2 2

1.
!
How many inches wider is the diameter of the hole make by a "# -inch-
$
diameter drill bit than the hole made by a #%
-inch-diameter drill bit?

&"
A. #%

!
B. #%

!
C. !&

#
D. −
%'

#
E. − #%

2.
An arithmetic sequence has 2 as its 1st term and 12 as its 6th term. What
is the sum of the first 6 terms of this sequence?

A. 14
B. 30
C. 42
D. 48
E. 104
 2 2
3.
What value of w satisfies the equation 2𝑤 − (−15) = 7 ?

A. −16
B. −6
C. −4
D. 4
E. 11

4.
If 𝑥 & + 5 = 30, then 𝑥 & − 5 = ?

A. 5
B. √20
C. 20
D. 25
E. 35

5.
For 5 weeks, Leah has been running each day as part of her exercise
routine. The table below shows how many kilometers she has run each
day of the week. There is a linear relationship between the week
number and the number of kilometers Leah ran each day that week.
Given that she continues running according to this linear relationship,
how many kilometers will Leah run each day of week 7 ?

Week Kilometers run each day

1 1
2 3.5
3 6
4 8.5
5 11

A. 12
B. 13.5
C. 14
D. 14.5
E. 16
 2 2
6.
Each week, Drayton puts money in a jar so that the total amount of
money, A dollars, he will have in the jar at the end of the 𝑛th week is
(
given by 𝐴 = & (0.2(1 + 𝑛)). How much money will Drayton have in
the jar at the end of the 15th week?

A. $4.80
B. $22.50
C. $24.00
D. $25.50
E. $48.00

7.
Given that 12% of a number is 18, what is 25% of the same number?

A. 0.54
B. 8.64
C. 37.5
D. 150
E. 600

8.
Isiah rented a car for a week and drove the car 650.0 miles. The cost to
rent the car was $175.00 for the week, plus $0.07 for each mile the car
was driven beyond 600.0 miles. What was the cost of Isiah’s car
rental?

A. $175.00
B. $175.07
C. $178.50
D. $217.00
E. $220.50
 2 2
9.
The measure of the vertex angle of an isosceles triangle is 48º.
What is the measure of each base angle of the isosceles triangle?

A 42º
B. 48º
C. 66º
D. 84º
E. 132º

10.
Beth is installing plumbing pipe in a new house. A sketch of a
section of pipe is shown below.

⃖7777⃗ to be parallel to ⃖7777⃗

For 𝐴𝐵 𝐶𝐷, what must be the measure of ∠𝐵𝐶𝐷 ?

A. 41º
B. 82º
C. 98º
D. 131º
E. 139º

11.
A square and a rectangle have the same area. The length of the
rectangle is 36 centimeters, and the width of the rectangle is 9
centimeters. What is the length, in centimeters, of a side of the square?

A. 3√10
B. 18
"
C. 22 &

D. 90
E. 324
 2 2
12.
Each card in a standard deck of 52 playing cards is identified by a
unique combination of two characteristics: rank and suit. There are
13 ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 suits (clubs,
diamonds, hearts, spades). You will select 1 card at random. What
is the probability you will select a 5 of diamonds (i.e., a card with
rank 5 and the suit of diamonds)?
"
A. )&
"
B. %'
"
C. "!
"
D. "&
"
E. %

13.
Nancy left the grocery store with n apples. On her way home, she
gave 7 apples to Paulo. Later, the bag broke and she lost half of the
remaining apples. Which of the following expressions gives the
number of apples Nancy was carrying when she arrived home?
(*+
A. &

