mastering the eoi, algebra 2, se - glencoe

Includes:

• Student Recording Sheet for Mastery• Diagnostic Test• Practice by Objective• Practice Test

Diagnose • Prescribe • Practice for the End of Instruction

Algebra II

the EOI

OKcover_ALG2_SE_894018.indd 1 7/10/09 12:01:07 PM

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027

ISBN: 978-0-07-894018-7MHID: 0-07-894018-4 Mastering the EOI, Algebra II

Printed in the United States of America.

1 2 3 4 5 6 7 8 9 10 009 18 17 16 15 14 13 12 11 10

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Contents

Diagnostic Test—Student Recording Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Diagnostic Test—Student Answer Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Diagnostic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Practice by Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Practice Test—Student Answer Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

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Mastering the EOI, Algebra II iii

00i_0vi_OK_SE_FM_ALG11_894018.in3 3 6/30/09 12:30:32 PM

Color in the bubble for each question that you answered correctly on the Diagnostic Test. For each question you did not answer correctly, your teacher may ask you to do the exercises on the practice page(s) listed from this workbook.

Question Objective Assessed Practice Page

1 AII.1.2.b 18

2 AII.2.1.d 23

3 AII.2.3.a 27

4 AII.2.3.b 28

5 AII.2.5.c 33

6 AII.2.1.a 20

7 AII.2.3.c 29

8 AII.3.1.a 42

9 AII.2.2.a 25

10 AII.2.4 30

11 AII.1.3.b 19

12 AII.1.2.a 17

13 AII.2.7.c 40

14 AII.2.6.d 37

15 AII.1.1.b 16

16 AII.2.1.e 24

17 AII.2.1.c 22

18 AII.2.4 30

19 AII.2.6.a 34

20 AII.2.5.a 31

21 AII.2.7.b 39

22 AII.3.1.b 43

23 AII.2.7.d 41

Question Objective Assessed Practice Page

24 AII.2.6.b 35

25 AII.2.7.a 38

26 AII.2.6.c 36

27 AII.2.7.c 40

28 AII.2.1.d 23

29 AII.2.2.b 26

30 AII.2.3.b 28

31 AII.2.1.b 21

32 AII.2.4 30

33 AII.2.5.b 32

34 AII.2.2.b 26

35 AII.2.5.b 32

36 AII.3.3 44

37 AII.2.1.a 20

38 AII.1.3.b 19

39 AII.2.1.a 20

40 AII.2.6.c 36

41 AII.1.1.a 15

42 AII.2.1.a 20

43 AII.2.5.a 31

44 AII.2.4 30

45 AII.2.6.c 36

Diagnostic TestStudent Recording Sheet

How many did you answer correctly? _______

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Mastering the EOI, Algebra II v


Record your answers by coloring in the appropriate bubble for the best answer to each question.

1 A B C D

2 F G H J

3 A B C D

4 F G H J

5 A B C D

6 F G H J

7 A B C D

8 F G H J

9 A B C D

10 F G H J

11 A B C D

12 F G H J

13 A B C D

14 F G H J

15 A B C D

16 F G H J

17 A B C D

18 F G H J

19 A B C D

20 F G H J

21 A B C D

22 F G H J

23 A B C D

24 F G H J

25 A B C D

26 F G H J

27 A B C D

28 F G H J

29 A B C D

30 F G H J

31 A B C D

32 F G H J

33 A B C D

34 F G H J

35 A B C D

36 F G H J

37 A B C D

38 F G H J

39 A B C D

40 F G H J

41 A B C D

42 F G H J

43 A B C D

44 F G H J

45 A B C D

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Mastering the EOI, Algebra II 1

Diagnostic TestStudent Answer Document

01_OK_EOI_SAD_894018.indd 1 6/23/09 8:36:48 AM

01_OK_EOI_SAD_894018.indd 2 7/10/09 11:08:29 AM

4 Which of the following statements is true about the vertex of the graph of y = 2 x 2 - 3?

F The vertex is at the origin, and the solution of the equation is x = 0.

G The vertex is at the minimum value for y, below the origin. The graph has 2 x-intercepts and 2 solutions.

H The vertex is at the maximum value for y, below the origin. There are no x-intercepts and no solutions.

J The vertex is 3 units to the left of the origin, and there are 2 negative x-intercepts and 2 solutions.

AII.2.3.b

1

AII.1.2.b

What is the simplified form of

2 _ x + 2

- 1 _ x - 1

?

A x _ x 2 + x - 2

B 3x _ x 2 + x - 2

C x - 4 _ x 2 + x - 2

D x - 4 _ x 2 - x + 2

3

AII.2.3.a

- p 2 + 4 = -8p

What is the solution of this equation?

A 4 ± √ � 5 B 4 ± 2 √ � 5 C 8 ± 4 √ � 5 D -8 ± 4 √ � 5

2 y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

What is the range of this function for the domain -1 ≤ x ≤ 2?

F -2 ≤ y ≤ 2G -2 < y < 1H -1 ≤ y ≤ 2J -1 < y < 2

AII.2.1.d

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Diagnostic Test

03_13_OK_EOI_DT_894018.indd 303_13_OK_EOI_DT_894018.indd 3 16/6/10 11:28:46 PM16/6/10 11:28:46 PM

5

AII.2.5.c

pH is the measure of hydrogen ion concentration [ H + ] in moles per liter of a solution. The measure is given by the formula below.

pH = log 10 1 _

[ H + ]

What is the pH of a solution if [ H + ] = 10 -6.4 ?

A -6.4B 0.0000004C 6.4D 2,511,866

7

AII.2.3.c

The height, y, of an electron in a cloud chamber is given by the equation y = 100 - x - x 2 , where x is the horizontal position of the electron. If the electron is at a height of 28 units, what is its horizontal position?

A 8B 9C 10D 28

8

AII.3.1.a

The graph below shows the amount of money spent each week for ten weeks on groceries by the Monroe family.

Amou

nt ($

)

200

175

150

125

100

75

50

25

0

Week1 2 3 4 5 6 7 8 9 10

y

x

What does the scatter plot imply about the grocery spending practices of the Monroe family?

F There is an infinite association between the values of dependent and independent variables.

G There is a positive association between the dependent and independent variables.

H There is a negative association between the dependent variable and the independent variable.

J There is no association between the dependent and independent variables.

6 Which statement best describes what happens to the graph of y = a x 2 when the value of a changes from 2 to -2?

F The graph translates 2 units down.G The graph translates 4 units down.H The graph is reflected in the x-axis.J The graph is reflected in the y-axis.

AII.2.1.a

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4 Mastering the EOI, Algebra II

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Diagnostic Test (continued)


9

AII.2.2.a

Late registration at the Super Sprint Triathlon at Oklahoma Community College was $55 for adults and $45 for students. $19,165 was collected during late registration. The number of adults that registered, a, was four more than twice the number of students, s, that registered. Which system of equations models this situation?

A a + s = 19,165 55a + 45s = 19,165B a - 2s = 4 55a + 45s = 19,165C a - 2s = 4 45a + 55s = 19,165D a + 2s = 4 45a + 55s = 19,165

11

AII.1.3.b

What is the quotient of (7 - 2i) and (7 + 2i)?

A 45 _ 53

- 28 _ 53

i

B 1 - 28 _ 53

i

C 1 - 28 _ 45

i

D 45 _ 53

+ 28 _ 53

i

12

AII.1.2.a

What is ( x 3 + 5 x 2 - 15x + 2) divided by (x - 2)?

F x 2 + 3x - 9G x 2 + 3x - 18H x 2 + 7x + 1J x 2 + 7x - 1

10

AII.2.4

What is the center of the circle with equation x 2 + 2x + y 2 + 8y = 152?

F (1, 4) G (1, -4) H (-1, 4) J (-1, -4)

AII.2.7.c

13 y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

What are all the x-intercepts of the function?

A 4B -1, 1C -2, 2D -2, -1, 1, 2

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03_13_OK_EOI_DT_894018.indd 5 7/1/09 2:00:39 PM

14

AII.2.6.d

The Cityplex Building in Tulsa, Oklahoma, is 648 feet tall. A ball is thrown upward by a person standing on top of the building. The ball’s height above the ground h, in feet, after t seconds, is given by the equation below.

h = -16 t 2 + 48t + 648

After how many seconds will the ball be 360 feet above the ground?

F 3 secondsG 3.5 secondsH 4 secondsJ 6 seconds

15

AII.1.1.b

n is an even integer. For what values

of a and b is n √ �� (ab) n = |ab| true?

A for all values of a and bB only when a and b are both

positiveC only when a and b are both

negativeD only when a and b have opposite

signs

17

AII.2.1.c

Which equation describes the composite function g ◦ f if f(x) = x 2 + 4x + 2 and g(x) = x + 1?

A (g ◦ f ) (x) = x 2 + 4x + 3B (g ◦ f ) (x) = x 2 + 5x + 3C (g ◦ f ) (x) = x 2 + 5x - 3D (g ◦ f ) (x) = x 2 + 6x + 7

16

AII.2.1.e

What is the inverse of f(x) = x - 7 _ 3 ?

F f -1 (x) = 1 _ 3 x - 7

G f -1 (x) = - 1 _ 3 x + 7

H f -1 (x) = 7x + 3J f -1 (x) = 3x + 7

18

AII.2.4

y

x−2−1−3−4

4321

−2−3−4

1 2 3 4

What is the equation of this circle?

F x 2 - y 2 - 2x = 8G x 2 + y 2 + 2x = 8H x 2 + y 2 - 2x = 8J x 2 - y 2 + 2x = 8

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03_13_OK_EOI_DT_894018.indd 6 7/1/09 2:00:41 PM

19

AII.2.6.a

Cleo found the solutions of 3 x 2 -

2x - 8 = 0 to be 4 _ 3 and 2. Are

these solutions correct? If not, why?

A correctB Incorrect; she factored to get

(3x + 4) (x - 2) = 0 but solved 3x + 4 = 0 incorrectly.

C Incorrect; she factored to get (3x + 4) (x - 2) = 0 but she solved x - 2 = 0 incorrectly.

D Incorrect; she factored incorrectly to get (x - 4) (3x - 2) = 0.

20

AII.2.5.a

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

Which function is represented by the graph?

F f (x) = x + 1G f (x) = 2 -x

H f (x) = ( 1 _ 2 )

x

J f (x) = ln x

21

AII.2.7.b

Which graph represents the functionf(x) = x _

x + 2 ?

