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Integrated
Math II
CALIFORNIA STANDARDS TEST
INTEGRATED MATHEMATICS 2
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS
Algebra I
3.0 Students solve equations and inequalities involving
absolute values.
9.0* Students solve a system of two linear equations in two
variables algebraically and are able to interpret the answer
graphically. Students are able to solve a system of two
linear inequalities in two variables and to sketch the
solution sets.
15.0* Students apply algebraic techniques to solve rate
problems, work problems, and percent mixture problems
16.0 Students understand the concepts of a relation and a
function, determine whether a given relation defines a
function, and give pertinent information about given
relations and functions.
17.0 Students determine the domain of independent variables
and the range of dependent variables defined by a graph,
a set of ordered pairs, or a symbolic expression.
18.0 Students determine whether a relation defined by a graph,
a set of ordered pairs, or a symbolic expression is a
function and justify the conclusion.
21.0* Students graph quadratic functions and know that their
roots are the x-intercepts.
22.0 Students use the quadratic formula or factoring techniques
or both to determine whether the graph of a quadratic
function will intersect the x-axis in zero, one, or two points.
23.0* Students apply quadratic equations to physical problems,
such as the motion of an object under the force of gravity.
*
**
# of
Items
%
20
31%
1
5
4
1/2**
1
1/2**
3
1
3
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years;
1/3 = rotated every three years)
© California Department of Education
1
CALIFORNIA STANDARDS TEST
INTEGRATED MATHEMATICS 2
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS
Standard Set 24.0 Students use and know simple aspects
of a logical argument:
24.1 Students explain the difference between inductive and
deductive reasoning and identify and provide examples of
each.
24.2 Students identify the hypothesis and conclusion in logical
deduction.
24.3 Students use counterexamples to show that an assertion
is false and recognize that a single counterexample is
sufficient to refute an assertion.
Geometry
1.0* Students demonstrate understanding by identifying and
giving examples of undefined terms, axioms, theorems,
and inductive and deductive reasoning.
2.0* Students write geometric proofs, including proofs by
contradiction.
3.0* Students construct and judge the validity of a logical
argument and give counterexamples to disprove a
statement.
4.0* Students prove basic theorems involving congruence and
similarity.
5.0 Students prove that triangles are congruent or similar, and
they are able to use the concept of corresponding parts of
congruent triangles.
7.0* Students prove and use theorems involving the properties
of parallel lines cut by a transversal, the properties of
quadrilaterals, and the properties of circles.
13.0 Students prove relationships between angles in polygons
by using properties of complementary, supplementary,
vertical, and exterior angles.
14.0* Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to determine
distance and find missing lengths of sides of right
triangles.
*
**
# of
Items
%
1/3**
1/3**
1/3**
40
61%
2
3
4
5
2
5 2/3**
2
1/3**
2
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years;
1/3 = rotated every three years)
© California Department of Education
2
CALIFORNIA STANDARDS TEST
INTEGRATED MATHEMATICS 2
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS
16.0* Students perform basic constructions with a straightedge
and compass, such as angle bisectors, perpendicular
bisectors, and the line parallel to a given line through a
point off the line.
18.0* Students know the definitions of the basic trigonometric
functions defined by the angles of a right triangle. They
also know and are able to use elementary relationships
between them. For example, tan(x) = sin(x)/cos(x), (sin
(x))2 + (cos (x))2 = 1.
19.0* Students use trigonometric functions to solve for an
unknown length of a side of a right triangle, given an angle
and a length of a side.
20.0 Students know and are able to use angle and side
relationships in problems with special right triangles, such
as 30°, 60°, and 90° triangles and 45°, 45°, and 90°
triangles.
22.0* Students know the effect of rigid motions on figures in the
coordinate plane and space, including rotations,
translations, and reflections.
# of
Items
4
3
3
1
3
Algebra II/ Probability and Statistics
18.0* Students use fundamental counting principles to compute
combinations and permutations.
19.0* Students use combinations and permutations to compute
probabilities.
Probability and Statistics
1.0 Students know the definition of the notion of independent
events and can use the rules for addition, multiplication,
and complementation to solve for probabilities of particular
events in finite sample spaces.
5
INTEGRATED 2 TOTAL
65
*
**
%
8%
2
2
1
100%
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years;
1/3 = rotated every three years)
© California Department of Education
3
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
Introduction - Algebra I
The following released test questions are taken from the Algebra I Standards Test. This test is one of the
California Standards Tests administered as part of the Standardized Testing and Reporting (STAR) Program
under policies set by the State Board of Education.
This document contains released test questions from the California Standards Test forms in 2003, 2004, 2005,
2006, and 2007. First on the pages that follow are lists of the standards assessed on the Algebra I Test. Next are
released test questions. Following the questions is a table that gives the correct answer for each question, the
content standard that each question is measuring, and the year each question last appeared on the test.
In selecting test questions for release, three criteria are used: (1) the questions adequately cover a selection of
the academic content standards assessed on the Algebra I Test; (2) the questions demonstrate a range of
difficulty; and (3) the questions present a variety of ways standards can be assessed. These released test
questions do not reflect all of the ways the standards may be assessed. Released test questions will not appear
on future tests.
For more information about the California Standards Tests, visit the California Department of Education’s
Web site at http://www.cde.ca.gov/ta/tg/sr/resources.asp.
Note: Not all Algebra I standards are covered on the Integrated Math test.
— 1 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
1
Released Test Questions
Is the equation 3(2 x 4) = 18 equivalent to
6 x 12 =18?
Which number does not have a reciprocal?
A
–1
Yes, the equations are equivalent by the
Commutative Property of Multiplication.
B
0
Yes, the equations are equivalent by the
Distributive Property of Multiplication over
Addition.
C
1
1000
D
3
A
Yes, the equations are equivalent by the
Associative Property of Multiplication.
B
C
D
4
No, the equations are not equivalent.
CSA10108
CSA10152
2
16 +3 8 =
A
4
B
6
C
9
D
10
5
What is the multiplicative inverse of
A
2
B
1
2
C
1
2
D
2
CSA00471
3
Which expression is equivalent to x6 x 2?
A
x 4 x3 B
x5 x3 C
x7 x3 D
x9 x3 1
?
2
CSA10153
CSA20167
6
What is the solution for this equation?
2 x 3 =5
A
x =4 or x =4
B
x =4 or x =3
C
x =1 or x =4
D
x =1 or x =3
CSA00264
— 6 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
7
What is the solution set of the inequality
5 x + 4 b3?
A
2 b xb 6
B
xb 2 or x p 6
C
12 b xb 4
D
xb 12 or x p 4
10
c = 120 + 60n.
If the total cost was $360, for how many days
was the sailboat rented?
CSA10036
8
A
2
B
4
C
6
D
8
Which equation is equivalent to
5x 2( 7 x + 1) = 14 x?
A
9x 2 = 14 x
B
9x+ 1 = 14 x
C
9x+ 2 = 14 x
D
12x1= 14x
CSA00485
11
CSA00206
9
The total cost (c) in dollars of renting a sailboat
for n days is given by the equation
8x=5
B
8x=17
C
29x=5
D
29x=17
3( x + 5) = 2 x+ 35
Step 1:
Step 2:
Step 3:
Step 4:
3x + 15 = 2 x+ 35
5x + 15 = 35
5x = 20
x= 4
Which is the first incorrect step in the solution
shown above?
Which equation is equivalent to
4 ( 2 5 x) = 6 3 (13 x)?
A
Solve:
A
Step 1
B
Step 2
C
Step 3
D
Step 4
CSA00332
CSA00059
12
A 120-foot-long rope is cut into 3 pieces. The
first piece of rope is twice as long as the second
piece of rope. The third piece of rope is three
times as long as the second piece of rope.
What is the length of the longest piece of rope?
A
20 feet
B
40 feet
C
60 feet
D
80 feet
— 7 —
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 © 2008 California Department of Education.
CSA10052
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
13
Released Test Questions
The cost to rent a construction crane is $750
per day plus $250 per hour of use. What is the
maximum number of hours the crane can be
used each day if the rental cost is not to exceed
$2500 per day?
A
2.5
B
3.7
C
7.0
D
13.0
16
Which number serves as a counterexample to
the statement below?
All positive integers are divisible by 2 or 3.
A
100
B
57
C
30
D
25
CSA10057
CSG10197
14
17
What is the solution to the inequality
x 5 > 14?
A
x>9
B
x>19
C
x<9
D
x<19
What is the conclusion of the statement in the
box below?
If x 2 =4, then x=2 or x=2.
A
x2 =4
B
x=2
C
x=2
D
x=2 or x =2
CSA00487
15
The lengths of the sides of a triangle are
y, y +1, and 7 centimeters. If the perimeter is
56 centimeters, what is the value of y?
A
24
B
25
C
31
D
32
CSA30045
18
CSA10046
Which of the following is a valid conclusion to
the statement “If a student is a high school band
member, then the student is a good musician”?
A
All good musicians are high school band
members.
B
A student is a high school band member.
C
All students are good musicians.
D
All high school band members are good
musicians.
CSA30095
— 8 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
19
The chart below shows an expression evaluated
for four different values of x.
x
x 2+ x+ 5
1
2
6
7
7
11
47
61
21
5
B
11
C
16
D
21
Given: n + 8( n + 20) = 110
Step 1: n + 8n + 20 = 110
Step 2:
9n + 20 = 110
Step 3:
Step 4:
Step 5:
Josiah concluded that for all positive values of
x, x 2 + x + 5 produces a prime number.
Which value of x serves as a counterexample to
prove Josiah’s conclusion false?
A
Stan’s solution to an equation is shown below.
Step 6:
9n = 110 20
9n = 90
9n 90
=
9
9
n = 10
Which statement about Stan’s solution is true?
A
Stan’s solution is correct.
B
Stan made a mistake in Step 1.
C
Stan made a mistake in Step 3.
