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VIRGINIA STANDARDS OF LEARNING
Spring 2007 Released Test
END OF COURSE
ALGEBRA II
Form M0117, CORE 1
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©2007 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia 23218-2120.
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ISD6736
Algebra II Formula Sheet
Geometric Formulas
b
l
h
h
h
h
b
A=
1
2
b
bh
A = bh
s
l
r
A=
1
2
h
h
h
p = 4s
A = s2
1
3
w
V = lwh
S.A.= 2(lw + lh + wh)
b1
s
r
V = 13 Bh
S.A.= 12 lp + B
b2
h(b1 + b2 )
w
l
B
c
a
r
b
l
c2 = a2 + b2
p = 2(l + w)
A = lw
Abbreviations
Pi
milligram
gram
kilogram
milliliter
liter
kiloliter
millimeter
centimeter
meter
kilometer
square centimeter
cubic centimeter
mg
g
kg
mL
L
kL
mm
cm
m
km
cm2
cm3
ounce
pound
quart
gallon
inch
foot
yard
mile
square inch
square foot
cubic inch
cubic foot
oz
lb
qt
gal.
in.
ft
yd
mi.
sq in.
sq ft
cu in.
cu ft
volume
total surface area
area of base
V
S.A.
B
year
month
hour
minute
second
yr
mon
hr
min
sec
22
7
Quadratic Formula
x=
–b ± b2 – 4ac
2a
Algebra II
Directions
Read and solve each question. Then mark the space on your answer document for the best
answer. For this test you may assume that the value of the denominator of a rational
expression is not zero.
SAMPLE
6 (a + 2 )
a
A
B
C
D
i
a3
a +2
=
6
a2
6(a + 2)
a
6a 2
6a 2 + 24a + 24
a4
5
1
Which is a simplified form of the following expression?
4
27 3
A
B
C
D
2
4
19, 683
36
81
177,147
Which is a true statement?
( )( )
= ( x − y )( x − y )
= ( x + y )( x + y )
= ( x − y )( x − y )
F
x2 −y2 = x +y x −y
G
x2 −y2
H
x2 +y2
J
x2 +y2
6
3
Which is equivalent to the following expression?
2
x −3
A
−
x
x −3
?
2−x
0
B
C
D
4
2x
x −3
2−x
x −3
2−x
(
2 x −3
)
If no denominator is equal to zero, which is a simplified form of the following
expression?
⎛
5x y
⎜
⎜ x −y x −y
⎝
(
F
G
H
J
)(
5 xy
(x + y )
2
5
(x + y )
2
5
( x − y )( x + y )
5 xy
( x − y )( x + y )
7
)
⎞⎛
⎞
⎟ ⎜ x −y ⎟
⎟ ⎝ x +y ⎠
⎠
5
Which is equivalent to
2 27 + 3 75 − 18 ?
6
A
18 6
B
4 120
C
21 3 − 3 2
D
24 3 − 9 2
Which statement is a result of applying the transitive property of inequalities?
Given: 2 x − 1 < 7x and 7x < x + 72
7
F
2 x − 1 < x + 72
G
x + 72 < 7 x
H
x + 72 < 2 x − 1
J
7x < 2x − 1
Which is equivalent to the expression below?
(1 + 3i)(3 + i)
A
B
C
D
3 − 10i
6 + 6i
6 + 10i
10i
8
8
What is the completely factored form of the following expression?
6 x 2 + 7x − 3
9
F
(2x + 3)(3x − 1)
G
(2x − 3)(3x + 1)
H
(6x − 3)( x + 1)
J
(6x − 1)( x + 3)
If x ≠ − 3, which is an equivalent form of the following expression?
6x + 7
(
2 x +3
A
B
C
D
−
) 2 ( x + 3)
2
x +1
x +3
2x + 1
x +3
(
2 2x + 3
2x + 5
)
x +3
9
10
Which is an equivalent form of the following?
−
11
F
−
8i
G
−
9i
H
i + 10
J
−
1 −5
−
4
9
Which equation represents the statement below?
“a is inversely proportional to b.”