A y

x−1−4−3

8

42

6

2 41 3−2

−4−6−8

B y

x−1−4−3

8

42

6

2 41 3−2

−4−6−8

C y

x−1−4−3

8

42

6

2 41 3−2

−4−6−8

D y

x−1−4−3

8

42

6

2 41 3−2

−4−6−8

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03_13_OK_EOI_DT_894018.indd 7 7/1/09 2:00:44 PM

22

AII.3.1.b

y

x−2−8−6

8

42

6

4 82 6−4

−4−6−8

What function best represents the function shown on the graph?

F f (x) = 9x + 15G f (x) = 1.5 x 2 + 10.5x + 7.5H f (x) = x 3 + 3 x 2 + 2x + 3J f (x) = -0.2 x 4 + x 3 + 3 x 2 + 2x + 3

23

AII.2.7.d

During the Oklahoma City Memorial Marathon, a runner ran at a speed of 5 miles per hour for 2 hours and at 7 miles per hour for t hours. Which function represents the average speed of the runner?

A S (t) = 2t _ 2 (5) (7t)

B S (t) = 2 (5) (7t)

_ 2t

C S (t) = 2 (5) + 7t

_ 2 + t

D S (t) = 2 + t _

2 (5) + 7t

24

AII.2.6.b

What is the graph of the polynomial f(x) = x 5 + 2 x 4 - x 3 + 2 x 2 - 4x + 5?

F y

x−1

8101214

42

6

2 4 5 61 3−2

G y

x−1−4−3

5

2 41 3−2

40353025201510

H y

x−1−4−3

8

42

6

2 41 3−2

−4−6−8

J y

x−1−4−3

8101214

42

6

2 41 3−2

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03_13_OK_EOI_DT_894018.indd 803_13_OK_EOI_DT_894018.indd 8 6/18/10 12:56:18 AM6/18/10 12:56:18 AM

25

AII.2.7.a

A worker can wash a car in 45 minutes. Another worker can wash a car in 35 minutes. How long will it take them to wash a car working together?

A 19.7 minutesB 35 minutesC 40 minutesD 80 minutes

26

AII.2.6.c

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

Which of the following is true of the function shown in the graph?

F y-intercept at (2, 0) G x-intercept at (0, -3) H relative minimum at (0, 0) J relative maximum at (-1, 2)

27

AII.2.7.c

y

x−1−4−5−6 −3 2 41 3−2

4

21

3

−2−3−4

What is the vertical asymptote(s) of this function?

A x = -2 and x = 4B x = -2C x = -4D x = -4 and x = 2

28

AII.2.1.d

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

What is the domain of this function?

F (-∞, 0 ] � [ 0, ∞) G (-∞, 0 ) � (0, ∞) H (-∞, 0 ] � [ 0, ∞) J (-∞, 0 ] � (0, ∞)

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03_13_OK_EOI_DT_894018.indd 9 7/1/09 2:00:49 PM

29

AII.2.2.b

y = 2x

2x - 4y = 12

What is the point of intersection of the two lines?

A (-2, -4) B (-1, -2) C (0, 0) D The lines do not intersect.

31

AII.2.1.b

If f(x) = 4 x 2 + 11x - 8 and g(x) = -2 x 2 - 3, which expression is equivalent to(f - g)(x)?

A 2 x 2 + 11x - 11B 2 x 2 + 11x - 5C 6 x 2 + 11x - 5D 6 x 2 + 11x - 11

30

AII.2.3.b

y

x

567

321

4

3 5 6 721 4−1

Which statement best describes this graph?

F It has no zeros and a minimum point at (3, 0) .

G It has a single zero and a minimum point at (3, 0) .

H It has a single zero and a maximum point at (3, 0) .

J It has zeros at x = 3 and y = 2 1 _ 4 ,

and a minimum point at (3, 0) .

32

AII.2.4

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

What is the equation of this hyperbola?

F x 2 _ 4 -

y 2 _

9 = 1

G x 2 _ 4 +

y 2 _

9 = 1

H x 2 _ 9 -

y 2 _

4 = 1

J x 2 _ 9 +

y 2 _

4 = 1

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03_13_OK_EOI_DT_894018.indd 10 7/1/09 2:00:51 PM

33

AII.2.5.b

If lo g 12 1 2 2n = x, what is the value of x?

A 2nB 12C 144D 1 2 n

34

AII.2.2.b

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

This graph shows the solution set of which system of linear inequalities?

F y ≥ x + 1 and y < -0.5x - 1G y > x + 1 and y < -0.5x - 1H y ≥ x + 1 and y ≤ -0.5x - 1J y > x + 1 and y ≤ -0.5x - 1

35

AII.2.5.b

Which equation is equivalent to lo g 2 32 = 5?

A 5 2 = 32B 3 2 2 = 5C 2 5 = 32D 3 2 5 = 2

36

AII.3.3

Use the pattern below. The area of the shaded region in the first figure is 1.

What is the value of the sum of the areas of the shaded regions in the first six figures?

F 2

G 63 _ 32

H 31 _ 32

J 63 _ 128

37

AII.2.1.a

y

x−1−4−3 2 41 3−2

4567

21

3

What type of function is represented by this parent graph?

A exponentialB logarithmicC radicalD quadratic

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38

AII.1.3.b

What is the product of (-4 + 5i ) and (1 - 6i )?

F -26 - 19i

G -26 + 19i

H 26 + 29i

J 26 - 29i

39

AII.2.1.a

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

If this graph is translated up 3 units and reflected in the y-axis, what would be the new equation?

A y = x 2 + 3B y = x 2 - 3C y = - x 2 + 3D y = - x 2 - 3

40

AII.2.6.c

y

x−1−4−3 2 41 3−2

123

−2−3−4−5−6−7−8−9

What is the approximate x-value of the relative maximum?

F x = 2.1G x = 0.7H x = -0.4J x = -0.8

41

AII.1.1.a

Which is equivalent to (-8) 2 _ 3 ?

A -4

B - 1 _ 4

C 1 _ 4

D 4

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43

AII.2.5.a

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

Which function is graphed?

A y = 2 x B y = lo g 2 xC y = 0. 2 x D y = 2 -x

44

AII.2.4

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

What is the equation of the ellipse?

F x 2 - y 2

_ 9

= 1

G x 2 _ 9 - y 2 = 1

H x 2 _ 9 + y 2 = 1

J x 2 + y 2

_ 9 = 1

42

AII.2.1.a

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

What type of graph is represented by this parent graph?

F exponentialG logarithmicH radicalJ quadratic

45

AII.2.6.c

y

x−1−4−3 2 41 3−2

4

21

3

−2−3−4

Which of the following is true of the function shown in the graph?

A an x-intercept = (2, 0) B a y-intercept = (0, 2) C a relative minimum at (0, 0) D a relative maximum at (-1, 0)

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03_13_OK_EOI_DT_894018.indd 14 7/10/09 11:09:31 AM

5

4

3

2

1

If 4 x = 2 x + 1 _ 2 , what is the value of x?

A -1

B - 1 _ 2

C 1 _ 2

D 1

What is the value of (-64) - 2 _

3 ?

A -16 C 1 _ 16

B - 1 _ 16

D 16

What is the value of ( 5 √ � 8 ) 2 ?F 8

2 _ 5

G 8 5 _ 2

H 10

√ � 8

J 8 10

Which is equivalent to 4 √ �� 64 x 8 ?

F 4 3 x 2

G 2 1 _ 2 x 4

H 2 3 _ 2 x 4

J 2 3 _ 2 x 2

The table shows the radii of a series of spheres.

Sphere Radius

1 3 r 1 _ 2

2 9 r 3 _ 2

3 27 r 5 _ 2

4 81 r 7 _ 2

Which of these spheres has a volume

of 26,244π r 15

_ 2 ?

V = 4 _ 3 π r 3

A sphere 1B sphere 2C sphere 3D sphere 4

6 What is the simplified form of 3 3 _ 2 ?

F 3

G √ � 3

H 3 √ � 3

J 9

7 What value, when substituted for x, makes the statement 4 x =

8 √ �� 64 true?

A - 3 _ 8

B 3 _ 8

C 8 _ 3

D 3

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Practice by ObjectiveAII.1.1.a

15_29_OK_EOI_PO_894018.indd 15 7/8/09 12:35:43 PM

1 What is the simplified form of

3 √ �� 64 ·

√ �� 64 ?

A 3 √ �� 64

B 4 √ �� 64 C 16D 32

2What is the simplified form of 4

5 _ 8 _

4 1 _ 4 ?

F 2

G 4 3 _ 8

H 4 3 _ 2

J 4


3 √ �� 4 (108) -

3 √ �� 16 ?

A 4 3 √ �� 27 - 4

B 2 3 √ �� 108 - 4

C 4 3 √ � 2

D 3 √ �� 416

4 Which radical is considered a like radical with 3

4 √ � 2 ?

F √ � 2

G 3 √ � 2

H 7 4 √ � 2

J 4 √ � 2

5What is the value of 9

1 _ 2 + ( 1 _

3 ) 2 ?

A 1B 3

C 3 1 _ 6

D 3 1 _ 9

6 m

1 _ 2 + 3 _

m 1 _ 2 - 1

What is the simplified form of this expression?

F 5 m 1 _ 2 + 3

G m 1 _ 2 - 3 _

m - 1

H m + 4 m 1 _ 2 + 3 __

m - 1

J 5 m 1 _ 2 + 3

7 What is the value of the expression

(32) - 3 _

5 ?

A -8

B - 1 _ 8

C 1 _ 8

D 8

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Practice by ObjectiveAII.1.1.b

15_29_OK_EOI_PO_894018.indd 16 7/8/09 12:35:46 PM

1 Which expression is equivalent to

( x 2 + 5x - 6) (x + 1) -1 ?

A x 3 + 6 x 2 - x - 6

B x + 6 - 12 _ x + 1

C x - 4 - 2 _ x + 1

D x + 4 - 10 _ x + 1


(6 y 3 + 5 y 2 - 11y - 4) ÷ (3y + 1)?

F 2 y 2 + 5y

G 2 y 2 + 4y - 4

H 2 y 2 + y - 4

J -2 y 2 - y + 4

3 What is the quotient for (8 x 3 + 10 x 2 - 13x - 15) ÷ (2x + 3)?

A 4 x 2 + 11x - 5

B 4 x 2 - x - 5

C 4 x 2 + 11x + 10

D 4 x 2 - 5

4 What is the simplified expression of

x 3 - 7x - 6 __

x - 2 ?

