Name
RELEASED FORM
Algebra II
K
SE
D
Form K
EA
North Carolina Test of
R
EL
Algebra II
Public Schools of North Carolina
www.ncpublicschools.org
State Board of Education
Department of Public Instruction
Division of Accountability Services/North Carolina Testing Program
Raleigh, North Carolina 27699-6314
© 2009 All rights reserved. This document may not be reproduced by any means, in whole or in part, without prior
written permission from the North Carolina Department of Public Instruction, Raleigh, North Carolina.
NCDPI
1.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
Which expression is equivalent to
3.
2x + 6
x2 + 2x − 24 ?
• 2
x + 2x − 24 x − 7x + 12
Multiply:
2
B
2 ( x + 3)
x−3
C
2 ( x + 3)
( x − 4 )( x − 3 )
D
2 ( x + 3)
( x + 4 )( x − 3 )
A
6x ( 3 7x )
B
6x ( 3 21x )
C
6x2 ( 3 42 )
D
6x2 ( 3 63 )
SE
D
2
x−4
12 x 2 • 3 126 x2
4.
Which polynomial function has as
zeros 3 and 4 + i?
A
f (x) = x3 − 11 x 2 + 41 x − 51
Which expression is equivalent to
B
f (x) = x3 − 5 x2 − 7x + 51
EA
2.
A
3
x + 3 ÷ x 2 + 2x − 3 ?
6x − 3
2x − 1
C
f (x) = x3 + 5 x2 − 7x − 51
D
f (x) = x3 + 11 x2 + 41 x + 51
A
3( x − 1 )
B
x −1
3
5.
3
x −1
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C
D
Page 1
1
3 ( x − 1)
If h(x) = 2 x and g(x) = 3x2 + 1,
what is h ( g(x) ) ?
A
6x2 + 1
B
6x2 + 2
C
12 x2 + 1
D
12 x2 + 2
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NCDPI
7.
What are the zeros of the polynomial
p (x) = x3 − 2x 2 − 23x + 60?
8.
The following list shows the number
of people (in millions) in the
United States whose only means
of getting to work was walking.
A
{—15, — 2, 2}
B
{— 5, 3, 4}
Year
(x)
Number
( y)
C
{2, 3, 10}
1940
1950
7.6
7.0
{1, 2, 30}
1960
6.4
D
1970
5.7
1980
1990
5.4
4.5
SE
D
6.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
In 1950, a U.S. population model
t −1950
million
was y = 151 • (1.013 )
If x = 0 for the year 1940, which
equation is the best-fit linear model
for the data?
people, where t is the year. What did
the model predict the U.S. population
would be in the year 2000?
EA
A
y = — 16.5 x + 125
247 million
B
y = —0.06 x + 7.6
B
255 million
C
y = 0.06 x + 10
C
263 million
D
y = 7.6 x − 0.06
D
288 million
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A
Page 2
9.
Given: 5 x − 2 y + z = 0
2 x − y + z = —3
3 x + 4 y = 18
What is the value of x in the solution
of this system?
A
—
B
—
C
—
2
D
—
3
4
1
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NCDPI
(
)
A
( x − 5) + ( y + 1) = 7
B
( x − 5 ) + ( y + 1 ) = 49
3x = 2 + 4 y
2 y = 6 − 5x
2
2
C
( x + 5) + ( y − 1) = 7
D
( x + 5 ) + ( y − 1 ) = 49
2
2
2
2
—1
2
2x + 6 + 2 = 0
A
x = 5 or x = 1
B
x=5
C
x = —5 or x = — 1
D
x = —1
14.
Which circle has the smallest area?
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12.
A
x 2 + y2 = 12
B
( x − 2)
C
( x + 1) + ( y + 3) = 6
D
Page 3
Which matrix equation should be
used to find the intersection of these
two lines?
2
2
Solve for x:
13.
A
⎡3 —4 ⎤ ⎡ x ⎤ ⎡2⎤
⎢⎣2 5 ⎥⎦ ⎢⎣ y ⎥⎦ = ⎢⎣6 ⎥⎦
B
⎡3 ⎤ ⎡ x ⎤ ⎡ —4 ⎤ ⎡ x ⎤ ⎡2⎤
⎢⎣2⎥⎦ ⎢⎣ y ⎥⎦ + ⎢⎣ 5 ⎥⎦ ⎢⎣ y ⎥⎦ = ⎢⎣6 ⎥⎦
C
⎡3 —4 ⎤ ⎡ x ⎤ ⎡2⎤
⎢⎣5 2 ⎥⎦ ⎢⎣ y ⎥⎦ = ⎢⎣6 ⎥⎦
D
⎡3 ⎤ ⎡ x ⎤ + ⎡ 5 ⎤ ⎡ x ⎤ = ⎡2⎤
⎢⎣2⎥⎦ ⎢⎣ y ⎥⎦ ⎢⎣ —4 ⎥⎦ ⎢⎣ y ⎥⎦ ⎢⎣6 ⎥⎦
SE
D
11.