(
B. &
−7

C. 2𝑛 − 14

D. 2𝑛 − 7

E. 2𝑛 + 14

14.
The functions f and g below are defined for all real values of x.
For what real value of x is 𝑓(𝑥) = 𝑔(𝑥) ?

𝑓(𝑥) = 2𝑥 − 3
𝑔(𝑥) = 𝑥 + 5
A. 1
B. 2
C. 4
D. 6
E. 8
 2 2
15.
Kallee and her dog Sammi achieved the following 9 times, in
minutes, in completing the dog agility obstacle course at the Pup
Club: 2.3, 2.3, 2.8, 2.4, 2.9, 7.6, 2.5, 2.7, and 2.1. Which of the
following numbers is closest to the median time, in minutes, that
Kallee and Sammi achieved in completing the dog agility obstacle
course?
A. 2.3
B. 2.5
C. 2.9
D. 3.1
E. 5.5

16.
Which of the following expressions is equivalent to
3[(5𝑥 + 4𝑦)(3𝑥 + 5𝑦)] ?

A. 15𝑥 & + 37𝑥𝑦 + 20𝑦 &

B. 45𝑥 & + 87𝑥𝑦 + 20𝑦 &

C. 45𝑥 & + 60𝑦 &

D. 45𝑥 & + 37𝑥𝑦 + 20𝑦 &

E. 45𝑥 & + 111𝑥𝑦 + 60𝑦 &

17.
A roof slopes such that it rises 3 inches for each 1 foot of horizontal
run. The horizontal run of the roof is 12 feet 6 inches. What is the
vertical rise, in inches, of the roof?
"
A. 3 '

"
B. 31 &

"
C. 37 &

%
D. 37 )

E. 54
 2 2
18.
When 𝑦 = 4 and 𝑦 = 𝑥 + 1 are graphed in the standard (𝑥, 𝑦)
coordinate plane, what is the point of intersection of the 2 lines?

A. (3, 4)
B. (4 3)
C. (4, 4)
D. (4, 5)
E. (5, 4)

19.
The results of a recent survey of 101 pet owners are given in the table
below. Each pet owner responding owns at least 1 cat or dog. When an
individual pet owner is selected at random from dog owners only, what
is the probability that the individual is male?

Type of owners Pet owners

Male Female Total
Cat owners only 12 18 30
Dog owners only 24 21 45
Cat and dog owners 14 12 26
Total 50 51 101

+
A. "+

+
B. ")

"&
C. &)

'
D. ")

+
E. "!
 2 2
20.
The graph of 𝑦 = √𝑥 is shown in the standard (𝑥, 𝑦) coordinate plane
below.

One of the following graphs in the standard (𝑥, 𝑦) coordinate plane

shows the result of reflecting the graph of 𝑦 = √𝑥 across the x-axis and
then translating that reflection 3 coordinate units down. Which graph is
it?

A.

B.

C.

D.
 2 2
21.
!
Hideaki feeds his dog % of a can of dog food each day. How many
days can he feed his dog with 24 cans of dog food?

A. 18
B. 24
C. 28
D. 32
E. 36

Use the following informa1on to answer ques1ons 22-24

In ∆𝐴𝐵𝐷 shown below, point C is on 𝐵𝐷DDDD, all right angles are marked,
and the given lengths are in inches.

22.
What is the area, in square inches, of ∆𝐴𝐵𝐷 ?

"
A. 87 &

B. 180
C. 210
D. 240
E. 340

23.
What is the perimeter, in inches, of ∆𝐴𝐵𝐷 ?

A. 52
B. 65
C. 77
D. 90
E. 102
 2 2
24.
What is the value of tan ∠𝐴𝐵𝐶 ?

)
A. "&
!+
B. %,
"&
C. )
%,
D. !+
",
E. !

25.
Standing in sunlight on level ground, a 6-foot-tall man casts a
4-foot-long shadow at the same time that a nearby vertical tree
casts a 12-foot-long shadow. What is the height, in feet, of the
tree?

A. 2
B. 8
C. 10
D. 14
E. 18

26.
In the standard (𝑥, 𝑦) coordinate plane, 𝐵 (1, −6) is an
DDDD. The midpoint of DDDD
endpoint of 𝐴𝐵 𝐴𝐵 is (−5, 4). What
are the coordinates of A ?

