Test Success Cover Grade 8 No Algebra - SHSPHOTOS Students compute the volumes and surface areas of prisms ... Students apply these techniques in solving word problems. ... in problems

Summative Math

CALIFORNIA STANDARDS TEST SUMMATIVE HIGH SCHOOL MATHEMATICS (Blueprint adopted by the State Board of Education 10/02)

* 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 CONTENT STANDARDS # ofItems %

Algebra I 18 28% 4.0* Students simplify expressions prior to solving linear

equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.

1

5.0* Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

3

6.0* Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able

to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

2

7.0* Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula.

1

8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

1

10.0* Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.

3

11.0 Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

1

12.0* Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

1

14.0* Students solve a quadratic equation by factoring or completing the square. 1

15.0* Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. 2

20.0* Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.

1

23.0* Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. 1





Geometry 19 29% 3.0* Students construct and judge the validity of a logical

argument and give counterexamples to disprove a statement.

1

4.0* Students prove basic theorems involving congruence and similarity. 3

5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

2

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.

2

8.0* Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.

1

9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

1

10.0* Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

1

11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.

1

15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. 2

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.

2

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.

1

21.0* Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

2





Algebra II 23 35% 1.0* Students solve equations and inequalities involving

absolute value. 1

2.0* Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

3

3.0* Students are adept at operations on polynomials, including long division. 1

4.0* Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.

1

6.0* Students add, subtract, multiply, and divide complex numbers. 1

7.0* Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.

2

8.0* Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.

3

10.0* Students graph quadratic functions and determine the maxima, minima, and zeros of the function. 2

11.1* Students understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents.

1

12.0* Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

2

14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.

1

15.0* Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.

1





18.0* Students use fundamental counting principles to compute combinations and permutations. 1

19.0* Students use combinations and permutations to compute probabilities. 1

22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. 1/2**

23.0* Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. 1/2**

24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.

1

Probability and Statistics 5 8% 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.

2

2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces. 2

7.0 Students compute the variance and the standard deviation of a distribution of data. 1

SUMMATIVE HIGH SCHOOL MATHEMATICS TOTAL 65 100%

CA LI FOR N I A STA N DA R DS T E ST

Released Test Questions Algebra I

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.

— 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.

Note: Not all Algebra I standards are covered on the Summative Math test.

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1 Is the equation 3(2 x 4) = 18 equivalent to

6x 12 = 18?

A Yes, the equations are equivalent by the Associative Property of Multiplication.

B Yes, the equations are equivalent by the Commutative Property of Multiplication.

C Yes, the equations are equivalent by the Distributive Property of Multiplication over Addition.

D No, the equations are not equivalent.

CSA10108

�2

A

B

C

D

4

6

9

10

16 + 3 8 =

CSA00471

3 Which expression is equivalent to x x� 6 2?

4 3A x x

5 3B x x

7 3C x x

9 3D x x

CSA20167

4 Which number does not have a reciprocal?

A –1

B 0

C1

1000

D 3

CSA10152

�5 What is the multiplicative inverse of 1

?2

A 2

1 B2

1C2

D 2

CSA10153

�6 What is the solution for this equation?

2x 3 = 5

A

B

C

D

x= 4 or x= 4

x= 4 or x= 3

x= 1 or x= 4

x= 1 or x= 3

CSA00264




� 7 What is the solution set of the inequality 5 x+ 4 3?

A 2 x 6

B x 2 or x 6

C 12 x 4

D x 12 or x 4

CSA10036

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 12x 1=14x

CSA00206

� 9 Which equation is equivalent to 4 2( 5x)= 6 3(1 3x)?

A 8x= 5

B 8x=17

C 29x= 5

D 29x=17

CSA00059

� 10 The total cost (c) in dollars of renting a sailboat for n days is given by the equation

c= 120+ 60n.

If the total cost was $360, for how many days was the sailboat rented?

A 2

B 4

C 6

D 8

CSA00485�


�11 Solve: 3(x+ =5) 2x+ 35

Step 1: 3x+ 15= 2x+ 35 Step 2: 5x+ 15= 35 Step 3: 5x= 20 Step 4: x= 4

Which is the first incorrect step in the solutionshown above?

A Step 1

B Step 2

C Step 3

D Step 4

CSA00332

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

CSA10052

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13 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

CSA10057

�14 What is the solution to the inequality x >5 14?

A x> 9

B x>19

C x< 9

D x<19

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

CSA10046

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

CSG10197

17 What is the conclusion of the statement in the box below?

If x2 = 4, then x= 2 or x= 2.

A 2 4x =

B 2x=

C 2x=

D 2 or 2x x= =

CSA30045

18 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



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19 The chart below shows an expression evaluated for four different values of x.

x x + x + 52

1 72 116 477 61

Josiah concluded that for all positive values of x x x 5, 2 + + produces a prime number. Which value of x serves as a counterexample to prove Josiah’s conclusion false?

A 5

B 11

C 16

D 21

CSA20027

20 John’s solution to an equation is shown below.

Given: x2 + + = 05x 6

Step 1: (x+ 2)(x+ 3)= 0

Step 2: x 2 0 or x+ =3 0+ =

Step 3: x= 2 or x= 3

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

CSA20034

21 Stan’s solution to an equation is shown below.

Given: n+ 8( n+ 20) = 110

Step 1: n+ 8n+ 20= 110

Step 2: 9n+ 20= 110

Step 3: 9n= 110 20

Step 4: 9n= 90

9n 90 Step 5: =

9 9Step 6: n= 10

Which statement about Stan’s solution is true?

A

B

C

D

Stan’s solution is correct.

Stan made a mistake in Step 1.



CSA20035

22 When is this statement true?

The opposite of a number is less than the original number.

A This statement is never true.

B This statement is always true.

C This statement is true for positive numbers.

D This statement is true for negative numbers.

CSA20147



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23 What is the y-intercept of the graph of 4x+ 2 y= 12?

A – 4

B – 2

C 6

D 12

CSA00239

24 Which inequality is shown on the graph below?

y

76

5

4

3

21

2 3 4 5 6 7-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7 1-10

x

A1

y x< 12

B1

y x 12

C1

y x> 12

D1

y x 12

CSA10130

�25 Which best represents the graph of y x= 2 2?

y y

x x

y y

x x

CSA00299

7654321-1-3-4-5-6-7 -2 0

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

A

7654321-1-3-4-5-6-7 -2 0

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

C

7654321-1-3-4-5-6-7 -2 0

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

B

7654321-1-3-4-5-6-7 -2 0

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

D




26 Which inequality does the shaded region of the graph represent?

y

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1

-2

-3

-4

-5

-6

-7

x

�


A

B

C

D

3x y+ 2

3x y+ 2

3x y+ 2

3x y+ 2

CSA20055

� y

27

-3-4-5 -2 -1 0 1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

x

Which equation best represents the graph above?

