Module 1

1. The graph of the function f is shown, where y = f ( x). What is the

value of f (0) ?

(A) −6
(B) −4
(C) −3
(D) −5

Note : Figure not drawn to scale

2. In the figure, two lines intersect at a point. If r = 61, what is the

value of s ?
3. The function f is defined by f ( x) = 5 x 2 . What is the value of
f (7) ?

(A) 35
(B) 45
(C) 70
(D) 245

x + 5y =
5
x − 5y =
7
4. The solution to the given system of equations is ( x, y ). What is the
value of x ?
(A) 1.2
(B) 5
(C) 6
(D) 12

5. Which expression is equivalent to 6 x( x + 3) ?

(A) 6 x 2 + 3
(B) 6 x 2 + 18 x
(C) 7 x 2 + 3
(D) 7 x 2 + 9 x
6. The function f is defined by f ( x) = 3 x 5 . In the xy -plane, the graph
of y = g ( x) is the result of shifting the graph of y = f ( x) up 9 units.
Which equation defines the function g ?

x) 3x5 + 9
(A) g (=

x) 3x5 − 9
(B) g (=

(C) g ( x) = 3 x 45

(D) g ( x) = 27 x 5

7. For the linear function f , the graph of y = f ( x) in the xy -plane has

a slope of 69 and f (0) = 3. Which equation defines f ?

(A) f ( x) = 3 x
(B) f ( x=
) 3x + 3
(C) f ( x) = 69 x
(D) f (=
x) 69 x + 3

8. 5% of w is 741.41. What is the value of w ?

(A) 778.481
(B) 3,707.05
(C) 14,828.2
(D) 70,433.95
9. The graph of a system of a linear and a quadratic equation is shown.
What system is represented by the graph?

 7 2
 y = − 16 x
(A) 
 y= −7 x
 4

 7 2
 y = − 16 x
(B) 
y=7x
 4

 7 2
 y = 16 x
(C) 
 y= −7 x
 4

 7 2
 y = 16 x
(D) 
y=7x
 4
 W ( x=
) 4 x + 80
10. The function W gives the total time, in minutes, it takes for a
gardener to water x plants and mow the grass. According to the
function, how many minutes does it take the gardener to mow the
grass?

19= x + y
9
x− y =
11. The solution to the given system of equations is ( x, y ). What is the
value of x ?

(A) 9
(B) 10
(C) 14
(D) 19

x 2 − 16 x + y 2 − 10 y − 55 =
0
12. In the xy -plane, the graph of the given equation is a circle. If this
circle is inscribed in a square, what is the perimeter of the square?
(A) 24
(B) 48
(C) 96
(D) 220
13. If 5(3 x + 6)= 3(3 x + 6) + 78 what is the value of 3 x + 6?
(A) 78
(B) 39
(C) 33
(D) 11

14. If f ( x)= x + 5 and g ( x) = 5 x, what is the value of 7 f (4) − g (4) ?

(A) −11
(B) 13
(C) 35
(D) 43

t −15
 53 
=C (t ) 240   +7
 52 
15. The function C gives the estimated number of cephalopods, a class
of marine animal, in a certain area, where t is the number of months
since a study began. How many months after the study began was the
number of cephalopods in the area estimated to be 247?
 3
16. An object moves at a speed of feet per second. What is this speed
17
in yards per second? (3 feet = 1 yard)

x g ( x)
1 34
2 31
3 28
4 25

17. For the linear function g , the table shows four values of x and their
corresponding values of g ( x). The function can be written as
g ( x=
) mx + b, where m and b are constants. What is the value of
b?

18. The current value of a house is $174,000, and this value increases by
2.4% each year from the value of the previous year. Which function
f gives the value, in dollars, of the house x years from now?

(A) f ( x) = 174, 000(0.024) x

(B) f ( x) = 174, 000(0.24) x

(C) f ( x) = 174, 000(1.024) x

(D) f ( x) = 174, 000(1.24) x

19. What is the value of sin18π ?
(A) 0
1
(B)
2

2
(C)
2
(D) 1

Note: Figure not drawn to scale.

20. In triangle QRS shown, QR < RS . Which expression represents the

length of QS ?

(A) 17 cos Q
(B) 17 sin Q
17
(C)
cos Q
17
(D)
sin Q
 1 3r
34
x− y =
9 7
21. One of the equations in a system of two linear equations is given,
where r is a nonzero constant. The system has no solution. If the
other equation in the system is graphed in the xy -plane, what is the
slope of the graph?

27 r
(A) −
7
27
(B) −
7r
7r
(C)
27
7
(D)
27r

22. A machine makes 8-inch, 9-inch, and 3-inch parts. During a certain
day, the number of 8-inch parts that the machine makes is 4 times the
number n of 9-inch parts, and the number of 3-inch part is 30.
During this day, the machine makes 100 parts total, Which equation
represents this situation?

(A) 8(4n) + 9n + 3(30) =

100
(B) 8n + 9n + 3n =
100
(C) 4n + 30 =
100
(D) 5n + 30 =
100
Module 2

1. The ratio of the base to the height of a triangle is 1 to 8. The base of

the triangle is 104 centimeters. What is the height, in centimeters, of
the triangle?
(A) 13
(B) 42
(C) 104
(D) 832
 q ( x) = 15(3x )

2. Which table gives three values of x and their corresponding values of

q(x) for function q?

(A)

x −1 0 2

q( x) −45 0 45

(B)
x −1 0 1
1
q( x) 3 45
5

(C)
x −1 0 1
1
q( x) 15 45
5

(D)
x −1 0 1
q( x) 5 15 45
3. A plant nursery classifies a perennial flower species as tall if its
typical height when fully grown is more than 100 centimeters. Each
of the following inequalities represents the possible heights h, in
centimeters, for a specific perennial flower species when fully
grown. Which inequality represents the possible heights h, in
centimeters, for a tall perennial flower species?

