includes - glencoe • north carolina course of study ... north carolina algebra 1 end-of-course...

GLENCOE MATHEMATICSGLENCOE MATHEMATICS

Includes:

• North Carolina Course of Study Content Standards Covered on the Algebra 1 EOC Test

• Student Recording Chart

• Diagnostic Test

• Practice for Each Content Standard

• Full-Size Sample Test

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United Statesof America. Except as permitted under the United States Copyright Act, no part of this book maybe reproduced in any form, electronic or mechanical, including photocopy, recording, or anyinformation storage or retrieval system, without prior written permission of the publisher.

Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027

ISBN: 0-07-868597-4 Preparing for the North Carolina Algebra 1 End-of-Course TestPractice and Sample Test Workbook

1 2 3 4 5 6 7 8 9 10 009 13 12 11 10 09 08 07 06 05 04

Test-Taking Tips• Go to bed early the night before the test. You will think more clearly

after a good night's rest.

• Read each problem carefully and think about ways to solve theproblem before you try to answer the question.

• Relax. Most people get nervous when taking a test. It's natural. Justdo your best.

• Answer questions you are sure about first. If you do not know theanswer to a question, skip it and go back to that question later.

• Think positively. Some problems may seem hard to you, but you maybe able to figure out what to do if you read each question carefully.

• If no figure is provided, draw one. If one is furnished, mark it up tohelp you solve the problem.

• When you have finished each problem, reread it to make sure youranswer is reasonable.

• Become familiar with a variety of formulas and when they shouldbe used.

• Make sure that the number of the question on the answer sheetmatches the number of the question on which you are working inyour test booklet.

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Algebra 1 EOC Test iii

Contents

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivStudent Recording Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vAlgebra 1 Competency Goals Tested on the EOC Correlated to

Glencoe Algebra 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Test PracticeDiagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Standards Practice1.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Test PracticeSample Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Sample Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Overview

The material in this booklet is designed to help you prepare for the North Carolina Algebra 1 End-of-Course Test (EOC).

It contains:

• a Student Recording Chart,

• the competency goals tested on the EOC,

• a Diagnostic Test,

• practice for each competency goal, and

• two Sample Tests.

How to Use This Book

Diagnostic Test This test will help you identify any weaknesses youmay have as you prepare to take the EOC. Once you’ve taken the test andit’s been graded, complete the Student Recording Chart that is found onpage iv. Mark an × in the square for each question that you answeredincorrectly.

Individual Practice You can use each student’s chart to determine whereextra practice is needed. Assign each student the appropriate StandardsPractice worksheet(s) from pages 17 to 64 in the Student Workbook.

Practice If you missed one or two of the questions for a particularcompetency goal, you could probably use some extra practice with thatgoal. The Student Recording Chart lists practice pages for eachcompetency goal. Complete the appropriate practice pages. If you areunsure about how to do some of the problems, you may want to refer toyour mathematics book.

Sample Tests After you have completed your practice worksheet(s),take the Sample Tests on pages 65 to 96.

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iv Algebra 1 EOC Test

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Algebra 1 EOC Test v

Student Recording Chart

Directions Mark an × by each question from the Diagnostic Test that youanswered incorrectly. If there are one or two ×s marked for a competency goal,write Yes in the Need Practice? box. Then complete the practice pages for thatcompetency goal.

Strand Number and Operations

Goal 1.01 1.02 1.03

Test Questions 14 ■■ 26 ■■ 33 ■■ 46 ■■ 11 ■■ 21 ■■ 24 ■■ 51 ■■ 4 ■■ 12 ■■ 28 ■■ 45 ■■47 ■■ 67 ■■ 79 ■■ 25 ■■ 52 ■■ 61 ■■ 80 ■■ 25 ■■ 53 ■■ 62 ■■ 25 ■■ 25 ■■

Need Practice?

Practice Pages 17–20 21–24 25–28

Strand Geometry and Measurement

Goal 2.01 2.02

Test Questions 5 ■■ 18 ■■ 25 ■■ 29 ■■ 15 ■■ 40 ■■ 48 ■■ 50 ■■38 ■■ 43 ■■ 56 ■■ 25 ■■ 60 ■■ 63 ■■ 64 ■■ 25 ■■

Need Practice?

Practice Pages 29–32 33–36

Strand Data Analysis and Probability

Goal 3.01 3.02 3.03

Test Questions 1 ■■ 7 ■■ 8 ■■ 13 ■■ 10 ■■ 27 ■■ 35 ■■ 36 ■■ 16 ■■ 34 ■■ 41 ■■ 55 ■■42 ■■ 49 ■■ 25 ■■ 25 ■■ 37 ■■ 73 ■■ 25 ■■ 25 ■■ 57 ■■ 71 ■■ 72 ■■ 25 ■■

Need Practice?

Practice Pages 37–40 41–44 45–48

Strand Algebra

Goal 4.01 4.02 4.03 4.04

Test Questions 19 ■■ 30 ■■ 65 ■■ 2 ■■ 3 ■■ 6 ■■ 20 ■■ 22 ■■ 54 ■■ 17 ■■ 23 ■■ 44 ■■75 ■■ 77 ■■ 78 ■■ 9 ■■ 31 ■■ 32 ■■ 59 ■■ 66 ■■ 74 ■■ 58 ■■ 68 ■■ 69 ■■

39 ■■ 25 ■■ 25 ■■ 76 ■■ 25 ■■ 25 ■■ 70 ■■ 25 ■■ 25 ■■

Need Practice?

Practice Pages 49–52 53–56 57–60 61–64

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vi Algebra 1 EOC Test

Competency Goals Tested on the EOCCOMPETENCY GOAL 1: The learner will perform operations with numbers andexpressions to solve problems.