F x 2 + 2x - 3

G x 2 + 2x - 3 - 12 _ x - 2

H x 2 - 5 - 16 _ x - 2

J x 2 - 5

5

x 2 + 1

OKA2-PO-002A-894018.ai

be

Area = 2x 4 - 3x 3 + 2x 2 - 3xb

What is the length of side b of the rectangle?

A 2 x 2 - 3xB 2x 2 - 3x + 2 C x 2 - 3x D x 2 - 3x + 2

6 What is the quotient of 8t 4 - 2t 3 - t 2 + 2t - 1divided by 2t - 1?

F 4t 3 + t 2 + 1G 4t 3 + t + 1H 4t 3 + t 2 - 1J 4t 3 + t - 1C

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15_29_OK_EOI_PO_894018.indd 17 7/9/09 9:44:05 AM

1 Which expression represents the sum

of x + 1

_ x - 3

+ x _ x + 2

?

A 2 _ x - 3

B 2 x 2 + 2 _

x 2 - x - 6

C 2x + 2 _

2x - 1

D 2 x 2 + 6x + 2 __

x 2 - x - 6

2 x 2 + 2x

_ x 2 - 1

÷ x 2 - x - 6 _

x + 1

What is the quotient?

F x _ -3x + 3

G 2 x 2 + x - 6 _

x 2 - 1

H 1 _ -3x + 3

J x _ x 2 - 4x + 3

3What is the simplest form of

3 _ n + 2 _

(2n) -2 ?

A 2n + 3 _

4 n 3

B 3 _ 2 n 2

C 4 n 2 + 6n

D 8 n 2 + 12n

4 y _

3 + 3 _ y _

(3y) -1

What is the quotient?

F y + 3

G y + 9

H y 2 + 9

J y 2 + 9

_ 9 y 2

5 The amount of light, L, admitted through the aperture of a camera lens is related to the f-stop setting, f, where k is a constant value dependent on the particular lens being used.

L = k _ f 2

What is the ratio of the amount of light admitted at an f-stop setting of 22 to the amount of light admitted at an f-setting of 11?

A 4 to 1B 2 to 1C 1 to 2D 1 to 4

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15_29_OK_EOI_PO_894018.indd 18 7/9/09 11:20:29 AM

1 What is the sum of (2 - 3i) and (-4 + 6i)?

A iB -2 - 9iC 2 - 3iD -2 + 3i

2 What is the product of (-4 - 5i) and (2 + i)?

F -7 + 4iG -13 - 14iH -3 - 14iJ 3 + 14i

3 What is the product of -3 + 5i and its conjugate?

A -15i B 2iC √ �� 34 D 34

4 What is the quotient of (1 - i) ÷ (2 + 2i)?

F - 1 _ 2 i

G 1 _ 2

H 1 _ 2i

J 1 _ 2 - 1 _

2 i

5 What is the difference of (-4 - 5i) and (3 - i)?

A -7 + 4i C -7 - 4iB -1 - 6i D 1 - 4i

6 What is (-6 + 4i)(1 - 3i) in simplest form?

F -5 + iG 6 + 22iH 18 - 22iJ -18 + 22i

7 What is the product of -2 - 6i and its conjugate?

A √ �� 40 B 36 + 4iC 40 - 24iD 40

8 What is (-5 + 3i) + (2 - 7i) in simplest form?

F -3 + 4iG -7 - 4iH -3 - 4iJ -10 - 21i

9 What is the quotient of(1 + 0i) ÷ (2 - 2i)?

A 1 _ 4 + 1 _

4 i

B 1 _ 2

C 1 _ 4 - 1 _

4 i

D 1 _ 2 - 1 _

2 i

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15_29_OK_EOI_PO_894018.indd 19 7/8/09 12:35:54 PM

1 The two exponential functions shown on the graph are translations of each other. The equation for one of the functions is y = 1. 5 x .

OKA2-PO-003A-894018.ai

be

45

321

−2−1−3−4

−2−1

−3

1 2 3 4

y

x

What is the equation of the other function?

A y = 2 (1. 5 x ) B y = 1. 5 x - 1C y = 1. 5 x - 2D y = 1. 5 x + 2

2 For the function f (x) = ( 1 _ 2 )

x , which

statement is true?

F As x increases, y approaches 0.G As x decreases, y approaches 0.H As y increases, x approaches 0.J As y decreases, x approaches 0.

3

OKA2-PO-004A-894018.ai

be

4321

−1

−2−1

−3−4

1 2 3 4 5 6 7

y

x

What type of function is represented by this parent graph?

A exponentialB logarithmicC radicalD quadratic

4 What effect does the transformation have on the parent graph for the function f (x) = x 2 + 1?

F translates graph 1 unit leftG translates graph 1 unit rightH translates graph 1 unit downJ translates graph 1 unit up

5 What is the equation of the image when the graph of y = x 2 is translated 2 units up and then reflected in the x-axis?

A y = 1 _ 2 x 2 + 2

B y = x 2 + 2

C y = - x 2 + 2D y = - x 2 - 2

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15_29_OK_EOI_PO_894018.indd 20 7/9/09 9:46:02 AM

1 Which expression equals (f + g)(x) if f (x) = x 2 - 2x + 9 and g (x) = x + 5?

A 14B x 2 - x + 4C x 2 - 3x + 14D x 2 - x + 14

2 If f (x) = x 2 + 4x - 3 and g(x) = 3x + 6, what is the value of f · g?

F x 2 + 7x + 3G 3 x 3 + 12 x 2 - 9x - 18H 3 x 3 + 18 x 2 + x - 18J 3 x 3 + 18 x 2 + 15x - 18

3 If f (x) = 2 x 2 - 4x - 3 and g(x) = x 2 + 5x - 1, what is the value of (f - g)(x)?

A x 2 + x - 4B x 2 - 9x - 2C x 2 - 9x - 4D x 2 + x - 2

4 Which value must be excluded

from the solution of ( f _ g ) (x) if

f (x) = x 2 - 5x + 8 and g(x) = 5x - 4?

F -4

G 4 _ 5

H 5 _ 4

J 4

5 What is the product of f and g if

f (x) = 2 _ 3 x + 3 and g(x) = 3x + 6?

A (fg) (x) = 2 x 2 + 13x + 18

B (fg) (x) = 11 _ 3 x + 9

C (fg) (x) = 2 x 2 + 18D (fg) (x) = 2x + 7

6 Which definition represents the quotient rule for functions?

F ( f _ g ) (x) = f (x)

_ g (x) , g (x) ≠ 0

G ( f _ g ) (x) = f (x)

_ g (x) , f (x) ≠ 0

H ( f _ g ) (x) = f (x)

_ g (x) , g (x) > 0

J ( f _ g ) (x) = f (x)

_ g (x) , f (x) > 0

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15_29_OK_EOI_PO_894018.indd 21 7/9/09 11:20:32 AM

1 By which of the following is the domain of a composed function, (f ◦ g)(x), determined?

A range of f (x) B domain of f (x) C domain of g (x) D domains of both f (x) and g (x)

2 If f (n) = n 2 + 2n - 3 and g(n) = n + 4, which equation describes the composite function f ◦ g?

F (f ◦ g) (n) = n 2 + 10n + 13G (f ◦ g) (n) = n 2 + 2n + 1H (f ◦ g) (n) = n 2 + 10n + 21J (f ◦ g) (n) = n 2 + 3n + 1

3 If f (x) = x 2 + 3x - 1 and g(x) = x + 4, which equation describes the composite function g ◦ f ?

A (g ◦ f ) (x) = x 2 + 3x + 3B (g ◦ f ) (x) = x 2 + 4x + 3C (g ◦ f ) (x) = x 3 + 7 x 2 + 11x - 4D (g ◦ f ) (x) = x 2 + 11x + 27

4 If f(n) = n 2 - n - 2 and g(n) = n - 1, which equation describes the composite function f ◦ g?

F (f ◦ g) (n) = n 2 - n - 1G (f ◦ g) (n) = n 2 - 3H (f ◦ g) (n) = n 2 - 3nJ (f ◦ g) (n) = n 2 - 3n + 4

5 If p(x) = 2x + 1 and p (q(x)) = 14x + 1, what is q(x)?

A q (x) = 2xB q (x) = 7xC q (x) = 7x + 2D q (x) = 7

6 Which equation describes the composite function f ◦ g if f(n) = 2 n -1 and g(n) = n - 1?

F (f ◦ g) (n) = -1G (f ◦ g) (n) = 2(n - 1)

H (f ◦ g) (n) = 2 _ n - 1

J (f ◦ g) (n) = 2 _ n - 1

, n ≠ 1

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Practice by ObjectiveAII.2.1.c

15_29_OK_EOI_PO_894018.indd 22 7/8/09 12:36:03 PM

1 y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

Which inequality best describes the range of the function shown in the graph?

A -2 < x < 2B -2 ≤ x < 2C -1 ≤ y D -1 < y

2 y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

What is the domain of the function shown in the graph?

F y ≥ 0 G y > 0 H x ≥ -2J x > -2

3 What is the domain of the function y = x + 2 for the range -1 ≤ y ≤ 2?

A {x | 0 < x < 3}B {x | 0 ≤ x ≤ 3}C {x | -3 < x < 0}D {x | -3 ≤ x ≤ 0}

4 What is the range of the function y = 2x - 1 for the domain 0 < x < 3?

F {y | -1 < y < 5}G {y | -1 ≤ y ≤ 5}

H {y | 1 _ 2 < y < 2}

J {y | 1 _ 2 ≤ y ≤ 2}

5 What is the domain of the function y = x 2 - 1 for the range 3 < y ≤ 8 in interval notation?

A [-3, 3]B [-3, -2) ∪ (2, 3]C (-3, -2) ∪ (2, 3) D (2, 3]

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Practice by ObjectiveAII.2.1.d

15_29_OK_EOI_PO_894018.indd 2315_29_OK_EOI_PO_894018.indd 23 6/21/10 9:45:42 PM6/21/10 9:45:42 PM

1 Which graph represents the inverse

of the function f(x) = x + 6

_ 2 ?