D
Stan made a mistake in Step 5.
CSA20035
CSA20027
20
John’s solution to an equation is shown below.
22
When is this statement true?
The opposite of a number is less than the
original number.
Given:
x 2 + 5x + 6 = 0 Step 1:
( x + 2 )( x + 3) = 0
Step 2:
x + 2 = 0 or x + 3 = 0
A
This statement is never true.
Step 3:
x = 2 or x = 3
B
This statement is always true.
C
This statement is true for positive numbers.
D
This statement is true for negative numbers.
Which property of real numbers did John use
for Step 2?
A
multiplication property of equality
B
zero product property of multiplication
C
commutative property of multiplication
D
distributive property of multiplication over
addition
CSA20147
CSA20034
— 9 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
23
Released Test Questions
25
What is the y-intercept of the graph of
4x +2 y =12?
A
–4
B
–2
C
Which best represents the graph of y =2 x 2?
y
6
y
7
7
6
6
5
5
4
4
3
3
2
2
1
D
12
-7 -6 -5 -4 -3 -2 -1 0
-1
CSA00239
24
Which inequality is shown on the graph below?
y
7
6
5
4
2
3
4
5
6
7
4 5 6 7
1
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
A
C
y
7
7
6
6
5
5
4
4
3
3
2
2
1
2
3
4
5
6
7
x
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
1
B
C
1
y> x 1
2
D
1
yp x 1
2
5
6
7
x
2
3
4
5
6
7
x
CSA00299
-6
-7
1
yb x 1
2
4
D
-4
B
3
x
-5
1
y< x 1
2
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
A
1
y
-7 -6 -5 -4 -3 -2 -1 0
-1
1 2 3
x
-2
1
3
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
1
CSA10130
— 10 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
26
Which inequality does the shaded region of the
graph represent?
y
27
5
4
y
3
7
2
6
1
5
-5
-4
-3
3
-1 0
-1
2
-2
4
-2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
1
2
3
4
5
6
7
1
2
3
4
x
5
-3
x
-4
-2
-5
-3
-4
-5
Which equation best represents the graph
above?
-6
-7
A
y =[
A
3x + y b 2
B
y = 2x
B
3x + y p 2
C
y= x+2
C
3x + y b 2
D
y = 2x + 2
D
3x + y p 2
CSA00508
CSA20055
28
Which point lies on the line defined by
3x +6 y =2?
A
(0, 2)
B
(0, 6)
C
⎛
⎞
⎜⎜1, −1 ⎟⎟
⎟
⎜
⎝
6⎠
D
⎛
⎞
⎜⎜1, − 1 ⎟⎟
⎟
⎜
⎝
3⎠
CSA00009
— 11 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
29
Released Test Questions
What is the equation of the line that has a slope
of 4 and passes through the point ( 3,10) ?
A
y=4x22
B
y=4x+22
C
y=4x43
D
y=4x+43
31
Some ordered pairs for a linear function of x
are given in the table below.
CSA10150
30
A
y=2x+1
Renting a Bicycle
B
y=2x1
Hours (h) Cost in dollars (c)
2
15
5
30
8
45
C
y=3x2
D
y=4x 3
1
1
3
7
5
13
7
19
CSA10181
If hours, h, were graphed on the horizontal axis
and cost, c, were graphed on the vertical axis,
what would be the equation of a line that fits
the data?
B
y
Which of the following equations was used to
generate the table above?
The data in the table show the cost of renting a
bicycle by the hour, including a deposit.
A
x
32
c=5h
1
c= h+5
5
The equation of line l is 6 x +5 y =3, and the
equation of line q is 5x 6 y =0. Which
statement about the two lines is true?
A
Lines l and q have the same y-intercept.
B
Lines l and q are parallel.
C
Lines l and q have the same x-intercept.
D
Lines l and q are perpendicular.
CSA00241
C
c=5h+5
D
c=5h5
CSA10005
— 12 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
33
34
Which equation represents a line that is
Which graph best represents the solution to this
system of inequalities?
5
parallel to y = x +2?
4
A
B
£¦¦ 2 x p y 1
¤
¦¦¥2 x 5 y 10
5
y= x+1
4
y
4
y= x+2
5
D
5
4
4
3
3
2
2
1
-5
C
y
5
-4 -3
-2
4
y= x+3
5
5
y= x+4
4
1
-1 0
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1 0
-1
-2
-2
-3
-3
-4
-4
-5
-5
A
-4
-3
-2
5
4
4
3
3
2
2
-1 0
-1
3
4
5
1
2
3
4
5
1
1
2
3
4
5
x
-5
-4
-3
-2
-1 0
-1
-2
-2
-3
-3
-4
-4
-5
-5
B
D
CSA00516
35
x
y
5
1
-5
2
C
y
CSA10112
1
What is the solution to this system of
equations?
£¦¦ y =3x 2
¤
¦¦¥6 x +2 y =4
A
(6, 2)
B
(1, –5)
C
no solution
D
infinitely many solutions
CSA00027
— 13 —
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 © 2008 California Department of Education.
x
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
36
Released Test Questions
£
¦ x +3 y =7
¦
¤
¦
¦
¥x +2 y =10
A
2x 4
B
A
 7 13 ¬­
žž , ­
žŸ2 4 ­®
1
2x 4
B
 7 17 ¬
ž
žž , ­­­
Ÿ2 5 ®
C
1
5x 4
C
(2,
D
x4
5
D
(16, 3)
CSA00303
40 (
CSA10131
37
4x 2 2 x +8) ( x 2 +3x 2 ) =
A
Marcy has a total of 100 dimes and quarters. If
the total value of the coins is $14.05, how many
quarters does she have?
3x 2 + x+ 6
B
3x 2 + x+ 10
C
3x 2 5x+ 6
A
27
D
3x 2 5x+10
B
40
C
56
D
73
CSA00086
41
CSA20083
38
5 x3
=
10x 7
39
Which ordered pair is the solution to the
system of equations below?
Which of the following best describes the graph
of this system of equations?
£¦¦y =2 x +3
¤
¦¦
¥5 y =10x +15
A
two identical lines
B
two parallel lines
C
two lines intersecting in only one point
D
two lines intersecting in only two points
The sum of two binomials is 5x 2 6 x. If one of
the binomials is 3x 2 2 x, what is the other
binomial?
A
2x 2 4x
B
2x 2 8x
C
8x 2 + 4x
D
8x 2 8x
CSA10160
CSA00509
— 14 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
42
45
Which of the following expressions is equal to
(x + 2 )+ (x 2)(2 x + 1)?
A
2x 2 2x
B
2x 2 4x
C
2x 2
D
4x 2 +2x
3x
B
2x 2
C
3x 2
D
2x 3
x+3
B
x 3
C
x+4
D
x4
CSA00503
46
Which of the following shows 9t 2 + 12 t + 4
factored completely?
C
(3t+2)
(3t+4)(3t+1)
(9t+4)(t+1)
D
9t 2 +12t+4
A
A volleyball court is shaped like a rectangle.
It has a width of x meters and a length of 2x
meters. Which expression gives the area of the
court in square meters?
A
A
+x
CSA10191
43
Which is a factor of x 2 11x + 24?
B
2
CSA20106
47
CSA00496
44
Which is the factored form of
3a2 24 ab + 48 b2 ?
A
(3a8b)(a 6b)
B
(3a16b)(a 3b)
C
3(a4b)(a4b)
D
3(a8b)(a8b)
What is the complete factorization of 32 8z 2?
A
8(2 +z)(2 z)
B
8(2 +z )(2 z )
C
8(2 +z )
D
8(2 z )
2
2
CSA20105
48
CSA00066
If x 2 is added to x, the sum is 42. Which of the
following could be the value of x?
A
–7
B
–6
C
14
D
42
CSA10171
— 15 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
49
Released Test Questions
What quantity should be added to both sides of
this equation to complete the square?
x2
52
Carter is solving this equation by factoring.
10x 2 25x +15 =0
8x =5
A
4
Which expression could be one of his correct
factors?
B
–4
A
x+ 3
C
16
B
x 3
D
–16
C
2x+ 3
D
2x 3
CSA00478
CSA00162
50
What are the solutions for the quadratic
equation x 2 +6 x =16?
A
2, 8
B
2, 8
C
2, 8
D
2, 8
53
ax 2 +bx +c =0 (where a p0)
ax 2 +bx =c
b
c
x 2 + x =
a
a
?
Step 1:
Step 2:
CSA10062
51
Toni is solving this equation by completing the
square.
Step 3:
Which should be Step 3 in the solution?
Leanne correctly solved the equation
x 2 +4x =6 by completing the square.
Which equation is part of her solution?
A
B
C
D
(x+2) = 8
2
(x+ 2) = 10
2
(x+4) = 10
2
(x+ 4) = 22
2
A
c b
x 2 = x
b a
B
x+
C
b
b
c b
x 2 + x+ = +
a
2a
a 2a
D
x2
CSA20139
b
c
= a
ax
2
 b ¬­2
b
c ž b ¬­
ž
+ x+ ž ­­ = + ž ­­
ž
ž
Ÿ2a®
a
a Ÿ2a®
CSA00072
— 16 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
54
Four steps to derive the quadratic formula are
shown below.
56
Which statement best explains why there is no
real solution to the quadratic equation
2 x2 + x + 7 = 0 ?
A
The value of 12 4 i 2 i 7 is positive.
B
The value of 12 4 i 2 i 7 is equal to 0.
C
The value of 12 4 i 2 i 7 is negative.
D
The value of 12 4 i 2 i 7 is not a perfect
square.
CSA10147
What is the correct order for these steps?
A
I, IV, II, III
B
I, III, IV, II
C
II, IV, I, III
D
II, III, I, IV
57
What is the solution set of the quadratic
equation 8x 2 + 2 x + 1 = 0?