A
a =k +b
B
a = kb
C
a=
D
a=
b
k
k
b
10
12
What type of function is
( ) (
f x = 3 x −2
F
G
H
J
13
)
2
+ 1?
Quadratic
Linear
Exponential
Step
Ohm’s Law relates to a simple electric circuit and states:
The resistance is directly proportional to
the voltage and inversely proportional to
the current.
One circuit has a resistance of 8 ohms when the voltage is 48 volts and the
current is 6 amperes. What is the resistance of a second circuit that has a
voltage of 128 volts and a current of 8 amperes?
A
B
C
D
120 ohms
64 ohms
28 ohms
16 ohms
11
14
Which graph best represents the following equation?
y=
−
(
)
2
x −3 − 1
y
5
4
3
2
F
1
-5 -4 -3 -2 -1
O
1
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
-1
-2
-3
-4
-5
y
5
4
3
2
G
1
-5 -4 -3 -2 -1
O
-1
-2
-3
-4
-5
y
5
4
3
2
H
1
-5 -4 -3 -2 -1
O
-1
-2
-3
-4
-5
y
5
4
3
2
J
1
-5 -4 -3 -2 -1
O
-1
-2
-3
-4
-5
12
15
( )
If f x = x 3 + x 2 − 8, what is f
A
B
C
D
16
−
−
( 8) ?
−
568
456
456
568
The table below shows the value of a certain collectible baseball card over
eight years.
Year (x)
1
2
3
4
5
6
7
8
Value (y )
(in dollars)
3
5
9
18
29
43
51
69
Which exponential equation best represents the data?
( )
x
F
y = 2.18 6.1
G
y = 14.8 9.58
H
y = 0.53 1.01
J
y = 2.25 1.59
( )
( )
x
x
( )
x
13
17
What are the first three terms of the sequence defined by the following
equation?
)
(
an = 7 + n − 1 5
18
A
12, 17, 22
B
7, 2,
C
7, 12, 17
D
7, 35, 175
−
3
This table of ordered pairs contains elements of a function of x.
x
y
0
11
1
6
2
3
3
2
4
3
Which equation could define the function?
F
y = − 5 x + 11
G
y = − 2 x + 11
H
y = x −3 +2
( )
y = ( x − 2) + 7
2
2
J
14
19
Which appears to be the graph of a quadratic function?
y
8
7
6
5
4
3
2
1
A
–
2 –1 –O
1
–
2
1 2 3 4 5 6 7 8
x
2 4 6 8 10 12 14 16
x
y
8
7
6
5
4
3
2
1
B
–
4 –2 –O
1
–
2
y
25
20
15
10
C
5
–
25 –20 –15 –10 –5 O
–
5
–
10
–
15
–
20
–
25
5 10 15 20 25
x
1 2 3 4 5
x
y
16
14
12
10
8
6
4
2
D
–
5 –4 –3 –2 –1 –O
2
–
4
15
20
Which lists four consecutive terms of a geometric sequence?
F
G
H
J
21
1, 4, 8, 16
6, 9, 12, 15
12, 48, 192, 768
7, 14, 42, 168
( )
Which is a root of f x = 0 if
( ) (
)(
)
f x = x +5 x −4 ?
A
B
C
D
−
−
5
4
0
5
( )
g ( x ) = 3x
f x = 2x − 1
22
( ( )) is
Given the functions defined above, the composite function g f x
equal to —
F
5x − 1
G
6x − 3
H
6x − 1
J
6x 2 − 3
16
23
y
10
5
x
-15 -10 -5
5
10
15 20
25
-5
-10
-15
-20
Which equation best represents the line of best fit for the data in the
scatterplot above?
24
A
y = 4x − 1
B
y = −x + 4
C
y = − 9x + 3
D
y =x
Assuming the domain is the set of all real numbers, what is the range of the
following function of x ?
y = x2 +2
F
G
H
J
All
All
All
All
integers
real numbers
real numbers greater than or equal to 0
real numbers greater than or equal to 2
17
25
x
4
4.5
5
5.5
6
y
0.5
0.6
0.8
0.9
1.2
Which is most likely the equation of the line of best fit for the data given in
the table?
