C) 10  2 2 
D) 5
D) (−3, 4)

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 Module
1

- 12 - - - - - - - - 15 - - - - - - -

...............................................................................................................................................................................................................................................................................................................
y = 6x + 3 A circle in the xy-plane has the equation
One of the two equations in a system of linear (x − 13)2 + ( y − k)2 = 64. Which of the following
equations is given. The system has infinitely many
gives the center of the circle and its radius?
solutions. Which equation could be the second
equation in this system? A) The center is at (13, k) and the radius is 8.
A) y = 2(6x) + 3 B) The center is at (k, 13) and the radius is 8.
B) y = 2(6x + 3) C) The center is at (k, 13) and the radius is 64.
C) 2( y) = 2(6x ) + 3 D) The center is at (13, k) and the radius is 64.
D) 2( y) = 2(6x + 3)

-
16 - - - - - - -

-
13 - - - - - - - The function f is defined by f (x ) = 1x − 4x I. What
6 value of a satisfies f (5) − f (a) = −15 ?
If p + 18 = 54, what is the value of 7p ?
7 A) −20
B) 5
C) 10
D) 45

-
14 - - - - - - -
y = 9x + 12
x + 7y = 20
The solution to the given system of equations is 17
- - - - - - - -
(x , y ). What is the value of y ?
For the exponential function f, the value of f (0) is c,
where c is a constant. Of the following equations that
define the function f, which equation shows the value
of c as the coefficient or the base?

A) f (x ) = 22(1.5)x+1
B) f (x ) = 33(1.5)x
C) f (x ) = 49.5(1.5)x−1
D) f (x ) = 74.25(1.5)x−2

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 Module
1

-18 - - - - - - - - ~ -20 - - - - - - - - ~

...............................................................................................................................................................................................................................................................................................................
t During a study, the temperature, in degrees
The function f (t ) = 40,000(2) 790 gives the number Celsius (°C), of the air in a chamber was recorded to
the nearest integer at certain times. The scatterplot
of bacteria in a population t minutes after an initial
shows the recorded temperature y, in °C , of the air in
observation. How much time, in minutes, does it the chamber x minutes after the start of the study.
y
take for the number of bacteria in the population to
30
28
double? 26
24
22
A) 2 20
18
B) 790 Temperature 16
C) 1,580 coc) l42
10
D) 40,000 8
6
4
2
X
0 1 2 3 4 5 6 7 8
Time (minutes)
What was the average rate of change, in °C per
minute, of the recorded temperature of the air in the
-
19 - - - - - - - - ~ chamber from x = 5 to x = 7 ?
12 2 2
− =−
n t w
The given equation relates the variables n, t, and w,
where n > 0 , t > 0, and w > t . Which expression is
equivalent to n ?

A) 12tw
-21 - - - - - - - - ~
In August, a car dealer completed 15 more than
B) 6(t − w ) 3 times the number of sales the car dealer completed
in September. In August and September, the car
w−t dealer completed 363 sales. How many sales did the
C) car dealer complete in September?
6tw
6tw
D)
w−t

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 Module
1

22 24

...............................................................................................................................................................................................................................................................................................................
Points Q and R lie on a circle with center P. The x y
radius of this circle is 9 inches. Triangle PQR has a −2s 24
perimeter of 31 inches. What is the length, in inches, −s 21
s 15
of QR ?

A) 13 2 The table shows three values of x and their

corresponding values of y, where s is a constant.
B) 13 There is a linear relationship between x and y.
Which of the following equations represents this
C) 9 2
relationship?
D) 9
A) sx + 3y = 18s
B) 3x + sy = 18s
C) 3x + sy = 18
D) sx + 3y = 18

23
In a set of four consecutive odd integers, where the
integers are ordered from least to greatest, the first
integer is represented by x. The product of 12 and
the fourth odd integer is at most 26 less than the sum
25
of the first and third odd integers. Which inequality
represents this situation? Which of the following expressions is equivalent
A) 12(x + 6) ≤ x + (x + 4) − 26 to (sin 24°)(cos 66°) + (cos 24°)(sin 66°) ?