A
£ 1 1 ²¦
¤¦ , »
¥¦¦ 2 4 ¦¦¼
B
{1 +
C
£¦1 + 7 1 7 ²¦
¦»
¦
,
¤
¦¦ 8
¦¦
8
¥
¼
D
no real solution
2, 1 2
}
CSA20062
55
Which is one of the solutions to the equation
2 x 2 x 4 = 0?
A
1
33
4
B
1
+ 33
4
C
1+ 33
4
D
1 33
4
CSA10179
CSA00314
— 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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
58
Released Test Questions
The graph of the equation y =x 2 3x 4 is
shown below.
59
Which best represents the graph of
y = x 2 +3?
9
8
7
6
5
5
4
4
3
3
2
2
1
1
5
-5 -4 -3 -2 -1 0
-1
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
-6
-7
-8
-9
y
y
y
1 2 3 4
5 6 7 8 9
x
1
2
3
4
5
x
-5 -4 -3 -2 -1 0
-1
-2
-2
-3
-3
-4
-4
-5
-5
A
C
y
y
5
5
4
4
3
3
2
2
For what value or values of x is y =0?
A
x=1 only
B
x=4 only
C
x=1 and x=4
D
x= 1 and x=4
2
3
4
5
1
2
3
4
5
1
2
3
4
5
x
-5 -4 -3 -2 -1 0
-1
-2
-2
-3
-3
-4
-4
-5
-5
B
D
CSA00519
CSA00514
60
x
1
1
-5 -4 -3 -2 -1 0
-1
1
Which quadratic function, when graphed, has
x-intercepts of 4 and 3?
A
y= ( x 3)( x+4)
B
y= ( x+3)(2x8)
C
y= (3x1)(4x+1)
D
y= (3x+1)(8x 2)
CSA20115
— 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 © 2008 California Department of Education.
x
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
61
64
How many times does the graph of
y = 2 x 2 2 x + 3 intersect the x-axis?
A
none
B
one
C
two
D
three
2
What is
x 4xy + 4 y2
reduced to lowest
3xy 6 y2
terms?
A
x 2y
3
B
x 2y
3y
C
x+2y
3
D
x+2y
3y
CSA10084
62
An object that is projected straight downward
with initial velocity v feet per second travels a
distance s = vt + 16t 2 , where t = time in seconds.
If Ramón is standing on a balcony 84 feet above
the ground and throws a penny straight down
with an initial velocity of 10 feet per second, in
how many seconds will it reach the ground?
A
2 seconds
B
3 seconds
C
6 seconds
D
8 seconds
CSA00463
65
Simplify
A
B
6 x 2 + 21 x + 9
to lowest terms.
4x 2 1
3( x+1)
2x1
3( x+3)
2x1
CSA00158
C
63
The height of a triangle is 4 inches greater
than twice its base. The area of the triangle is
168 square inches. What is the base of the
triangle?
A
7 in.
B
8 in.
C
12 in.
D
14 in.
D
3(2 x+3)
4 ( x1)
3( x+3)
2x+1
CSA10025
CSA00104
— 19 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
66
What is
A
B
Released Test Questions
x 2 4x +4
reduced to lowest terms?
x 2 3x +2
68
A
x2
x1
B
x2
x+1
C
C
x+2
x1
D
D
x+2
x+1
7( z 2)
4 ( z +1)
7( z +2)
4 ( z 1)
7z ( z +1)
4 ( z +2)
7z (z 1)
4 ( z +2)
CSA00067
CSA10189
67
12 a3 20
a2
What is
reduced to lowest terms?
16a2 +8a
69
Which fraction equals the product
x +5 ¬
­­ žž 2 x 3 ¬­­ ?
žž
žŸ3x +2 ­®Ÿx
ž 5 ­®
A
a
2
A
2x 3
3x +2
B
3a 5
2a +1
B
3x +2
4x 3
C
2a
4 +2 a
C
x2 25
6x2 5x 6
D
a (3a 5)
2 (2 a +1)
D
2x2 +7x 15
3x2 13x 10
CSA00013
CSA10029
— 20 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
72
x 2 +8x + 16 2 x +8
÷ 2
=
x +3
x 9
70
2 (x+4)
2
A
B
C
(x 3)(x+3)
A pharmacist mixed some 10%-saline solution
with some 15%-saline solution to obtain
100 mL of a 12%-saline solution. How much of
the 10%-saline solution did the pharmacist use
in the mixture?
2
A
60 mL
2 (x+3)(x 3)
B
45 mL
x+4
C
40 mL
D
25 mL
(x+4)(x 3)
CSA00333
2
73
(x+4)(x 3)
2 (x+3)
2
D
CSA20164
71
3x
5 ?
Which fraction is equivalent to
x x
+
4 2
A
x2
5
B
9x 2
20
C
4
5
D
Andy’s average driving speed for a 4-hour trip
was 45 miles per hour. During the first 3 hours
he drove 40 miles per hour. What was his
average speed for the last hour of his trip?
A
50 miles per hour
B
60 miles per hour
C
65 miles per hour
D
70 miles per hour
CSA00576
74
9
5
One pipe can fill a tank in 20 minutes, while
another takes 30 minutes to fill the same tank.
How long would it take the two pipes together
to fill the tank?
A
50 min
B
25 min
C
15 min
D
12 min
CSA10141
CSA00161
— 21 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
75
Released Test Questions
Two airplanes left the same airport traveling
in opposite directions. If one airplane averages
400 miles per hour and the other airplane
averages 250 miles per hour, in how many
hours will the distance between the two planes
be 1625 miles?
A
2.5
B
4
C
5
D
10.8
78
For which equation graphed below are all the
y-values negative?
y
9 8 7 6 5 4 3 2 10
1
2
3
4
5
6
7
8
9
CSA10055
y
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
x
A
76
Lisa will make punch that is 25% fruit juice by
adding pure fruit juice to a 2-liter mixture that
is 10% pure fruit juice. How many liters of pure
fruit juice does she need to add?
A
0.4 liter
B
0.5 liter
C
2 liters
D
8 liters
9 8 7 6 5 4 3 2 10
1
2
3
4
5
6
7
8
9
1 2 3 4 5 6 7 8 9
x
1 2 3 4 5 6 7 8 9
x
C
y
y
9
8
7
6
5
4
3
2
1
9 8 7 6 5 4 3 2 10
1
2
3
4
5
6
7
8
9
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
x
9
8
7
6
5
4
3
2
1
9 8 7 6 5 4 3 2 10
1
2
3
4
5
6
7
8
9
CSA10186
B
77
D
Which relation is a function?
A
{(–1, 3), (–2, 6), (0, 0), (–2, –2)}
B
{(–2, –2), (0, 0), (1, 1), (2, 2)}
C
{(4, 0), (4, 1), (4, 2), (4, 3)}
D
{(7, 4), (8, 8), (10, 8), (10, 10)}
CSA00522
CSA10070
— 22 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
79
What is the domain of the function shown on
the graph below?
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
1
2
3
4
5
6
7
x
-2
-3
-4
-5
-6
-7
A
B
C
D
{1, 2, 3, 4}
{1, 2, 4, 5}
{1, 2, 3, 4}
{1, 2, 4, 5}
CSA10072
— 23 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
80
Released Test Questions
Which of the following graphs represents a relation that is not a function of x?
A
y
C
7
7
6
6
5
5
4
4
3
3
2
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
B
y
1
1
2
3
4
5
6
7
x
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
y
D
7
6
6
5
5
4
4
3
3
2
2
-7 -6 -5 -4 -3 -2 -1 0
-1
2
3
4
5
6
7
1
2
3
4
5
6
7
x
y
7
1
1
1
1
2
3
4
5
6
7
x
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
x
CSA30002
— 24 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
Question Number
Correct Answer
Standard
Year of Release
1
C
1.1
2006
2
B
2.0
2003
3
B
2.0
2005
4
B
2.0
2006
5
D
2.0
2007
6
C
3.0
2003
7
D
3.0
2004
8
A
4.0
2003
9
C
4.0
2005
10
B
5.0
2003
11
B
5.0
2004
12
C
5.0
2004
13
C
5.0
2006
14
B
5.0
2007
15
A
5.0
2007
16
D
24.1
2004
17
D
24.2
2006
18
D
24.2
2007
19
A
24.3
2005
20
B
25.1
2005
21
B
25.2
2006
22
C
25.3
2005
23
C
6.0
2003
24
D
6.0
2004
25
A
6.0
2006
26
A
6.0
2007
27
B
6.0
2007
28
C
7.0
2003
29
A
7.0
2004
30
C
7.0
2005
31
C
7.0
2007
32
D
8.0
2003
33
A
8.0
2004
34
C
9.0
2003
35
D
9.0
2004
— 25 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
Question Number
Correct Answer
Standard
Year of Release
36
D
9.0
2006
37
A
9.0
2006
38
A
9.0
2007
39
B
10.0
2004
40
D
10.0
2005
41
A
10.0
2006
42
A
10.0
2006
43
B
10.0
2007
44
C
11.0
2003
45
B
11.0
2004
46
A
11.0
2005
47
B
11.0
2007
48
A
14.0
2004
49
C
14.0
2005
50
C
14.0
2005
51
B
14.0
2006
52
D
14.0
2007
53
D
19.0
2003
54
A
19.0
2005
55
C
20.0
2003
56
C
20.0
2005
57
D
20.0
2005
58
C
21.0
2003
59
B
21.0
2006
60
B
21.0
2007
61
A
22.0
2004
62
A
23.0
2003
63
C
23.0
2004
64
B
12.0
2003
65
B
12.0
2005
66
A
12.0
2006
67
D
12.0
2007
68
A
13.0
2003
69
D
13.0
2005
70
C
13.0
2006
— 26 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra I
Released Test Questions
Question Number
Correct Answer
Standard
Year of Release
71
C
13.0
2007
72
A
15.0
2003
73
B
15.0
2004
74
D
15.0
2006
75
A
15.0
2006
76
A
15.0
2007
77
B
16.0
2004
78
A
17.0
2004
79
D
17.0
2005
80
D
18.0
2007
— 27 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
Introduction - Algebra II
The following released test questions are taken from the Algebra II Standards Test. This test is one of the
California Standards Tests administered as part of the Standardized Testing and Reporting (STAR) Program
under policies set by the State Board of Education.
