VIRGINIA STANDARDS OF LEARNING

Spring 2010 Released Test

END OF COURSEALGEBRA II (2001 Revised)

Form M0110, CORE 1

Property of the Virginia Department of Education

Copyright ©2010 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia 23218-2120. All rights reserved. Except as permitted by law, this material may not be reproduced or used in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system, without written permission from the copyright owner. Commonwealth of Virginia public school educators may reproduce any portion of these released tests for non-commercial educational purposes without requesting permission. All others should direct their written requests to the Virginia Department of Education, Division of Student Assessment and School Improvement, at the above address or by e-mail to Student_Assessment@doe.virginia.gov.

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Algebra II Formula Sheet

Geometric Formulas

Pi

227

V = lwhS.A.= 2(lw + lh + wh)

l

h

w13

hl

r

p = 4sA = s2

s

s

A = h(b1 + b2 )12

b1

b2

h

r

h

p = 2(l + w)A = lw

l

w r

c2 = a2 + b2

ac

b

Abbreviations

milligram mggram gkilogram kgmilliliter mLliter Lkiloliter kLmillimeter mmcentimeter cmmeter mkilometer kmsquare centimeter cm2

cubic centimeter cm3

volume Vtotal surface area S.A.area of base B

ounce ozpound lbquart qtgallon gal.inch in.foot ftyard ydmile mi.square inch sq in.square foot sq ftcubic inch cu in.cubic foot cu ft

year yrmonth monhour hrminute minsecond sec

V = BhS.A.= lp + B

13

12

h l

B

A = bh12

b

h

A = bhb

b

h

Quadratic Formula

x =–b ± b2 – 4ac

2a

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3

SAMPLE

A

B

C

D 6 24 242

4a a

a+ +

6 2a

6 2( )aa+

62a

6 22

3( )aa

aa

++=i

Algebra II

Directions

Read each question and choose the best answer. For this test you may assume that the valueof the denominator is not zero.

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4

2 What is the factored form of

FGHJ ( )x z−6 2

( )x z+ 6 2

( )( )x z x z+ −36( )( )x z x z+ −6 6

x z2 236− ?

1 For non-zero denominators, which of the following is equivalent

to

A

B

C

D 3 55

( )( )

aa

−+

( )( )aa

−+

55

− 12a

−3

3 755 5

3a aa a a

−+ +( )( )

?

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5

3 Which of these is equivalent to 1 ?

ABCD i82

i66

i42

i24

4 Which complex number is equivalent to

FGHJ 8 12− i

8 6− i6 12− i6 6− i

( ) ( ) ?7 9 1 3− − +−i i

5 What is the simplified form of

ABC 21D 63

14 33 14

6 21i ?

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6

6 The equation is an example of which

property of real numbers?

F Associative propertyG Transitive propertyH Identity propertyJ Reflexive property

( cos )( ) cos2 17 1 2 171 1− −− = −θ π θ π

7 Which expression is equivalent to

A

B

C

D 325

50 10x y

325

12

52x y

2 5 3x y−

2 225x y

32 10 25 x y ?

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7

8 Which is equivalent to

F 4GHJ 22

13 9+ i13 9− i

13 81− − ?

9 Which property would justify the following statement?

A Distributive propertyB Reflexive property of equalityC Symmetric property of equalityD Transitive property of equality

If and , then .x y y x+ = = + =2 20 2 20

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8

10 Which expression is equivalent to

F

G

H

J 425

52

2

3 8xy

yx

i

25

425

8 2

3xy

xy

i

25

254

8 3

2xy

yx

i

24

525

8

2 3xx

yy

i

254

25

0 0

8

2

3

xyxy

x y, where and ?≠ ≠

11 Using what is the 10th term in this geometric sequence?

A 78,125B 390,625C 1,953,125D 9,765,625

0 2 1 5 25 125. , , , , , . . .

a a rnn= −

11 ,

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9

12 If what is the value of

FGH 60J 92

−4

−44

f ( ) ?−4f x x x( ) ,= −2 72

13 Given:

What is the vertex of the graph for this function?

