VIRGINIA STANDARDS OF LEARNING
Spring 2010 Released Test
END OF COURSE
ALGEBRA II (2001 Revised)
Form M0110, CORE 1
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Algebra II Formula Sheet
Geometric Formulas
b
h
l
h
h
h
b
A=
1
2
b
bh
A = bh
s
l
V = lwh
S.A.= 2(lw + lh + wh)
r
A=
1
2
h
h
h
p = 4s
A = s2
1
3
w
b1
s
r
B
V = 13 Bh
S.A.= 12 lp + B
b2
h(b1 + b2 )
w
l
c
a
r
b
l
c2
p = 2(l + w)
A = lw
=
a2
+ b2
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 each question and choose the best answer. For this test you may assume that the value
of the denominator is not zero.
SAMPLE
6(a + 2)
a
A
B
C
D
i
a3 =
a +2
6
a2
6(a + 2)
a
6 a2
6 a2 + 24 a + 24
a4
3
1
For non-zero denominators, which of the following is equivalent
to
A
B
C
D
2
3 a3 − 75 a
?
a(a + 5)(a + 5)
−
−
3
1
a2
(a − 5)
(a + 5)
3(a − 5)
(a + 5)
What is the factored form of x2 − 36 z2 ?
F
G
H
J
(x + 6 z )(x − 6 z )
(x + z )(x − 36 z )
(x + 6 z )2
(x − 6 z )2
4
3
Which of these is equivalent to 1 ?
A
B
C
D
4
Which complex number is equivalent to (7 − 9i) − (−1 + 3i) ?
F
G
H
J
5
i24
i 42
i 66
i 82
6 − 6i
6 − 12i
8 − 6i
8 − 12i
What is the simplified form of
A
B
C
D
6 i 21 ?
3 14
14 3
21
63
5
6
−
−
The equation (2cos 1θ − 17π)(1) = 2 cos 1θ − 17π is an example of which
property of real numbers?
F
G
H
J
7
Associative property
Transitive property
Identity property
Reflexive property
Which expression is equivalent to
5
32 x10 y2 ?
2
A
2x2 y5
B
2x5 y
C
32 2 2
x y
5
D
32 50 10
x y
5
−
1
3
5
6
8
Which is equivalent to 13 −
F
G
H
J
9
−
81 ?
4
13 − 9i
13 + 9i
22
Which property would justify the following statement?
If x + 2 = y and y = 20 , then x + 2 = 20.
A
B
C
D
Distributive property
Reflexive property of equality
Symmetric property of equality
Transitive property of equality
7
10
11
2 x8
5y
Which expression is equivalent to
, where x ≠ 0 and y ≠ 0 ?
4 x2
25 y3
F
2x8 5 y
i
4 x 2 25 y3
G
2 x 8 25 y3
i
5 y 4 x2
H
2x8 4 x2
i
5 y 25 y3
J
4 x2 5 y
i
25 y3 2 x 8
Using an = a1 r n−1 , what is the 10th term in this geometric sequence?
0.2 , 1, 5, 25, 125, . . .
A
B
C
D
78,125
390,625
1,953,125
9,765,625
8
12
If f (x) = 2 x2 − 7 x , what is the value of f (− 4) ?
F
G
H
J
13
−
−
44
4
60
92
Given: f (x) = (x − 4)2 − 1
What is the vertex of the graph for this function?
A
(− 4, −1)
B
(− 4, 1)
C
( 4, −1)
D
( 4, 1)
9
14
The graph shown most accurately represents which of the
following functions?
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
-3
-4
-5
-6
-7
-8
-9
⎛ ⎞x
⎝2⎠
F
f (x ) = −⎜⎜ 1 ⎟⎟⎟
G
⎛ 1 ⎞⎟x
f (x ) = ⎜⎜ ⎟⎟
⎝2⎠
H
f (x ) = − 2 x
J
f (x ) = 2 x
10
2
3
4
5
6
7
8
9
x
15
Given: Sn =
1 ⎡
n 2 a + (n − 1) d ⎤⎦
2 ⎣ 1
An outdoor theater has 37 seats in the first row, 40 seats in the second row,
and 43 seats in the third row. If this pattern continues, what is the total
number of seats in the first 10 rows?