A y=

B y= 2x

C y x 2= +

D y= 2x+2

CSA00508

�28 Which point lies on the line defined by 3x+ 6 y= 2?

A (0, 2)

B (0, 6)

⎛ 1⎞⎜C ⎜1, − ⎟⎟⎜ ⎟⎝ 6⎠

⎛ 1⎞⎜D ⎜1, − ⎟⎟⎜ ⎟⎝ 3⎠

CSA00009



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29 What is the equation of the line that has a slope of 4 and passes through the point (3 10)?,

A y= 4x 22

B y= 4x+ 22

C y= 4x 43

D y= 4x+ 43

CSA10150

30 The data in the table show the cost of renting a bicycle by the hour, including a deposit.

Renting a Bicycle

Hours (h) Cost in dollars (c)

2 15

5 30

8 45

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?

A c= 5h

1B c= h+5

5

C c= 5h+ 5

D c= 5h 5

CSA10005

31 Some ordered pairs for a linear function of xare given in the table below.

x y

1 1

3 7

5 13

7 19

Which of the following equations was used to generate the table above?

A y= 2x+1

B y= 2x 1

C y= 3x 2

D y= 4x 3

CSA10181

32 The equation of line l is 6x+ 5 y= 3, and the equation of line q is 5x 6 y= 0. Whichstatement 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




33 Which equation represents a line that is

5parallel to y= x+ 2?

4

5A y= x+1

4

4 B y= x+2

5

4 C y= x+3

5

5 D y= x+ 4

4

CSA10112

�34 Which graph best represents the solution to this system of inequalities?

2x y 1

2x 5 y 10y y

-5 -4 -3 -2 -1-1

-2

-3

-4

-5

10 2 3 4 5 -5 -4 -3 -2 -1-1

-2

-3

-4

-5

10 2 3 4 5x x

1

2

3

4

5

1

2

3

4

5

B D

A C

y y

-5 -4 -3 -2 -1-1

-2

-3

-4

-5

1

2

3

4

5

10 2 3 4 5 -5 -4 -3 -2 -1-1

-2

-3

-4

-5

1

2

3

4

5

10 2 3 4 5x x

CSA00516

�35 What is the solution to this system of equations?

y= 3x 2

6x+ 2 y= 4

A (6, 2)

B (1, –5)

C no solution

D infinitely many solutions

CSA00027

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Released Test QuestionsAlgebra I

�36 Which ordered pair is the solution to the system of equations below?

x+ 3 y= 7

x+ 2 y=10

7 13A ,2 4

7 17B ,

2 5

C ( 2,

D (16, 3)

CSA10131

� 37 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?

A

B

C

D

27

40

56

73

CSA20083

�38 Which of the following best describes the graph of this system of equations?

2x+ 3y=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

CSA00509

� 539 x3=

10x7

A 2x4

1B

2x4

1C

5x4

x4D

5

CSA00303

�40 (4x2 2x+8) (x2 + 3x 2)=A 3x2 + +x 6

B 3x2 + +x 10

C 3x2 5x+6

D 3x2 5x+10

CSA00086

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41 The sum of two binomials is 5x2 6x. If one of the binomials is 3x2 2x, what is the other binomial?

A 2x2 4x

B 2x2 8x

C 8x2 + 4x

D 8x2 8x

CSA10160



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42 Which of the following expressions is equal to

2 1 ? ( ) ( )x+ + x 2 (2x+ )

A 2x2 2x

B 2x2 4x

C 2x2 + x

D 4x2 +2x

CSA10191

43 A volleyball court is shaped like a rectangle. It has a width of x meters and a length of 2xmeters. Which expression gives the area of the court in square meters?

A 3x

B 2x2

C 3x2

D 2x3

CSA00496

44 Which is the factored form of 3a2 24 ab + 48 b2 ?

A (3a 8b)( a 6b)

B (3a 16 b)( a 3b)

C 3(a 4b)( a 4b)

D 3(a 8b)( a 8b)

CSA00066

� 45 Which is a factor of x2 11x+ 24?

A x+3

B x 3

C x+ 4

D x 4

CSA00503

46 Which of the following shows 9t2 + +12 t 4factored completely?

A (3t+2)2

B (3t+ 4)(3t+1)C (9t+ 4)(t+1)D 9t2 +12 t+ 4

CSA20106

47 What is the complete factorization of 32 8z2?

A 8 2( + z)(2 z)

B 8 2( + z)(2 z)

C 8 2( + z)2

D 8 2( 2 z)

CSA20105

48 If x2 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



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Released Test QuestionsAlgebra I

49 What quantity should be added to both sides of this equation to complete the square?

x2 8x= 5

A 4

B – 4

C 16

D –16

CSA00478

50 What are the solutions for the quadratic equation x2 + 6x= 16?

A 82,

B 2 8 ,

C 2, 8

D 2 8,

CSA10062

51 Leanne correctly solved the equation x2 + 4x= 6 by completing the square.Which equation is part of her solution?

A ( )2 2 = 8x+

B (x+2 )2 =10

C ( )4 2 =10 x+

D ( )4 2 = 22 x+

CSA20139

52 Carter is solving this equation by factoring.

10x2 25x+ 15= 0

Which expression could be one of his correct factors?

A x+3

B x 3

C 2x+3

D 2x 3

CSA00162

�53 Toni is solving this equation by completing the square.

ax2 + bx+ c= 0 (where a 0)

Step 1: ax2 + bx= c

2 b c Step 2: x + x=

a a Step 3: ?

Which should be Step 3 in the solution?

c bA x2 = x

b a

b cB x+ =

a ax

C x2 b b c b+ x+ = +

a 2a a 2a

2 2

D x2 b b c b+ x+ = +

a 2a a 2a

CSA00072




54 Four steps to derive the quadratic formula are shown below.

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

CSA20062

�55 Which is one of the solutions to the equation 2x2 x 4= 0?

CSA00314

1A 334

1B + 33

4

1+ 33 C

4

1 33 D

4

56 Which statement best explains why there is no real solution to the quadratic equation

2 + +2x x 7= 0 ?

A The value of 12 i i is positive.4 2 7

B The value of 12 i i is equal to 0.4 2 7

C The value of 12 i i is negative.4 2 7

D The value of 12 i i is not a perfect4 2 7square.