Which equation describes the circle
with center 5, —1 and radius 7?
EA
10.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
2
2
+ y2 = 8
2
( x + 8) + ( y − 9) = 3
2
2
The profit (P), in dollars, for a
company is modeled by the function
P (x) = — 750 x2 + 15,000 x, where x is
the number of items produced. For
which values of x will the company
lose money?
A
x<2
B
2 < x ≤ 10
C
10 ≤ x < 20
D
x > 20
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NCDPI
16.
In which direction is the graph
of f (x) = 5 translated when
x+b
b increases?
A
left
B
right
C
up
D
down
A company that manufactures
jeans estimates that the profit
for selling a particular style is
given by the equation:
17.
Copper production increased at a rate
of about 4.9% per year between 1988
and 1993. In 1993, copper
production was approximately
1.801 billion kilograms. If this trend
continued, which equation best models
the copper production (P), in billions of
kilograms, since 1993?
(Let t = 0 for 1993.)
SE
D
15.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
P = —250x3 + 1,505x2 − 300, for 0 < x < 6
A
P = 1.801 ( 4.900 )
t
B
P = 1.801 (1.490 )
t
C
P = 1.801 (1.049 )
t
D
P = 1.801 ( 0.049 )
t
the number of times the company
spent zero dollars on advertising
R
EL
A
EA
where P is profit in tens of
thousands of dollars and x is the
advertising expense in tens of
thousands of dollars. What does
an x-intercept mean in the context
of the problem?
B
the profit when the company
spent zero dollars on advertising
C
the advertising expense when the
company had the most profit
D
the advertising expense when the
company’s profit was zero dollars
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NCDPI
18.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
Divide:
20.
( 6x3 − 11 x2 − 47x − 20 ) ÷ ( 2 x + 1)
19.
3 x2 − 7x − 20
B
3 x2 + 7x − 20
C
3 x2 − 4 x − 20
D
3 x2 + 4 x − 20
A
ln 7 x3 = ln 25
B
ln 7x3 = ln 32
C
ln 10x = ln 10
D
ln 21x = ln 10
SE
D
A
Which equation is equivalent to
ln 7 + 3 ln x = 5 ln 2?
By which matrix should both sides
21.
Simplify:
1−1
y x
1+1
y x
of the equation be multiplied to solve
x
for ⎡⎢ ⎤⎥ ?
⎣ y⎦
A
EA
⎡3 1⎤ ⎡ x ⎤ = ⎡5⎤
⎣⎢ 5 2 ⎦⎥ ⎢⎣ y ⎦⎥ ⎢⎣ 9 ⎦⎥
B
x− y
x+ y
x+ y
x− y
A
⎡3 1⎤
⎣⎢ 5 2 ⎥⎦
B
⎡3 5⎤
⎢⎣ 5 9 ⎥⎦
C
0
C
⎡ 2
⎢ —5
⎣
D
—
D
⎡ 2
⎢ —1
⎣
1⎤
3 ⎥⎦
R
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—
Page 5
—
1
5⎤
3 ⎥⎦
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NCDPI
22.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
Let x and y be real numbers. If
24.
1
x = 8, y = 7
B
x = 8, y = 1
C
D
—
x = 4, y = 7
—
x = 4, y = 1
25.
23.
A
right
B
left
C
up
D
down
SE
D
(x + yi) − (2 − 3i) = 6 + 4i, what are
the values of x and y?
A
In which direction does the graph
of y = ( x + 2 ) 2 + c shift as c decreases?
—
What is the value of z in the solution
of this system?
If f ( x ) = 2 x + 1 and g( x ) = x3, what is
f ( g ( 3 ) )?
343
B
189
55
D
34
B
—
7
—
1
C
3
D
5
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C
A
EA
A
x + y − z = —5
2 x + z + 1 = —2 y
x − y = 3z + 3
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NCDPI
What is the domain of
f (x) = —2 x3 + x2 + 1?
the set of all real numbers
B
{x —3 < x < 2}
C
{x
D
27.
—
2 < x < 3}
the empty set
A
The population of a small town in
North Carolina is 4,000, and it has
a growth rate of 3% per year. Which
expression can be used to calculate the
town’s population x years from now?
A
3( 4,000 )
B
4,000(1.03 )
C
29.