This document contains released test questions from the California Standards Test forms in 2003, 2004, 2005,
2006, and 2007. First on the pages that follow are lists of the standards assessed on the Algebra II Test. Next are
released test questions. Following the questions is a table that gives the correct answer for each question,
the content standard that each question is measuring, and the year each question last appeared on the test.
In selecting test questions for release, three criteria are used: (1) the questions adequately cover a selection
of the academic content standards assessed on the Algebra II Test; (2) the questions demonstrate a range
of difficulty; and (3) the questions present a variety of ways standards can be assessed. These released test
questions do not reflect all of the ways the standards may be assessed. Released test questions will not appear
on future tests.
For more information about the California Standards Tests, visit the California Department of Education’s
Web site at http://www.cde.ca.gov/ta/tg/sr/resources.asp.
Note: Not all Algebra II standards are covered on the Integrated Math test.
— 1 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
1
Released Test Questions
What is the complete solution to the equation
3 6 x = 15?
A
x = 2; x = 3
B
x = 2; x = 3
C
x = 2; x = 3
D
x = 2; x = 3
4
£¦2 x y + 3 z = 8
¦¦
¤x 6 y z = 0
¦¦
¦¦¥6 x + 3 y 9 z = 24
CST00507
2
What are the possible values of x in
12 4 x = 2 ?
A
x = 2.50 or x = 3.50
B
3.50 < x < 2.50
C
3.5 > x > 2.5
D
x = 2.50 or x = 3.50
5
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
6 dozen
B
7 dozen
C
8 dozen
D
9 dozen
A
(0, 4, 4)
B
 10 ­¬
žž1, 4, ­
žŸ
3 ­®
C
no solution
D
infinitely many solutions
CST00203
CST20085
3
What is the solution to the system of equations
shown below?
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
6
B
8
C
9
D
12
CST00491
CST00099
— 6 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
6
What system of inequalities best represents
the graph shown below?
8
Which system of linear inequalities is
represented by this graph?
y
y
9
8
7
6
5
4
3
2
1
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
1
2
3
4
5
x
-2
-9 -8 -7 -6 -5 -4 -3
-3
-4
-3
-4
-5
-6
-7
-8
-9
-5
A
y > 2 and y > x + 1
B
y > 2 and y < x + 1
C
y < 2 and y > x + 1
D
y < 2 and y < x + 1
A
£¦
1
¦¦ y p x + 3
2
¤
¦¦
y
p
x
2
¥¦
B
¦¤£¦ y p 2x + 3
¦¥¦ y b x 2
C
£¦¦2 x y p 3
¤
¦¥¦ x + y b 2
D
£¦¦2 x + y p 3
¤
¦¥¦ x y p 2
CST00500
7
Which point lies in the solution set for the
£¦ 2 y x t 6
?
system ¦
¤
¦¥¦ 2 y 3 x < 6
A
B
C
D
(4, 1)
(3, 1)
(0, 3)
(4, 3)
CST20079
CST10059
— 7 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
9
Released Test Questions
12
)
2 x + 7 2 x 4 + 21 x 3 + 35 x 2 37 x + 46
A
B
C
D
x3 + 7 x 2 7 x + 6 4
2x + 7
2 x 3 + 14 x 2 14 x + 12 x3 7 x2 + 7 x 6 +
4
2x + 7
4
2x + 7
x3 + 7 x2 7 x + 6 +
Which expression is equivalent to
(6 y2 2)(6 y + 2)?
A
36y 2 4
B
36y3 4
C
36y 2 +12y 2 +12y 4
D
36y3 +12y 2 12y 4
CST20008
4
2x + 7
CST00109
13
What is the volume of the figure below?
10
(
Which polynomial represents
3x 2 + x 4) ( 2 x 5) ?
A
6x 3 13 x 2 13 x 20
B
6x 3 13 x 2 13 x + 20
C
6x 3
D
6x 3 +13 x 2 + 3x + 20
+13 x 2
x+6
x+1
+ 3x 20
x+4
A
x 3 +10x 2 + 34x + 24
B
x 3 +11x 2 + 34x + 24
C
x 3 +10x 2 + 24x + 24
D
x 3 +11x 2 + 24x + 24
CST10024
11 (
2 x 2 + 6 x + 1) 2 (4x 2 3x + 1) =
A
6x 2 1
B
10x 2 1
C
6x 2 + 12 x 1
D
10x 2
CST10285
14
+ 12x 1
CST00233
8a3 + c3 =
A
(2 a + c)(2a + c)(2a + c)
B
(2 a c)(4a 2 + 2ac + c 2 )
C
(2 a c)(4a 2 + 4ac + c 2 )
D
(2 a + c)(4a 2 2ac + c 2 )
CST00118
— 8 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
15
The total area of a rectangle is 4x 4 9 y2 .
Which factors could represent the length
times width?
A
B
C
D
x+3
6
=
+ 2
x + 5 x + 3x 10
18
A
(2x 2 3y)(2x 2 + 3y)
(2x2 + 3y )(2x2 + 3y )
B
(2x 3y )(2x 3y )
(2x + 3y )(2x 3y )
x2
7x 9
+ 3x 10
C
x 2 + x + 12
x 2 + 3x 10
D
x2 + x + 1
x 2 + 3x 10
CST10028
16
(
x2 + x
x 2 + 3x 10
Which product of factors is equivalent to
CST00295
x + 1) y2 ?
A
2
(x + 1 + y)2
B
(x + 1 y)2
C
(x 1 + y)( x 1 y)
D
(x + 1 + y)( x + 1 y)
19
Which is a simplified form of
A
3a 5
b3 c 5
B
3ab
c5
CST10030
17
Which expression shows the complete
factorization of 12 x 2 147?
A
(3x 7)(4x + 2)
B
(4x 21)(3x + 7)
C
12 ( x 7)( x + 7)
D
3(2 x 7)(2x + 7)
C
D
3a2 b3 c2
?
(a1 b2 c)3
3
b2 c 5
3
ab3c 5
CST00267
CST20117
— 9 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
20
What is
A
Released Test Questions
23
20x 4
8x 3
÷
?
27 y2
15 y5
32y3
81x
What is the simplest form of
5x 3 y + 20 x 2 y2 + 20 xy3
?
5xy
B
( x + 2)
2
( x + 2y)
C
x 2 + y2
D
x 2 + 4y 2
A
B
C
32
81xy 7
25y3
18x
2
CST10049
D
25
18xy 7
CST20321
21
Which product is equivalent to
A
4(x 2)
B
4(x + 2)
C
4(x 2)
D
4(x + 2)
24
Imaginary
4x 2 16
?
2x
9
A
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
1
B
x
C
x+4
D
x +3
x 3
B
C
1 2 3 4 5 6
7 8 9
Real
D
-4
x 2 + 4x
x 2 9
i 2
=
x+ 3
x + x 12
A
8
7
6
5
4
3
2
1
CST10041
22
If i = 1, which point shows the location of
5 2 i on the plane?
-5
-6
-7
-8
-9
A
point A
B
point B
C
point C
D
point D
CST00510
CST10043
— 10 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
25
27
If i = 1, what is the value of i 4 ?
A
i
B
If i = 1, then 4 i(6 i ) =
A
48
i
B
24
C
1
C
24
D
1
D
48
CST00238
26
CST00512
Which of the following complex numbers is
represented by the point on the graph below?
28
Imaginary
What is an equivalent form of
A
3i
4
B
3i
5
C
4i
4
D
4i
5
2
?
3+ i
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
1
2
3
4
5
6
7
Real
-2
-3
CST10040
-4
-5
29
(
-6
-7
A
4 + 3i
B
4 3i
C
3 4i
D
3 + 4i
What is the product of the complex numbers
3 + i) and ( 3 i) ?
A
8
B
10
C
9–i
D
10 6i
CST10038
CST30142
— 11 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
30
Released Test Questions
If i = 1 and a and b are non-zero real
1
numbers, what is
?
a + bi
33
There are two numbers with the following
properties.
1) The second number is 3 more than the
first number.
A
a + bi
a 2 + b2
B
a bi
a 2 + b2
C
a + bi
a 2 b2
A
6, 3
B
4, 1
D
a bi
a 2 b2
C
1, 4
D
3, 6
2) The product of the two numbers is 9 more
than their sum.
Which of the following represents possible
values of these two numbers?
CST10371
CST20109
31
34
What are the solutions to the equation
x 2 + 2 x + 2 = 0?
A
x = 0; x = 2
B
x = 0; x = 2i
C
x = 1+ i; x = 1 i
D
x = 1 + 2 2; x = 1 2 2
CST00114
32
What are the solutions to the equation
1
3
1+ 2 = ?
x
x
x=
B
x=3+
C
x=
D
13
13
x=3+
; x =3
2
2
A
2
B
4
C
8
D
16
CST00508
35
5
3
5
3
+
;x= 2
2
2
2
A
Jenny is solving the equation x 2 8x = 9 by
completing the square. What number should be
added to both sides of the equation to complete
the square?
5
5
; x =3
2
2
Which of the following most accurately
describes the translation of the graph
2
y = ( x + 3) 2 to the graph of
y = ( x 2) + 2 ?
2
13
3
13
3
+
;x= 2
2
2
2
A
up 4 and 5 to the right
B
down 2 and 2 to the right
C
down 2 and 3 to the left
D
up 4 and 2 to the left
CST10074
CST00197
— 12 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
36
Which of the following sentences is true about
2
the graphs of y = 3 ( x 5) + 1 and
37
y = 3 ( x + 5) + 1?