CSA10147

57 What is the solution set of the quadratic equation 8x2 + 2x+ 1= 0?

1 1A ,

2 4

B { 1+ 12, 2}

D no real solution

CSA10179

1+ 7 1C ,

7

8 8

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58 The graph of the equation y= x2 3x 4 is shown below.

y

5-

5-

4-

4-3-

3-

2-2- 1-

1-01

1

2

2

3

3

4

4

5

5

6-

6-

7-

7-

8-

8-

9-

9- 6 7 8 9

6

7

8

9

x

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

CSA00514

59 Which best represents the graph of y= x2 + 3?

5

4

3

2

1

-5 -4 -3 -2 -1 0 1 2 3 4 5 -1

-2

-3

-4

-5

y

x

A

y

3

5

4

2

1

-5 -4 -3 -2 -1 0 1 2 3 4 5 -1

-2

-3

-4

-5

x

C

y

5

4

3

2

1

-5 -4 -3 -2 -1 0 1 2 3 4 5 -1

-2

-3

-4

-5

x

B

y

-3

-2

5

4

3

2

1

-5 -4 -3 -2 -1 0 1 2 3 4 5 -1

-4

-5

x

D

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CSA00519

60 Which quadratic function, when graphed, has x-intercepts of 4 and 3?

A y=(x 3)(x+ 4)

B y=(x+3 2x 8 ))(

C y=(3x 1)(4x+1)

D y=(3x+1)(8x 2)

CSA20115




61 How many times does the graph of y= 2x2 2x+ 3 intersect the x-axis?

A none

B one

C two

D three

CSA10084

62 An object that is projected straight downward with initial velocity v feet per second travels a distance s vt time in seconds.= + 16t2 , where t=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

CSA00158

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.

CSA00104

x2

4xy + 4 y264 What is reduced to lowest

3xy 6 y2

terms?

x 2yA3

x 2yB

3y

x+2yC

3

x+2yD

3y

CSA00463

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6x2 + 21 x+ 965 Simplify to lowest terms. 4x2 1

3(x+1)A

2x 1

3(x+3)B

2x 1

3 2( x+3 )C

4(x 1)

3(x+3)D

2x+1

CSA10025

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Algebra I Released Test Questions

�66 x2 4x+ 4What is reduced to lowest terms?

x2 3x+ 2

x 2A

x 1

x 2Bx+1

x+2Cx 1

x+2D

x+1

CSA10189

� 12 3 20 267 a a

What is reduced to lowest terms? 16a2 + 8a

aA2

3a 5 B

2a+1

2aC

4 2+ a

a a(3 5 )D

2 2( a+1)CSA00013

� 68

7(z 2)A

4(z+1)

7(z+ 2)B

4(z 1)

7z z( +1 )C

4(z+ 2)

7z z( 1 )D

4(z+ 2)CSA00067

69 Which fraction equals the product

x+ 5 2 x 3 ?

3x+ 2 x 5

2x 3A3x+2

3x+2B4x 3

x2 25C

6x2 5x 6

2x2 +7x 15D3x2 13x 10

CSA10029

�





�70 x2 +8x+16 2x+8÷ =x+ 3 x2 9

( + )2 2 x 4

A(x 3)(x+ 2

3)

2(x+3)(x 3)B

x+ 4

(x+ 4)(x 3)C2

(x+ 4)(x )2 3D

2(x+3)CSA20164

3x

71 5 Which fraction is equivalent to ?x x +4 2

x2 A

5

9x2 B

20

4 C 5

9 D 5

CSA10141

�

�

�

�


72 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?

A

B

C

D

60 mL

45 mL

40 mL

25 mL

CSA00333

73 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

B

C

D

50 miles per hour

60 miles per hour

65 miles per hour

70 miles per hour

CSA00576

74 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

B

C

D

50 min

25 min

15 min

12 min

CSA00161



�

�

�

�



75 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

CSA10055

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

CSA10186

77 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)}

CSA10070

78 For which equation graphed below are all the y-values negative?

y y

5

5

4

43

3

2

2 110

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9 6 7 8 9

6789

5

5

4

43

3

2

2 110

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9 6 7 8 9

6789

x x

A C

y y

5

5

4

43

3

2

2 110

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9 6 7 8 9

6789

5

5

4

43

3

2

2 110

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9 6 7 8 9

6789

x x

B D

CSA00522




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 2 3 4 5 6 7 -1

-2

-3

-4

-5

-6

-7

x

�


A

B

C

D

{ 1, 2 3 4, , }{ 1 2, , 4, 5}{1 2, , 3, 4}{1 2, , 4, 5}

CSA10072




80 Which of the following graphs represents a relation that is not a function of x?

A y

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1

-2

-3

-4

-5

-6

-7

x

C y

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1

-2

-3

-4

-5

-6

-7

x

B y

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1

-2

-3

-4

-5

-6

-7

x

D y

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1

-2

-3

-4

-5

-6

-7

x

�


CSA30002



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



Question Number Correct Answer Standard Year of Release

C 1.1 2006

B 2.0 2003

B 2.0 2005

B 2.0 2006

D 2.0 2007

C 3.0 2003

D 3.0 2004

A 4.0 2003

C 4.0 2005

B 5.0 2003

B 5.0 2004

C 5.0 2004

C 5.0 2006

B 5.0 2007

A 5.0 2007

D 24.1 2004

D 24.2 2006

D 24.2 2007

A 24.3 2005

B 25.1 2005

B 25.2 2006

C 25.3 2005

C 6.0 2003

D 6.0 2004

A 6.0 2006

A 6.0 2007

B 6.0 2007

C 7.0 2003

A 7.0 2004

C 7.0 2005

C 7.0 2007

D 8.0 2003

A 8.0 2004

C 9.0 2003

D 9.0 2004






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






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



�

�

�


Released Test QuestionsAlgebra II

� 1 What is the complete solution to the equation 3 6x = 15?

A x= 2; x= 3

B x= 2; x= 3

C x= 2; x= 3

D x= 2; x= 3

CST00507

�2 What are the possible values of x in 12 4 2=x ?

A

B

C

D

x x= =2 50 3 50. .or

< <3 50 2 50. .x

3 5 2 5. .> >x

x x= =2 50 3 50. .or

CST20085

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 6 dozen

B 7 dozen

C 8 dozen

D 9 dozen

CST00099

4 What is the solution to the system of equations shown below?

A

B

2 3 8

6 0

6 3 9 24

x y z

x y z

x y z

+ ==

+ =

0 4 4, ,( )

1 410

3, ,

C no solution

D infinitely many solutions

CST00203

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 6

B 8

C 9

D 12

CST00491



Released Test Questions Algebra II


� 6 What system of inequalities best represents the graph shown below?

