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Subject: MA, Grade: HS
CST High School Algebra II Part 1
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Author: California
District: California Released Tests
Printed: Wednesday January 15, 2014
CST High School Algebra II Part 1
1 What is the complete solution to the equation
|3 − 6x| = 15 ?
A
B
C
D
x = 2; x = 3
x = −2; x = 3
x = 2; x = −3
x = −2; x = −3
2 What are the possible values of x in
|12 − 4x| = 2 ?
A
B
C
D
x = −2.50 or x = −3.50
−3.50 < x < −2.50
MA:HS
5 A restaurant manager bought 20 packages of
bagels. Some packages contained 6 bagels each,
and the rest contained 12 bagels each. There were
168 bagels in all. How many packages of 12 bagels
did the manager buy?
A
B
C
D
6
8
9
12
6 What system of inequalities best represents the
graph shown below?
3.5 > x > 2.5
x = 2.50 or x = 3.50
3 For a wedding, Shereda bought several dozen roses
and several dozen carnations. The roses cost $15
per dozen, and the carnations cost $8 per dozen.
Shereda bought a total of 17 dozen flowers and
paid a total of $192. How many roses did she buy?
A
B
C
D
6 dozen
7 dozen
8 dozen
9 dozen
4 What is the solution to the system of equations
shown below?

 2x − y + 3z = 8
x − 6y − z = 0

−6x + 3y − 9z = 24
A
B
C
D
Page 1
(0, 4, 4)
1, 4,
10
3
no solution
infinitely many solutions
A
B
C
D
y > −2 and y > x + 1
y > −2 and y < x + 1
y < −2 and y > x + 1
y < −2 and y < x + 1
7 Which
point lies in the solution set for the system
2y − x ≥ −6
2y − 3x < −6
A
B
C
D
?
(-4, -1)
(3, 1)
(0, -3)
(4,3)
Go On
CST High School Algebra II Part 1
8 Which system of linear inequalities is represented
MA:HS
10
by this graph?
A
B
C
D
x3 + 7x2 − 7x + 6 −
2x3 + 14x2 − 14x + 12 −
4
2x + 7
x3 + 7x2 − 7x + 6 +
4
2x + 7
polynomial
(3x2 + x − 4) (2x − 5) ?
A
B
C
D
y ≥ 12 x + 3
y ≥ x − 2
y ≥ 2x + 3
y ≤ x − 2
Page 2
6x3 + 13x2 + 3x − 20
6x3 + 13x2 + 3x + 20
12 (−2x2 + 6x + 1) − 2 (4x2 − 3x + 1) =
2x + y ≥ 3
x − y ≥ 2
13 Which
A
B
C
D
6x3 − 13x2 − 13x + 20
2x − y ≥ 3
x + y ≤ 2
equations?
2x − 3y = 4
4x + y = −6
represents
6x3 − 13x2 − 13x − 20
A
B
C
D
9 What is the solution to the following system of
4
2x + 7
x3 − 7x2 + 7x − 6 +
11 Which
A
B
C
D
4
2x + 7
6x2 − 1
−10x2 − 1
6x2 + 12x − 1
−10x2 + 12x − 1
expression
(6y 2 − 2) (6y + 2) ?
A
B
C
D
is
equivalent
36y 2 − 4
36y 3 − 4
36y 2 + 12y 2 + 12y − 4
36y 3 + 12y 2 − 12y − 4
(5,-2)
(-2, 5)
(-1,-2)
(-2,-1)
Go On
to
CST High School Algebra II Part 1
14 What is the volume of the figure below?
MA:HS
17 The total area of a rectangle is 4x4 − 9y2 ? Which
factors could represent the length times width?
A
B
C
D
(2x2 − 3y) (2x2 + 3y)
(2x2 + 3y) (2x2 + 3y)
(2x − 3y) (2x − 3y)
(2x + 3y) (2x − 3y)
18 Which product of factors is equivalent to
(x + 1)2 − y 2 ?
A
B
C
D
x3 + 10x2 + 34x + 24
A
B
C
D
x3 + 11x2 + 34x + 24
x3 + 10x2 + 24x + 24
3
2
x + 11x + 24x + 24
15 What is (5x3 − 2x) (3x2 + x − 8) ?
A
B
C
D
16
3
A
B
C
D
2
15x + 5x − 46x − 2x + 16x
15x6 − 35x3 − 6x2 + 14x
3
(x − 1 + y) (x − 1 − y)
(x + 1 + y) (x + 1 − y)
tion of 12x2 − 147 ?
15x5 − x4 − 42x3 + 16x
4
(x + 1 − y)2
19 Which expression shows the complete factoriza-
5x3 + 3x2 − x − 8
5
(x + 1 + y)2
(3x − 7) (4x + 2)
(4x − 21) (3x + 7)
12 (x − 7) (x + 7)
3 (2x − 7) (2x + 7)
3
8a + c =
A
B
C
D
Page 3
(2a + c) (2a + c) (2a + c)
(2a − c) (4a2 + 2ac + c2 )
(2a − c) (4a2 + 4ac + c2 )
(2a + c) (4a2 − 2ac + c2 )
20
25x2 − 40xy + 16y 2
A
B
C
D
(5x − 4y)2
(5x + 10 − 4y)3
5 (5x − 4y)2
5 (4xy)2
Go On
CST High School Algebra II Part 1
x+3
x+5
21
A
B
x2 + x
x2 + 3x −10
C
x2 + x + 12
x2 + 3x −10
D
x2 + x + 1
x2 + 3x −10
+
6
x2 + 3x − 10
2
24 Which product is equivalent to 4x2 −−x16 ?
=
A
B
C
D
7x − 9
x2 + 3x −10
22 Which is a simplified form of
A
B
C
D
MA:HS
3a2 b3 c−2
(a−1 b2 c)3
?
