Final Ver Anthongy

8/14/2019 Final Ver Anthongy

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CALIFORNIA STANDARDS TEST

Released Test QuestionsAlgebra II

1 What is the complete solution to the equation3 6 x =15?A x= 2;x= 3B x= 2;x= 3C x= 2;x= 3D x= 2;x= 3

CST00507

2 What are the possible values ofx in12 4 2 =x ?A

B

C

D

x x= = 2 5 0 3 50. .or < < 3 5 0 2 50. .x3 5 2 5. .> >xx x= =2 5 0 3 50. .or

CST20085

3 For a wedding, Shereda bought several dozenroses and several dozen carnations. The rosescost $15 per dozen, and the carnations cost $8per dozen. Shereda bought a total of 17 dozenflowers and paid a total of $192. How manyroses 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 equationsshown 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 4

10

3, ,

C no solution

D infinitely many solutions

CST00203

5 A restaurant manager bought 20 packagesof bagels. Some packages contained 6 bagelseach, and the rest contained 12 bagels each.

There were 168 bagels in all. How manypackages of 12 bagels did the manager buy?

A 6

B 8

C 9

D 12

CST00491

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.


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Released Test Questions Algebra II


6 What system of inequalities best representsthe 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 the2 6y x

system ?


3/22



2x +7 2x4 +21x3 +35x2 37x +469 )A x x x

x3 27 7 6

4

2 7

+ + +

B 2 14 14 124

2 73 2x x x

x+ + +C x x x

x3 27 7 64

2 7 + +

+D x x x

x3 27 7 64

2 7+ + +

+CST00109

10 Which polynomial represents

(3x2 +x 4)(2x 5)?A 6x3 13x2 13x 20B 6x3 13x2 13x + 20

C 6x3 +13x2 + 3x 20D 6x3 +13x2 + 3x + 20

CST10024

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

B 10x2 1

C 6x2 + 12x 1

D 10x2 + 12x 1

CST00233

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

B

C

D

36y2 436y3 436y2 +12y2 +12y 436y3 +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 (2a c + )(2a c + )(2a c + )B (2a c)(4a2 + 2ac +c 2 )C (2a c)(4a2 + 4ac +c 2 )D (2a c 2 2ac + c+ )(4a 2 )

CST00118

8




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15 The total area of a rectangle is 4x 2 . 4 9yWhich factors could represent the lengthtimes 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

y

2

?

A (x+ + y)21B (x+ 1 y)2C (x1 + 1y)(x y)D (x+ + y)(x+ y)1 1

CST10030

17Which expression shows the completefactorization of12x2 147?

A (3x7)(4x+ 2)B (4x21)(3x+ 7)C 12(x7)(x+ 7)D 3 2 2x+( x7)( 7)

CST20117

x +3 6

18x +5 +x2 +3x 10 =

x2 + xA

x2 + 3x107x 9

Bx2 + 3x10

2+ +x x 12

Cx2 + 3x10

2+ +

Dx2 + 3x10

x x 1CST00295

2 3 2

19 Which is a simplified form of3a b c

?1 2 3 (a b c)

3a5A

3 5 b c 3ab

B5c3

C 2 5 b c

3D

3 5 ab cCST00267

9




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2020x 8x

What is ?2 527y 15y

32y3A

81x32

B81xy7

25y3C

18x25

D18xy7

CST20321

214x2 16

?2 xWhich product is equivalent to

A 4(x2)B 4(x+2)C 4(x2)D 4(x+2)

CST10041

22x2 +4x x2 9

i =x +3 x2 +x 12

A 1

B x

C x+4D

x+3x3

CST10043

23 What is the simplest form of3 2 2 35x y +20x y +20xy

?5xy

A (x+2)2B (x+2y)2C x2 +y2D x2 +4y2

CST10049

24 If i = 1, which point shows the location of5 2 i on the plane?

Imaginary

Real

A pointAB

C

pointBpoint C

D pointDCST00510

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

-2

-1

1

2

3

4

5

9

8

7

6A

B

C0 1 2 3 4 5 6 7 8 9

D

-3

-4

-5

-6

-7

-8

-9


4 3

10




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

C 1

D 1

CST00238

26 Which of the following complex numbers isrepresented 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+ iB 4 3 iC 3 4 iD 3 4+ i