54321-1-3-4-5 -2 0x

-5

-4

-3

-1

1

2

3

4

5

-2

y

A y y> 2 1and > +x

B y y> 2 1and < +x

C y y< 2 1and > +x

D y y< 2 1and < +x

CST00500

� 7 Which point lies in the solution set for the

2 6y xsystem ?

<<2 3y x 6

A ( )4 1,

B ( )3 1,

C ( )0 3,

D ( )4 3,

CST10059

� 8 Which system of linear inequalities is represented by this graph?

-3-4-5-6-7-8-9

987654321

-3-4-5-6-7-8-9

y

A1

y x+32

y x 2

By 2x+3

y x 2

C2x y 3

x y+ 2

D2x y+ 3

x y 2CST20079



�

�

�

�

�



� 2x+ 7 2x4 + 21 x3 + 35 x2 37 x+ 46 9 )A x x x

x3 27 7 6

4

2 7 + +

+

B 2 14 14 12 4

2 7 3 2x x x

x+ +

+

C x x xx

3 27 7 6 4

2 7 + +

+

D x x xx

3 27 7 6 4

2 7 + + +

+CST00109

10 Which polynomial represents

(3x2 + x 4)(2x 5)?

A 6x3 13 x2 13 x 20

B 6x3 13 x2 13 x+20

C 6x3 +13 x2 +3x 20

D 6x3 +13 x2 +3x+20

CST10024

11 ( 2x2 +6x+1) 2(4x2 3x+1) =A 6x2 1

B 10x2 1

C 6x2 +12 x 1

D 10x2 +12x 1

CST00233

12 Which expression is equivalent to (6 y2 2)( 6 y+ 2)?

A

B

C

D

36y2 4

36y3 4

36y2 +12y2 +12y 4

36y3 +12y2 12y 4

CST20008

13 What is the volume of the figure below?

x + 6

x + 1 x + 4

A x3 +10x2 +34x+24

B x3 +11x2 +34x+24

C x3 +10x2 +24x+24

D x3 +11x2 +24x+24

CST10285

14 8a3 + c3 =

A (2 a c + )( 2a c + )( 2a c + )

B (2 a c)( 4a2 + 2ac+ c 2 )

C (2 a c)( 4a2 + 4ac+ c 2 )

D (2 a c 2 2ac+ c + )( 4a 2 )

CST00118





15 The total area of a rectangle is 4x 2 . � 4 9 yWhich factors could represent the length times width?

A (2x2 3y)(2x2 +3y) B (2x2 + 3y)(2x2 + 3y) C (2x 3y)(2x 3y) D (2x+ 3y)(2x 3y)

CST10028

�16 Which product of factors is equivalent to

(x+ 1)2 y2 ?

A (x+ + y)21

B (x+1 y)2

C (x 1+ 1 y)( x y)

D (x+ + y)( x+ y) 1 1

CST10030

�17 Which expression shows the complete factorization of 12x2 147?

A (3x 7)(4x+2)

B (4x 21 )(3x+7)

C 12(x 7)(x+7)

D 3 2 2x+( x 7)( 7)

CST20117

� x+ 3 6

18x+ 5

+x2 + 3x 10

=

x2 + x A

x2 + 3x 10

7x 9 B

x2 + 3x 10

2 + +x x 12 C

x2 + 3x 10

2 + +D

x2 + 3x 10

x x 1

CST00295

2 3 2 19 Which is a simplified form of

3a b c ?

1 2 3 � (a b c )

3a5 A

3 5 b c

3ab B 5 c

3 C 2 5 b c

3 D 3 5 ab c

CST00267




20� 20x 8xWhat is ÷ ?

2 527 y 15 y

32y3A

81x

32 B

81xy7

25y3

C18x

25 D

18xy7

CST20321

�21 4x2 16?

2 x Which product is equivalent to

A 4(x 2)

B 4(x+2)

C 4(x 2)

D 4(x+2)

CST10041

�22x2 + 4x x2 9i =

x+ 3 x2 + x 12

A 1

B x

C x+ 4

Dx+3

x 3

CST10043

�23 What is the simplest form of 3 2 2 35x y+ 20 x y + 20 xy

?5xy

A (x+2)2

B (x+2y)2

C x2 + y2

D x2 + 4y2

CST10049

�24 If i= 1, which point shows the location of 5 2i on the plane?

Imaginary

Real

A point A

B

C

point B

point C

D point D

CST00510

-2 -1-3-4-5-6-7-8-9

-2

-1

1234

5

9

87

6A

B

C0 1 2 3 4 5 6 7 8 9

D

-3-4-5-6-7-8-9


4 3




�25 If i= 1, what is the value of i4 ?

A i

B i

C 1

D 1

CST00238

�26 Which of the following complex numbers is represented by the point on the graph below?

�

�


Imaginary

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1

-2

-3

-4

-5

-6

-7

Real

A 4 3+ i

B 4 3i

C 3 4i

D 3 4+ i

CST30142

27 If i= 1, then 4 6i i( )=

A 48

B 24

C 24

D 48

CST00512

28 What is an equivalent form of ?� 23+ i

3 iA

4

3 i B

5

4 i C

4

4 i D

5

CST10040

29 What is the product of the complex numbers (3+ i) and (3 i)?

A 8

B 10

C 9 – i

D 10 6i

CST10038




�30 If i= 1 and a and b are non-zero real

CST10371

1numbers, what is ?

a bi+

a biA +a2 +b2

a biBa2 +b2

a biC +a2 b2

a biDa2 b2

�

CST00114

31 What are the solutions to the equation x2 + 2x+ 2= 0?

A x= 0; x= 2

B x= 0; x= 2i

C x= 1+ ; x= 1 ii

D x= + 2; x= 11 2 2 2

�32 What are the solutions to the equation 1 3

1+ = ?x2 x

3 5 3 5A x= + ; x=

2 2 2 2

5 5B x 3 ; x= 3= +

2 2

3 13 3 13C x= + ; x=

2 2 2 2

13 13D x 3 ; x= 3= +

2 2

CST00197

� 33 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 morethan their sum.

Which of the following represents possible values of these two numbers?

A 6 3,

B 4 1,

C 1 4,

D 3 6,

CST20109

�34 Jenny is solving the equation x2 8x= 9 bycompleting the square. What number should beadded to both sides of the equation to complete the square?