B) 12(x + 6) ≥ 26 − (x + (x + 4)) A) 2(cos 66°)(sin 24°)

C) 12(x + 4) ≤ x + (x + 3) − 26 B) 2(cos 66°) + 2(cos 24°)
D) 12(x + 4) ≥ 26 − (x + (x + 3))
C) (cos 66°)2 + (cos 24°)2
D) (cos 66°)2 + (sin 24°)2

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 Module
1

26 27

................................................................................................................................................................................................................................................
The cost of renting a carpet cleaner is $52 for the first f (x) = (x − 2)(x + 15)
day and $26 for each additional day. Which of the
The function f is defined by the given equation. For
following functions gives the cost C(d ), in dollars, of
what value of x does f (x ) reach its minimum?
renting the carpet cleaner for d days, where d is a
positive integer?

A) C(d ) = 26d + 26
B) C(d ) = 26d + 52
C) C(d ) = 52d − 26
D) C(d ) = 52d + 78

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. 38

 Module
2

Math
27 QUESTIONS

The questions in this section address a number of important math skills.

Use of a calculator is permitted for all questions.

,a-nH
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 fis the set of all real numbers x for which f(x)
is a real number.

li04ii1Ut31

G
£

CJw
~ b
b~
a
~ 0

x--../3
x
'~
45°
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. 40 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. 41 CO NTI N U E

 Module
2

-1 - - - - - - - - ~ -3 ----

...............................................................................................................................................................................................................................................................................................................
A total of 165 people contributed to a charity event as y
either a donor or a volunteer. 130 people contributed 12
as a donor. How many people contributed as a \ 11 I
volunteer? \ 10 I
\ 9 I
A) 35 \ 8
I
B) 130
\ 7 I
\ 6 I
'
C) 165 I
5
D) 330 \ 4 J
\3 I
., /
"(

1
X
-2
f 2

The graph of the quadratic function y = f (x) is

shown. What is the vertex of the graph?
-2 - - - - - - - - ~ A) (0, −2)
There are 250 trees in a park. Of these trees, 6% are
birch trees. How many birch trees are in the park? B) (0, −3)
A) 6 C) (0, 2)
B) 15 D) (0, 3)
C) 75
D) 244

-4 - - - - - - - - ~
The number of raccoons in a 131-square-mile area is
estimated to be 2,358. What is the estimated
population density, in raccoons per square mile, of
this area?
A) 18
B) 131
C) 149
D) 2,376

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 Module
2

-5 ------~ -8 ------~

...............................................................................................................................................................................................................................................................................................................
−11, −9, 26 If 8x = 6, what is the value of 72x ?
A data set of three numbers is shown. If a number A) 3
from this data set is selected at random, what is the B) 15
probability of selecting a positive number?
C) 54
A) 0 D) 57

1
B)
3
2
C)
3

D) 1 -9 - - - - - - ~
Which expression is equivalent to 23x 3 + 2x 2 + 9x ?

A) 23x(x 2 + 2x + 9)
B) 9x(23x 3 + 2x 2 + 1)
C) x(23x 2 + 2x + 9)
D) 34(x 3 + x 2 + x)
-6 - - - - - - ~
f (x ) = 45x + 600
The function f gives the monthly fee f (x ), in dollars,
a facility charges to keep x crates in storage. What is
the monthly fee, in dollars, the facility charges to
keep 50 crates in storage?
- 10 - - - - - - ~
Which expression is equivalent to
(9x 3 + 5x + 7) + (6x 3 + 5x 2 − 5) ?

A) 15x 6 + 5x 2 − 5x − 35
B) 15x 3 + 10x 2 + 2
-7 - - - - - - ~
C) 15x 6 + 5x 2 + 5x + 2
1 2 11
The function f is defined by f (x ) = 5 − x + . D) 15x 3 + 5x 2 + 5x + 2
 4  4
1
What is the value of f   ?
 4 

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 Module
2

-11 - - - - - - - - ~ -12 - - - - - - - - ~

...............................................................................................................................................................................................................................................................................................................
At a state fair, attendees can win tokens that are In the given scatterplot, a line of best fit for the data
worth a different number of points depending on the is shown.
shape. One attendee won S square tokens and y
C circle tokens worth a total of 1,120 points. The
equation 80S + 90C = 1,120 represents this 14 ~

/
situation. How many more points is a circle token -/
worth than a square token? 12
/
- ,/
10
A) 950 /
/
B) 90 8
/
C) 80 6
/ =
- /_
D) 10 / -
4 /
2 , /

u 1 2 3 4 5 6 7
X

Which of the following is closest to the slope of the

line of best fit shown?