A

B

C

D ( , )4 1

( , )4 1−

( , )−4 1

( , )− −4 1

f ( ) ( )x x= − −4 12

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10

14 The graph shown most accurately represents which of the following functions?

F

G

H

J f x x( ) = 2

f x x( ) = −2

f xx

( ) =⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

12

f xx

( ) =⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

− 12

9

8

7

6

5

4

3

2

1

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

-9 -8 -7 -6 -5 -4 -3 -2 21 3 4 5 6 7 8 9-1 O

y

x

9

8

7

6

5

4

3

2

1

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

-9 -8 -7 -6 -5 -4 -3 -2 21 3 4 5 6 7 8 9-1 O

y

x

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11

15 Given:

An outdoor theater has 37 seats in the first row, 40 seats in the second row,and 43 seats in the third row. If this pattern continues, what is the totalnumber of seats in the first 10 rows?

A 120B 320C 505D 520

S n a n dn = + −⎡⎣ ⎤⎦12

2 11 ( )

16 The graph of a 4th-degree polynomial is shown.

Exactly how many real zeros does this function have?

F 1G 2H 3J 4

9

8

7

6

5

4

3

2

1

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

-9 -8 -7 -6 -5 -4 -3 -2 21 3 4 5 6 7 8 9-1 O

y

x

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12

18 Which of the following equations best models the data in this table?

F

G

H

J y x x= − +12

12

y x= +−34

2

y x= +2 1

yx

=⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟2 4

5

x

–2–0.5

0

1.5

2.5

3

y

5

2

1

0.5

1.5

2.5

17 What is the value of

A 2B 19C 36D 57

( ) ?17 151

3n

n−∑

=

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13

19 The time it takes to do a job is inversely proportional to the number ofworkers. If 8 workers can do a job in 6 days, then 16 workers can do thesame job in —

A 1.5 daysB 3 daysC 6 daysD 12 days

20 What type of function is

F ExponentialG QuadraticH LinearJ Step

y x= +2 8 ?

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14

21 The graph most accurately represents which of the following functions?

A

B

C

D y x= + +2 3

y x= − +2 3

y x= − +3 2

y x= + +3 2

9

8

7

6

5

4

3

2

1

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

-9 -8 -7 -6 -5 -4 -3 -2 21 3 4 5 6 7 8 9-1 O

y

x

22 The graph of is translated up 8 units. Which equation representsthe translated graph?

FGHJ y x= −4 3

y x= −12 11y x= −12 3y x= −4 19

y x= −4 11

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15

23 Which equation represents the statement

“r is inversely proportional to s and directly proportional to the cube of t”?

A

B

C

D r kts

=3

r kst

=3

r kst

=3

r kts

=3

3

24 Which equation best represents the data in this table?

F

G

H

J y x= +1

y x x= + −−12

2 12

y x= 12

y x= ln

x0.511.523

y 0.75 0 0.5 0.75 1

–

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16

25 Given what is the value of

ABC 5D 7

−18

−23

g f( ( )) ?2f x x g x x( ) and ( ) ,= + = +−3 4 7

26 Which lists four consecutive terms of an arithmetic sequence?

F 3, 10, 17, 24G 1, 4, 9, 16H 1, 2, 4, 8J −5 6 10 13, , ,

27 What are all the roots for the equation

A 19B 23C 5 and 23D 9 and 19

3 14 6 21w − − = ?

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17

28 Which graph best represents the solutions to the inequality

F

G

H

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

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

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

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

3 7 5x − ≤ ?

29 What is the solution set for

A

B

C

D { }4{ }−{ }124

−{ }28

k + − = −64 8 2 ?

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18

30 What is the solution set of the equation

F

G

H

J − −− +{ }1 2 1 2i i,

1 2 1 2− +{ }i i,

−{ }1, 3

−{ }3,1

x x2 2 5 0− + = ?

31 What is the solution to

ABCD x = 129

x = 29x = −1x = −121

x − = −4 53 ?

32 Which is the solution set for

F

G

H

J −{ }5 5,

−{ }5

5{ }

25{ }

( ) ?x + =5 02

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19

33 What is the solution set for

A

B

C

D 6{ }

265{ }

185{ }

2{ }

53

2 8 0− = ≠x x

xif ?

