A
y
=
x
2
B
y
=
2
x
C
x
=
y
2
D
x
=
2
y
CST00516
57
Which is the first
incorrect
step in simplifying
4
log
4
?
64
4
Step 1
:
log
4
=
log
4
4
−
log
4
64
64
Step 2
:
=
−
1
16
Step 3
:
=
−
15
A
Step 1
B
Step 2
C
Step 3
D
Each step is correct.
CST00517
CALIFORNIA STANDARDS TEST
—
17
—
This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected
based on performance on released test questions. Copyright © 2009 California Department of Education.

Released Test Questions
Algebra II
58
Jeremy, Michael, Shanan, and Brenda
each worked the same math problem at
the chalkboard. Each student’s work is
shown below. Their teacher said that while
two of them had the correct answer, only
one of them had arrived at the correct
conclusion using correct steps.
Jeremy’s work
Shanan’s work
3
−
7
x
3
3
−
7
x
3
x x
=
x x
=
−
7
7
x
x
=
x
10
,
x
≠
0
=
1
4
,
x
≠
0
x
Michael’s work
Brenda’s work
3
−
7
x
3
3
−
7
x
3
x x
=
x x
=
−
7
7
x
x
=
x
−
4
,
x
≠
0
=
4
,
≠
0
x
x
Which is a completely correct solution?
A
Jeremy’s work
B
Michael’s work
C
Shanan’s work
D
Brenda’s work
CST10301
59
A student showed the following steps in his
solution of the equation below, but his answer
was not correct.
log
5
(
2
x
2
−
3
x
+
1
)
−
log
5
(
x
−
1
)
+
log
5
125
=
6
Step 1
:
log
5
(
2
x
−
1
)(
x
−
1
)
−
log
5
(
x
−
1
)
+
=
3
6
Step 2
:
log
5
(
2
x
−
1
)(
x
−
1
)
−
log
5
(
x
−
1
)
=
3
Step 3
:
log
5
(
x
−
1
)
=
3
Step 4
:
x
−
=
1
125
Step 5
:
x
=
126
In which step did he make his first error?
A
Step 1
B
Step 2
C
Step 3
D
Step 4
CST10336
60
Which is the first
incorrect
step in simplifying
(
)
3
x
2
−
(
)
−
1
x
5
?
1
S ep 1:
(
)
3
−
t
x
2
−
(
)
x
5
=
x
6
−
x
−
5
1
Step 2:
=
x
6
−
x
5
x
6
Step 3:
=
x
5
Step 4:
=
x
A
Step 1
B
Step 2
C
Step 3
D
Step 4
CST00139
CALIFORNIA STANDARDS TEST
—
18
—
This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected
based on performance on released test questions. Copyright © 2009 California Department of Education.

Released Test Questions
Algebra II
CALIFORNIA STANDARDS TEST
61
A certain radioactive element decays over
time according to the equation
t
⎛
1
⎞
y
=
A
⎜
⎟
300
⎜
⎟
,
⎝
⎜
2
⎠
⎟
where A = the number of grams present
initially and
t
= time in years. If 1000 grams
were present initially, how many grams will
remain after 900 years?
A
500 grams
B
250 grams
C
125 grams
D
62.5 grams
CST00367
62
Bacteria in a culture are growing exponentially
with time, as shown in the table below.
Bacteria Growth
Day
Bacteria
0
100
1
200
2
400
Which of the following equations expresses the
number of bacteria,
y
, present at any time,
t
?
A
y
=
+
100
2
t
B
y
=
(
)
100
i
( )
t
2
C
y
=
2
t
t
D
y
=
(
)
200
i
(
2
)
CST10253
63
If the equation
y
=
2
x
is graphed, which of
the following values of
x
would produce a point
closest to the
x
-axis?