A 2

B 4

C 8

D 16

CST00508

� 35 Which of the following most accurately describes the translation of the graph y=(x+ 2

3) 2 to the graph of

=(x 2)2y + 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




� �



36 Which of the following sentences is true about the graphs of y= 3(x 5)2 + 1 and

y= 3(x+ 5)2 + 1?

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, while the other graph has a vertex that is a minimum.

CST10294

37 What are the x-intercepts of the graph of y= 12x2 5x 2?

A1

1and 6

B1

1and 6

C2 1

and 3 4

D2 1

and 3 4

CST00297





� 238 Which is the graph of y= 2(x 1) + 1?

y y

76

5

4

3

21

0 1 2 3 4 5 6 7 -1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7

76

5

4

3

21

0 1 2 3 4 5 6 7 -1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7xx

A C

y y

76

5

4

3

21

0 1 2 3 4 5 6 7 -1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7

76

5

4

3

21

0 1 2 3 4 5 6 7 -1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7x x

B D

CST10292



�

�



39 Which ordered pair is the vertex of

f x( )= x2 + 6x+ 5?

A ( 4)3,

B ( 3)2,

C ( ,1 0)

D ( ,0 5)

CST10084

2 2

40 The graph of x y

= 1 is a hyperbola.� 2 3

Which set of equations represents the

asymptotes of the hyperbola’s graph?

3 3A y= x, y= x

2 2

2 2B y= x, y= x

3 3

1 1C y= x, y= x

2 2

1 1D y= x, y= x

3 3

CST10304

�41 Which of the following represents a parabola?

A x y r2 2 2+ =

B y

a

x

b

2

2

2

2+ 1=

C 4 2px= y

D y

a

x

b

2

2

2

21=

CST20065

42 4x2 5 y2 16x 30 y 9= 0

What is the standard form of the equation of the conic given above?

(x 4)2 (y 3)2A =1

11 4

(y+ 3)2 (x 2)2B =1

4 5

(y 3)2 (x+ 2)2C =1

6 9

(x 4)2 (y 3)2D + =1

11 4

CST00146



�

�

�


Released Test QuestionsAlgebra II

43 Which statement describes the graph of the equation x2 + y2 + 4x 6 y 3= 0?

A a hyperbola with center ( 2 3) and vertices,(4, 3) and ( 4 3),

B a hyperbola with center ( 2 3) and vertices,(2, 3) and (3, 2)

C a circle with center ( 2 3) and radius 8,

D a circle with center ( 2 3) and radius 4,

CST20127

� x44 What is the solution to the equation 5 = 17?

A x= 2

B x= log10 2

C x= log10 17+ log10 5

log10 17 D x=

log10 5

CST00132

45 If log10 x= 2, what is the value of x ?

1A x=

10

1B x=

10

1C x=

100

D x=100

CST10255

46 Which equation is equivalent to log3 = x?� 19

A

B

1

9

33= x

1

9

3

= x

C 31

9x=

D 319 = x

CST10151

47 Which is the first incorrect step in simplifying4

log4 ?64

4Step 1: log4 = log4 4 log4 64

64Step 2: = 1 1 6

Step 3: = 15

A Step 1

B Step 2

C Step 3

D Each step is correct.

CST00517



� �

�



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 Shanan’s work

3 7 x33 7 x3

x x = x x =7 7 x x

= x10 , x 0 =14

, x 0 x

Michael’s work Brenda’s work 3 3

3 7 x 3 7 x x x = x x =

7 7 x x

= x 4 , x 0 x x , 0= 4

Which is a completely correct solution?

A Jeremy’s work

B Michael’s work

C Shanan’s work

D Brenda’s work

CST10301

49 A student showed the following steps in his solution of the equation below, but his answer was not correct.

log5 (2x2 3x+ 1) log5 (x 1)+ log5 125= 6

Step 1:( )( 1) ( ) 3log5 2x 1 x log5 x 1 + = 6

Step 2:log5 (2x 1)(x 1) log5 (x 1)= 3

Step 3: log5 (x 1)= 3

Step 4: x 1= 125

Step 5: x= 126

In which step did he make his first error?

A

B

C

D

Step 1

Step 2

Step 3

Step 4

CST10336

50 A certain radioactive element decays over t

1time according to the equation 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

— 17 — This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected


� �

�

�



51 Bacteria in a culture are growing exponentially with time, as shown in the table below.

Bacteria Growth

Day Bacteria

0 1001 2002 400

Which of the following equations expresses the number of bacteria, y, present at any time, t?

A y=100+2t

B y= i t(100) (2)C y= 2t

D y= i t(200) (2)CST10253

52 If the equation y= 2x is graphed, which of the following values of x would produce a point closest to the x-axis?

1A

4

3 B

4

5 C

3

8 D

3

CST20145

53 Which table below correctly describes points of ( ) 3 xthe exponential function f x = 2?

A

x – 2 – 1 0

f(x) – 18 – 6 – 2

B

x – 2 – 1 0

f(x) – 4 – 5 – 2

C

x – 2 – 1 0

8 2f(x) – 1 –1 – 1 9 3

D

x – 2 – 1 0

f(x) 7 1 – 1

CST20196

54 log6 40=

A log10 6+ log 10 40

B log10 6 log 10 40

C (log 10 6)(log 10 40 )

logD 10 40

log10 6CST00199



�

�

�

�



55 Jonathan wrote the equation log6 (x 4)= 0on the board. He needs one clue for problem solving. Which fact provides the correct information that he needs to solve the equation?

A 60 =1

B 61= 6

C 4 4= 0

D 6 4= 2

CST10484

�56 What is the value of log327?

A 2

B 3

C 6

D 9

CST00519

� . .57 If log 2 0 301 and log 3 0 477 , what is the approximate value of log 72?

A 0.051

B 0.778

C 0.861

D 1.857

CST10362

58 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

B some values of x

C no values of x

D impossible to determine

CST00032

59 On a recent test, Jeremy wrote the equation

x2 16x 4.= + Which of the following

x 4

statements is correct about the equation

he wrote?

A The equation is always true.

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.

CST10260

60 Given the equation y= xn where x>0and n<0, which statement is valid for real values of y?

A y> 0

B y= 0

C y< 0

D y 0

CST20140

— 19 —

� 61 If x is a real number, which best describes the

values of x for which the inequality x>0

is true?

A all x> 0

B all x 0

C all values of x

D no values of x

CST00396

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.

�

�

�

�

�

�



62 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.

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

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

CST10391

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?