A
B
C
D
16
120
320
505
520
The graph of a 4th-degree polynomial is shown.
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
2
3
4
5
6
7
8
9
x
-3
-4
-5
-6
-7
-8
-9
Exactly how many real zeros does this function have?
F
G
H
J
1
2
3
4
11
17
3
What is the value of ∑ (17n − 15) ?
n=1
A
B
C
D
18
2
19
36
57
Which of the following equations best models the data in this table?
x
F
⎛ 4 ⎞⎟x
y = 2 ⎜⎜⎜ ⎟⎟
⎝5⎠
G
y = x2 + 1
H
−
y = 3 x +2
J
y = 1 x2 − x + 1
y
–2
5
– 0.5
2
0
1
1.5
0.5
2.5
1.5
3
2.5
4
2
12
19
The time it takes to do a job is inversely proportional to the number of
workers. If 8 workers can do a job in 6 days, then 16 workers can do the
same job in —
A
B
C
D
20
1.5 days
3 days
6 days
12 days
What type of function is y = 2 x + 8 ?
F
G
H
J
Exponential
Quadratic
Linear
Step
13
21
The graph most accurately represents which of the following functions?
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
2
3
4
5
6
7
8
9
x
-3
-4
-5
-6
-7
-8
-9
22
A
y = x +3 +2
B
y = x −3 + 2
C
y = x −2 + 3
D
y = x +2 +3
The graph of y = 4 x − 11 is translated up 8 units. Which equation represents
the translated graph?
F
G
H
J
y = 4 x − 19
y = 12 x − 3
y = 12 x − 11
y = 4x − 3
14
23
Which equation represents the statement
“r is inversely proportional to s and directly proportional to the cube of t”?
A
B
C
D
24
3
r = kt3
s
k
r= 3
st
ks
r= 3
t
3
r = kt
s
Which equation best represents the data in this table?
F
y = ln x
G
y= 1x
H
−
y = 1 x2 + 2x − 1
J
y = x +1
x
y
0.5
1
1.5
2
3
– 0.75
0
0.5
0.75
1
2
2
15
25
Given f (x) = − 3 x + 4 and g(x) = x + 7, what is the value of g( f (2)) ?
A
B
C
D
26
−
23
18
5
7
Which lists four consecutive terms of an arithmetic sequence?
F
G
H
J
27
−
3, 10, 17, 24
1, 4, 9, 16
1, 2, 4, 8
−
5, 6, 10, 13
What are all the roots for the equation 3 w − 14 − 6 = 21 ?
A
B
C
D
19
23
5 and 23
9 and 19
16
28
29
Which graph best represents the solutions to the inequality 3 x − 7 ≤ 5 ?
F
-5 -4 -3 -2 -1 0
1
2
3
4
5
G
-5 -4 -3 -2 -1 0
1
2
3
4
5
H
-5 -4 -3 -2 -1 0
1
2
3
4
5
J
-5 -4 -3 -2 -1 0
1
2
3
4
5
What is the solution set for
A
B
C
D
k + 64 − 8 = −2 ?
{ 28}
{ 124}
{ 4}
{}
−
−
17
30
31
What is the solution set of the equation x2 − 2 x + 5 = 0 ?
F
{ − 3, 1 }
G
{ −1, 3 }
H
{ 1 − 2i, 1 + 2i }
J
{ −1 − 2i, −1 + 2i }
What is the solution to
A
B
C
D
32
3
x − 4 = −5 ?
x = −121
x = −1
x = 29
x = 129
Which is the solution set for (x + 5)2 = 0 ?
F
{ 25 }
G
{5}
H
{ −5 }
J
{ − 5, 5 }
18
33
What is the solution set for
A
B
C
D
34
5 2 8
− = if x ≠ 0 ?