What are the x-intercepts of the graph of
y = 12 x 2 5x 2?
2
A
1 and 1
6
B
1 and
1
6
A
Their vertices are maximums.
B
The graphs have the same shape with
different vertices.
C
The graphs have different shapes with
different vertices.
C
One graph has a vertex that is a maximum,
while the other graph has a vertex that is a
minimum.
2
1
and 3
4
D
2
1
and
3
4
D
CST10294
— 13 —
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 © 2008 California Department of Education.
CST00297
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
38
Released Test Questions
Which is the graph of y = 2 ( x 1) + 1?
2
y
y
7
6
7
6
5
4
5
4
3
2
1
3
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
1 2 3
4 5 6 7
x
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
-4
-5
-6
-6
-7
-7
A
C
y
y
7
6
5
4
7
6
5
4
3
2
1
3
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
1 2 3
4 5 6 7
x
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
-4
-5
-6
-7
-6
-7
B
1 2 3
4 5 6 7
1 2 3
4 5 6 7
x
x
D
CST10292
— 14 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
39
41
Which ordered pair is the vertex of
f ( x ) = x 2 + 6 x + 5?
A
Which of the following represents a parabola?
A
x 2 + y2 = r 2
B
y2 x 2
+
=1
a 2 b2
C
4 px = y 2
D
y2 x 2
=1
a 2 b2
(3, 4)
B
(2, 3)
C
(1, 0)
D
(0, 5)
CST20065
CST10084
40
 x ¬2  y ¬2
The graph of žž ­­­ žž ­­­ = 1 is a hyperbola.
žŸ 2 ®
žŸ 3 ®
42
Which set of equations represents the
4x 2 5 y2 16 x 30 y 9 = 0
What is the standard form of the equation
of the conic given above?
asymptotes of the hyperbola’s graph?
A
B
C
D
y=
y=
y=
3
3
x, y = x
2
2
2
2
x, y = x
3
3
1
1
x, y = x
2
2
1
1
y = x, y = x
3
3
A
(x 4)2 (y 3)2
=1
11
4
B
(y + 3)2 (x 2)2
=1
4
5
C
(y 3)2 (x + 2)2
=1
6
9
D
(x 4)2 (y 3)2
+
=1
11
4
CST00146
CST10304
— 15 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
43
Released Test Questions
46
Which statement describes the graph of the
equation x 2 + y2 + 4x 6 y 3 = 0?
A
a hyperbola with center (2, 3) and vertices
(4, 3) and (4, 3)
A
13
= x3
9
B
a hyperbola with center (2, 3) and vertices
(2, 3) and (3, 2)
B
C
a circle with center (2, 3) and radius 8
 1 ¬­3
žž ­ = x
žŸ 9 ­®
C
3x =
D
3 =x
D
a circle with center (2, 3) and radius 4
CST20127
44
1
= x?
9
1
9
1
9
CST10151
What is the solution to the equation 5 x = 17?
47
A
x=2
B
x = log10 2
C
x = log10 17 + log10 5
D
x=
Which is the first incorrect step in simplifying
4
log 4 ?
64
Step 1:
Step 2:
Step 3:
log10 17
log10 5
CST00132
45
Which equation is equivalent to log 3
log 4
4
= log 4 4 log 4 64
64
= 1 16
= 15
A
Step 1
B
Step 2
C
Step 3
D
Each step is correct.
If log10 x = 2, what is the value of x ?
CST00517
1
10
A
x =
B
x=
1
10
C
x=
1
100
D
x = 100
CST10255
— 16 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
48
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
x3
x 3 x7 = 7
x
= x10 , x v 0
Michael’s work
x3
x 3 x7 = 7
x
= x4 , x v 0
49
A student showed the following steps in his
solution of the equation below, but his answer
was not correct.
log 5 ( 2 x 2 3x + 1) log 5 ( x 1) + log 5 125 = 6
Step 1:
log 5 ( 2 x 1)( x 1) log 5 ( x 1) + 3 = 6
Shanan’s work
x3
x 3 x7 = 7
x
1
= 4 , xv0
x
Brenda’s work
x3
x 3 x7 = 7
x
= x4 , x v 0
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
Which is a completely correct solution?
B
Step 2
A
Jeremy’s work
C
Step 3
B
Michael’s work
D
Step 4
C
Shanan’s work
D
Brenda’s work
CST10336
CST10301
50
A certain radioactive element decays over
t
 1 ¬ 300
time according to the equation y = A žž ­­­ ,
žŸ 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
— 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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
51
Released Test Questions
Bacteria in a culture are growing exponentially
with time, as shown in the table below.
53
Bacteria Growth
Day
Bacteria
0
1
2
100
200
400
Which table below correctly describes points of
the exponential function f ( x) = 3x 2?
A
y = 100 + 2t
B
y = (100) i (2)
C
y = 2t
D
y = (200) i (2)
–1
0
f(x)
– 18
–6
–2
x
–2
–1
0
f(x)
–4
–5
–2
x
–2
–1
0
f(x)
–1
x
–2
–1
0
f(x)
7
1
–1
C
t
t
8
9
–1
2
3
–1
D
CST10253
52
–2
B
Which of the following equations expresses the
number of bacteria, y, present at any time, t?
A
x
If the equation y = 2 x is graphed, which of
the following values of x would produce a point
closest to the x-axis?
CST20196
A
1
4
B
3
4
C
5
3
D
8
3
54
CST20145
log 6 40 =
A
log10 6 + log10 40
B
log10 6 log10 40
C
(log10 6)(log10 40)
D
log10 40
log10 6
CST00199
— 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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
55
Jonathan wrote the equation log 6 ( x 4) = 0
on the board. He needs one clue for problem
solving. Which fact provides the correct
information that he needs to solve the equation?
59
On a recent test, Jeremy wrote the equation
x 2 16
= x + 4. Which of the following
x 4
statements is correct about the equation
A
60 = 1
B
61 = 6
he wrote?
C
44 = 0
A
The equation is always true.
D
64 = 2
B
The equation is always true, except
when x = 4.
C
The equation is never true.
D
The equation is sometimes true when x = 4.
CST10484
56
What is the value of log327?
A
2
B
3
C
6
D
9
CST10260
60
CST00519
57
If log 2 x 0.301 and log 3 x 0.477, what is the
approximate value of log 72?
A
0.051
B
0.778
C
0.861
D
1.857
A
y>0
B
y=0
C
y<0
D
yb0
CST20140
61
If x is a real number, which best describes the
values of x for which the inequality
x >0
is true?
CST10362
58
Given the equation y = x n where x >0
and n <0, which statement is valid for
real values of y?
If x is a real number, for what values of x is the
3x 9
equation
= x 3 true?
3
A all values of x
A
all x > 0
B
all x p 0
C
all values of x
D
no values of x
CST00396
B
some values of x
C
no values of x
D
impossible to determine
CST00032
— 19 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
62
Released Test Questions
Which of the following conclusions is true about
the statement below?
x2 = x
A
The statement is always true.
B
The statement is true when x is negative.
C
The statement is true when x = 0.
D
The statement is never true.
65
Teresa and Julia are among 10 students who
have applied for a trip to Washington, D.C.
Two students from the group will be selected
at random for the trip. What is the probability
that Teresa and Julia will be the 2 students
selected?
A
1
45
B
2
45
C
1
5
D
2
5
CST10162
63
Abelardo wants to create several different
7-character screen names. He wants to use
arrangements of the first 3 letters of his
first name (abe), followed by arrangements
of 4 digits in 1984, the year of his birth.
How many different screen names can
he create in this way?
A
72
B
144
C
288
D
576
CST00071
66
(3 y 1)4 =
A
81y 4 108y3 + 54y 2 12y + 1
B
81y 4 + 108y3 54y 2 12y + 1
C
81y 4 54y3 108y 2 12y + 1
D
81y 4 + 54y3 108y 2 12y + 1
CST10401
64
A train is made up of a locomotive, 7 different
cars, and a caboose. If the locomotive must
be first, and the caboose must be last, how
many different ways can the train be ordered?
A
5040
B
181,440
C
362,880
D
823,543
CST00308
67
CST10391
How many terms does the binomial expansion
of ( x 2 + 2 y3 ) contain?
20
A
20
B
21
C
40
D
60
CST10316
— 20 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
68
What are the first 4 terms in the expansion of
( 1 + 2 x) ?
6
71
Which expression represents f ( g ( x))
if f ( x) = x 2 1 and g ( x) = x + 3?
A
1 + 12x + 30 x 2 + 40 x 3
A
x 3 + 3x 2 x 3
B
1 + 12x + 24 x 2 + 48 x 3
B
x 2 + 6x + 8
C
1+12x + 30x 2 +120x 3
C
x2 + x + 2
D
1+12x + 60x 2 +160x 3
D
x2 + 8
CST20032
CST20022
69
What is the sum of the infinite geometric series
1 1 1
1
+ + + +...?
2 4 8 16
A
1
B
1.5
C
2
D
2.5
72
Given that f ( x) = 3x 2 4 and g ( x) = 2 x 6,
what is g ( f ( 2 )) ?
A
2
B
6
C
8
D
10
CST30049
CST20167
70
73
What is the nth term in the arithmetic
series below?
3 + 7 + 11 + 15 + 19 ...
A
4n
B
3 + 4n
C
2n +1
D
4n 1
If f ( x) = x 2 + 2 x + 1 and g ( x) = 3 ( x + 1) ,
2
which is an equivalent form of f ( x) + g ( x)?
A
x 2 + 4x + 2
B
4x 2 + 2x + 4
C
4x 2 + 8x + 4
D
10x 2 + 20x +10
CST10204
CST10178
— 21 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
74
Released Test Questions
A math teacher is randomly distributing
15 rulers with centimeter labels and 10 rulers
without centimeter labels. What is the probability
that the first ruler she hands out will have
centimeter labels and the second ruler will
not have labels?
