North Carolina Early Mathematics
Placement Testing Program
January 2013
Volume 2
KEY
These mathematics questions were most often answered incorrectly by high school students across North
Carolina on NC EMPT practice placement test versions (2010-2011 and 2011-2012). The questions are typical
of those found on actual college math placement exams throughout UNC institutions and NC community
colleges so it is important to practice and avoid the same errors. Pages 1-3 list the 30 questions. The last sheet
contains the scrambled answers. Show all work for each problem on notebook paper and then write the correct
answer from the last sheet next to the appropriate problem on pages 1-3.
Question
Answer
Find the equation that represents a line that passes through the point
1.
2.
Solve the equation dx  ey  f for y (where d  0, e  0 ).
The function f ( x )  
3.
4.
5.
6.
7.
4x  7 y  7  0
4
(7, 5) and has slope  .
7
3
x  4 has an x  intercept when x has
2
y
dx  f
e
8
3
what value?
How long is the hypotenuse of a right isosceles triangle in which
one leg measures 10x units (where x  0) ?
2
5
3
The number
is equivalent to ?
1
 8.5
2
13
24
Justin works at Target after school to earn gas money for his truck.
The manager increased his hours on the weekly schedule and his
salary rose from $150 to $200. What is the percentage increase?
Find the solution of the equation
 2.3   2.3    2.3  .
5 x
10 x 2
3
17
1
33 %
3
4
1
What kind of function would best model the data below, where x
is the independent variable and y is the dependent variable?
8.
9.
x
y
4
5
3
3
2
1
Find the simplified form of
1
1
0
1
1
3
3
2
5
absolute value
7
3
2x
2
1

(where x  0) .
x
2x
Figure FGH is a triangle with angle
10.
measures of 3x ,  7 x  15 ,  2 x  9  .
Find the measure of the smallest angle.
G
F
25
H
How many of the following five statements are TRUE?
11.
2 5

3 9
14  13
12.
13.
14.
1
2 %  0.225
4
3.14159  
1
3
 0.38
8
A tire has a circumference of 60 inches. Approximately how many
revolutions does the tire make when the tire rolls 1 mile (5,280 ft.)?
1, 056
Simplify the expression   x  3(2 x  1)  1.
5x  4
Find the simplified form of
2
3

(where x  0, x  1) .
x 1
x
A ladder 30 feet long leans against a building and
5 x  3
x2  x
A
makes an angle of 72 with the ground. In the
15.
16.
17.
18.
diagram, AB represents the ladder and
mABC  72 . CA represents how high
the ladder reaches on the side of the building.
Find CA in feet.
30sin 72
B
C
A television is marked down 20% to a sale price of $320. Write an
equation that could be used to determine its original price, P.
Which equation represents a line that is perpendicular to the line
1
y  x  4 and passes through the point (1, 2)?
2
Solve the equation S  2 rh  2 r 2 for h and simplify your
answer (where r  0 ).
0.80P  $320
2x  y  0
h
S
r
2 r
2
20.
Professor Ed bought a set of books from Red Bank Publishing for
$250 and was charged another $20 for “shipping and handling.”
What is the rate Red Bank Publishing charges for “shipping and
handling”?
How long is the hypotenuse of a right
isosceles triangle whose leg measures
7x
7x units (where x  0) ?
21.
A tire has a circumference of 36 inches. Approximately how many
revolutions does the tire make when the tire rolls 1 mile (5,280 ft.)?
19.
22.
Find the solution of the equation
8%
7x 2
1, 760
 4.5   4.5    4.5  .
5 x
17
3
4
A lighthouse built at sea level is 170 feet high.
23.
24.
A
In the diagram, AC represents the lighthouse.
A buoy is in the water and is represented by
point B. The angle of elevation from the
buoy to the top of the lighthouse is 75 .
Find BC , the distance from the buoy to
the base of the lighthouse in feet.
170
75
B
x
C
If the measurements of the area and height of a triangle are known,
how would you calculate the measurement of the base of the
triangle?
Figure FGH is an acute triangle with angle
25.
 twice the area   height
G
measures of 2 x ,  3x  5  ,  5 x  15  .
Find the measure of the smallest angle.
38
F
26.
tan 75
170
H
PQ  10mn
Find the product of P  10m and Q  10n.
What kind of function would best model the data below, where x
is the independent variable and y is the dependent variable?
27.
x
y
3
13.5
2
4
1
0.5
0
0
1
0.5
2
4
3
13.5
cubic
4
32
How many of the following five statements are TRUE?
28.
2
 0.667
3
8  9
29.
30.
5 9

8 16
3
 0.38
8
1
3
5 %  0.575
4
If you travel a given distance and know your average speed
throughout the trip, how would you calculate the time it took to
complete the trip?
If P  10m is raised to the n power, it is equivalent to ?
distance

speed
P  10
n
mn
3
Scrambled Answers for the Top 30 Missed Questions Puzzle
January 2013
Volume 2
NOTE that there are more possible answers than questions, so choose carefully!
1
33 %
3
7x 2
y f 
dx
e

1
x
0.80P  $320
4
170
absolute value
147
17
1
linear
8%
34
5x  4
P  10
n
mn
30
170 tan 75
h
 speed
S
2 r
12.5%
r
PQ  100
1
2
 area  height 
y
cubic
25
distance
sin 72
8
3
2x  y  4  0
10 x 2
tan 75
m n
dx  f
e
13
24
2
3
2x
0.5417
2x  y  0
88
1,760
1
4x  7 y  7  0
0.20P  $320
5 x  3
x2  x
h
2 r
S  2 r 2
30sin 72
20x
 twice the area   height
25%
38
4
PQ  10mn
4x  7 y  7  0
1,056
5 x  1
x2  1
Visit our awesome website for a wealth of information about
college math placement testing: www.ncempt.org
This puzzle was created in January 2013 by Ellen Hilgoe, Associate Director,
NC Early Mathematics Placement Testing Program, [email protected].
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