B
down
C
left
D
right
x
Solve for x: x − 1 =
x + 5 2( x + 5 )
A
x
up
—
5
B
2
C
—
D
5 or — 2
5 or 2
1.03
4,000x
4,000x
3
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D
x
The graph of f (x) = x 2 + 3 is
translated to produce the graph
2
of g (x) = ( x + 2 ) + 3. In which
direction was the graph of f
translated?
SE
D
A
28.
EA
26.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
Page 7
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NCDPI
30.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
Which graph shows the solution set for the following inequality?
x 2 > x + 12
—6 —5 —4 —3 —2 —1
B
—6 —5 —4 —3 —2 —1
C
D
0
1
2
3
4
5
6
SE
D
A
1
2
3
4
5
6
—6 —5 —4 —3 —2 —1
0
1
2
3
4
5
6
—6 —5 —4 —3 —2 —1
0
1
2
3
4
5
6
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EA
0
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NCDPI
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
31. Which graph represents the system of inequalities below?
2x − 3 y ≥ 9
4x + 2 y < 8
A
B
+6
+6
+5
+5
+4
+4
+3
+3
+2
+2
+1
+1
—6
—5
—4
—3
—2
—1 0
—1
y
SE
D
y
+ 1 +2 +3 +4 +5 +6
x
—6
—5
—4
—3
—2
—4
—4
—5
—5
—6
EA
—6
y
D
—4
—3
—2
y
+6
+6
+5
+5
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Page 9
—5
+4
+4
+3
+3
+2
+2
+1
+1
—1 0
—1
x
—3
—3
—6
+ 1 +2 +3 +4 +5 +6
—2
—2
C
—1 0
—1
+ 1 +2 +3 +4 +5 +6
x
—6
—5
—4
—3
—2
—1 0
—1
—2
—2
—3
—3
—4
—4
—5
—5
—6
—6
+ 1 +2 +3 +4 +5 +6
x
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NCDPI
32.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
The dimensions of this rectangular
prism are given algebraically.
33.
A single microscopic organism divides
into two organisms every 3 days. Use
t
the formula N (t) = N0 ( 2 ) 3 , where t is
the time in days, N (t) is the number
3—w
SE
D
of organisms at t days, and N0 is
the number of organisms at t = 0.
w+2
w
Approximately how long would it
take one organism to produce a
What is the approximate width (w)
that will maximize the volume?
A
1 unit
B
11 units
C
1 3 units
D
2 units
4
A
1,667 days
B
333 days
C
126 days
D
40 days
EA
2
population of about 10,000 organisms?
34.
What is an equation of the circle that
has center
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( —1, 1) ?
Page 10
( —2, 3) and passes through
A
( x + 2)
B
( x − 2) 2 + ( y + 3 ) 2
= 5
C
( x + 2) 2 + ( y − 3) 2
= 25
D
( x − 2) 2 + ( y + 3) 2
= 25
2
+ ( y − 3) = 5
2
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NCDPI
37.
Simplify:
(x )
3
4
A
B
36.
x
3
27
64
9
x4
9
12
C
x
D
x4
15
38.
The area of a rectangular window
is ( 4 x 2 − 21x − 18 ) . Both the length
and the width are polynomials
Which binomial is a factor of
( x 3 − x 2 + 3 x − 3) ?
A
x−3
B
x +1
C
x2 − 1
D
x2 + 3
SE
D
35.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
If 5 tractors can plow a field in
4 hours, how many hours will it take
3 tractors to plow the field?
A
62
B
61
EA
with integer coefficients. Which of
the following could represent the
length of the window?
4x + 6
B
4x + 3
C
x+6
D
x+3
2
C
52
D
51
3
2
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A
3
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NCDPI
Solve: 3 x − 7 x + 2 = 0
40.
9
x = 1, x = 4
C
−
x = 1, x = 1
9
3
D
2
the function f ( x ) = 42x − 100 ?
2x + x − 15
x = 1, x = 4
B
What are the vertical asymptotes of
A
x = — 5, x = 5
B
x = — 5, x = 4, x = 5
C
x = — 3, x = 5
D
x = — 3, x = 5 , x = 20
3
x = 1, x = 1
3
9
SE
D
A
41.
2
2
3
What is the approximate value of the
greatest zero of f (x) = x3 − 6x2 − x + 3?
A
—
0.75
EA
39.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
2.84
C
6.08
D
6.31
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B
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NCDPI
42.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
A poll shows that it is likely that, with a margin of error of ± 2 percentage points,
78% of those randomly selected from a population would vote for a particular candidate.
This situation can be described by the inequality x — 78 ≤ 2. Which graph shows the
A
B
80
76
80
C
76
80
D
76
80
Which equation represents
the graph of y = x translated
1 unit right and 2 units down?