CST30142

27 If i = 1, then 4 6i i( ) =A 48

B 24C 24

D 48

CST00512

28 What is an equivalent form of ?2

3 +i3 i

A4

3 iB

5

4 iC

4

4 iD

5

CST10040

29 What is the product of the complex numbers(3 +i) and (3 i)?A 8

B 10

C 9 iD 10 6i

CST10038

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30 If i = 1 anda andb are non-zero real

CST10371

1numbers, what is ?

a bi+a bi

A+

a2 + b2

a biB

a2 + b2

a biC

+a2 b2

a biD

a2 b2

CST00114

31 What are the solutions to the equationx2 +2x +2 =0?A x = 0;x = 2

B x = 0;x = 2iC x = 1+ ;x = 1 ii

D x=

+

2;x=

11 2 2 2

32 What are the solutions to the equation1 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 followingproperties.

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 completethe square?

A 2

B 4

C 8

D 16

CST00508

35 Which of the followingmost accuratelydescribes the translation of the graph

y = (x + 23) 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


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36 Which of the following sentences is true aboutthe graphs ofy =3(x 5)2 +1 andy =3(x +5)2 +1?A Their vertices are maximums.

B The graphs have the same shape withdifferent vertices.

C The graphs have different shapes withdifferent 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 thex-intercepts of the graph ofy =12x2 5x 2?A

11 and 6

B1

1 and6

C2 1

and 3 4

D2 1

and3 4

CST00297

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238 Which is the graph ofy =2(x 1) +1?

y y7

6

5

4

3

2

1

0 1 2 3 4 5 6 7

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7

7

6

5

4

3

2

1

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 y7

6

5

4

3

2

1

0 1 2 3 4 5 6 7

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7

7

6

5

4

3

2

1

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

14




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39 Which ordered pair is the vertex off x( ) =x2 +6x +5?

A ( 4)3,

B ( 3)2,

C ( ,1 0)

D ( ,0 5)

CST10084

2 240 The graph of

x y =1 is a hyperbola. 2 3Which set of equations represents the

asymptotes of the hyperbolas 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+ =

Bya

xb

2

2

2

2+ 1=

C 4 2px=y

Dya

xb

2

2

2

2 1=

CST20065

42 4x2 5y2 16x 30y 9 =0What is the standard form of the equationof 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

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43 Which statement describes the graph of theequation x2 +y2 +4x 6y3 =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 17D x= log10 5CST00132

45 If log10 x =2, what is the value ofx ?1

A x=10

1B x= 101

C x=100

D x= 100CST10255

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

B

1

9

33

=x1

9

3

=x

C 31

9x

=

D 319

=xCST10151

47 Which is the first incorrect step in simplifying4

log4 ?64

4Step 1: log4 =log4 4 log4 64

64Step 2: =1 1 6Step 3: =15

A Step 1

B Step 2

C Step 3

D Each step is correct.

CST00517

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48 Jeremy, Michael, Shanan, and Brendaeach worked the same math problem atthe chalkboard. Each students work isshown below. Their teacher said that whiletwo of them had the correct answer, onlyone of them had arrived at the correctconclusion using correct steps.

Jeremys work Shanans work

3 7 x3

3 7 x3

x x = x x =7 7 x x

=x10 ,x 0= 1

4,x 0

x

Michaels work Brendas work3 3

3 7x

3 7x

x x = x x =7 7 x x=x4 ,x 0 x x , 0= 4

Which is a completely correct solution?

A Jeremys work

B Michaels work

C Shanans work

D Brendas work

CST10301

49 A student showed the following steps in hissolution of the equation below, but his answerwas 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 1Step 2Step 3Step 4

CST10336

50 A certain radioactive element decays overt

1time according to the equation y = A

300 ,2

where A = the number of grams present

initially andt = 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




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

Bacteria Growth

Day Bacteria

0 100

1 200

2 400

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

A y= 100 +2tB y= i t(100) (2)C y=2tD y= i t(200) (2)

CST10253

52 If the equation y = 2x is graphed, which ofthe following values ofx would produce a pointclosest to thex-axis?

1A4

3B

4

5C

3

8D

3

CST20145

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

A

x 2 1 0f(x) 18 6 2

B

x 2 1 0f(x) 4 5 2

C

x 2 1 08 2

f(x) 1 1 19 3

D

x 2 1 0f(x) 7 1 1

CST20196

54 log6 40 =A log10 6 +log10 40

B log10 6 log10 40

C (log10 6)(log10 40)

logD 10

40

log10 6

CST00199

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14/22



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

A 60 = 1

B 61 =6C 4 4 =0D 6 4 =2

CST10484

56 What is the value of log327?A 2

B 3

C 6

D 9

CST00519

. .57 Iflog2 0 301 and log 3 0 477, what is theapproximate value of log 72?A 0.051

B 0.778

C 0.861

D 1.857

CST10362

58 Ifx is a real number, for what values ofx is the3x 9equation =x 3 true?

3

A all values ofxB some values ofxC no values ofxD 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, exceptwhen x=4.