A

OKA2-PO-007A-894018.ai

be

45

321

−2−1−3−4

−2−1

−3

1 2 3 4

y

x

B

OKA2-PO-008A-894018.ai

be

1

−2−1−3−4

−2−1

−3−4−5−6−7

1 2 3 4

y

x

C

OKA2-PO-009A-894018.ai

be

21

−2−1−3−4

−2−1

−3−4−5−6

1 2 3 4

y

x

D

OKA2-PO-010A-894018.ai

be

321

−2−1−3−4

−2−1

−3−4−5

1 2 3 4

y

x

2 What is the inverse of f (x) = 1 _ 2 x + 4?

F f -1 (x) = 2x - 8G f -1 (x) = 2x - 4

H f -1 (x) = 2x + 1 _ 4

J f -1 (x) = 2x + 8

3 Two functions, f and g, are inverse functions if and only if both of their compositions are what type of function?

A oppositeB identityC reciprocalD real

4 What is the inverse of f if

f (x) = 2 _ 3 x - 8?

F f -1 (x) = 3 _ 2 x - 1 _

8

G f -1 (x) = 2 _ 3 x + 1 _

8

H f -1 (x) = 3 _ 2 x - 12

J f -1 (x) = 3 _ 2 x + 12

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Practice by ObjectiveAII.2.1.e

15_29_OK_EOI_PO_894018.indd 24 7/8/09 12:36:10 PM

1 At a doughnut shop, Manuel bought a box of 18 doughnuts that contained g glazed doughnuts and j jelly doughnuts. If the number of glazed doughnuts was 2 less than twice the number of jelly doughnuts, which system of equations could be used to determine the number of each type?

A g + 2j = 20 g + j = 18B g + 2j = 18 g + j = 20C 2j - g = 2 g + j = 18D 2j - g = 20 g + j = 18

2 The ages of Shelby and her father combined equals 50. Her father’s age, f, is 1 less than three times Shelby’s age, s. Which system of equations could be used to determine the ages of Shelby and her father?

F 3s - f = 1 s + f = 50G 3s - f = 1 f - s = 50H 3s + f = 60 s + f = 50J 3s + f = 1 f - s = 50

3 Jane’s Fudge Shop sells peanut butter fudge, p, for $6.75 a pound and walnut fudge, w, for $7.50 a pound. A customer asks for a 3-pound mixture of both kinds of fudge, which costs $7.00 a pound. Which system of equations can be used to find the number of pounds of each type of fudge in the mixture?

A 7.50p + 6.75w = 7 (3) p + w = 3B 7.50p + 6.75w = 7 (3) p + w = 7C 7.50w + 6.75p = 7 (3) p + w = 7D 7.50w + 6.75p = 7 (3) p + w = 3

4 The price of a new digital camera, n, is $50 less than twice the cost of a refurbished camera, r. The difference in price between the two cameras is $150. Which system of equations can be used to determine the price of each camera?

F 2r - n = 50 r - n = 150G n - 2r = 50 n - r = 150H 2r - n = 50 n - r = 150J 2r - n = 0 n - r = 150

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15_29_OK_EOI_PO_894018.indd 25 7/8/09 12:36:13 PM

1 The table below gives the slope and y-intercept of two lines.

m -1 2

y-intercept 3 -3

What is the solution to the system of equations for these two lines?

A (2, 1) B (3, 0) C (6, -3) D no solution

2 y = 1 _ 4 x - 4

2x - 2y = -4

Which of the following points is the solution to the system of equations?

F (0, 4) G (0, -4) H (-8, 6) J (-8, -6)

3 The equations of two lines are y = 3x + 2 and 2x + y = 4. Which is the point of intersection?

A (2, 0)

B (2, 16)

C ( 2 _ 5 , 16 _

5 )

D no intersection

4

OKA2-PO-011A-894018.ai

be

y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

The graph of the equation y = 3 - xis shown. If the graph of y + x = 6 is added to the diagram, what would be the solution to this system of equations?

F (-3, 6)G (0, 3)H (3, 0) J no solution

5 x - y = 1

y = 2 - x

Which of the following points is the solution to the system of linear equations?

A ( 1 _ 2 , 3 _

2 )

B ( 3 _ 2 , 1 _

2 )

C (3, 2) D no solution

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15_29_OK_EOI_PO_894018.indd 26 7/8/09 12:36:15 PM

1 What are the solutions of 2 x 2 - 5x - 3 = 0?

A - 3 _ 2 and 1 C -3 and 1 _

2

B - 1 _ 2 and 3 D -1 and 3 _

2

2 What is the solution(s) of 3 x 2 + x - 8 = 0?

F 1 + √ �� 33 _

6

G 1 ± √ �� 97 _

6

H -1 ± √ �� 97

_ 6

J -1 + i √ �� 95

_ 6

3 What are the solutions of 4 y 2 - 2y + 3 = 0?

A 1 ± i √ �� 11 _

4 C

1 ± √ �� 44 _

4

B 1 ± √ �� 11 _

4 D

-1 ± i √ �� 11 _

4

4 What is the solution(s) of 3 y 2 - 4y + 4 = 0?

F 2i √ � 2 _

3

G 2 ± 2 √ � 2 _

3

H 2 ± 2i √ � 2

_ 3

J 2 ± i √ � 2

_ 3

5 What are the solutions of 3 x 2 - x - 4 = 0?

A -4 and 1 _ 3 C - 4 _

3 and 1

B - 1 _ 3 and 4 D -1 and 4 _

3

6 What is the solution(s) of 5 x 2 - 2x - 1 = 0?

F -1 ± √ � 6 _

5 H

√ � 6 _

5

G 1 ± √ � 6 _

5 J 1 ± 2i

_ 5

7 The main cables supported by the towers of the Golden Gate Bridge can be modeled by a parabola. Suppose the lowest point of the cables shown in the figure is used as the origin for a coordinate system that has the horizontal roadway as the x-axis. Which equation best describes the curve formed by the cables?

A y = 0.000554 x 2 B y = 0.00012 x 2 C y = 0.35 x 2 D y = 0.18 x 2

1280 m

227 m227 m

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15_29_OK_EOI_PO_894018.indd 27 7/9/09 2:32:16 PM

1 f(x) = 2 x 2 + x - 6

What are the zeros of the function?

A -2 and 3 _ 2

B - 3 _ 2 and 2

C -2 and - 3 _ 2

D -2 and 4 _ 3

2 What is the minimum point of the graph of the function f(x) = 3 x 2 + 6x - 8?

F (-1, 11) G (-11, -1) H (1, 11) J (-1, -11)

3 The zeros of a quadratic function are 3 and -1. The graph of the function has a minimum point at (1, -8). Which is an equation for the function?

A f (x) = - x 2 + 2x + 3B f (x) = x 2 - 2x - 3C f (x) = 2 x 2 - 4x - 6D f (x) = - x 2 + 3x - 1

4 f(x) = -2 x 2 - 4x - 6

What is the maximum point of the function?

F (-1, 0) H (1,-8) G (-1, -4) J (1, -12)

5 Which is the graph of f(x) = -x 2 - x + 6?

A

OKA2-PO-013A-894018.ai

be

45

3

78

6

21

−2−1−3−4 1 2 3 4

y

x

B

OKA2-PO-014A-894018.ai

be

45

3

6

2

−2−1

1

−2−1−3−4 1 2 3 4

y

x

C

OKA2-PO-015A-894018.ai

be

45

3

67

21

−1−1 1 2 3 4 5 6 7

y

x

D

OKA2-PO-016A-894018.ai

be

2

−2−1

−3−4−5−6

1

−2−1−3−4 1 2 3 4

y

x

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15_29_OK_EOI_PO_894018.indd 28 7/8/09 12:36:22 PM

1 Juanita deposits her savings in an account that compounds interest. If she leaves the money in the account for 2 years, the final value (FV) of her deposit is a quadratic function of the interest rate (r ).

r FV2% $260.10

3% $265.23

4% $270.40

5% $275.63

Which equation does the table represent?

A FV = 250 (1 + r) 2 B FV = 250 (1 - r) 2 C FV = 250 (r) 2 D FV = 250 + (1 + r) 2

2 Javon travels as part of his job. He calculates that his current business trip can be described by the formula d = -30 t 2 + 510t, where d is the distance from home and t is the time in days of his trip. On what day(s) of his trip will he be 1,800 miles from home?

F day 5G day 5 and day 12H day 12 and day 15J day 13

3 The Mid-Continent Tower in Tulsa, Oklahoma, is 513 feet tall. Suppose a penny is thrown upward by a person standing at the edge of the top of the tower. Its height, h, in feet above the street, after t seconds is given by the equation below.

h = -16 t 2 + 64t + 513

What is the height of the penny after 5 seconds?

A 80 ft B 433 ft C 513 ftD 753 ft

4 To the nearest second, how long after being thrown will the penny in Question 3 land on the street? (Assume the coin makes it all the way to the street.)

F 6 s G 7 s H 8 sJ 10 s

5 What is the maximum height above the street reached by the penny in Question 3?

A 532 ft B 548 ft C 577 ftD 600 ft

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15_29_OK_EOI_PO_894018.indd 29 7/9/09 9:47:28 AM

1 The equation (x - h) 2 + (y - k) 2 = r 2 is the standard form of which type of conic section?

A parabolaB circleC ellipseD hyperbola

2 3 x 2 + 4x - 5y + 2 = 0

What is the shape of the graph of the equation?

F parabolaG circleH ellipseJ hyperbola

3 Which equation represents the equation of a hyperbola?

A x 2 + y 2 - 8x - 6y + 5 = 16B x 2 = 8yC 3 x 2 + 4 y 2 + 8y = 8D x 2 - y 2 + 8x = 16

4

OKA2-PO-017A-894018.ai

be

8642

−1

−4−2

−6−8

2 4 6 8 10 12 14

y

x

Which equation represents the conic shown on the graph?

F 8 x 2 - 2 y 2 = 25G (x + 8) 2 + (y - 2) 2 = 25H (x - 8) 2 + y 2 = 25J 2x 2 + 8y = 5

5

OKA2-PO-018A-894018.ai

be

4321

−2−1−3−4

−2−1

−3−4

1 2 3 4

y

x

What is the equation of the graph?

A 2 x 2 = 2yB 2 x 2 = 2 y 2 C 2 y 2 - 2 x 2 = 1D 2 y 2 + 2 x 2 = 1

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Practice by ObjectiveAII.2.4

30_44_OK_EOI_PO_894018.indd 30 7/9/09 11:28:48 AM

1 Which graph represents the function

f(x) = ( 1 _ 2 ) x ?