2
( x − 1)
—
2
A
y=
B
y = ( x − 1) − 2
−2
2
—
( x + 1)
2
y=
+2
D
y = ( x + 1) − 2
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C
Page 13
44.
Which is the solution set of the
equation x + 2 = 4 ?
x−2
EA
43.
76
SE
D
percentage of voters (according to the inequality) who favor the candidate?
A
{± 2 2 }
B
{2 2}
C
{ 1 ±2 17 }
D
{ 1 +2 17 }
2
—
—
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NCDPI
45.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
When interest is compounded n times
a year, the accumulated amount (A)
after t years is given by the formula
(
A = P 1+ r
n
)
47.
C
13.23 years
D
13.08 years
B
The graph widens.
SE
D
13.71 years
The graph narrows.
48.
C
The graph shifts up.
D
The graph shifts right.
Which is the inverse of the function
f ( x ) = x − 9?
A
f
B
f
C
f
D
f
EA
B
A
Alan has just started a job that pays a
salary of $21,500. At the end of each
year of work, he will get a 5% salary
increase. What will his salary be after
getting his fifth increase?
A
$22,631
B
$24,889
C
$26,133
D
$27,440
1
x+9
−1
( x) =
−1
( x) = x + 9
−1
( x) = 9 − x
−1
( x) =
1
x−9
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46.
13.98 years
2
nt
where P is the initial principal and
r is the annual rate of interest.
Approximately how long will it
take $2,000 to double at an annual
interest rate of 5.25% compounded
monthly?
A
In the function f (x) = a( x − 4 ) , where
a > 0, what happens to the graph of
f as the value of a increases?
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NCDPI
A
⎧7 ± 2 5 ⎫
⎨
⎬
2
⎩
⎭
B
⎧ —7 ± 2 5 ⎫
⎨
⎬
2
⎩
⎭
C
⎧ 7 ± 29 ⎫
⎨
⎬
2
⎩
⎭
D
⎧ — 7 ± 29 ⎫
⎨
⎬
2
⎩
⎭
The table below shows the number of families living in the city of Sunnyvale from 1965 to
2000.
EA
50.
What are the zeros of f ( x ) = x2 + 7x + 5?
SE
D
49.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
Year (after 1900)
65
70
75
80
85
90
95
100
Number of Families
31.1 30.5 30.1 28.7 27.1 25.7 23.2 20.3
(thousands)
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According to the best-fit quadratic model, approximately how many families will live in
Sunnyvale in 2010?
A
14,000
B
15,000
C
18,000
D
19,000
Page 15
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NCDPI
51.
North Carolina Test of Algebra II. Form K RELEASED Fall 2009
What is the solution set of the system
below?
A
{( 0, 0 )}
B
{( 0, 4 )}
C
{( 0, 0 ) , ( 4, 0 )}
D
{( 0, 0 ) , ( 8, 4 )}
EA
STOP
SE
D
x = 2y
x − y2 = — 2 y
R
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End of Algebra II Test
Page 16
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North Carolina Test of Algebra II
Form K RELEASED Fall 2009
Answer Key
6 August 2009
SE
D
Goal
1 – Number and Operations
1 – Number and Operations
1 – Number and Operations
1 – Number and Operations
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
1 – Number and Operations
1 – Number and Operations
1 – Number and Operations
1 – Number and Operations
1 – Number and Operations
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
1 – Number and Operations
1 – Number and Operations
1 – Number and Operations
1 – Number and Operations
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
EA
Correct Answer
C
D
A
A
B
B
D
B
C
B
C
D
C
D
A
D
C
A
C
B
A
D
C
D
C
A
B
C
B
B
D
C
D
A
B
B
D
A
A
C
C
D
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Item Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Page 1
North Carolina Test of Algebra II
Form K RELEASED Fall 2009
Answer Key
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
2 – Algebra
SE
D
B
A
C
D
A
B
D
A
D
R
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EA
43
44
45
46
47
48
49
50
51
6 August 2009
Page 2
Scale Score
127
127
128
128
129
129
130
131
131
132
133
134
135
136
137
138
139
140
141
143
144
145
146
147
148
149
150
150
151
152
153
154
154
155
156
157
158
158
159
160
161
162
R
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EA
SE
Raw Score
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
D
North Carolina Test of Algebra II
Form K RELEASED Fall 2009
Raw to Scale Score Conversion
10 August 2009
Page 1
163
164
165
166
167
169
170
172
175
177
R
EL
EA
SE
42
43
44
45
46
47
48
49
50
51
D
North Carolina Test of Algebra II
Form K RELEASED Fall 2009
Raw to Scale Score Conversion
10 August 2009
Page 2