C The equation is never true.

D The equation is sometimes true whenx=4.CST10260

60 Given the equation y =xn where x > 0and n 0B y=0C y 0

is true?

A all x>0B all x0C all values ofxD no values ofx

CST00396




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62 Which of the following conclusions is true aboutthe statement below?

x2 = xA 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 different7-character screen names. He wants to use

arrangements of the first 3 letters of hisfirst name (abe),followed by arrangementsof 4 digits in 1984, the year of his birth.How many different screen names canhe create in this way?

A 72

B 144

C 288

D 576

CST10401

64 A train is made up of a locomotive, 7 differentcars, and a caboose. If the locomotive mustbe first, and the caboose must be last, howmany different ways can the train be ordered?

A 5040

B 181,440

C 362,880D 823,543

CST10391

65 Teresa and Julia are among 10 students whohave applied for a trip to Washington, D.C.Two students from the group will be selectedat random for the trip. What is the probabilitythat Teresa and Julia will be the 2 studentsselected?

1A

45

2B

45

1C

5

2D

5

CST00071

66 (3y 1)4 =A 81y4 108y3 +54y2 12y+ 1B 81y4 + 108y3 54y2 12y+ 1C 81y4 54y3 108y2 12y+ 1D 81y4 +54y3 108y2 12y+ 1

CST00308

67 How many terms does the binomial expansion

of(x2 +2y3)20contain?A 20

B 21

C 40

D 60

CST10316

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68 What are the first 4 terms in the expansion of

(1 2 )6

?+ xA 1 1 30x2 + 3+ 2x+ 40xB 1 1+ 2x+ 24x2 + 48x3C 1+12x+ 30x2 +120x3D 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 thenth term in the arithmeticseries below?

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

A 4nB 3 4+ nC 2n+1D 4n1

CST10178

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

3+

3x

2

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 6C 8D 10

CST30049

73 ( ) and g x( ) =2

If f x =x2 + 2x + 1 3(x + 1) ,

which is an equivalent form of f x( )+ g( )x ?A x2 + 4x+ 2B 4x2 + 2x+ 4C 4x2 + 8x+ 4D 10x2 + 20x+10

CST10204

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74 A math teacher is randomly distributing15 rulers with centimeter labels and 10 rulers

without centimeter labels. What is the probabilitythat the first ruler she hands out will havecentimeter labels and the second ruler willnot have labels?

1A

24

1B

4

2C

5

23D

25

CST10435

75 On a certain day the chance of rain is 80%in San Francisco and 30%in Sydney. Assumethat the chance of rain in the two cities isindependent. What is the probability that

it willnot rain in either city?

A

B

C

D

7%

14%

24%

50%

CST20180

76 One bag contains 2 green marbles and 4 whitemarbles, and a second bag contains 3 greenmarbles and 1 white marble. If Trent randomlydraws one marble from each bag, what is theprobability that they are both green?

A 14

2B

5

C 12

5D

6

CST20181

77 A box contains 7 large red marbles, 5 largeyellow marbles, 3 small red marbles, and5 small yellow marbles. If a marble is drawnat random, what is the probability that it isyellow, given that it is one of the large marbles?

5A

12

7B

20

5C

8

1D

5CSN00211

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

Jamie

Try out for

guard80%

Try out forforward

20%

Try out forcatcher

70%

Try out forpitcher

30%

Try out forbasketball team

Try out forbaseball team

Jamie will definitely try out for either basketball or baseball, but not both. The probability that Jamiewill try out for baseball and try out for catcher is 42%. What is the probability that Jamie will try outfor basketball?

A

B

C

D

40%

60%

80%

90%

CST10210

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79 A small-business owner must hire seasonalworkers as the need arises. The following listshows 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 deviationfor these data? (Round the answer to thenearest 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 deviationof 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

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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

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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

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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

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