(A) 14 < h < 95

(B) 41 < h < 93
(C) 78 < h < 100
(D) 107 < h < 160

4. A linear function f gives a company’s profit, in dollars, for selling

x items. The company’s profit is $170 when it sells 4 items, and its
profit is $590 when it sells 10 items. Which equation defines f ?

( x) 170 x − 590
(A) f=
(B) f ( x) = 59 x
(C) f (=
x) 70 x − 10 x
(D) f (=
x) 70 x − 110
5. Each year, the value of an investment increases by 0.69% of its value
the previous year. Which of the following functions best models how
the value of the investment changes over time?
(A) Decreasing exponential
(B) Decreasing linear
(C) Increasing exponential
(D) Increasing linear

8
6. Line p in the xy -plane is defined by y= x + and passes through
3
the points (a,0) and (0, b), where a and b are constants. What is
the value of a ?

25 x x 20
2
= +
x − 25 x − 5 x + 5
7. What is the positive solution to the given equation?
8. How many solutions does the equation 7( x + 12) + 5 x= 12( x + 7)
have?

(A) Exactly one

(B) Exactly two
(C) Infinitely many
(D) Zero

9. The manager of a gym selected a sample of 142 members at random

to estimate the percentage of the gym’s members that would continue
to pay for a membership if the price increased. From the survey, the
manager estimates that 89% of the gym’s members would continue
to pay for a membership if the price increased, with an associated
margin of error of 5.15%. If the survey is repeated with a random
sample of 284 members and the results are calculated in the same
way, which of the following will be the most likely effect of using
the larger random sample compared to the smaller random sample?\

(A) The margin of error will be lower.

(B) The margin of error will be higher.
(C) The estimate of the percentage of the gym’s members that would
continue to pay for a membership if the price increased will be
lower.
(D) The estimate of the percentage of the gym’s members that would
continue to pay for a membership if the price increased will be
higher.
10. The function f is defined by f ( x) =−9 x + 9. What is the y -
coordinate of the y -intercept of the graph of y = f ( x) in the xy -
plane?

11. The histogram summarizes a data set of the weights, in pounds, of 14

salmon. If an additional weight of 68 pounds is added to the original
data set to create a new data set of 15 weights of salmon, which of
the following measures must be greater for the new data set than for
the original data set?

I. The median
II. The mean

(A) I only
(B) II only
(C) I and II
(D) Neither I nor II
 x y

−12 44
a 14
2 b

12. The table shows three values of x and their corresponding values of
y, where a and b are constants. There is a linear relationship
between x and y. In the xy -plane, the y -intercept of the line
representing this relationship is (0, −16). What is the value of a + b ?
(A) −32
(B) −31
(C) −22
(D) −21

( x + k ) 2 + 37 =
37
13. In the given equation, k is a constant. How many distinct real
solutions does this equation have?
(A) Zero
(B) Exactly one
(C) Exactly two
(D) Infinitely many
14. For a certain circuit, its power P, in watts; current C , in amperes;
voltage V , in volts, and resistance R, , in ohms, are related as

CV 2
= PR , where P, C ,V , and R are positive. When R = 18 ,
P
which equation correctly expresses P in terms of C and V ?

CV 2
(A) P =
18 P
CV 2
(B) P =
18

C 2V 4
(C) P = 3
18

18
(D) P = 3
C 2V 4
 y < −5 x − 21
y > −3 x − 8

15. For which of the following tables are all the values of x and their
corresponding values of y solutions to the given system of
inequalities?

(A)
x y
−8 14
−9 35
−11 −3

(B)
x y
−8 19
−9 22
−11 −3

(C)
x y
−8 19
−9 22
−11 27

(D)
x y
−8 19
−9 20
−11 24
16. A circle is inscribed in a square such that the circumference of the
circle touches the midpoint of each side of the square. The length of
the diagonal of the square is 228 units. What is the area, in square
units, of the circle?

(A) 6, 498π
(B) 12,996π
(C) 25,992π
(D) 51,984π

17. The expression kx represents the result of decreasing a positive

force, x, acting on an object by 0.34%. What is the value of k ?

18. A polygon has exactly 87 sides. If the measure of each of the 87

interior angles of this polygon is (180 p ) , what is the value of p ?
19. The number of bacteria in a liquid medium doubles every hour.
There are 66,000 bacteria in the liquid medium at the start of an
observation. Which of the following represents the number of
bacteria, y, in the liquid medium t hours after the start of the
observation?

1
(A) y = (66, 000)t
2
(B) y = 2(66, 000)t
t
1
(C) y = 66,000  
2
(D) y = 66, 000(2)t

n
20. The function f (n) = 7(20.44) 4 gives each term of a sequence as a
function of the term’s position, n, in the sequence, where n is a
whole number. The value of the term in position 14 is p % more than
the value of the term in position 10. What is the value of p ?

(A) 20.44
(B) 44
(C) 1,944
(D) 2,044
21. A right square pyramid has a total surface area of 28,160 square
inches, and the combined surface area of the four lateral faces of this
pyramid is 16,060 square inches. What is the height, in inches, of this
pyramid?

(A) 48
(B) 55
(C) 73
(D) 110

22. The expression 6 x 4 + 17 x 2 + 7 can be rewritten as

(3 x 2 + a )(2 x 2 + b), where a and b are positive integers, or as

(3 x 2 + c)(2 x 2 + d ), where c and d are positive non-integers. What

is the value of a + c ?