34 Which of the following represent the solutions to

F

G

H

J−

< <12

5x

x x< >−12

5or

− < <5 12

x

x x< >−5 12

or

4 9 11x + > ?

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20

35 What is the solution set of

A

B

C

D 432

⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

292

⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

192

⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

52

⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

2 7 6x + = ?

36 What is the solution set of

F

G

H

J 12

5,⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

1 52

,⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

−−⎧

⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

52

1,

−−⎧

⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

5 12

,

2 7 5 02x x+ + = ?

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21

37

Which best represents the equation of the graphed conic section?

A

B

C

D x y2 2

9 161− =

x y2 2

9 161+ =

x y2 2

16 91− =

x y2

161

2

9+ =

9

8

7

6

5

4

3

2

1

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

-9 -8 -7 -6 -5 -4 -3 -2 21 3 4 5 6 7 8 9-1 O

y

x

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22

38 Which graph most likely represents a function with a zero of 5 ?

F

7

6

5

4

3

2

1

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

-5-6-7 -4 -3 -2 21 3 4 5 6 7-1 O

y

x

G

7

6

5

4

3

2

1

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

-5-6-7 -4 -3 -2 21 3 4 5 6 7-1 O

y

x

H

7

6

5

4

3

2

1

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

-5-6-7 -4 -3 -2 21 3 4 5 6 7-1 O

y

x

J

7

6

5

4

3

2

1

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

-5-6-7 -4 -3 -2 21 3 4 5 6 7-1 O

y

x

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23

39 Which is a zero of the function

ABCD −2

−103

f ( ) ( )( )( ) ?x x x x= + − +3 2 1 2

40 What are the coordinates of the vertex of the graph of the

function

F

G

H

J ( , )− −2 5

( , )1 5−

( , )2 5

( , )−1 5

− − = +2 1 52( ) ?x y

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24

41 A polynomial function has a zero at Which of the following expressionsmust be one factor of the polynomial?

A

B

C

D x3

3x

( )x + 3

( )x −3

x = 3.

42 Where does the graph of cross the x-axis?

F

G

H

J−⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟

−53

0 45 0, and ( , )

−⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

53

0 9 0, and ( , )

53

0 3 0, and ( , )⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

−

53

0 9 0, and ( , )⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

−

f x x x( ) ( )( )= − +3 5 9

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25

43 If which matrix represents

A

B

C

D−⎡

⎣⎢⎢

⎤

⎦⎥⎥

14 20 9

49 10 9

⎡

⎣⎢⎢

⎤

⎦⎥⎥

−⎡

⎣⎢⎢

⎤

⎦⎥⎥

14 20 6

49 40 9

−⎡

⎣⎢⎢

⎤

⎦⎥⎥

M2 ?M =⎡

⎣⎢⎢

⎤

⎦⎥⎥

−7 10 3

,

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26

45 The dimensions of matrix P are The dimensions of matrix Z are What are the dimensions of matrix PZ ?

ABCD 1 6×

5 5×6 1×30 5×

5 1× .6 5× .