26
A
y = 0.34 x − 0.9
B
y = 0.25 x − 0.7
C
y = 0.45 x − 1
D
y = 0.50 x − 0.6
Assuming k is a constant of variation, which equation represents a situation
in which y varies jointly as a and b?
F
y = kab
G
y=
ab
H
y=
k
J
y=
k
ab
ka
b
18
27
Which shows the solution to the following inequality?
x −3 > 2
A
B
C
D
28
0
5
10
0
5
10
0
5
10
0
5
10
What is the solution set for the equation below?
x −2
8
F
{2, 8}
G
⎧⎪ 10 ⎫⎪
⎨ ⎬
⎪⎩ 3 ⎪⎭
H
J
−
x −2
x
{ 4}
{6}
19
=
−
1
4
29
What is the solution to the equation?
x +4
x
A
x = −7
B
x = −4
C
x = −1
D
x=
=
14
5
20
3
7
30
What is the apparent solution set for the equation associated with the
following graph?
y
7
6
5
4
3
2
1
-2
-1 O
-1
x
1
-2
F
{ 2, 2}
G
⎧−
⎫
⎪ 1 1⎪
⎨ , ⎬
⎪⎩ 2 2 ⎪⎭
H
⎧− ⎫
⎪ 1⎪
⎨ ⎬
⎪⎩ 4 ⎪⎭
J
−
{ 1, 1}
−
21
2
31
What is the solution for the equation below?
x −6 +5 = 8
32
A
x =9
B
x = 15
C
x = 19
D
x = 65
What is the solution set for the following equation?
x 2 + 6x − 7 = 0
F
G
H
J
{ 1, 7}
{ 2, 3}
{ 3, 2}
{ 7, 1}
−
−
−
−
22
33
What is the solution set for the following equation?
6 = x2 − x
A
⎧⎪ 1 i 23 ⎫⎪
⎨ ±
⎬
2 ⎪⎭
⎪⎩ 2
B
⎧⎪ − 1 i 23 ⎫⎪
⎨ ±
⎬
2 ⎪⎭
⎪⎩ 2
{ 2, 3}
{ 3, 2}
−
C
−
D
34
If
−
6 x + 11 = 4 , then —
F
x=
G
x=
H
x=
J
x=
−
5
2
−
7
6
−
5
2
7
6
−
or x =
6
or x =
5
or x =
7
or x =
7
2
6
5
2
23
35
Which graph best represents the given inequality?
y ≥ x +1
y
5
4
3
2
1
A
–
5 –4 –3 –2 –1 –O
1
–
2
–
3
–
4
–
5
1 2 3 4 5
x
1 2 3 4 5
x
1 2 3 4 5
x
1 2 3 4 5
x
y
B
5
4
3
2
1
–
5 –4 –3 –2 –1 –O
1
–
2
–
3
–
4
–
5
y
C
5
4
3
2
1
–
5 –4 –3 –2 –1 –O
1
–
2
–
3
–
4
–
5
y
D
5
4
3
2
1
–
5 –4 –3 –2 –1 –O
1
–
2
–
3
–
4
–
5
24
36
Which graph best represents the following equation?
y = 2x
y
5
4
3
2
F
1
- 5 - 4 - 3 - 2 -1
O
-1
1
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
-2
-3
-4
-5
y
5
4
3
2
G
1
- 5 - 4 - 3 - 2 -1
O
-1
-2
-3
-4
-5
y
5
4
3
2
H
1
- 5 - 4 - 3 - 2 -1
O
-1
-2
-3
-4
-5
y
5
4
3
2
J
1
- 5 - 4 - 3 - 2 -1
O
-1
-2
-3
-4
-5
25
37
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
O
1
2
3
4
5
6
7
8
9
x
-1
-2
-3
-4
-5
-6
-7
-8
-9
Which appears to be an x-intercept of the graph shown?
A
B
C
D
−
4
0
1
2
26
38
Which graph most closely represents
(
x +2
) (
2
+ y +1
y
5
4
3
2
F
1
5 4 3 2 1O
1
1 2 3 4 5
x
2
3
4
5
y
G
5
4
3
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1 2 3 4 5
x
y
5
4
3
2
H
1
5 4 3 2 1O
1
1 2 3 4 5
x
2
3
4
5
y
J
5
4
3
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1 2 3 4 5
x
27
)
2
= 9?