A. (−11, 14)
B. (−10, 6)
C. (−4, −2)
D. (−2, −1)
E. (36, 100)
 2 2
27.
Two sides of the triangle shown below are 12 inches long
and 20 inches long, respectively. The measure of the angle
formed by these 2 sides is 30º. What is the area, in square
inches, of the triangle?

"
(Note: The area of a triangle is & 𝑎𝑏 sin 𝐶, where C is the
angle formed by sides with lengths a and b.)

A. 34
B. 57
C. 60
D. 119
E. 120

28.
What are the solutions to the equation below?
𝑥 & + 2𝑥 = 24

A. −12 and 2
B. −6 and 4
C. −4 and 6
D. −2 and 12
E. 22 and 24

29.
Paula bought 3 textbooks-1 math, 1 science, and 1 history-for a total
"
price of $280. The price of the history textbook was ! the price of the
science textbook, and the price of the math textbook was equal to the
sum of the prices of the science textbook and the history textbook.
What was the price of the science textbook?

A. $35
B. $94
C. $105
D. $140
E. $210
 2 2
30.
−(𝑎& 𝑏 & − 3𝑎& 𝑏 & + 4𝑎 − 5𝑏) − (−5𝑏 + 4𝑎 − 2𝑎& 𝑏 & )
is equivalent to:

A. 0
B. 4𝑎& 𝑏 & − 8𝑎 + 10𝑏
C. 4𝑎% 𝑏 %& − 8𝑎& + 10𝑏 &
D. −6𝑎& 𝑏 & + 8𝑎 − 10𝑏
E. −6𝑎% 𝑏 % + 8𝑎& − 10𝑏 &

31.
Which of the following values is closest to the height, in centimeters, of
a cylinder that has a radius of 4 centimeters and a volume of 754 cubic
centimeters?
(Note: The volume of a cylinder with radius r and height h is π𝑟 & ℎ.)

A. 15
B. 30
C. 35
D. 47
E. 148

32.
- ! *&) -
For all 𝑎 > 25, - ! .)-
∙ -! *",-.&) = ?

!
A. "#$
!
B. !%("'$)
!
C. !%("! '$")

D. 𝑎−5
E. −(𝑎 − 5)
 2 2
33.
How many (𝑥, 𝑦) ordered pairs satisfy 4𝑥 − 6𝑦 = 3 ?

A. 0
B. 1
C. 2
D. 3
E. Infinitely many

34.
For all positive integer values of x, if 𝑦 = 4𝑥, and 𝑧 = 3𝑦, then the
greatest divisor of z is which of the following?

A. 1
B. 4
C. 4x
D. 12
E. 12x
 2 2
Use the following informa1on to answer ques1ons
35-37

A nonprofit organization that assists people in 50 underdeveloped

nations had an annual budget of $800 million last year. The budget was
divided into 6 expense categories as shown in the table below.

Category Expense amount

( in millions of dollars)
Administration $40
Relief $248
Food $186
Health $200
Training $74
Other $52
Total $800

35.
Last year’s budget will be displayed in a circle graph that consists of 1
sector for each of the 6 categories. Which of the following values is
closest to the measure of the central angle of the Relief sector of the
circle graph?

A. 31
B. 56
C. 60
D. 112
E. 224

36.
Last year, what was the average expense amount, in millions of dollars,
per nation for the Food category?
A. 0.2325
B. 3.72
C. 4
D. 4.96
E. 16
 2 2
37.
Next year, the expense amount for the Training category will increase
by 30%, while the expense amounts for the other 5 categories will
remain the same. What fraction of next year’s
total budget will be for the Training category?
&&.&
A. ',,
&&.&
B. '&&.&
+%
C. '&&.&
$#.&
D. ',,
$#.&
E. '&&.&

38.
Brian rode his bicycle at a constant speed along a bicycle trail
for 50 km in 3 hours 20 minutes. Which of the following times
is closest to how much time Brian took to ride 35 km on that
ride?