1A

45

2B

45

1C

5

2D

5

CST00071

66 (3 y 1)4 =

A 81y4 108y3 + 54y2 12y+1

B 81y4 +108y3 54y2 12y+1

C 81y4 54y3 108y2 12y+1

D 81y4 + 54y3 108y2 12y+1

CST00308

67 How many terms does the binomial expansion

of (x2 + 2 y3)20contain?

A 20

B 21

C 40

D 60

CST10316



�

�

�



68 What are the first 4 terms in the expansion of

(1 2 )6 ?+ x

A 1 1 30 x2 + 3+ 2x+ 40 x

B 1 1+ 2x+24 x2 + 48 x3

C 1+12x+30x2 +120x3

D 1+12x+60x2 +160x3

CST20022

69 What is the sum of the infinite geometric series

1 1 1 1 + + + + . . . ? 2 4 8 16

A

B

C

D

1

1.5

2

2.5

CST20167

70 What is the nth term in the arithmetic series below?

3+ + 11+ 19 . . .7 15 +

A 4n

B 3 4+ n

C 2n+1

D 4n 1

CST10178

71 Which expression represents f g x � ( ( ))if f x = 2 1 and g x = + 3?( ) x ( ) x

A x3 +3x2 x 3

B x 6x2 + +8

C x x 22 + +

D x2 +8

CST20032

� ( ) ( )72 Given that f x = 3x2 4 and g x = 2x 6,

what is g f 2 )?( ( )

A 2

B 6

C 8

D 10

CST30049

�73 ( ) and g x( )= 2If f x = x2 + 2x+ 1 3(x+1) ,

which is an equivalent form of f x( )+ g( )x ?

A x2 + 4x+2

B 4x2 +2x+ 4

C 4x2 +8x+ 4

D 10x2 +20x+10

CST10204



�

�

�

�



74 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?

1A

24

1 B

4

2 C

5

23 D

25

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

B

C

D

7%

14%

24%

50%

CST20180

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 1

4

2B5

C 1

2

5D6

CST20181

77 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?

5A

12

7B

20

5C

8

1D

5

CSN00211



�



78 The probabilities that Jamie will try out for various sports and team positions are shown in the chart below.

Jamie

Try out for guard 80%

Try out for forward

20%

Try out for catcher

70%

Try out for pitcher

30%

Try out for basketball team

Try out for baseball team

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

B

C

D

40%

60%

80%

90%

CST10210



� �



79 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.

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.)

A 3.3

B 7.4

C 10.8

D 13.5

CST20052

80 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



123456789

1011121314151617181920212223242526272829303132333435



Question Number Correct Answer Standard Year of Release B 1.0 2004D 1.0 2007C 2.0 2003C 2.0 2004B 2.0 2006B 2.0 2006B 2.0 2007D 2.0 2007D 3.0 2003B 3.0 2004D 3.0 2005D 3.0 2006B 3.0 2007D 4.0 2003A 4.0 2005D 4.0 2006D 4.0 2007A 7.0 2003A 7.0 2004D 7.0 2005D 7.0 2006B 7.0 2006B 7.0 2006D 5.0 2003C 5.0 2005C 5.0 2007C 6.0 2003B 6.0 2004B 6.0 2005B 6.0 2007C 8.0 2003A 8.0 2004B 8.0 2005D 8.0 2006A 9.0 2004





Question Number Correct Answer Standard Year of Release 36 B 9.0 200537 C 10.0 200338 C 10.0 200439 A 10.0 200640 A 16.0 200441 C 16.0 200742 B 17.0 200343 D 17.0 200744 D 11.1 200345 C 11.1 200446 C 11.1 200547 B 11.2 200348 C 11.2 200549 C 11.2 200750 C 12.0 200351 B 12.0 200452 A 12.0 200553 D 12.0 200754 D 13.0 200455 A 13.0 200756 B 14.0 200357 D 14.0 200458 A 15.0 200359 B 15.0 200460 A 15.0 200661 A 15.0 200662 C 15.0 200763 B 18.0 200564 A 18.0 200665 A 19.0 200566 A 20.0 200367 B 20.0 200668 D 20.0 200769 A 22.0 200570 D 22.0 2006





Question Number Correct Answer Standard Year of Release 71 B 24.0 200572 D 24.0 200773 C 25.0 200474 B PS1.0 200475 B PS1.0 200676 A PS1.0 200777 A PS2.0 200378 A PS2.0 200679 A PS7.0 200580 D PS7.0 2006




Released Test Questions Geometry

Introduction - Geometry The following released test questions are taken from the Geometry Standards Test. This test is one of theCalifornia Standards Tests administered as part of the Standardized Testing and Reporting (STAR) Programunder 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 Summative Math test.

�



�1 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

CSG00185

2 In the diagram below, 1 4.

1l

2

3m

4

t

Which of the following conclusions does nothave to be true?

A 3 and 4 are supplementary angles.

B Line l is parallel to line m.

C 1 3

D 2 3

CSG10066

�3 Consider the arguments below.

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?

A I only

B II only

C both I and II

D neither I nor II

CSG00552

�4 Theorem: A triangle has at most one obtuse angle.

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?

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





�5 Use the proof to answer the question below.

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. ?

Given: AB BC; D is the midpoint of AC

Prove: ABD CBD

A

D

CB

What reason can be used to prove that the triangles are congruent?

A AAS

B ASA

C SAS

D SSS

CSG10068





�6 In the figure below, AB>BC.

A

BC

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 m B

C m A m C=

D m A m C

CSG00524





�7 Use the proof to answer the question below.

Given: 2 3

Prove: 1 4

12

34

t

m

�

Statement Reason

1. 2 3 1. Given

12. 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




�8 “Two lines in a plane always intersect in exactly one point.”

Which of the following best describes a counterexample to the assertion above?

A coplanar lines

B parallel lines

C perpendicular lines

D intersecting lines

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 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

�11 A conditional statement is shown below.

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

CSG20216



�

�

�

�



12 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

CSG00578

13 Which of the following facts would be sufficientto prove that triangles ABC and DBE aresimilar?

A

C B

D

E

A

B

CE and BE are congruent.

ACE is a right angle.

C

D

AC DEand are parallel.

A and B are congruent.

CSG00544

14 Parallelogram ABCD is shown below.

A B

C

E

D

Which pair of triangles can be established to be congruent to prove that DAB BCD ?

A ADC and BCD

B AED and BEC

C DAB and BCD

D DEC and BEA

CSG10146

15 If ABC and XYZ are two triangles such AB BC

that = , which of the following wouldXY YZ

be sufficient to prove the triangles are similar?

A A X

B B Y

C C Z

D X Y

CSG10218



�



�16 In parallelogram FGHI, diagonals IG and FHare drawn and intersect at point M. Which of the following statements must be true?