39
y
7
6
5
4
3
2
1
–
7
–
6
–
5
–
4
–
3
–
2
–
1 O
–
1
2
3
4
5
6
1
–
2
–
3
–
4
–
5
–
6
–
7
Which equation is best represented by the graph?
(
)
2
A
y = x − 3 +1
B
y=
−
C
y=
−
D
y=
−
( x + 3) + 1
( x − 3) − 1
( x − 3) + 1
2
2
2
28
7
x
40
y
5
4
3
2
1
-5 -4 -3 -2 -1
O
1
2
3
4
5
x
-1
-2
-3
-4
-5
Which is an apparent factor of the polynomial graphed above?
F
G
H
J
41
( x − 1)
( x − 2)
( x − 2.5)
( x + 2)
A polynomial function has zeros − 3 and 4. Which is one of the factors of the
polynomial?
A
B
C
D
( x + 1)
( x − 3)
( x + 3)
( x + 4)
29
42
y
5
4
3
2
1
- 5 - 4 - 3 - 2 -1
O
-1
1
2
3
4
5
x
-2
-3
-4
-5
This is a portion of the graph of a conic section. Which equation most likely
represents this graph?
F
y = 2x 2
G
x = 2y 2
H
y = 3x 2
J
x = − 2y 2
30
⎡ 4 5⎤ ⎡ x ⎤ ⎡20 ⎤
⎢
⎥⎢ ⎥ = ⎢ ⎥
⎣ 9 10 ⎦ ⎣ y ⎦ ⎣30 ⎦
43
Which system of linear equations is equivalent to the matrix equation above?
44
A
⎧ 4 x + 9y = 20
⎨
⎩5 x + 10y = 30
B
⎧ 4 x + 5y = 20
⎨
⎩ 9 x + 10y = 30
C
⎧ 4 x + 5 x = 20
⎨
⎩ 9y + 10y = 30
D
⎧ 4 x + 5y = 20
⎨
⎩5 x + 10y = 30
Which matrix is equivalent to
⎡1 1⎤ ⎡1⎤
⎢
⎥ ⎢ ⎥?
1
1
⎣
⎦ ⎣1⎦
F
⎡1⎤
⎢ ⎥
⎣1⎦
G
⎡1
⎢
⎣1
H
⎡2 ⎤
⎢ ⎥
⎣2 ⎦
J
⎡2 2 ⎤
⎢
⎥
⎣2 2 ⎦
1⎤
⎥
1⎦
31
45
Charlie bought jeans, j, and T-shirts, t, at a clothing store. The receipt showed
that a total of seven items was purchased and that the jeans were $28 each
and the T-shirts were $12 each. If he spent a total of $116 before tax, which
system of equations could be used to determine the number of jeans he
purchased?
A
⎧⎪7j + 12t = 28
⎨
⎩⎪ j + t = 116
B
⎧⎪28 j + 12t = 116
⎨
⎩⎪ j + t = 7
C
⎧⎪28 j + 12t = 7
⎨
⎩⎪ j + t = 116
D
⎧⎪12 j + 28t = 116
⎨
⎩⎪ j + t = 7
⎧
−
⎪y ≥ x −6
⎪
⎪ y ≤ x +2
⎨
⎪
11
⎪
x −6
⎪y ≥
3
⎩
46
What are the corner points of the feasibility region for the given system of
inequalities?
⎛ 1 −1 ⎞
2, 4 , 0, 2 , ⎜ ,
⎟
⎝ 2 2⎠
4, − 2 , 0, − 6 , 3, 5
) (
)
F
(
−
G
(
−
H
(
⎛1
0, − 2 , 1, − 1 , ⎜ ,
⎝2
J
(
−
−
−
) (
) (
⎛3
2, − 4 , ⎜ ,
⎝2
)
) ( )
)
−
−
1⎞
⎟
2⎠
1⎞
⎟ , 2, 0
2⎠
( )
32
47
y
5
4
3
2
1
- 5 - 4 - 3 - 2 -1
O
-1
1
2
3
4
5
x
-2
-3
-4
-5
Which system of inequalities is best represented by the graph above?