44

Apparently, the system of equations graphed above has —

F exactly 1 solutionG exactly 2 solutionsH exactly 3 solutionsJ no solutions

-1-1

-2

-3

-4

-5

1

1

2

3

4

5

3 52 4-2-3-4-5

y

x0

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27

46 If then what is the value of Q ?

F

G

H

J5 30 6

−⎡

⎣⎢⎢

⎤

⎦⎥⎥

5 105 12

⎡

⎣⎢⎢

⎤

⎦⎥⎥

20 307 9− −

⎡

⎣⎢⎢

⎤

⎦⎥⎥

110 15650 72

−

−

⎡

⎣⎢⎢

⎤

⎦⎥⎥

P P Q=⎡

⎣⎢⎢

⎤

⎦⎥⎥ =

⎡

⎣⎢⎢

⎤

⎦⎥⎥

−

−

−

−4 32 1

20 3010 12

and i ,,

47 What is the solution set for the following system of equations?

ABCD ( , ), ( , )− −{ }1 2 2 1

( , ), ( , )− −{ }1 2 1 2( , ), ( , )−{ }2 1 2 1( , ), ( , )1 2 1 2−{ }

x yx y

2 2 51

+ =+ =

⎧⎨⎪⎪⎩⎪⎪

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28

49 Which ordered pair represents a solution to the following system of inequalities?

A

B

C

D ( , )− −4 14

( , )−3 2

( , )2 6

( , )6 4

2 4 123 2x yx y

+ ≤− <

⎧⎨⎪⎪⎩⎪⎪

48 What appears to be the maximum value of for the feasible regionin the graph?

F 72G 74H 78J 80

0 1 2 3 4 5 6 7 8 9 10111213141516

123456789

10111213141516

y

x

P x y= +5 6

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29

50 The matrix equation represents which system of

linear equations?

F

G

H

J4 2

3 6

x yx y

+ =

− =

⎧⎨⎪⎪

⎩⎪⎪

−

−

4 3 2

6

x yx y

+ =

− =

⎧⎨⎪⎪

⎩⎪⎪

−

−

4 3 2

6

x yx y

− =

+ =

⎧⎨⎪⎪

⎩⎪⎪

−

−

4 2

3 6

x yx y− =

+ =

⎧⎨⎪⎪

⎩⎪⎪

−

−

4 31 1

26

−

−

−⎡

⎣⎢⎢

⎤

⎦⎥⎥⎡

⎣⎢⎢⎢

⎤

⎦⎥⎥⎥=

⎡

⎣⎢⎢

⎤

⎦⎥x

y ⎥⎥

VA526029_2A_RB 3/4/11 7:30 AM Page 29

Test Sequence Number Correct Answer

ReportingCategory Reporting Category Description

1 D 001 Expressions and Operations2 F 001 Expressions and Operations3 A 001 Expressions and Operations4 J 001 Expressions and Operations5 A 001 Expressions and Operations6 H 001 Expressions and Operations7 A 001 Expressions and Operations8 G 001 Expressions and Operations9 D 001 Expressions and Operations

10 G 001 Expressions and Operations11 B 002 Relations and Functions12 H 002 Relations and Functions13 C 002 Relations and Functions14 G 002 Relations and Functions15 C 002 Relations and Functions16 G 002 Relations and Functions17 D 002 Relations and Functions18 J 002 Relations and Functions19 B 002 Relations and Functions20 F 002 Relations and Functions21 B 002 Relations and Functions22 J 002 Relations and Functions23 D 002 Relations and Functions24 F 002 Relations and Functions25 C 002 Relations and Functions26 F 002 Relations and Functions27 C 003 Equations and Inequalities28 G 003 Equations and Inequalities29 A 003 Equations and Inequalities30 H 003 Equations and Inequalities31 A 003 Equations and Inequalities32 H 003 Equations and Inequalities33 D 003 Equations and Inequalities34 F 003 Equations and Inequalities35 C 003 Equations and Inequalities36 G 003 Equations and Inequalities37 C 004 Analytical Geometry38 F 004 Analytical Geometry39 D 004 Analytical Geometry40 H 004 Analytical Geometry41 A 004 Analytical Geometry42 F 004 Analytical Geometry43 A 005 Systems of Equations/Inequalities44 G 005 Systems of Equations/Inequalities45 B 005 Systems of Equations/Inequalities46 J 005 Systems of Equations/Inequalities47 D 005 Systems of Equations/Inequalities48 H 005 Systems of Equations/Inequalities49 C 005 Systems of Equations/Inequalities50 G 005 Systems of Equations/Inequalities

Answer Key-EOC041-M0110

VA526029_2A_RB 3/4/11 7:30 AM Page 30

If you get this many items

correct:

Then your converted scale

score is:0 0001 1682 2043 2264 2425 2556 2667 2758 2849 29110 29811 30512 31113 31714 32215 32816 33317 33818 34319 34720 35221 35722 36123 36624 37025 37526 37927 38328 38829 39330 39731 40232 40633 41134 41635 42136 42737 43238 43839 44440 45141 45842 46543 47444 48345 49446 50747 52348 54549 58150 600

Algebra II (2001 Revised), Core 1

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