A �FGI must be an obtuse triangle.

B �HIG must be an acute triangle.

C �FMG must be congruent to�HMG.

D �GMH must be congruent to�IMF.

CSG00559

17 Which of the following best describes the triangles shown below?

8 8

60°

30°

A both similar and congruent

B similar but not congruent

C congruent but not similar

D neither similar nor congruent

CSG00478

�18 Which of the following statements must be true if GHI JKL?

H K

G I

J L

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.

CSG20074




�19 In the figure below, AC DF and A D.

C

BA

F

ED

Which additional information would be enough to prove that ABC DEF?

A AB DE

B AB BC

C BC EF

D BC DE

CSG00517

�20 Given: AB and CD intersect at point E;

1 2


A

B

E1

34 2

C

D

Which theorem or postulate can be used to prove AED BEC ?

A AA

B SSS

C ASA

D SAS

CSG10074

�21 In the figure below, n is a whole number. What is the smallest possible value for n?

n

15

n

A 1

B 7

C 8

D 14

CSG00295




�22 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

CSG10041

�23 In the accompanying diagram, parallel lines land m are cut by transversal t.

t

1 l

2 m

Which statement about angles 1 and 2 mustbe true?

A 1 2.

B 1 is the complement of 2.

C 1 is the supplement of 2.

D 1and 2 are right angles.

CSG00579

�24 What values of a and b make quadrilateral MNOP a parallelogram?

N 21 O

3a – 2b 13

M 4a + b P

A a=1, b= 5

B a= 5, b=1

11 34C a= , b=

7 7

34 11 D a= , b=

7 7

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.

CSG20048





�26 For the quadrilateral shown below, what is m a+ m c?

C

c o

B 95o

32oD

a o

A

A 53°

B 137°

C 180°

D 233°

CSG10162

�27 If ABCD is a parallelogram, what is the length of segment BD?


B C

A D

E7

5

6

A 10

B 11

C 12

D 14

CSG20236

�28 A right circular cone has radius 5 inches and height 8 inches.

8 in.

5 in.

l

What is the lateral area of the cone? (Lateral area of cone = rl, where l= slant height )

A 40 sq in.

B 445 sq in.

C 5 39 sq in.

D 5 89 sq in.

CSG00053




�29 Figure ABCD is a kite.


B

D

17 cm

17 cm

8 cm

8 cm

15 cm6 cm

10 cm

10 cm

A C

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 121 in.

B 168 in.

C 176 in.

D 228 in.

CSG00564

�31 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

�32 The four sides of this figure will be folded up and taped to make an open box.

5 centimeters

What will be the volume of the box?

A 50 cm3

B 75 cm3

C 100 cm3

D 125 cm3

CSG00299




�33 A classroom globe has a diameter of 18 inches.

Which of the following is the approximate surface area, in square inches, of the globe? (Surface Area = 4 r2 )

A 113.0

B 226.1

C 254.3

D 1017.4

CSG20238

�34 The rectangle shown below has length 20 meters and width 10 meters.


4 m 4 m

4 m

4 m

4 m 4 m

4 m

4 m

If four triangles are removed from the rectangle as shown, what will be the area of the remaining figure?

A 136 m2

B 144 m2

C 168 m2

D 184 m2

CSG00012

�35 If RSTW is a rhombus, what is the area of WXT?

X60o

R W

12

S T

A 18 3

B 36 3

C 36

D 48

CSG00227




�36 What is the area, in square units, of the trapezoid shown below?

y

(0, 5) (8, 5)

x0 (12, 0)

A 37.5

B 42.5

C 50

D 100

CSG20226

�37 The figure below is a square with four congruent parallelograms inside.

35

12

What is the area, in square units, of the shaded portion?

A 60

B 84

C 114

D 129

CSG20225

�38 What is the area, in square meters (m), of the trapezoid shown below?

5 m 5 m

12 m

6 m

A 28

B 36

C 48

D 72

CSG10047

�39 What is the area, in square inches (in.), of the triangle below?

10 in.

10 in.10 in.

A 25

B 25 3

C 50

D 50 3

CSG10048





�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?

A 2 to 3

B 4 to 9

C 16 to 27

D 16 to 81

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?

A 320 cm3

B 640 cm3

C 960 cm3

D 1280 cm3

CSG20116

�42 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?

A 115°

B 120°

C 125°

D 130°

CSG00571

�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 quadrilateral

B hexagon

C octagon

D decagon

CSG00305

�44 What is m x ?


B x

A 60 25 C

A 35°

B 60°

C 85°

D 95°

CSG20086

�45 If the measure of an exterior angle of a regular polygon is 120°, how many sides does the polygon have?

A 3

B 4

C 5

D 6

CSG20204




46 In the figure below, AB C .

A D

(x + 40)º (x – 40)º

B C

What is the value of x?

A 40

B 50

C 80

D 90

CSG00244

�47 The measures of the interior angles of a pentagon are 2 6x x x, , 4 6, 2x 16 , and6x+ 2. What is the measure, in degrees, of the largest angle?

A 28

B 106

C 170

D 174

CSG10028

� �48 What is m 1?


36

88

1

o

o

A 34°

B 56°

C 64°

D 92°

CSG20179

�49 What is m WZX ?

V

Y

132º

52º

Z

X

W

A 80°

B 90°

C 100°

D 110°

CSG30022




�50 What is the measure of an exterior angle of a regular hexagon?

A 30°

B 60°

C 120°

D 180°

CSG00570

�51 A diagram from a proof of the Pythagorean theorem is pictured below.

a b

c

Which statement would not be used in the proofof the Pythagorean theorem?

1A The area of a triangle equals ab.

2B The four right triangles are congruent.

C The area of the inner square is equal to half of the area of the larger square.

D The area of the larger square is equal to the sum of the areas of the smaller square and the four congruent triangles.

CSG10192

�52 A right triangle’s hypotenuse has length 5. If one leg has length 2, what is the length of the other leg?

A 3

B 21

C 29

D 7

CSG00566

�


53 A new pipeline is being constructed to re-routeits oil flow around the exterior of a national wildlife preserve. The plan showing the old pipeline and the new route is shown below.

60 mile

s

32 miles

OLD PIPE LINENEW PIPELIN

E

About how many extra miles will the oil flowonce the new route is established?

A 24

B 68

C 92

D 160

CSG10016




�54 Marsha is using a straightedge and compass to do the construction shown below.

P

l

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

CSG00526

�55 Given: angle A

What is the first step in constructing the angle bisector of angle A?


BD

AC

A Draw ray AD.