A

OKA2-PO-019A-894018.ai

be

45

321

−2−1−3−4

−2−1

−3

1 2 3 4

y

x

B

OKA2-PO-020A-894018.ai

be

45

321

−2−1−3−4

−2−1

−3

1 2 3 4

y

x

C

OKA2-PO-021A-894018.ai

be

321

−2−1−3−4

−2−1

−3−4−5

1 2 3 4

y

x

D

OKA2-PO-022A-894018.ai

be

321

−2−1−3−4

−2−1

−3−4−5

1 2 3 4

y

x

3 What is the domain of the logarithmic function y = log x?

A all real numbersB all negative real numbersC all positive real numbersD all real numbers greater than or

equal to 0

2

OKA2-PO-023A-894018.ai

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321

−2−1−3−4

−2−1

−3−4−5

1 2 3 4

y

x

Which function is graphed above?

F f(x) = x - 1G f(x) = 3 x

H f(x) = ( 1 _ 3 )

x

J f(x) = log x

4 Which point is on the graph of every exponential function given by y = a x where a > 0?

F (0, 1) G (0, -1) H (1, 0) J (-1, 0)

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30_44_OK_EOI_PO_894018.indd 31 7/9/09 11:28:56 AM

1 Which equation is equivalent to 2 5 = 32?

A log 5 2 = 32B log 2 5 = 32C log 2 32 = 5D log 5 32 = 2

2 What is the value of x if log 4 4 3 = x?

F 3G 4 H 64 J 81

3 What is the value of x if log 3 x = 2.5?

A 27B 243C √ � 3 D 9 √ � 3

4 What is 5 log 5 (2x - 1) using the properties of logarithms?

F ∅G 25H 2x - 1J 10x - 5

5 Which equation is equivalent to 125 = 5 3 ?

A log 3 5 = 125B log 3 125 = 5C log 5 3 = 125D log 5 125 = 3

6 How is the graph of y = log 3 x related to the graph of y = 3 x ?

F The graphs are reflections of each other over the x-axis.

G The graphs are reflections of each other over the y-axis.

H The graphs are reflections of each other over the line y = x.

J The graphs are reflections of each other over the line y = -x.

7 What is the value of x if log 2 x = 3.5?

A √ � 2 B 8 √ � 2 C 64D 128

8 Which of the following is equivalent to log 6 6 3x ?

F 3xG 6H 216 J 6 x

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30_44_OK_EOI_PO_894018.indd 32 7/9/09 11:28:59 AM

1 The loudness, L, of a sound in decibels is given by the formula

L = 10 log 10 I _ I 0

, where I is the

intensity of the sound and I 0 is the intensity of the softest sound detectable by humans. The softest sound audible to humans has an intensity of 1 0 -12 , so I 0 = 1 0 -12 . Jose Rodriguez installed a new muffler on his car, and, as a result, the noise level of the car dropped from 73 decibels to 64 decibels. What was the percent decrease of the intensity of sound with the new muffler?

A 8.74% B 12.3% C 79.4% D 87.4%

3 The population of Oklahoma City grew exponentially each year from 2000 according to the function P(x) = 506,132 (1.0103) x , where x is measured in years. To the nearest year, how long will it take for the population to reach 555,031?

A 8 yearsB 9 years C 10 years D 12 years

2 The formula that models the amount A of a decaying radioactive substance that remains in a sample is A = A 0 · e kt , where A 0 is the original amount of the substance, k is a constant, and t is the time in years. If a fossil contains one-fourth of the amount of radioactive isotope carbon-14 it originally contained, how old is the fossil? For carbon-14, k = -0.00012.

F 2,083 yearsG 5,017 years H 11,552 years J 115,520 years

4 In 2000, the average growth rate of Oklahoma’s population was about 0.7% per year. The population in Oklahoma in 2000 was about 3,450,640. If the growth rate remainsthe same, which is a good estimate of the population in 2010?

F 37,000,000G 3,700,000H 5,500,000J 5,440,000

5The formula A = A 0 (2)

- t _ h , where A 0 is

the original amount and h is the half-life of the substance, gives the amount of the original substance that remains after t years. The half-life of radium-226 is 1,620 years. Of a sample of 351 grams of radium-226, about how much will remain at the end of 4,860 years?

A 4.39 gramsB 43.9 gramsC 117 grams D 2,808 grams

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30_44_OK_EOI_PO_894018.indd 33 7/9/09 11:29:03 AM

1 2 x 2 = x

What is the solution to this equation?

A 0

B 1 _ 2

C 0 and 1 _ 2

D 0 and - 1 _ 2

2 3 x 2 - x - 2 = 0

What are the solutions?

F - 2 _ 3 and -1

G - 2 _ 3 and 1

H 2 _ 3 and -1

J 2 _ 3 and 1

3 x 3 + 3 x 2 + 2x = 0

What are the solutions of the equation?

A 0, -2, -1B -2, -1C 2, 1, 0 D 0

4 Which polynomial has 1 _ 3 as one of

its solutions?

F 3 x 2 - 3 = 0G x 2 - x + 3 = 0H 3 x 2 + 10x - 3 = 0J 3 x 2 - 10x + 3 = 0

5 One zero of the polynomial function

f(x) = 2 x 3 + 3 x 2 - 39x - 20 is - 1 _ 2 .

What are all the other zeros of this function?

A -4, -5B 4, 5 C -4, 5 D 4, -5

6 When using synthetic division to divide x 3 - 3 x 2 - 6x + 8 by x - 4, what divisor should be used?

F 4G -4 H x J -x

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30_44_OK_EOI_PO_894018.indd 34 7/9/09 11:29:05 AM

1 Which of the following is a polynomial function with a degree of 4?

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

C x 6 - x 2 + 4 _ x

D - x 4 + x 3 - x + 9

3

221

−2−1−3−4

−2−1

−3−4−5−6

1 2 3 4

y

x

Which equation is represented by this graph?

F 4x - 4G x 2 - 4H x 3 - 4xJ - x 4 - 4 x 2

Which graph represents the functionf(x) = -4 x 6 + 3 x 4 - 2x + 5?

A

432

78

65

1

−2−1−3−4 1 2 3 4

y

x

B

432

78

65

1

−2−1−3−4 1 2 3 4

y

x

C

432

78

65

1

−2−1−3−4 1 2 3 4

y

x

D

432

78

65

1

−2−1−3−4 1 2 3 4

y

x

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1

2 What is the point on the graph of a function that has no nearby points that have a greater y-coordinate called?

F x-interceptG y-interceptH relative minimumJ relative maximum

3

4

OKA2-PO-029A-894018.ai

be

864

−4−2

−6−8

2

−2−1−3−4 1 2 3 4

y

x

Which type of function is shown?

A a quadratic function with a positive leading coefficient

B a quadratic function with a negative leading coefficient

C a cubic function with a positive leading coefficient

D a cubic function with a negative leading coefficient

OKA2-PO-030A-894018.ai

be

810

64

−4−2

−6−8−10

2

−2−1−3−4−5 1 2 3 4 5

y

x

The graph shown is the function f(x) = x 3 + 5 x 2 - 8. What appears to be the relative maximum point and relative minimum point?

A max. = (-3.3, 10.5); min. = (0, 8)B max. = (3.3, 10.5); min. = (0, -8)C max. = (-3.3, 10.5); min. = (0, -8)D max. = (10.5, -3.3); min. = (-8, 0)

OKA2-PO-031A-894018.ai

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864

−4−2

−6−8

2

−2−1−3−4 1 2 3 4

y

x

Which of the following appears to be true of the function shown in the graph?

F y-intercept = (1, 0)G y-intercept = (0, 1)H rel. minimum = (-1.5, 8.5)J rel. maximum = (0.5, -0.5)

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30_44_OK_EOI_PO_894018.indd 36 7/9/09 11:29:18 AM

1 The top of the Oklahoma State Capital in Oklahoma City is approximately 255 feet above the street. Suppose a penny is thrown upward and outward by a person standing at the edge of the roof. The penny’s height, h, in feet above the street after t seconds is given by the following equation.

h = -16 t 2 + 48t + 255

How high above the street is the penny 3 seconds after being thrown?

A 68 ft B 240 ftC 255 ftD 256 ft

2 After how many seconds will the penny be 95 feet above the street in Question 1?

F 3.5 sG 4 sH 4.5 sJ 5 s

3 What is the maximum height above the building reached by the penny in Question 1?

A 255 ftB 256 ftC 270 ftD 291 ft

4 If the penny is simply dropped rather than thrown, the equation describing its height, h, above the street after t seconds is h = -16 t 2 + 255. To the nearest tenth of a second, how long would it take the penny to reach the street in Question 1?

F 3.5 sG 3.7 sH 3.9 sJ 4.0 s

5 The table below shows the attendance for seminars each month.

Which cubic function models the data in the table?

A f (x) = 202 x 3 + 14 x 2 + 19x + 6B f (x) = 202 x 3 - 14 x 2 + 19x - 6C f (x) = 1,501 x 2 - 3,354x + 2,115D f (x) = 1,501 x 2 + 3,354x + 2,115

Month 1 2 3 4

Attendance 201 1,592 5,379 12,774

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30_44_OK_EOI_PO_894018.indd 37 7/9/09 11:29:21 AM

1

2 What are the solutions to

1 _ x - 1

+ 2 _ x = 9 _ 2 ?

F -3, -4

G 1 _ 3 , 4 _

3

H - 1 _ 3 , -

4 _ 3

J 3, -4

4

5

What is the solution of 5 _ x + 3 _ 8 = 61

_ 56

?

A 6B 7 C 8 D 9

A carpenter can build a frame for a certain room in 4 hours. Another carpenter can build the same frame in 5 hours. How long will it take them to build the frame working together?

F 1 hr

G 20 _ 9 hr

H 9 _ 2 hr

J 9 hr

An airplane flies 150 miles east, then returns to the Will Rogers World Airport in Oklahoma City. The total flight time is 2 hours. The flight to the east is with the wind, and the return trip is against the wind. The wind is blowing at 25 miles per hour. What is the speed of the plane with no wind, to the nearest tenth?

A 76.1 miles per hourB 150.0 miles per hourC 152.1 miles per hourD 304.2 miles per hour

3 1 _ x 2 - 4

- 1 _ x + 2

= 8

What are the approximate solutions?