A
⎧x ≥ 0
⎪
⎨y ≤ 3
⎪y ≤ 4 − 2 x
⎩
B
⎧x ≥ 0
⎪
⎪y ≥ 0
⎨
⎪y ≤ 3
⎪⎩y ≥ 4 − 2 x
C
⎧x ≥ 0
⎪
⎨y ≥ 0
⎪y ≤ 4 − 2 x
⎩
D
⎧x ≥ 0
⎪
⎪y ≥ 0
⎨
⎪y ≤ 3
⎪⎩y ≤ 4 − 2 x
33
⎧⎪y = x 2 + 6 x + 1
⎨
⎪⎩y = − 2 x − 14
48
What is the solution set for the given system of equations?
F
G
H
J
49
{( 3, 8),( 5, 4)}
{( 7, 0),(0,1)}
{( 5, 4),(0,1)}
{( 3, 8)}
−
−
−
−
−
−
−
−
−
Which is the apparent solution set to the system of equations shown on
the graph?
y
13
12
11
10
9
8
7
6
5
4
3
2
1
-2 -1
O
1
2
-1
A
B
C
D
{(3, 9),( 1, 9)}
{(0,3),(0,5)}
{( 1, 9),(1,1)}
{( 1, 9)}
−
−
−
34
3
4
x
⎡ 5 10 ⎤
⎡25 30 ⎤
Given: A = ⎢
⎥ and B = ⎢
⎥
⎣25 30 ⎦
⎣ 5 10 ⎦
50
Which matrix is the product B × A ?
F
⎡175 250 ⎤
⎥
⎢
⎣775 1, 050 ⎦
G
⎡250 600 ⎤
⎥
⎢
⎣ 425 1, 050 ⎦
H
⎡125 300 ⎤
⎢
⎥
⎣125 300 ⎦
J
⎡875 1,150 ⎤
⎥
⎢
⎣275 350 ⎦
35
Answer Key-EOC041-M0117
Test Sequence
Number
Correct Answer
1
C
2
F
3
C
4
J
5
C
6
F
7
D
8
F
9
C
10
G
11
D
12
F
13
D
14
J
15
B
16
J
17
C
18
H
19
A
20
H
21
A
22
G
23
B
24
J
25
A
26
F
27
A
28
H
29
A
30
G
31
B
32
J
33
C
34
J
35
D
36
G
37
D
38
F
39
D
40
F
41
C
42
J
43
B
44
H
45
B
46
G
47
D
48
F
49
C
50
J
Reporting
Category
001
001
001
001
001
001
001
001
001
001
002
002
002
002
002
002
002
002
002
002
002
002
002
002
002
002
003
003
003
003
003
003
003
003
003
003
004
004
004
004
004
004
005
005
005
005
005
005
005
005
Reporting Category Description
Expressions and Operations
Expressions and Operations
Expressions and Operations
Expressions and Operations
Expressions and Operations
Expressions and Operations
Expressions and Operations
Expressions and Operations
Expressions and Operations
Expressions and Operations
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Relations and Functions
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Equations and Inequalities
Analytical Geometry
Analytical Geometry
Analytical Geometry
Analytical Geometry
Analytical Geometry
Analytical Geometry
Systems of Equations/Inequalities
Systems of Equations/Inequalities
Systems of Equations/Inequalities
Systems of Equations/Inequalities
Systems of Equations/Inequalities
Systems of Equations/Inequalities
Systems of Equations/Inequalities
Systems of Equations/Inequalities
Algebra II, Core 1
If you get this
many items
correct:
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
42
43
44
45
46
47
48
49
50
Then your
converted scale
score is:
000
163
200
222
238
252
262
272
281
288
295
302
308
314
320
326
331
336
341
346
351
355
360
365
369
374
378
383
388
392
397
402
407
412
417
423
428
434
440
446
453
460
468
477
487
498
511
528
550
587
600