3 x
x
{2}
{ 185 }
{ 265 }
{6}
Which of the following represent the solutions to 4 x + 9 > 11 ?
F
x < − 5 or x > 1
G
−
H
−
x < 1 or x > 5
J
2
5< x <
1
2
2
−
1
< x <5
2
19
35
What is the solution set of
A
B
36
2x + 7 = 6 ?
⎪⎧ 5 ⎪⎫
⎨ ⎬
⎪⎪⎩ 2 ⎪⎪⎭
⎪⎧ 19 ⎪⎫
⎬
⎨
⎪⎪⎩ 2 ⎪⎪⎭
C
⎧⎪ 29 ⎫⎪
⎬
⎨
⎪⎪⎩ 2 ⎪⎪⎭
D
⎧⎪ 43 ⎫⎪
⎬
⎨
⎪⎪⎩ 2 ⎪⎪⎭
What is the solution set of 2 x2 + 7 x + 5 = 0 ?
F
G
H
J
⎧⎪ −
⎨ 5,
⎪⎪⎩
−
1 ⎫⎪
⎬
2 ⎪⎪⎭
⎪⎧ − 5 − ⎫⎪
⎨ , 1⎬
⎪⎪⎭
⎪⎪⎩ 2
⎧⎪
5 ⎪⎫
⎨ 1, ⎬
⎪⎪⎩
2 ⎪⎪⎭
⎫⎪
⎧⎪ 1
⎨ , 5⎬
⎪⎪⎭
⎪⎪⎩ 2
20
37
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
2
3
4
5
6
7
8
9
x
-3
-4
-5
-6
-7
-8
-9
Which best represents the equation of the graphed conic section?
A
B
x 2 + y2 = 1
16
9
x 2 − y2 = 1
16
9
C
x 2 + y2 = 1
D
x 2 − y2 = 1
9
9
16
16
21
38
Which graph most likely represents a function with a zero of 5 ?
y
7
6
5
4
3
2
F
1
-7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
x
-3
-4
-5
-6
-7
y
7
6
5
4
3
2
G
1
-7 -6 -5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
-6
-7
y
7
6
5
4
3
2
H
1
-7 -6 -5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
-6
-7
y
7
6
5
4
3
2
J
1
-7 -6 -5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
-6
-7
22
39
Which is a zero of the function f (x) = (x + 3)(2 x − 1)(x + 2) ?
A
B
C
D
40
3
0
−
1
−
2
What are the coordinates of the vertex of the graph of the
function
−
2(x − 1)2 = y + 5 ?
F
(−1, 5)
G
(2, 5)
H
(1, − 5)
J
( − 2, − 5)
23
41
42
A polynomial function has a zero at x = 3. Which of the following expressions
must be one factor of the polynomial?
A
(x − 3)
B
(x + 3)
C
3x
D
x3
Where does the graph of f (x) = (3 x − 5)(x + 9) cross the x-axis?
F
⎛ 5 ⎞⎟
⎜⎜ , 0 ⎟ and ( − 9, 0)
⎜⎝ 3 ⎟⎠
G
⎛ 5 ⎞⎟
⎜⎜ , 0 ⎟ and ( − 3, 0)
⎜⎝ 3 ⎟⎠
H
⎛ − 5 ⎞⎟
⎜⎜
⎜⎝ 3 , 0 ⎟⎟⎠ and ( 9, 0)
J
⎛ − 5 ⎞⎟
⎜⎜
, 0 and ( − 45, 0)
⎜⎝ 3 ⎟⎟⎠
24
43
⎡ −7
If M = ⎢
⎢ 0
⎣
1 ⎤⎥
, which matrix represents M 2 ?