76
One bag contains 2 green marbles and 4 white
marbles, and a second bag contains 3 green
marbles and 1 white marble. If Trent randomly
draws one marble from each bag, what is the
probability that they are both green?
A
A
1
24
1
4
B
B
1
4
2
5
C
C
2
5
1
2
D
D
23
25
5
6
CST20181
CST10435
75
On a certain day the chance of rain is 80%
in San Francisco and 30%in Sydney. Assume
that the chance of rain in the two cities is
independent. What is the probability that
it will not rain in either city?
A
7%
B
14%
C
24%
D
50%
77
CST20180
A box contains 7 large red marbles, 5 large
yellow marbles, 3 small red marbles, and
5 small yellow marbles. If a marble is drawn
at random, what is the probability that it is
yellow, given that it is one of the large marbles?
A
5
12
B
7
20
C
5
8
D
1
5
CSN00211
— 22 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
78
The probabilities that Jamie will try out for various sports and team positions are shown
in the chart below.
Jamie
Try out for
basketball team
Try out for
guard
80%
Try out for
baseball team
Try out for
forward
20%
Try out for
catcher
70%
Try out for
pitcher
30%
Jamie will definitely try out for either basketball or baseball, but not both. The probability that Jamie
will try out for baseball and try out for catcher is 42%. What is the probability that Jamie will try out
for basketball?
A
40%
B
60%
C
80%
D
90%
CST10210
— 23 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
79
Released Test Questions
A small-business owner must hire seasonal
workers as the need arises. The following list
shows the number of employees hired monthly
for a 5-month period.
80
4, 13, 5, 6, 9
If the mean of these data is approximately 7,
what is the population standard deviation
for these data? (Round the answer to the
nearest tenth.)
3, 6, 2, 1, 7, 5
James found the mean and standard deviation
of the set of numbers given above. If he adds 5 to
each number, which of the following will result?
A
The mean will be multiplied by 5.
B
The standard deviation will increase by 5.
C
The mean will not change.
D
The standard deviation will not change.
CSN00127
A
3.3
B
7.4
C
10.8
D
13.5
CST20052
— 24 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
Question 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
Correct Answer
B
D
C
C
B
B
B
D
D
B
D
D
B
D
A
D
D
A
A
D
D
B
B
D
C
C
C
B
B
B
C
A
B
D
A
Standard
1.0
1.0
2.0
2.0
2.0
2.0
2.0
2.0
3.0
3.0
3.0
3.0
3.0
4.0
4.0
4.0
4.0
7.0
7.0
7.0
7.0
7.0
7.0
5.0
5.0
5.0
6.0
6.0
6.0
6.0
8.0
8.0
8.0
8.0
9.0
Year of Release
2004
2007
2003
2004
2006
2006
2007
2007
2003
2004
2005
2006
2007
2003
2005
2006
2007
2003
2004
2005
2006
2006
2006
2003
2005
2007
2003
2004
2005
2007
2003
2004
2005
2006
2004
— 25 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
Question Number
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Correct Answer
B
C
C
A
A
C
B
D
D
C
C
B
C
C
C
B
A
D
D
A
B
D
A
B
A
A
C
B
A
A
A
B
D
A
D
Standard
9.0
10.0
10.0
10.0
16.0
16.0
17.0
17.0
11.1
11.1
11.1
11.2
11.2
11.2
12.0
12.0
12.0
12.0
13.0
13.0
14.0
14.0
15.0
15.0
15.0
15.0
15.0
18.0
18.0
19.0
20.0
20.0
20.0
22.0
22.0
Year of Release
2005
2003
2004
2006
2004
2007
2003
2007
2003
2004
2005
2003
2005
2007
2003
2004
2005
2007
2004
2007
2003
2004
2003
2004
2006
2006
2007
2005
2006
2005
2003
2006
2007
2005
2006
— 26 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Algebra II
Released Test Questions
Question Number
71
72
73
74
75
76
77
78
79
80
Correct Answer
B
D
C
B
B
A
A
A
A
D
Standard
24.0
24.0
25.0
PS1.0
PS1.0
PS1.0
PS2.0
PS2.0
PS7.0
PS7.0
Year of Release
2005
2007
2004
2004
2006
2007
2003
2006
2005
2006
— 27 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
Introduction - Geometry
The following released test questions are taken from the Geometry Standards Test. This test is one of the
California Standards Tests administered as part of the Standardized Testing and Reporting (STAR) Program
under policies set by the State Board of Education.
This document contains released test questions from the California Standards Test forms in 2003, 2004, 2005,
2006, and 2007. First on the pages that follow are lists of the standards assessed on the Geometry Test. Next
are released test questions. Following the questions is a table that gives the correct answer for each question,
the content standard that each question is measuring, and the year each question last appeared on the test.
In selecting test questions for release, three criteria are used: (1) the questions adequately cover a selection of
the academic content standards assessed on the Geometry Test; (2) the questions demonstrate a range of
difficulty; and (3) the questions present a variety of ways standards can be assessed. These released test
questions do not reflect all of the ways the standards may be assessed. Released test questions will not appear
on future tests.
For more information about the California Standards Tests, visit the California Department of Education’s
Web site at http://www.cde.ca.gov/ta/tg/sr/resources.asp.
Note: Not all Geometry standards are covered on the Integrated Math test.
— 1 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
1
Released Test Questions
Which of the following best describes deductive
reasoning?
A
using logic to draw conclusions based on
accepted statements
B
accepting the meaning of a term without
definition
C
defining mathematical terms to correspond
with physical objects
D
inferring a general truth by examining a
number of specific examples
3
I. Every multiple of 4 is even. 376 is a multiple
of 4. Therefore, 376 is even.
II. A number can be written as a repeating
decimal if it is rational. Pi cannot be written
as a repeating decimal. Therefore, pi is not
rational.
Which one(s), if any, use deductive reasoning?
CSG00185
2
Consider the arguments below.
In the diagram below, ¸1 ! ¸4.
A
I only
B
II only
C
both I and II
D
neither I nor II
CSG00552
4
1
l
Theorem: A triangle has at most one obtuse
angle.
2
Eduardo is proving the theorem above by
contradiction. He began by assuming that in
+ABC, ¸A and ¸B are both obtuse. Which
theorem will Eduardo use to reach a
contradiction?
3
m
4
t
Which of the following conclusions does not
have to be true?
A
·3 and ·4 are supplementary angles.
B
Line l is parallel to line m.
C
·1 ! ·3
D
·2 ! ·3
A
If two angles of a triangle are equal, the sides
opposite the angles are equal.
B
If two supplementary angles are equal, the
angles each measure 90°.
C
The largest angle in a triangle is opposite the
longest side.
D
The sum of the measures of the angles of a
triangle is 180°.
CSG00025
CSG10066
— 6 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
5
Use the proof to answer the question below.
Given: AB!BC; D is the midpoint of AC
Prove: + ABD!+CBD
A
D
B
C
Statement
Reason
1.
AB!BC; D is the midpoint of AC
1.
Given
2.
AD ! CD
2.
Definition of Midpoint
3.
BD ! BD
3.
Reflexive Property
4.
+ ABD!+CBD
4.
?
What reason can be used to prove that the triangles are congruent?
A
AAS
B
ASA
C
SAS
D
SSS
CSG10068
— 7 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
6
Released Test Questions
In the figure below, AB > BC.
A
C
B
If we assume that m ¸A = m ¸C , it follows that
AB = BC. This contradicts the given statement
that AB > BC. What conclusion can be drawn
from this contradiction?
A
m ·A = m ·B
B
m ·A v m ·B
C
m ·A = m ·C
D
m ·A v m ·C
CSG00524
— 8 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
7
Use the proof to answer the question below.
Given: ¸ 2 ! ¸ 3
Prove: ¸ 1 ! ¸ 4
1
2
3
m
4
t
Statement
Reason
1.
¸ 2 !¸ 3
1. Given
2.
¸ 1 ! ¸ 2; ¸ 3 ! ¸ 4
2. ?
3.
¸ 1 !¸ 4
3. Transitive Property
What reason can be used to justify statement 2?
A
Complements of congruent angles are congruent.
B
Vertical angles are congruent.
C
Supplements of congruent angles are congruent.
D
Corresponding angles are congruent.
CSG10069
— 9 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
8
Released Test Questions
“Two lines in a plane always intersect in exactly
one point.”
11
A conditional statement is shown below.
Which of the following best describes a
counterexample to the assertion above?
A
coplanar lines
B
parallel lines
C
perpendicular lines
D
intersecting lines
If a quadrilateral has perpendicular
diagonals, then it is a rhombus.
Which of the following is a counterexample to
the statement above?
A
C
B
D
CSG00320
9
Which figure can serve as a counterexample to
the conjecture below?
If one pair of opposite sides of a
quadrilateral is parallel, then the
quadrilateral is a parallelogram.
A
rectangle
B
rhombus
C
square
D
trapezoid
CSG10194
10
CSG20216
Given: TRAP is an isosceles trapezoid with
diagonals RP and TA. Which of the following
must be true?
A
RP ? TA
B
RP &TA
C
RP ! TA
D
RP bisects TA
CSG00260
— 10 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
12
14
Which triangles must be similar?
A
two obtuse triangles
B
two scalene triangles with congruent bases
C
two right triangles
D
two isosceles triangles with congruent
vertex angles
Parallelogram ABCD is shown below.
A
B
E
CSG00578
13
D
Which of the following facts would be sufficient
to prove that triangles ABC and DBE are
similar?
C
Which pair of triangles can be established to
be congruent to prove that ¸DAB !¸BCD ?
A
A
B
C
D
D
+ADC and +BCD
+AED and +BEC
+DAB and +BCD
+DEC and +BEA
CSG10146
15
C
E
A
CE and BE are congruent.