−4
C
D
25y 3
18x
25
18xy 7
−4 (x − 2)
−4 (x + 2)
x2 + 4x
x+3
8x−3
15y −5
x2 − 9
x2 + x − 12
=
26 What is the simplest form of
?
5x3 y + 20x2 y 2 + 20xy 3
5xy
A
B
C
D
(x + 2)2
(x + 2y)2
x2 + y 2
x2 + 4y 2
2x2 − 10x
x2 + 8x + 16
27
Page 4
·
A 1
B x
C x + 4
D xx −+33
23 What is 20x
÷
27y 2
32y 3
81x
32
81xy 7
4 (x + 2)
25
3a5
b3 c5
3ab
c5
3
b2 c5
3
ab3 c5
A
B
4 (x − 2)
A
8x
(x + 4)(x − 5)
B
2x + 4
(x + 4)(x −+ 5)
C
8x
(x + 4)(x + 5)
D
2x + 4
x2 + 20
·
4x + 16
x2 − 25
=
Go On
CST High School Algebra II Part 1
4(x + y)
5x2 y 3
28
A −
B
−2x − 2y
10
=
31 Which of the following complex numbers is
represented by the point on the graph below?
4
x2 y 3
4
x2 y 3
C −
D
÷
MA:HS
4(x + y)
x2 y 3 (x − y)
4(x + y)2
5x2 y 3
√
−1 , which point shows the location of
5 − 2i on the plane?
29 If i =
A
B
C
D
4 + 3i
4 − 3i
3 − 4i
3 + 4i
32 If i =
A
B
C
D
point A
point B
point C
√
Page 5
−1 , then 4i (6i) =
48
24
-24
-48
point D
30 If i = −1 , what is the value of i4 ?
A
B
C
D
A
B
C
D
√
i
-i
1
33 What is an equivalent form of 3 +2 i ?
A
B
C
D
3−i
4
3−i
5
4−i
4
4−i
5
-1
Go On
CST High School Algebra II Part 1
MA:HS
34 What is the product of the complex numbers
38 What are the solutions to the equation x2 + 2x +
(3 + i) and (3 − i) ?
2 = 0?
A
B
C
D
A
B
C
D
8
10
9–i
10 – 6 i
√
−1 and a and b are non-zero real
=
numbers, what is a +1 bi ?
35 If i
A
B
C
D
39 What are the solutions to the equation
1 +
1
x2
=
3
x
3
2
+
B x = 3 +
a + bi
a2 − b2
C x =
a − bi
a2 − b2
D x = 3 +
−
−8 − 3i
−8 − i
2 − i
2 − 3i
(12 − 5i) and (−3 + 4i) ?
9–i
15 − 9i
3
2
?
√
a − bi
a2 + b2
37 What is the sum of the complex numbers
Page 6
x = −1 + i; x = −1 − i
√
√
x = −1 + 2 2; x = −1 − 2 2
A x =
(−5 + i) ?
A
B
C
D
x = 0; x = −2i
a + bi
a2 + b2
36 Which expression represents (−3 − 2 i)
A
B
C
D
x = 0; x = −2
+
√
5
5
3
;
x
=
−
2
2
2
√
√
5
5
;
x
=
3
−
2
2
√
√
13
; x = 23 − 213
2
√
√
13
13
;
x
=
3
−
2
2
40 There are two numbers with the following
properties.
1) The second number is 3 more than the first
number.
2) The product of the two numbers is 9 more than
their sum.
Which of the following represents possible values
of these two numbers?
A
B
C
D
−6, −3
−4, −1
−1, 4
−3, 6
−16 + 63i
9 − 9i
Go On
CST High School Algebra II Part 1
41 Jenny is solving the equation x2 − 8x = 9
by completing the square. What number should be
added to both sides of the equation to complete the
square?
A
B
C
D
2
4
8
16
MA:HS
45 Which of the following sentences is true about
the graphs of y = 3 (x − 5)2
y = 3 (x + 5)2 + 1 ?
+
1 and
A Their vertices are maximums.
B The graphs have the same shape with different
vertices.
C The graphs have different shapes with different
vertices.
D One graph has a vertex that is a maximum,
42 Two consecutive positive integers have the property that one integer times twice the other equals
612. What is the sum of these two integers?
while the other graph has a vertex that is a
minimum.
46 What are the x -intercepts of the graph of y =
A
B
C
D
33
35
37
39
43 What are the solutions to the equation x2 − 6x +
12x2 − 5x − 2 ?
A 1 and 16
B −1 and 16
C 23 and − 14
D − 23 and 14
5 = −8 ?
A
B
C
D
2 and 3
2i and 3i
3 + 2 · 3 and 3 − 2 · 3
3 + 2i and 3 − 2i
44 Which of the following most accurately describes
the translation of the graph y = (x + 3)2 − 2
to the graph of y = (x − 2)2 + 2 ?
A
B
C
D
Page 7
up 4 and 5 to the right
down 2 and 2 to the right
down 2 and 3 to the left
up 4 and 2 to the left
Go On
CST High School Algebra II Part 1
MA:HS
47 Which is the graph of y = −2 (x − 1)2 + 1 ?
A
C
B
D
48 Which ordered pair is the vertex of
f (x) = x2 + 6x + 5 ?
A
B
C
D
Page 8
(−3, −4)
(−2, −3)
(−1, 0)
(0, −5)
STOP