A -2.03 or 2.16B -2.16C 2.03D 2.03 or -2.16

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1 In the graph of a rational function, what are breaks in continuity called?

A point of continuityB vertical line testC vertical asymptoteD horizontal isotope

3

2 y

x

810

642

−4−2−6−8−10

−4−2

−6−8−10

2 4 6 8 10

OKA2-PO-032A-894018.aisp

Which function is represented by the graph above?

F f(x) = x + 4 _

x - 2

G f(x) = x - 4 _ x + 2

H f(x) = x + 4 _

x + 2

J f(x) = x - 4 _ x - 2

Which graph represents the function

f(x) = x _ x - 1

?

A y

x

810

642

−2−3−4−5

−4−6−8−10

1 2 3 4 5−2−1


B y

x

810

642

−2−3−4−5

−4−6−8−10

1 2 3 4 5−2−1


C y

x

810

642

−2−3−4−5

−4−6−8−10

1 2 3 4 5−2−1


D y

x

810

642

−2−3−4−5

−4−6−8−10

1 2 3 4 5−2−1


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30_44_OK_EOI_PO_894018.indd 39 7/9/09 11:29:38 AM

1 f(x) = x + 1 __

x 2 + 6x + 8

Which is the vertical asymptote(s) of the function?

A x = -2 and x = -4B x = -2C x = 2D x = 2 and x = 4

2

3

4 What must be true of the function

f(x) = p(x)

_ q(x)

in order for the function

to be rational?

F p(x) ≠ 0G q(x) ≠ 0H p(x) > 0J q(x) > 0

y

x

78

654

−2−3−4−5

1

3

−1−2

1 2 3 4 5

2

−1


What are the x- and y-intercepts of the function shown in the graph?

A x = 0 and y = 0B x = 0C y = 0D no x- or y-intercepts

y

x

810

642

−4−2−6−8−10

−4−2

−6−8−10

2 4 6 8 10


Which is the vertical asymptote(s) of the function shown in the graph?

F x = -3 and x = 5G x = -5H x = 3J x = -5 and x = 3

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30_44_OK_EOI_PO_894018.indd 40 7/9/09 11:29:47 AM

1 The profit, P, for a manufacturing company, in thousands of dollars, that produces x products can be modeled by the function below.

P(x) = 100x _ 200 - x

How much more profit will the company make if they increase production from 100 products to 125 products?

A $66.67B $66,667C $100,000D $166,667

3 The formulas for the volume and surface area of a cylinder are shown below.

V = π r 2 h

SA = 2π r 2 + 2πrh

Which rational function represents the ratio of the surface area to volume of the cylinder in simplified form?

A f(r) = r _ 2r + 2

B f(r) = πr 2 h __ 2 πr 2 + 2πrh

C f(r) = 2 πr 2 + 2πrh __

πr 2 h

D f(r) = 2r + 2h _

rh

2 The function shown below represents the growth of bacteria in hundreds, B, over a certain period of time, t.

B(t) = 4t - 1 _

t + 1 , t ≥ 0

What is the difference in the number of bacteria between t = 4 and t = 8?

F 0.44G 3H 3.44J 44

4 A cyclist rode at a speed of 15 miles per hour for 3 hours, and at a speed of 19 miles per hour for t hours. Which function represents the average speed of the cyclist?

F S(t) = 3t _ 3(15)(19t)

G S(t) = 3(15)(19t)

_ 3t

H S(t) = 3(15) + 19t

_ 3 + t

J S(t) = 3 + t _

3(15) + 19t

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30_44_OK_EOI_PO_894018.indd 41 7/9/09 11:29:50 AM

1 If the points on a scatter plot show that the dependent variable generally increases as the independent variable increases, what association does the scatter plot show?

A negative associationB positive associationC infinite associationD no association

2

3


Wei

ght(

lb)

155

145

165

135

0

175

185

Time (months)321 54 6

y

x

The graph shows the decrease in Kris’ weight over a 6-month period while she was on a diet. Which is a reasonable conclusion about Kris’ weight during the time shown on the graph?

A Kris lost weight during every consecutive month on the diet.

B Kris’ weight decreased by 10 pounds every month.

C Kris gained weight between the 4th and 5th months.

D Kris gained weight between the 5th and 6th months.

OKA2-PO-039A-894018.ai

sp

y

x

Exam

Gra

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40

20

0

60

80

100

Hours Studying21 3 5 7 984 6 10

What conclusion can be accurately made from the scatter plot?

F the more study hours the lower the grade

G the more study hours the higher the grade

H study hours do not affect the grade

J the more study hours lead to the honor roll

4 Which data would likely show a negative association?

F people’s height and the distance between their fingertips when their arms are extended to the side

G height of trees over timeH height of candles as they burnJ people’s height and their area code

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30_44_OK_EOI_PO_894018.indd 42 7/10/09 9:55:17 AM

1Month Average

Temperature 1 47

2 54

3 62

4 72

5 78

6 86

7 94

8 92

9 84

10 75

11 62

12 51

The table shows the average high temperatures for Okmulgee, Oklahoma, for each month of the year. Which function best models the data in the table?

A f(x) = -1.1x + 64.2B f(x) = -1.7 x 2 + 18.8x + 22.9C f(x) = - 0.1 x 3 + 0.6 x 2 +

8.1x + 36.8D f(x) = 47 (1.03) x

3 Hours Wages15 $236.2529 $456.7540 $63032 $50437 $582.75

What equation best models the scatter plot of the data shown in the table?

A f(x) = 1.04 (135) x B f(x) = 135 (1.04) x C f(x) = 15.75xD f(x) = 15.75x + 40

2 When using a graphing calculator, what is the name of the value that indicates the strength of the correlation?

F dependent variable (y)G independent variable (x)H correlation coefficient (r)J association variable (a)

4 Year Population 0 1.65

10 1.75

20 1.87

30 2.09

40 2.32

What equation best models the scatter plot of the data shown in the table?

F f(x) = 1.01 (1.62) x G f(x) = 1.62 (1.01) x H f(x) = 0.017xJ f(x) = x + 1.6

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1 15, 7, -1, -9, ...

Which expression represents the general term of this arithmetic sequence?

Arithmetic Sequences & Series

n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )

Geometric Sequences & Series

n th term: a n = a 1 r (n - 1)

Sum: s n = a 1 (1 - r n )

_ (1 - r)

A 15 - 8n C 23 - 8nB n - 8 D -8 + 15n

3

2

4

8, 12, 18, 27, ...

Whic expression represents the general term of this geometric sequence?


n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )



Sum: s n = a 1 (1 - r n )

_ (1 - r)

F 4n + 4 H 4 · ( 3 _ 2 )

n

G 8 · ( 3 _ 2 )

n - 1 J 8 · ( 2 _

3 )

n - 1

Find the sum of the first 100 positive even integers.


n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )



Sum: s n = a 1 (1 - r n )

_ (1 - r)

A 5,000 C 10,000B 5,050 D 10,100

1 _ 9 - 1 _

27 + 1 _

81 - 1 _

243 + ...

What is the sum of this infinite sequence?


n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )



Sum: s n = a 1 (1 - r n )

_ (1 - r)

F 1 _ 6 H 1 _

12

G 1 _ 9 J 1

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Practice by ObjectiveAII.3.3

30_44_OK_EOI_PO_894018.indd 44 7/9/09 2:39:49 PM

Record your answers by coloring in the appropriate bubble for the best answer to each question.

1 A B C D

2 F G H J

3 A B C D

4 F G H J

5 A B C D

6 F G H J

7 A B C D

8 F G H J

9 A B C D

10 F G H J

11 A B C D

12 F G H J

13 A B C D

14 F G H J

15 A B C D

16 F G H J

17 A B C D

18 F G H J

19 A B C D

20 F G H J

21 A B C D

22 F G H J

23 A B C D

24 F G H J

25 A B C D

26 F G H J

27 A B C D

28 F G H J

29 A B C D

30 F G H J

31 A B C D

32 F G H J

33 A B C D

34 F G H J

35 A B C D

36 F G H J

37 A B C D

38 F G H J

39 A B C D

40 F G H J

41 A B C D

42 F G H J

43 A B C D

44 F G H J

45 A B C D

46 F G H J

47 A B C D

48 F G H J

49 A B C D

50 F G H J

51 A B C D

52 F G H J

53 A B C D

54 F G H J

55 A B C D

56 F G H J

57 A B C D

58 F G H J

59 A B C D

60 F G H J

61 A B C D

62 F G H J

63 A B C D

64 F G H J

65 A B C D

66 F G H J

67 A B C D

68 F G H J

69 A B C D

70 F G H J

71 A B C D

72 F G H J

73 A B C D

74 F G H J

75 A B C D

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Practice TestStudent Answer Document

37_OK_EOI_SAD_894018.indd 45 6/23/09 8:21:33 AM

7/10/09 11:09:31 AM046_OK_EOI_SAD_894019 46

4

5 1

_ 2 , 1

_ 4 , 1

_ 8 , 1

_ 16 , …

What is the sum of the infinite geometric series?


n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )



Sum: s n = a 1 (1 - r n )

_ (1 - r)

A - 1 _ 2

B 1 _ 2

C 1

D 2

1 Which equation models exponential growth?

A y = 0.4 (1.08) x B y = 7 e -1.5x C y = 8000 (0.9) x D y = 6.4 (2.7) -4

What are the factors of 2 x 2 - 7x - 4?

F (2x + 1) and (x - 4) G (2x - 1) and (x + 4) H (2x - 1) and (x - 4) J (2x + 1) and (x + 4)

2 10 + 10

_ 3 +

10

_ 9 + 10

_ 27 + …

What is the sum of this infinite series?


n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )



Sum: s n = a 1 (1 - r n )

_ (1 - r)

F The sum does not exist.

G 31 _ 3

H 15J 20

3 Which statement is equivalent to 5 4 = 625?

A lo g 4 625 = 5B lo g 5 625 = 4C lo g 5 4 = 625D lo g 4 5 = 625

6(1024 )

- 2 _ 5

What is the value of this expression?