B
¸ACE is a right angle.
C
AC and DE are parallel.
D
¸ A and ¸ B are congruent.
B
If + ABC and +XYZ are two triangles such
AB BC
that
=
, which of the following would
XY YZ
be sufficient to prove the triangles are similar?
A
·A!·X
B
· B ! ·Y
C
·C ! · Z
D
· X ! ·Y
CSG10218
CSG00544
— 11 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
16
Released Test Questions
In parallelogram FGHI, diagonals IG and FH
are drawn and intersect at point M. Which of
the following statements must be true?
18
Which of the following statements must be true
if +GHI +JKL?
H
A
FGI must be an obtuse triangle.
B
C
HIG must be an acute triangle.
FMG must be congruent to HMG.
D
GMH must be congruent to IMF.
G
K
I
CSG00559
17
Which of the following best describes the
triangles shown below?
J
A
The two triangles must be scalene.
B
The two triangles must have exactly one acute
angle.
C
At least one of the sides of the two triangles
must be parallel.
D
The corresponding sides of the two triangles
must be proportional.
30°
8
8
L
CSG20074
60°
A
both similar and congruent
B
similar but not congruent
C
congruent but not similar
D
neither similar nor congruent
CSG00478
— 12 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
19
20
In the figure below, AC ! DF and ¸A ! ¸D.
Given: AB and CD intersect at point E;
¸1 ! ¸2
C
A
B
A
3
1
C
E
2
4
D
F
B
E
D
Which theorem or postulate can be used to
prove + AED +BEC ?
Which additional information would be enough
to prove that + ABC ! +DEF ?
A
AB ! DE
B
AB ! BC
C
BC ! EF
D
BC ! DE
A
AA
B
SSS
C
ASA
D
SAS
CSG10074
CSG00517
21
In the figure below, n is a whole number. What
is the smallest possible value for n?
n
n
15
A
1
B
7
C
8
D
14
CSG00295
— 13 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
22
Released Test Questions
Which of the following sets of numbers could
represent the lengths of the sides of a triangle?
A
2, 2, 5
B
3, 3, 5
C
4, 4, 8
D
5, 5, 15
24
What values of a and b make quadrilateral
MNOP a parallelogram?
21
N
O
3a – 2b
13
CSG10041
23
M
In the accompanying diagram, parallel lines l
and m are cut by transversal t.
4a + b
A
a = 1, b = 5
B
a = 5, b = 1
C
a=
11
34
,b=
7
7
D
a=
34
11
,b=
7
7
P
t
l
1
2
m
Which statement about angles 1 and 2 must
be true?
A
·1 ! ·2.
B
·1 is the complement of ·2.
C
·1 is the supplement of ·2.
D
·1 and ·2 are right angles.
CSG10163
25
Quadrilateral ABCD is a parallelogram. If
adjacent angles are congruent, which statement
must be true?
A
Quadrilateral ABCD is a square.
B
Quadrilateral ABCD is a rhombus.
C
Quadrilateral ABCD is a rectangle.
D
Quadrilateral ABCD is an isosceles
trapezoid.
CSG00579
CSG20048
— 14 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
26
28
For the quadrilateral shown below, what is
m¸a + m¸c ?
A right circular cone has radius 5 inches and
height 8 inches.
C
co
B 95o
32o
D
l
8 in.
ao
A
5 in.
A
53°
B
137°
C
180°
D
233°
What is the lateral area of the cone? (Lateral
area of cone = Qrl, where l = slant height )
CSG10162
27
If ABCD is a parallelogram, what is the length
of segment BD?
B
A
40Q sq in.
B
445Q sq in.
C
5Q 39 sq in.
D
5Q 89 sq in.
C
CSG00053
5
E
7
6
A
D
A
10
B
11
C
12
D
14
CSG20236
— 15 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
29
Released Test Questions
31
Figure ABCD is a kite.
B
17 cm
10 cm
A
8 cm
6 cm
15 cm
C
A sewing club is making a quilt consisting of 25
squares with each side of the square measuring
30 centimeters. If the quilt has five rows and five
columns, what is the perimeter of the quilt?
A
150 cm
B
300 cm
C
600 cm
D
900 cm
CSG20111
8 cm
10 cm
32
17 cm
The four sides of this figure will be folded up
and taped to make an open box.
D
5 centimeters
What is the area of figure ABCD, in square
centimeters?
A
120
B
154
C
168
D
336
CSG20157
30
If a cylindrical barrel measures 22 inches in
diameter, how many inches will it roll in
8 revolutions along a smooth surface?
A
121Q in.
B
168Q in.
C
176Q in.
What will be the volume of the box?
D
228Q in.
A
50 cm 3
B
75 cm 3
C
100 cm 3
D
125 cm 3
CSG00564
CSG00299
— 16 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
33
A classroom globe has a diameter of 18 inches.
34
The rectangle shown below has length
20 meters and width 10 meters.
4m
4m
4m
4m
4m
4m
4m
If four triangles are removed from the
rectangle as shown, what will be the area of the
remaining figure?
Which of the following is the approximate
surface area, in square inches, of the globe?
( Surface Area = 4Qr 2 )
A
113.0
B
226.1
C
254.3
D
1017.4
4m
A
136 m2
B
144 m2
C
168 m2
D
184 m2
CSG00012
CSG20238
35
If RSTW is a rhombus, what is the area of
+WXT?
R
W
X
S
60o
12
T
A
18 3
B
36 3
C
36
D
48
CSG00227
— 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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
36
Released Test Questions
38
What is the area, in square units, of the
trapezoid shown below?
What is the area, in square meters (m), of the
trapezoid shown below?
12 m
y
(0, 5)
(8, 5)
5m
5m
6m
0
(12, 0)
x
28
B
36
A
37.5
C
48
B
42.5
D
72
C
50
D
100
CSG10047
39
CSG20226
37
A
What is the area, in square inches (in.), of the
triangle below?
The figure below is a square with four
congruent parallelograms inside.
10 in.
5
3
12
10 in.
What is the area, in square units, of the shaded
portion?
A
60
B
84
C
114
D
129
10 in.
A
25
B
25 3
C
50
D
50 3
CSG20225
— 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 © 2008 California Department of Education.
CSG10048
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
40
The perimeters of two squares are in a ratio of
4 to 9. What is the ratio between the areas of
the two squares?
43
The sum of the interior angles of a polygon is
the same as the sum of its exterior angles. What
type of polygon is it?
A
2 to 3
A
quadrilateral
B
4 to 9
B
hexagon
C
16 to 27
C
octagon
D
16 to 81
D
decagon
CSG00013
41
Lea made two candles in the shape of right
rectangular prisms. The first candle is 15 cm
high, 8 cm long, and 8 cm wide. The second
candle is 5 cm higher but has the same length
and width. How much additional wax was
needed to make the taller candle?
CSG00305
44
B x
A
320 cm3
B
640 cm3
C
960 cm3
A
35°
D
1280 cm3
B
60°
C
85°
D
95°
60
A
CSG20116
42
What is m¸ x ?
Two angles of a triangle have measures of 55°
and 65°. Which of the following could not be a
measure of an exterior angle of the triangle?
25
C
CSG20086
45
If the measure of an exterior angle of a regular
polygon is 120°, how many sides does the
polygon have?
A
115°
B
120°
C
125°
A
3
D
130°
B
4
C
5
D
6
CSG00571
CSG20204
— 19 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
46
Released Test Questions
48
In the figure below, AB & C .
A
What is m¸ 1?
D
(x + 40)º
36 o
(x – 40)º
88 o
B
C
What is the value of x?
A
40
B
50
C
80
D
90
1
CSG00244
47
The measures of the interior angles of a
pentagon are 2 x, 6 x, 4 x 6, 2 x 16, and
6 x + 2. What is the measure, in degrees, of the
largest angle?
A
28
B
106
C
170
D
174
A
34°
B
56°
C
64°
D
92°
CSG20179
49
What is m¸ WZX ?
V
132º
CSG10028
W
Z
52º
Y
A
80°
B
90°
C
100°
D
110°
X
CSG30022
— 20 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
50
52
What is the measure of an exterior angle of a
regular hexagon?
A
30°
B
60°
C
120°
D
180°
A right triangle’s hypotenuse has length 5. If
one leg has length 2, what is the length of the
other leg?
A
B
21
C
29
D
CSG00570
3
7
CSG00566
51
53
A diagram from a proof of the Pythagorean
theorem is pictured below.
a
b
A new pipeline is being constructed to re-route
its oil flow around the exterior of a national
wildlife preserve. The plan showing the old
pipeline and the new route is shown below.
32
m
W
NE
s
6
ile
s
ile NE
m ELI
0 IP
P
E
IPELIN
OLD P
c
Which statement would not be used in the proof
of the Pythagorean theorem?
1
A The area of a triangle equals ab.
2
B The four right triangles are congruent.
About how many extra miles will the oil flow
once the new route is established?
C
D
The area of the inner square is equal to half of
the area of the larger square.
A
24
B
68
C
92
D
160
The area of the larger square is equal to the
sum of the areas of the smaller square and the
four congruent triangles.
CSG10192
— 21 —
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 © 2008 California Department of Education.
CSG10016
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
54
Released Test Questions
Marsha is using a straightedge and compass to
do the construction shown below.
55
Given: angle A
What is the first step in constructing the angle
bisector of angle A?
P
B
A
l
A
Which best describes the construction Marsha
is doing?
A
a line through P parallel to line l
B
a line through P intersecting line l
C
a line through P congruent to line l
D
a line through P perpendicular to line l
D
C
JJJG
Draw ray AD.
B
Draw a line segment connecting points B
and C.
C
From points B and C, draw equal arcs that
intersect at D.
D
From point A, draw an arc that intersects the
sides of the angle at points B and C.