A. 2 hours 14 minutes
B. 2 hours 20 minutes
C. 2 hours 24 minutes
D. 2 hours 33 minutes
E. 3 hours 5 minutes

39.
For 𝑥 > 1, which of the following equations is equivalent to
log 0 8 = 2 ?

A. 2𝑥 = 8
B. 𝑥 = 2'
C. 𝑥 = 8&
D. 𝑥 & = 8
E. 𝑥 ' = 2
 2 2
40.
In the standard (𝑥, 𝑦) coordinate plane, the circle that is
centered at (−1, 5) and passes through (2, 1) is represented
by which of the following equations?

A. (𝑥 − 1)& + (𝑦 + 5)& = 5
B. (𝑥 − 1)& + (𝑦 + 5)& = 25
C. (𝑥 − 1)& + (𝑦 + 5)& = 37
D. (𝑥 + 1)& + (𝑦 − 5)& = 25
E. (𝑥 + 1)& + (𝑦 − 5)& = 37

41.
&0*1 ) 0
If 0.1 = ' , then 1 = ?

&
A. ""

)
B. '

"!
C. ""

"!
D. !

"!
E. &

42.
There are 3 types of toppings available for your ice cream. You may
choose to have no toppings at all, or any single topping, or any 2
toppings, or all 3 toppings. How many different possibilities are there?

A. 4
B. 6
C. 7
D. 8
E. 11
 2 2
43.
A house has an assessed value of $360,000. Insurance on the house
costs 𝑥 dollars per $1,000 of its assessed value. Which of the following
expressions represents the cost, in dollars, of insurance for this house?

A. 360x
B. 360,000x
C. 360,000,000x
0
D. !#,,,,,,,,,
0
E. !#,

44.
When 𝑓(𝑥) = 2𝑥 & − 3 and 𝑔(𝑥) = 𝑥 + 4, 𝑓(𝑔(𝑥)) ?

A. 2𝑥 & + 1
B. 2𝑥 & + 13
C. 2𝑥 & + 29
D. 2𝑥 & + 16𝑥 + 29
E. 2𝑥 ! + 8𝑥 & − 3𝑥 − 12

45.
Bobbi made the conjecture: “If a quadrilateral has one set of opposite
sides equal in length and the other set of opposite sides parallel, then
the quadrilateral is a parallelogram.” A figure in one of the following
categories serves as a counterexample to Bobbi’s conjecture. Which
one?

A. Hexagon
B. Kite
C. Rectangle
D. Square
E. Trapezoid
 2 2
46.
Point 𝐼 (1, 2) is shown in the standard (x, y) coordinate plane below.
Point I is reflected across the line 𝑦 = 4 and, after the reflection, is
labeled J. What are the coordinates of J ?

A. (−3, 2)
B. (1, − 2)
C. (1, 6)
D. (5, 2)
E. (7, 2)

47.
The midpoints of the sides of square ABCD are vertices of square
KLMN, shown below. The side length of square ABCD is 10 feet.
What is the area, in square feet, of the shaded region?

A. 5√2
B. 12.5
C. 10√2
D. 25
E. 50
 2 2
48.
DDDD and 𝐵𝐷
In the circle below, chords 𝐴𝐶 DDDD intersect at point E, the measure
X is 90º, and the measure of 𝐶𝐷
of 𝐴𝐵 X is 88º. The measure of ∠𝐴𝐸𝐵 is
the average of the measures of arcs 𝐴𝐵X and 𝐶𝐷 X . What is the measure of
∠𝐴𝐸𝐵 ?

A. 88º
B. 89º
C. 90º
D. 91º
E. 92º

49.
DDDD, 𝐵𝐶
In the figure below, D, E, and F are the midpoints of 𝐴𝐵 DDDD , and DDDD
𝐴𝐶 ,
respectively. The measure of ∠𝐴 is 70º and the measure of ∠𝐶 is 15º.
What is the sum of the measures of ∠𝐷𝐹𝐸 and ∠𝐷𝐸𝐹 ?