A) 0

1
B)
2

C) 1

D) 2

-
13 - - - - - - - - ~

A circle has a radius of 2.1 inches. The area of the

circle is bπ square inches, where b is a constant.
What is the value of b ?

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 Module
2

-14 - - -16 -y < x-

...............................................................................................................................................................................................................................................................................................................
In triangle XYZ , angle Y is a right angle, point P lies
on XZ , and point Q lies on YZ such that PQ is x < 22
parallel to XY . If the measure of angle XZY is 63° , For which of the following tables are all the values of
what is the measure, in degrees, of angle XPQ ? x and their corresponding values of y solutions to the
given system of inequalities?

A) x y
19 18
20 19
21 20

-15 - - B) x
19
y
20
An investment account was opened with an initial
20 21
value of $890 . The value of the account doubled 21 22
every 10 years. Which equation represents the value
of the account M(t), in dollars, t years after the C) x y
account was opened? 23 22
t
24 23
10 25 24
1
A) M(t ) = 890 
 2  D) x y
t 23 24
1 2 24 25
B) M(t ) = 890  25 26
 10 

t
10
C) M(t ) = 890(2)

t
2
D) M(t ) = 890(10)

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 Module
2

- 17 - - - - - - ~ - 19 - - - - - - ~

...............................................................................................................................................................................................................................................................................................................
h15q7 h(t) = −16t 2 + b
Which expression is equivalent to 5 21 ,
hq The function h estimates an object’s height, in feet,
above the ground t seconds after the object is
where h > 0 and q > 0 ? dropped, where b is a constant. The function
estimates that the object is 3,364 feet above the
h10 ground when it is dropped at t = 0. Approximately
A) how many seconds after being dropped does the
q14
function estimate the object will hit the ground?
h3 A) 7.25
B)
q3 B) 14.50
C) 105.13
C) h10q14 D) 210.25

D) h3q3

-
20 - - - - - - ~

2
2x − 8x − 7 = 0

- 18 - - - - - - ~ One solution to the given equation can be written as

3y = 4x + 17
8− k
−3y = 9x − 23 , where k is a constant. What is the value
4
The solution to the given system of equations is
of k ?
(x, y). What is the value of 39x ?
A) −18
B) −6
C) 6
D) 18

- 21 - - - - - - ~
A line intersects two parallel lines, forming
four acute angles and four obtuse angles. The
measure of one of the acute angles is (9x − 560) °.
The sum of the measures of one of the acute angles
and three of the obtuse angles is (−18x + w) ° . What
is the value of w ?

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 Module
2

- 22 - - -24 - - - - - - - -

...............................................................................................................................................................................................................................................................................................................
x f(x) In triangle XYZ , angle Z is a right angle and the
12
–4 0 length of YZ is 24 units. If tan X = , what is the
35
perimeter, in units, of triangle XYZ ?
– 19 1
5
A) 188
– 18 2
5 B) 168
C) 84
For the linear function f, the table shows three values
D) 71
of x and their corresponding values of f (x ). If
h(x) = f (x ) − 13, which equation defines h ?

A) h(x) = 5x − 4
B) h(x) = 5x + 7
C) h(x) = 5x + 9
D) h(x) = 5x + 20
-25 - - -
2
- 2- - - -
x + 14x + y = 6y + 109
In the xy-plane, the graph of the given equation is a
circle. What is the length of the circle’s radius?

A) 109
B) 149
-23 - - - - - - - -
C) 167
The linear function g is defined by g (x) = b − 15x ,
c D) 341
where b is a constant. If g (c + 7) = , where c is a
4
constant, which of the following expressions

represents the value of b ?

15c
A)
4
19c
B) +7
4
61c
C) + 105
4

D) 15c + 105

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 Module
2

26 27

...............................................................................................................................................................................................................................................
The speed of a vehicle is increasing at a rate of y = −2.5
7.3 meters per second squared. What is this rate, in y = x 2 + 8x + k
miles per minute squared, rounded to the nearest
In the given system of equations, k is a positive
tenth? (Use 1 mile = 1,609 meters.)
integer constant. The system has no real solutions.
A) 0.3 What is the least possible value of k ?
B) 16.3
C) 195.8
D) 220.4

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. 48