F -16 H 1 _ 16

G - 1 _ 16

J 16

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Practice Test

47_65_OK_EOI_PT_894018.indd 4747_65_OK_EOI_PT_894018.indd 47 17/6/10 2:49:17 PM17/6/10 2:49:17 PM

7 Which is the graph of y = x 2 + 4x + 4?

A y

x−1

4567

321

1 2 3 4 5 6 7

B y

x−2−1−3−4

4567

321

−4

1 2 3 4

C y

x−2−1−3−4−5−6−7

4567

321

1

D y

x−2−1−3−4

4321

−2−3−4

1 2 3 4

9 Ian, Sarah, and Jeremy were hired to paint classrooms at a school last summer. Ian painted 2 more classrooms than Sarah. Sarah painted twice as many classrooms as Jeremy. Together they painted a total of 17 classrooms. How many classrooms did Sarah paint?

A 2B 3 C 6D 8

10 The First Place Tower in Tulsa, Oklahoma, is 516 feet tall. Suppose a ball is thrown upward by a person standing on the top of the building so that its height above the ground, h, in feet, after t seconds is given by the equation h = -16 t 2 + 32t + 516. What will be the height of the ball after 2 seconds?

F 540 ftG 532 ftH 516 ftJ 388 ft

11 Which expression is equivalent to (8 y 3 - 10 y 2 - 9y + 9) ÷ (2y - 3)?

A 4 y 2 + y - 3

B 4 y 2 - y + 3

C 4 y 2 - 3

D y 3 + 4 y 2 + y - 38 What is the simplified form of

4 √ �� 256 · √ �� 256 ?

F 5 √ �� 256 H 32

G 16 J 64

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47_65_OK_EOI_PT_894018.indd 48 7/9/09 12:32:04 PM

12 14

13 (2 x 3 - x 2 - 2x + 1) ÷ (x + 1)

Which expression represents the quotient?

A 2x - 3B 2 x 2 - 3x + 1C 2x + 1D x2 - 2x + 1

A landscaper in Fair Oaks, Oklahoma received the bids shown in the graph below for cedar chips.

Cost

/ton

($)

150

100

50

0

Weight (tons)

Bids for Cedar Chips

1 2 3 4 5 6

KEYFennelGregoryHoweJackson

y

x

If the landscaper needs 5 tons of cedar chips, which bidder is the cheapest?

F FennelG GregoryH Howe J Jackson

y

x−2−1−3−4

4321

−2−3−4

1 2 3 4

Which inequality best describes the domain of the function represented by the graph?

F x ≥ 0G x ≤ 3H y ≥ 0J y ≤ 3

15 If f (x) = 3x - 8 and g (x) = 9 x 2 - 64, which expression is equivalent to g (x) ÷ f (x)?

A 3x + 8B 3x - 8

C 1 _ 3x + 8

D 27 x 3 + 512

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47_65_OK_EOI_PT_894018.indd 49 7/9/09 10:01:11 AM

16 The second tallest building in Oklahoma is the Bank of Oklahoma Tower. It has 8 fewer stories than the tallest building in Oklahoma, the Citiplex. Together these buildings have 112 stories. How many stories are in the Bank of Oklahoma Tower?

F 42G 52H 60J 70

18 x + y ≥ 6

2x - y ≥ 0

x ≤ 4

Which graph shows the solutions of the system of equations?

F y

x−1

4567

321

1 2 3 4 5 6 7

G y

x−1

4567

321

1 2 3 4 5 6 7

H y

x−1

4567

321

1 2 3 4 5 6 7

J y

x−1

4567

321

1 2 3 4 5 6 7

17 What are solutions of x 2 + 6x - 2 = 0?

If a x 2 + bx + c = 0

then x = -b ± √ �� b 2 - 4ac

__ 2a

A -3 ± √ �� 11 B 3 ± √ �� 11 C -3 ± √ � 2 D 3 ± √ � 2

�

�

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47_65_OK_EOI_PT_894018.indd 50 7/9/09 10:01:14 AM

19 y = (x - 1 ) 2 - 3

Which graph represents this equation?

A y

x−2−1−3−4−5−6−7

4567

321

1

B y

x−2−1−3−4

21

−2−3−4−5−6

1 2 3 4

C y

x−2−1

21

−2−1

−3−4−5−6

1 2 3 4 5 6

D y

x−2−1−3−4−5

21

−2−3−4−5−6

1 2 3

21 An amount of $200 is invested in a savings account paying 6.25% compounded continuously. How long would it take for the account to be worth $300?

A = P e rt

A 6.7 years C 6.3 yearsB 6.5 years D 6.0 years

22 4, 10, 25, 62.5, …

What is the general term of this geometric sequence?


n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )



Sum: s n = a 1 (1 - r n )

_ (1 - r)

F 2n + 4 H 4 · (5 2)

n - 1

G 4 · (5 2)

n

J 4 · (3 2)

n - 1

20 What is the product of (4 - 2i) and (3 + 2i)?

F 8 + 2iG 16 - 14iH 16 + 2iJ 8 - 2i

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47_65_OK_EOI_PT_894018.indd 51 7/9/09 10:01:17 AM

23 Which graph represents the function f (x) = 1 - x 2 ?

A y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

B y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

C y

x−2−1−3−4

4321

−2−3−4

1 2 3 4

D y

x−2−1−3−4

4321

−2−3−4

1 2 3 4

25 The function f (s) = 2s + 24 is used to convert women’s shoe sizes in the United States to shoe sizes in Italy. The function g (s) = 1 _

2 s - 14 is used

to convert shoe sizes in Italy to shoe sizes in Great Britain. What is a function for converting women’s shoe sizes in the United States to shoe sizes in Great Britain?

A (f · g) (s) = s + 17

B (f + g) (s) = 2 1 _ 2 s + 10

C (g · f) (s) = s - 2D fg (s) = s 2 + 16s - 336

24 Which equation represents the equation of a hyperbola?

F x 2 = 2yG 3 x 2 + 3 y 2 + 9y = 7H 2 x 2 - 3 y 2 + x = 10J x 2 + 2 y 2 - 4x - 3y + 5 = 11

26 -4, -1, 2, 5, …

What is the formula for the nth term of this sequence?


n th term: a n = a 1 + (n - 1)d

Sum: s n = n _ 2 ( a 1 + a n )

F a n = 3n - 4G a n = 3n - 3H a n = 2n - 4J a n = 3n - 7

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47_65_OK_EOI_PT_894018.indd 52 7/9/09 10:01:20 AM

29 Which is the graph of y = log (x + 1)?

A y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

B y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

C y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

D y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

28 7x y 2 - x 2 y

_ xy

Which expression represents the quotient?

F 7y - x 2 yG 7 - x 2 yH 7y - x J 7y - 1

27 3a _ a 2 - 4

1 _ 2 - a

- 1 _ 2 + a

What is the simplest form of this expression?

A 3 _ 2

B 3a _ 2a - 4

C - 3a _ 2a + 4

D - 3 _ 2

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47_65_OK_EOI_PT_894018.indd 53 7/9/09 10:01:23 AM

3330 If a > 1, for what values of x is lo g a x > 0 true?

F for all values of xG for all x such that 0 < x < 1H for all x such that x > 1J for no values of x

y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

What is the range of the function shown on the graph?

A y > 3B y ≤ 3C -3 < y < 3D all real numbers

34 Which polynomial represents the area of a circle with a radius of x - 3?

F π ( x 2 + 9) G π ( x 2 - 6x - 9) H π ( x 2 - 6x + 9) J π ( x 2 - 6x)

31 Kumar can paint his room in 10 hours. Julio can paint the same room in 8 hours. To the nearest minute, how long will it take if they paint the room together?

A 4 h 4 minB 4 h 27 minC 6 h 22 minD 9 h

32 x - 2y + z = -1

2x + y - z = -4

-x + 3y + 2z = 15

What is the solution to this system of equations?

F �G { (-1, 2, 4) }H { (2, 3, 4) }J { (2, -1, 7) }

�

�

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47_65_OK_EOI_PT_894018.indd 54 7/9/09 10:01:25 AM

35 How does the graph of y = x 2 - 2 differ from the graph of y = x 2 + 2?

A The vertex of y = x 2 - 2 is 4 units below the vertex for y = x 2 + 2.

B The vertex of y = x 2 - 2 is 4 units above the vertex for y = x 2 + 2.

C The vertex of y = x 2 - 2 is 4 units to the left of the vertex for y = x 2 + 2.

D The vertex of y = x 2 - 2 is 4 units to the right of the vertex of y = x 2 + 2.

37

y

x−2−1−3−4

4321

−2−3−4

1 2 3 4−1

What is the parent function of this graph?

A absolute valueB exponentialC linearD quadratic

38 y

x−2−1

456

321

−2−1 1 2 3 4 5 6

What is the equation of the graphed circle?

F (x - 2) 2 + (y - 3) 2 = 3G (x + 2) 2 + (y + 3) 2 = 3H (x - 2) 2 + (y - 3) 2 = 9J (x + 2) 2 + (y + 3) 2 = 9

36

What is the solution to this system of equations?

F all (x, y) such that 2x - 3y = -5G �

H ( 7 3)

J ( )

7 _

4 , 19 _

3

1,

2 x - 3y = -5

6 x - 9y = 6

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47_65_OK_EOI_PT_894018.indd 55 7/9/09 12:32:07 PM

39 Ladawn threw a coin from the second story of the mall into the fountain on the ground floor. The table below shows the relationship between the elapsed time and the coin’s height above the bottom of the fountain.

Time (sec) Height (ft)0 64

0.5 60

1.0 48

1.5 28

2.0 0

If the height of the coin can be modeled by a quadratic function of time, which equation best represents the height, h, at time, t?

A h = 64 - 16 t 2 B h = 64 - t 2 C h = 48 t 2 D h = t 2 + 64

41 y

x−2−3−4−5 −1

45

321

−2−3−4−5

−1 1 2 3 4 5

Which rotational function is shown in this graph?

A x + 1 __

(x - 1) (x + 2)

B x + 1 __

(x + 1) (x - 2)

C x + 1 __

(x + 1) (x + 2)

D x + 1 __

(x - 1) (x - 2)

40 When is the equation lo g a a k = k true?

F when a = kG neverH when a > 0 and a ≠ 1J when k > 0

42 What is the length of side b of the rectangle shown?

Area = 2 + 5 - 24x + 5x 3 x 2

x + 5

F x 2 - 3x + 1G 2 x 2 - 5x + 1H 2 x 2 + 5x + 1J 2 x 2 + 5x - 1

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47_65_OK_EOI_PT_894018.indd 5647_65_OK_EOI_PT_894018.indd 56 6/28/10 7:22:59 PM6/28/10 7:22:59 PM

43 3n

_ n - 5 + 3 _ 5 - n

Which expression represents the result of this addition?