⎥
3⎦
4 ⎤⎥
9 ⎥⎦
A
⎡ 49
⎢
⎢ 0
⎣
B
⎡ −14
⎢
⎢ 0
⎣
2 ⎤⎥
6 ⎥⎦
C
⎡ 49
⎢
⎢⎣ 0
1⎤
⎥
9 ⎥⎦
D
⎡ −14
⎢
⎢ 0
⎣
2 ⎤⎥
9 ⎥⎦
−
25
44
y
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
1
2
3
4
5
x
-2
-3
-4
-5
Apparently, the system of equations graphed above has —
F
G
H
J
45
exactly 1 solution
exactly 2 solutions
exactly 3 solutions
no solutions
The dimensions of matrix P are 6 × 5. The dimensions of matrix Z are 5 ×1.
What are the dimensions of matrix PZ ?
A
B
C
D
30 × 5
6 ×1
5 ×5
1× 6
26
46
47
⎡ 4
If P = ⎢ −
⎢ 2
⎣
F
⎡ 110
⎢
⎢ − 50
⎣
G
⎡ 20
⎢
⎢⎣ − 7
H
⎡
⎢
⎢⎣
5
5
J
⎡
⎢
⎢
⎣
5
0
−
−
⎡ 20
3 ⎤⎥
and P i Q = ⎢ −
⎢ 10
1 ⎥⎦
⎣
−
30 ⎤⎥
, then what is the value of Q ?
12 ⎥⎦
156 ⎤⎥
72 ⎥⎦
30 ⎤
⎥
9 ⎥⎦
−
10 ⎤
⎥
12 ⎥⎦
−
3 ⎤⎥
6 ⎥⎦
What is the solution set for the following system of equations?
⎪⎧⎪ x2 + y2 = 5
⎨
⎪⎪⎩ x + y = 1
A
B
C
D
{ (1, − 2), (1, 2) }
{ (− 2, 1), (2, 1) }
{ (−1, − 2), (1, 2) }
{ (−1, 2), (2, −1) }
27
48
What appears to be the maximum value of P = 5 x + 6 y for the feasible region
in the graph?
y
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
F
G
H
J
49
1 2 3 4 5 6 7 8 9 10111213141516
x
72
74
78
80
Which ordered pair represents a solution to the following system
of inequalities?
⎧⎪⎪ 2 x + 4 y ≤ 12
⎨
⎪⎪⎩ 3 x − y < 2
A
(6, 4 )
B
(2, 6 )
C
(− 3, 2)
D
(− 4, −14 )
28
50
⎡ 4
The matrix equation ⎢⎢ −
⎣ 1
linear equations?
F
⎪⎧⎪ 4 x − y = − 2
⎨−
⎪⎪ 3 x + y = 6
⎩
G
⎧⎪ 4 x − 3 y = − 2
⎪⎨
⎪⎪ − x + y = 6
⎩
H
⎪⎧⎪ 4 x + 3 y = − 2
⎨−
⎪⎪ x − y = 6
⎩
J
⎧⎪ 4 x + y = − 2
⎪⎨
⎪⎪ − x − 3 y = 6
⎩
3 ⎤⎥ ⎡⎢ x ⎤⎥ ⎡⎢ −2 ⎤⎥
=
represents which system of
1 ⎥⎦ ⎢⎢⎣ y ⎥⎥⎦ ⎢⎣ 6 ⎦⎥
−
29
Answer Key-EOC041-M0110
Test Sequence
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
43
44
45
46
47
48
49
50
Correct Answer
D
F
A
J
A
H
A
G
D
G
B
H
C
G
C
G
D
J
B
F
B
J
D
F
C
F
C
G
A
H
A
H
D
F
C
G
C
F
D
H
A
F
A
G
B
J
D
H
C
G
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 (2001 Revised),
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
168
204
226
242
255
266
275
284
291
298
305
311
317
322
328
333
338
343
347
352
357
361
366
370
375
379
383
388
393
397
402
406
411
416
421
427
432
438
444
451
458
465
474
483
494
507
523
545
581
600
A total raw score (left column) is
converted to a total scaled score
(right column). The total scaled
score may range from 0 to 600.
A scaled score of 400 or more
means the student passed the
SOL test, while a scaled score of
399 or less means the student
did not pass the test. A scaled
score of 500 or more indicates
the student passed the SOL test
at an advanced level.