A. 70º
B. 85º
C. 95º
D. 110º
E. 165º
 2 2
50.
A triangle has sides of length 6 inches, 6 inches, and 10 inches,
respectively. What is the area, in square inches of the triangle?

A. 5√11
B. 10√11
C. 20
D. 22
E. 30

51.
A new operation, 𝛼, is defined as 𝑥 𝛼 𝑦 = −𝑥 & − 6𝑦 for all integers x
and y. What is the value of 5 𝛼 2 ?

A. −37
B. −26
C. −22
D. 13
E. 26

52.
#" ## "
For what real value of x is (## )$
= !# true?

A. 2
B. 4
C. 5
D. 7
E. 9

53.
Let y be an integer. For all values of x, which of the following could
be the product of (2𝑥 + 𝑦) and (𝑥 + 2) ?

A. 𝑥 & + 5𝑥 + 4
B. 2𝑥 & + 2
C. 2𝑥 & + 4𝑥 + 2
D. 2𝑥 & + 7𝑥 + 6
E. 4𝑥 & + 2𝑥 + 4
 2 2
54.
A multiple of 42 is multiplied by a multiple of 5. What is the
units digit of the product?

A. 0
B. 2
C. 3
D. 5
E. 7

55.
When a wheel is modeled by a circle, the center of the hub of the
wheel corresponds to the center of the circle. Given that the center
of the hub travels a distance of 640 cm when the wheel makes 4
revolutions along a level surface, what is the radius, in centimeters,
of the wheel?
&,
A. 5
',
B. 5
"#,
C. 5
!&,
D. 5
#%,
E. 5
 2 2
56.
The system of equations

𝑦 = 𝑥&
\ &
𝑥 + 𝑦& = 9

is graphed in the standard (𝑥, 𝑦) coordinate plane below. The graph of

one of the following systems of inequalities is shown shaded. Which
system?

!"# !
A. !
# ! $! ! "%

!&# !
B !
# ! $! ! &%

!&# !
C. !
# ! $! ! "%

!"# !
D. !
# ! $! ! &%

!'# !
E. !
# ! $! ! &%
 2 2
57.
A line through the points (2, −6) and (𝑘, 9) in the standard (𝑥, 𝑦)
&
coordinate plane is perpendicular to a line with slope − !.
What is the value of k ?

A. −20.5
B. −8
C. 8
D. 12
E. 24.5

58.
A ship is 16 km from Lighthouse A and 28 km from Lighthouse B, as
shown in the figure below. The 2 lighthouses and the ship form a 120º
angle with the ship at its vertex. Which of the following expressions
gives the straight-line distance, in kilometers, between Lighthouse A
and Lighthouse B?

A. 16 + 28

"&,
B. ^"',_ (16 + 28)

C. √28& + 16&

D. `28& + 16& − 2(28)(16) sin 120°

E. `28& + 16& − 2(28)(16) cos 120°

 2 2
59.
) !5
If tan 𝜃 = "& with π < 𝜃 < & , then cos 𝜃 = ?

"!
A. − "&

"&
B. − "!

)
C. − "&

"&
D. "!

"!
E. "&

60.
Consider all the nonzero real values of a and b such that
|𝑎 − 3| = |𝑏 − 3| is true. Which of the following statements
about these values of a and b is true?

A. 𝑎 = 𝑏 is always true
B. 𝑎 − 𝑏 = 6 is always true
C. 𝑎 + 𝑏 = 6 is always true
D. 𝑎 = 𝑏 is sometimes true and 𝑎 − 𝑏 = 6 is sometimes true
E. 𝑎 = 𝑏 is sometimes true and 𝑎 + 𝑏 = 6 is sometimes true