B Draw a line segment connecting points Band 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




�56 Scott is constructing a line perpendicular to line l from point P. Which of the following should be his first step?

P

A l

P

lB

P

C l

P

D l

CSG00308

�57 Which triangle can be constructed using the following steps?

1. Put the tip of the compass on point A.

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.

5. Draw AC and BC.

C

A B


A right

B obtuse

C scalene

D equilateral

CSG10135



Released Test QuestionsGeometry

�58 The diagram shows ABC.

y

B

xCA

Which statement would prove that ABC is a right triangle?

A (slope AB)(slope BC)= 1

B (slope AB)(slope BC )= 1

C distance from A to B = distance from B to C

D distance from A to B = (distance from B to C)

CSG00475

�59 Figure ABCO is a parallelogram.


y

x

A B

CO (c, 0)

(a, b) (a + c, b)

What are the coordinates of the point ofintersection of the diagonals?

a b

A

,2 2

c b

B

,2 2

a c+

C

, 2 2

a c a+ +

D

,2 2

CSG20101




�60 What type of triangle is formed by the points

A(4 2, ), B(6, 1), and C( 1, 3)?

A right

B equilateral

C isosceles

D scalene

CSG10235

�61 The point ( 3 2, ) lies on a circle whose

equation is (x+ 3)2 +( y+ 1)2 = r2 . Which of

the following must be the radius of the circle?

A 3

B 10

C 9

D 10

CSG30048

� 562 In the figure below, if sin x= , what are 13cos x and tan x?

x

A cos = 12

13and tan =

5

12x x

B cos = 12

13and tan =

12

5x x

C cos = 13

12and tan =

5

12x x

D cos = 13

12and tan =

13

5x x

�


CSG00493

63 In the figure below, sin A= 0 7. .

C

21

B A

What is the length of AC?

A 14.7

B 21.7

C 30

D 32

CSG00432




�64 Approximately how many feet tall is the streetlight?

�


h

40º

20 ft

sin 0.64

0.77

40

40

40 0 84

°°°

cos

tan .

A 12.8

B 15.4

C 16.8

D 23.8

CSG20047

65 Right triangle ABC is pictured below.

B

32º

10.6

A C8.2

Which equation gives the correct value for BC?

BCA sin 32°=

.8 2

BCB cos 32°=

.10 6

8 2 C tan 58°=

.

BC

BCD sin 58°=

.10 6

CSG10210




�66 In the accompanying diagram, m A= 32° andAC= 10. Which equation could be used to find x in ABC ?

32°

B

x

A C10

A x=10 sin 32°

B x=10 cos 32°

C x=10 tan 32°

10D x=

cos32°CSG00555

�67 The diagram shows an 8-foot ladder leaning against a wall. The ladder makes a 53 angle with the wall. Which is closest to the distance up the wall the ladder reaches?


53°

8 ft ?

sin 53° 0.80 cos 53° 0.60 tan 53° 1.33

A 3.2 ft

B 4.8 ft

C 6.4 ft

D 9.6 ft

CSG00342




�68 Triangle JKL is shown below.

24oL

28

J

Which equation should be used to find the length of JK ?

JKA sin 24 °=2828

B sin 24 °=JK

JKC cos 24 °=

28

28D cos 24 °=

JKCSG20031

�69 What is the approximate height, in feet, of the tree in the figure below?

100 ft

50

sin .

cos .

tan .

50 0 766

50 0 643

50 1 192

°°°


K

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

bc

A 9

B 6 3

C 12 3

D 18CSG10052




�71 What is the value of x in the triangle below?

10B C

x x

A

A 5

B

C 10 3

D 20

5 2

CSG10056

�72 What is the value of x, in inches?

x30o

7 in.

A 7 3

B 14

C 14 3

D 21

CSG20099

�73 A square is circumscribed about a circle. What is the ratio of the area of the circle to the area of the square?

1A

4

1 B

2

2 C

D4

CSG00585

�74 In the circle below, AB and CD are chords intersecting at E.


A C

B

D

E

If AE= 5, BE= 12, and CE= 6, what is the

length of DE?

A 7

B 9

C 10

D 13

CSG00022




�75 RB is tangent to a circle, whose center is A, at

point B. BD is a diameter.


C

R

BA

D

25º

What is m CBR?

A 50°

B 65°

C 90°

D 130°

CSG20186

�76 In the figure below, AB is tangent to circle O at

point A, secant BD intersects circle O at points

C and D, mAC = 70°, and mCD = 110°.

A

110o

B

CO

D

70o

What is m ABC?

A 20°

B 40°

C 55°

D 70°

CSG10257




�77 In the circle shown below, the measure of

PR= 140° and the measure of RPQ = 50°.

�

�


P

140º

R

Q

50º

O

What is the measure of PQ?

A 50°

B 60°

C 70°

D 120°

CSG10003

78 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)

CSG00317

79 If triangle ABC is rotated 180 degrees about the origin, what are the coordinates of A ?

y

B A

C

76

5

4

3

21

0 1 2 3 4 5 6 7 -1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7x

A ( 5 , 4)B ( 5 4, )C ( 4 5, )D ( 4 , 5)

CSG10096





�80 Trapezoid ABCD below is to be translated to trapezoid A B C D by the following motion rule.

(x y (x 3, y 4), ) +

y

987

A6

B5432

CD 1

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-1-2-3-4-5-6-7-8-9

x

What will be the coordinates of vertex C ?

A (1 3),

B (2 1, )C 6 1)( ,

D (8, 3)CSG10214



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




A GE1.0 2004

A GE1.0 2005

C GE1.0 2007

D GE2.0 2003

D GE2.0 2004

D GE2.0 2005

B GE2.0 2007

B GE3.0 2003

D GE3.0 2004

C GE3.0 2005

A GE3.0 2006

D GE4.0 2003

C GE4.0 2004

C GE4.0 2005

B GE4.0 2005

D GE4.0 2006

A GE4.0 2007

D GE4.0 2007

A GE5.0 2003

A GE5.0 2004

C GE6.0 2003

B GE6.0 2007

C GE7.0 2003

B GE7.0 2004

C GE7.0 2005

D GE7.0 2006

A GE7.0 2006

D GE8.0 2003

C GE8.0 2005

C GE8.0 2006

C GE8.0 2007

A GE9.0 2006

D GE9.0 2006

C GE10.0 2003

A GE10.0 2004






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






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



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Test Success Cover Grade 8 No Algebra - SHSPHOTOS Students compute the volumes and surface areas of prisms ... Students apply these techniques in solving word problems. ... in problems