CSG10131
CSG00526
— 22 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
56
57
Scott is constructing a line perpendicular to
line l from point P. Which of the following
should be his first step?
1. Put the tip of the compass on point A.
P
l
A
Which triangle can be constructed using the
following steps?
2. Open the compass so that the pencil tip
is on point B.
3. Draw an arc above AB.
4. Without changing the opening, put the
metal tip on point B and draw an arc
intersecting the first arc at point C.
P
l
B
5. Draw AC and BC.
C
P
C
l
P
D
l
A
A
right
B
obtuse
C
scalene
D
equilateral
B
CSG10135
CSG00308
— 23 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
58
Released Test Questions
59
The diagram shows + ABC.
Figure ABCO is a parallelogram.
y
y
A (a, b)
B (a + c, b)
B
A
C
x
What are the coordinates of the point of
intersection of the diagonals?
Which statement would prove that + ABC is a
right triangle?
A
B
C
D
x
C (c, 0)
O
(slope AB)(slope BC ) = 1
(slope AB)(slope BC ) = 1
A
a
žž ,
žŸ 2
b ¬­
­
2 ­®
B

žž c ,
žŸ 2
b ¬­
­
2 ­®
C
a + c
žž
,
žŸ 2
D
a + c a +
žž
,
žŸ 2
2
distance from A to B = distance from B to C
distance from A to B = (distance from
B to C)
CSG00475
¬­
­
2 ­®
¬­
­­
®
CSG20101
— 24 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
60
63
What type of triangle is formed by the points
A(4, 2 ), B(6,1), and C(1, 3)?
In the figure below, sin A = 0.7.
C
A
right
B
equilateral
C
isosceles
D
scalene
21
CSG10235
61
2
equation is ( x + 3) + ( y + 1) = r 2 . Which of
2
the following must be the radius of the circle?
A
3
B
10
C
9
D
10
A
B
The point (3, 2 ) lies on a circle whose
What is the length of AC ?
A
14.7
B
21.7
C
30
D
32
CSG00432
CSG30048
62
5
In the figure below, if sin x = , what are
13
cos x and tan x?
x
A
cos x =
12
5
and tan x =
13
12
B
cos x =
12
12
and tan x =
13
5
C
cos x =
13
5
and tan x =
12
12
D
cos x =
13
13
and tan x =
12
5
CSG00493
— 25 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
64
Released Test Questions
Approximately how many feet tall is the
streetlight?
65
Right triangle ABC is pictured below.
B
10.6
A
32º
8.2
C
Which equation gives the correct value for BC?
h
A
sin 32° =
BC
8.2
B
cos 32° =
BC
10.6
C
tan 58° =
8.2
BC
D
sin 58° =
BC
10.6
40º
20 ft
sin 40° x 0.64
cos 40° x 0.77
tan 40° x 0.84
A
12.8
B
15.4
C
16.8
D
23.8
CSG10210
CSG20047
— 26 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
66
In the accompanying diagram, m¸A = 32° and
AC = 10. Which equation could be used to find
x in +ABC ?
67
The diagram shows an 8-foot ladder leaning
against a wall. The ladder makes a 53D angle
with the wall. Which is closest to the distance
up the wall the ladder reaches?
B
x
A
A
53°
8 ft
32°
10
?
C
x = 10 sin 32°
B
x = 10 cos 32°
C
x = 10 tan 32°
D
10
x=
cos32°
sin 53° 0.80
cos 53° 0.60
tan 53° 1.33
CSG00555
A
3.2 ft
B
4.8 ft
C
6.4 ft
D
9.6 ft
CSG00342
— 27 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
68
Released Test Questions
69
Triangle JKL is shown below.
K
24o
What is the approximate height, in feet, of the
tree in the figure below?
100 ft
L
28
50
J
Which equation should be used to find the
length of JK ?
JK
A sin 24° =
28
28
B sin 24° =
JK
JK
C cos 24° =
28
28
D cos 24° =
JK
sin 50° x 0.766
cos 50° x 0.643
tan 50° x 1.192
CSG20031
A
64.3
B
76.6
C
119.2
D
130.5
CSG20126
70
If a = 3 3 in the right triangle below, what is
the value of b?
a
b
c
A
9
B
6 3
C
12 3
D
18
CSG10052
— 28 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
71
73
What is the value of x in the triangle below?
10
B
x
C
x
A
A
A square is circumscribed about a circle. What
is the ratio of the area of the circle to the area
of the square?
A
1
4
B
1
2
C
2
Q
D
Q
4
5
B
5 2
C
10 3
D
20
CSG10056
72
CSG00585
74
What is the value of x, in inches?
In the circle below, AB and CD are chords
intersecting at E.
C
A
7 in.
E
30o
x
D
A
7 3
B
14
C
14 3
D
21
B
If AE = 5, BE = 12, and CE = 6, what is the
length of DE?
CSG20099
A
7
B
9
C
10
D
13
CSG00022
— 29 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
75
Released Test Questions
HJJG
RB is tangent to a circle, whose center is A, at
point B. BD is a diameter.
76
HJJJG
In the figure below, AB is tangent to circle O at
HJJG
point A, secant BD intersects circle O at points
p
p = 110°.
C and D, mA
C = 70°, and mCD
C
A
R
B
o
70
D
C
25º
O
A
B
110
o
D
What is m¸ CBR?
What is m¸ABC ?
A
50°
B
65°
A
20°
C
90°
B
40°
D
130°
C
55°
D
70°
CSG20186
CSG10257
— 30 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
77
79
In the circle shown below, the measure of
p
PR = 140° and the measure of ¸ RPQ = 50°.
If triangle ABC is rotated 180 degrees about the
origin, what are the coordinates of Aa ?
P
140º
y
7
6
50º
5
4
O
3
2
1
R
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
Q
C
1 2 3
4 5 6 7
x
-6
-7
A
50°
B
60°
C
70°
A
D
120°
B
CSG10003
A
-4
-5
What is the measure of p
PQ?
78
B
C
The vertices of ABC are A(2, 1), B(3, 4), and
C(1, 3). If ABC is translated 1 unit down and
3 units to the left to create DEF, what are the
coordinates of the vertices of DEF ?
A
D(0, 1), E(1, 2), F(1, 3)
B
D(0, –1), E(0, 3), F(–2, –2)
C
D(–2, 2), E(0, 3), F(–1, 0)
D
D(–1, 0), E(0, 3), F(–2, 2)
D
(5, 4)
(5, 4)
(4, 5)
(4, 5)
CSG00317
— 31 —
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 © 2008 California Department of Education.
CSG10096
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
80
Released Test Questions
Trapezoid ABCD below is to be translated to
trapezoid Aa Ba C aD a by the following motion
rule.
( x, y) l( x + 3, y 4)
y
A
D
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
-6
-7
-8
-9
B
C
1
2 3 4 5 6 7 8 9
x
What will be the coordinates of vertex C a ?
A
B
C
D
(1, 3)
(2, 1)
(6, 1)
(8, 3)
CSG10214
— 32 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
Question Number
Correct Answer
Standard
Year of Release
1
A
GE1.0
2004
2
A
GE1.0
2005
3
C
GE1.0
2007
4
D
GE2.0
2003
5
D
GE2.0
2004
6
D
GE2.0
2005
7
B
GE2.0
2007
8
B
GE3.0
2003
9
D
GE3.0
2004
10
C
GE3.0
2005
11
A
GE3.0
2006
12
D
GE4.0
2003
13
C
GE4.0
2004
14
C
GE4.0
2005
15
B
GE4.0
2005
16
D
GE4.0
2006
17
A
GE4.0
2007
18
D
GE4.0
2007
19
A
GE5.0
2003
20
A
GE5.0
2004
21
C
GE6.0
2003
22
B
GE6.0
2007
23
C
GE7.0
2003
24
B
GE7.0
2004
25
C
GE7.0
2005
26
D
GE7.0
2006
27
A
GE7.0
2006
28
D
GE8.0
2003
29
C
GE8.0
2005
30
C
GE8.0
2006
31
C
GE8.0
2007
32
A
GE9.0
2006
33
D
GE9.0
2006
34
C
GE10.0
2003
35
A
GE10.0
2004
— 33 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
Question Number
Correct Answer
Standard
Year of Release
36
C
GE10.0
2005
37
B
GE10.0
2006
38
B
GE10.0
2007
39
B
GE10.0
2007
40
D
GE11.0
2004
41
A
GE11.0
2005
42
D
GE12.0
2003
43
A
GE12.0
2003
44
C
GE12.0
2005
45
A
GE12.0
2005
46
D
GE12.0
2006
47
C
GE12.0
2007
48
A
GE13.0
2005
49
A
GE13.0
2006
50
B
GE13.0
2007
51
C
GE14.0
2004
52
B
GE15.0
2003
53
A
GE15.0
2004
54
A
GE16.0
2003
55
D
GE16.0
2004
56
D
GE16.0
2006
57
D
GE16.0
2007
58
B
GE17.0
2004
59
C
GE17.0
2005
60
D
GE17.0
2006
61
A
GE17.0
2007
62
A
GE18.0
2003
63
C
GE18.0
2004
64
C
GE18.0
2006
65
C
GE18.0
2007
66
C
GE19.0
2003
67
B
GE19.0
2005
68
A
GE19.0
2006
69
B
GE19.0
2007
70
A
GE20.0
2004
— 34 —
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 © 2008 California Department of Education.
CA L I F O R N I A S TA N DA R D S T E S T
Geometry
Released Test Questions
Question Number
Correct Answer
Standard
Year of Release
71
B
GE20.0
2005
72
A
GE20.0
2007
73
D
GE21.0
2003
74
C
GE21.0
2004
75
B
GE21.0
2005
76
C
GE21.0
2006
77
D
GE21.0
2007
78
D
GE22.0
2003
79
A
GE22.0
2004
80
D
GE22.0
2006
— 35 —
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 © 2008 California Department of Education.