A 3n - 3 _ n - 5

B 3n + 3 _ n - 5

C 3n - 3 _ 5 - n

D 3n2 + 18n - 15 __

-n2 + 10n - 25

46 Jan can mow her neighbor’s lawn in 3 hours. Ian can mow the same lawn in 2 hours. To the nearest minute, how long will it take if they mow the lawn together?

F 1 hG 1 h 5 minH 1 h 12 minJ 1 h 15 min

44 y

x−2−1−3−4

21

−2−3−4−5−6

1 2 3 4

What is the minimum point of the graph?

F (1, 5) G (-2, -4) H (-1, -7) J (-1, -13)

45 The price, u, of a laptop computer at Store A is $175 more than half the price, �, of the same computer at Store B. The difference in price between the computer at Store A and Store B is $250. Which system of equations can be used to determine the price of the computer at each store?

A u + 1 _ 2 � = 175

u + � = 250

B u - 2� = 250

� - u = 175

C u - 1 _ 2 � = 250

� - u = 175

D u - 1 _ 2 � = 175

u - � = 250

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47_65_OK_EOI_PT_894018.indd 57 7/9/09 10:01:35 AM

47 When is the equation

√ �� a 2 + b 2 = a + b true?

A when a = 0 and b ≥ 0 or when b = 0 and a ≥ 0

B alwaysC neverD when a ≥ 0 and b > 0

48 Radioactive substances decay over time. If the amount of carbon-14 in an animal bone was P 0 grams at the time the animal died, then the amount of carbon-14 remaining in the bone t years later is given by the function P(t) = P 0 e -0.00012t . If 10% of the original carbon-14 remains in a bone found at Spiro Mounds in Oklahoma, about how old is the bone?

F 19,000,000 yearsG 19,000 yearsH 8,000 yearsJ 1,900 years

50 At a manufacturing plant, machine A can produce 500 parts for a rush order in 6 hours and machine B can produce the same 500 parts in 8 hours. How long to the nearest minute, would it take both machines working together to produce the 500 parts?

F 3 h 15 minG 3 h 26 minH 3 h 30 minJ 3 h 44 min

51T = �n2

_ log (1 + r )

This formula gives the number of years, T, required for your money to double when invested at an interest rate, r, compounded continuously. If the interest rate is 5%, what is the value of T to the nearest tenth?

A 1.4 yearsB 3.9 yearsC 14.6 yearsD 32.7 years

49What is the simplified form of 5

3 _ 2 ?

A 5B √ � 5 C 5 √ � 5 D 25

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47_65_OK_EOI_PT_894018.indd 58 7/9/09 10:01:37 AM

5552 21, 17, 13, 9, …

What is the next term in this sequence?

F -5G 3H 5J 7

Which graph represents the function

f (x ) = (1 4)

x

?

A y

x−2−1−3−4

4321

−2−3−4

1 2 3 4−1

B y

x−2−1−3−4

4321

−2−3−4

1 2 3 4−1

C y

x−2−1−3−4

4321

−2−3−4

1 2 3 4−1

D y

x−2−1−3−4

4321

−2−3−4

1 2 3 4−1

53 The equation y = a(x - h ) 2 + k is the standard form of which type of conic section?

A circleB parabolaC hyperbolaD ellipse

54 What is the product of (-2 + 3i) and (-9 - i)?

F 15 - 25iG 21 - 25iH 15 + 25iJ 21 + 25i

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47_65_OK_EOI_PT_894018.indd 59 7/9/09 10:01:40 AM

57 - 1 _ 3 and 1 are the roots of which

polynomial equation?

A 3 x 2 - 2x - 1 = 0

B 3 x 2 - 1 = 0

C x 2 - 1 _ 3 = 0

D x 2 + 1 _ 9 = 0

58

y

x−2

8

42

6

4 8 102 6−4−6

−4−6−8

Which function represents this graphed function?

F f (x) = x + 3 _ x - 1

G f (x) = x - 3 _ x + 1

H f (x) = x + 1 _ x + 3

J f (x) = x + 1 _ x - 3

56 Which graph shows the equation (x + 4 ) 2 + (y - 2 ) 2 = 3 2 ?

F y

x−2−1−3−4−5−6−7

123

−2−1

−3−4−5

1

G y

x−2−1−3−4−5−6−7

123456

−2−1 1

H y

x−1

123

−2−3−4−5

−1 1 2 3 4 5 6 7

J y

x−1

123456

−2−1 1 2 3 4 5 6 7

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47_65_OK_EOI_PT_894018.indd 60 7/9/09 10:01:43 AM

59

60 12, 18, 27, 40.5, …

What is the next term in the sequence?

F 46.5G 54H 60.75J 81

G.P.

A.5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

Hours Watching TV per week5 10 15 20 25 30 35 40 45

What conclusion can be made from the scatter plot?

A There is no association.B The more hours spent watching

TV per week, the higher the G.P.A.C The fewer hours spent watching

TV per week, the lower the G.P.A.D The more hours spent watching

TV per week, the lower the G.P.A.

61 (6 - 7i) - (-2 + 8i)

Which expression represents the result of this subtraction?

A 4 - iB 4 - 15iC 8 - 15iD 8 + i

62 Which expression is equivalent to

x - 2 _ x - 1

+ x + 3

_ x + 1

?

F 2 x 2 + x - 5 _

x 2 + 1

G 2 x 2 + x - 5 _

x 2 - 1

H 2x2 + 3x + 5 __

x2 + 1

J 2x 2 + 3x + 5 __

x 2 - 1

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47_65_OK_EOI_PT_894018.indd 61 7/9/09 10:01:45 AM

63 y

x−2−1−3−4

4321

−2−3−4

1 2 3 4−1

Which equation represents the conic shown on the graph?

A 9 x 2 + 3 y 2 = 10B 9 x 2 - 3 y 2 = 10C 3 x 2 - 9 y 2 = 10D 3 x 2 + 9 y 2 = 10

65 The graph shows the increase in Sally’s salary over a 10-year period while working for her current company.

Sala

ry (i

n th

ousa

nd $

) 70

60

50

40

30

20

10

0

Years Worked

Sally’s Salary

1 2 3 4 5 6 7 8 9 10

Which is a reasonable conclusion about Sally’s salary during the time shown on the graph?

A Her salary doubled in 10 years.B Her salary increased by 50% over

the first 5 years.C Her salary increased by 50% over

the first 10 years.D Her salary increased by 5% each

year.

64 When two lenses are put together, the combined focal length is given by the equation below, where f 1 and f 2 are the focal lengths of each lens.

f = f 1 f 2 _

f 2 + f 1

What is the combined focal length to the nearest tenth of a centimeter when f 1 is 5 cm and f 2 is 8 cm?

F 3.0G 3.1H 0. 3 2 J 0.4

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47_65_OK_EOI_PT_894018.indd 62 7/9/09 10:01:48 AM

66 What is the product of -1 + 7i and its conjugate?

F -48G 50 - 14iH -48 - 14iJ 50

69 What is the vertical asymptote(s) of the following function?

y

x−2−3−4−5 −1

45

321

−2−3−4−5

−1 1 2 3 4 5

A x = -4 and x = 3B x = 3C x = 4D x = -3 and x = 4

67 The graph shown is the function f (x) = x3 + 4x2 + 2.

y

x−1−4−3

810

42

6

2 41 3−2

−4−6

What is the relative maximum and relative minimum?

A max. = (11.5, -2.67) ; min. = (2, 0)

B max. = (-2.67, 11.5) ;min. = (0, 2)

C max. = (11.5, -2.67) ; min. = (0, 2)

D max. = (-2.67, 11.5) ; min. = (2, 0)

68 4 _ x + 1

_ (3x ) -2

What is the simplest form of this expression?

F 4 + x _ 3 x 3

G 5 _ 3x

H 12 x 3 + 3 x 4 J 9 x 2 + 36x

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47_65_OK_EOI_PT_894018.indd 63 7/9/09 10:01:51 AM

7270 What are the solutions of 4 x 2 - 5x - 1 = 0?

F 1 _ 4 , 1

G 5 ± √ �� 41 _

8

H 5 ± √ �� 29 _

8

J -1 and - 1 _ 4

Which graph represents the function f (x) = 3 x 3 + 2 x 2 - x + 5?

F y

x−1−4−3

8

42

6

2 41 3−2

−4−6−8

G y

x−1−4−3

81012

42

6

2 41 3−2

−4

H y

x−1−4−3

810

42

6

2 41 3−2

−4−6

J y

x−2−8−6

8101214

42

6

4 82 6−4

71 y

x−2−1−3−4

4321

−2−1

−3−4

1 2 3 4

Which system of linear inequalities is graphed?

A y ≤ 2x + 1y ≥ -x - 2

B y < 2x + 1y ≥ -x + 2

C y < 2x - 1y ≥ -x - 2

D y < 2x + 1y ≥ -x - 2

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47_65_OK_EOI_PT_894018.indd 64 7/9/09 10:01:54 AM

7573

y

x−2−1−3−4

4321

−2−3−4

1 2 3 4−1

What is the equation of the graph?

A 9y2

_ 4 + 4x2

_ 4 = 25

B 9y2

_ 4 - 4x2

_ 4 = 25

C 36 y 2 + 16 x 2 = 25D 36 y 2 - 16 x 2 = 25

The scatter plot below shows the height and weight of some high school athletes.

Wei

ght (

kilo

gram

s)

140

120

100

80

60

40

20

0

Height (inches)55 60 65 70 75 80

Which equation best models the data?

A y = -3.1x + 87B y = 2.8x - 115C y = x2 - 2x + 54D y = 7 (2x)

74 The table shows Portia’s test scores in math at Western Oklahoma State College during her first semester. Which function best represents the data in the table?

Test Test Score1 96

2 85

3 83

4 85

5 87

6 86

7 81

8 70

9 53

F f (x) = -1.36x + 94.3G f (x) = -0.27 x 2 + 2.17x + 86.1H f (x) = -0.07 x 3 + x 2 - 4.8x + 95J f (x) = 0.04 x 4 - 1.2 x 3 + 10.4 x 2 -

35x + 122

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mastering the eoi, algebra 2, se - glencoe

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