1.01 Write equivalent forms of algebraic expressions to solve problems.(a) Apply the laws of exponents.(b) Operate with polynomials.(c) Factor polynomials.

1.02 Use formulas and algebraic expressions, including iterative and recursive forms, tomodel and solve problems.

1.03 Model and solve problems using direct variation.

COMPETENCY GOAL 2: The learner will describe geometric figures in the coordinateplane algebraically.

2.01 Find the lengths and midpoints of segments to solve problems.

2.02 Use the parallelism or perpendicularity of lines and segments to solve problems.

COMPETENCY GOAL 3: The learner will collect, organize, and interpret data withmatrices and linear models to solve problems.

3.01 Use matrices to display and interpret data. Operate (addition, subtraction, scalar multiplication) with matrices to solve problems.

3.02 Operate (addition, subtraction, scalar multiplication) with matrices to solve problems.

3.03 Create linear models, for sets of data, to solve problems.(a) Solve using tables, graphs, and algebraic properties.(b) Interpret constants and coefficients in the context of the problem.

COMPETENCY GOAL 4: The learner will use relations and functions to solve problems.

4.01 Use linear functions or inequalities to model and solve problems; justify results.

(a) Solve using tables, graphs, and algebraic properties.

(b) Interpret constants and coefficients in the context of the problem.

4.02 Graph, factor, and evaluate quadratic functions to solve problems.

4.03 Use systems of linear equations or inequalities in two variables to model and solveproblems. Solve using tables, graphs, and algebraic properties; justify results.

4.04 Graph and evaluate exponential functions to solve problems.

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Algebra 1 EOC Test 1

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Diagnostic Test

1 In a controlled study, ten randomly selected subjects are given varyingamounts of a pain medication. The number of minutes before pain isrelieved is recorded in the table. Which describes a pattern in the data?

3.01

A The subjects get very little pain relief from the medication.B The greater a subject’s pain, the more medication is required.C As the amount of drug increases, the number of minutes until a

subject feels pain relief decreases.D There is no connection between the medication’s dosage and the

timing of a subject’s relief.

Use the following information to answer Questions 2 and 3.

The sum s of the first n even counting numbers is given by the function s � n2 � n.

2 Which set includes the first 5 elements of the function’s range? 4.02A {0, 2, 6, 12, 20} B {2, 6, 12, 20, 30}C {2, 4, 6, 8, 10} D {3, 6, 10, 15, 20}

3 Which is the sum of the first 20 counting numbers? 4.02A 60 B 80 C 420 D 1,600

4 Which equations are equivalent to �W

W1

2� � �

D

D1

2�? 1.03

I. D2 � �D

W1W

1

2� II. W1 � �D

W1W

2

1� III. W2 � �D

D2W

1

1�

A II only B I and III C II and III D I, II, and III

5 Which is the midpoint of A�D� if the coordinates of the endpoints areA(�7, 2) and D(8, �3)? 2.01A (�0.5, �0.5) B (�0.5, 0.5)C (0.5, �0.5) D (0.5, 0.5)

6 Which function has a minimum value? 4.02

A y � �x2 � 6x � 8 B y � 28 � 5x � �12

�x2

C y � 3x2 � 10x � 8 D x2 � y � 36

Amount of Drug (mg) 1 2 5 7 8 10Relief Time (min) 9 5 6 4 3 11

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Read each question and choose the best answer. Then write the letter for the answer you have chosen in the blank at the right of each question.

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2 Algebra 1 EOC Test

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Diagnostic Test (continued)


A farmer in North Carolina tests the effects of three different fertilizers onthe yield of his fruit trees. He randomly selects three fruit trees from fourdifferent sections of his field and applies a fertilizer to each tree. The fruityield from each tree is recorded in the table.

7 Which has the consistently best yields for all three fertilizers? 3.01A North Section B South SectionC East Section D West Section

8 What was the total yield for Fertilizer C? 3.01A 147 B 164 C 195 D 219

9 Which are the zeros of the function y � 2x2 � x � 6? 4.02

A �1 and 5 B �5 and �12

�

C �2 and �32

� D 2 and ��23

�

10 If C � , D � , E � , and F � ,

which statement is true? 3.02A C � D � E B CD � FC 2C � F D 2D � E � F

11 Construction slowed Jan’s average speed on the 120-mile trip from Bensonto Warsaw to 45 miles per hour. On her return trip, Jan was able to average60 miles per hour. How much faster was her return trip? (d � rt) 1.02

A 7�12

� hours B 1.8 hours C 1.2 hours D 40 minutes

12 The resistance R of a wire varies directly as its length L. If the constantof proportionality between R and L is 0.007, what is the ratio of theresistance of a 20-foot wire to its length? 1.03

A �1,0

700� B �

21

04� C �

1240� D �

1,0700�

�12 �2�50 �6

8 15 5

�2 �1�5 �3

6 210 2

Fertilizer North Section South Section East Section West SectionA 47 54 50 50B 47 52 47 49C 53 58 53 55

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13 A high school store sells clothing with the school logo. The matrixshows the current inventory, where the sizes are small (S), medium (M),and large (L). Which clothing item is located in row 2, column 3? 3.01

A shorts, size medium B sweatshirts, size largeC shorts, size large D T-shirts, size medium

14 Which property justifies the statement (p � 3) � 5q � p � (3 �5q)?A Associative Property of Addition 1.01B Commutative Property of AdditionC Commutative Property of MultiplicationD Distributive Property

15 Which is an equation of a line perpendicularto A�B�? 2.02

A y � ��12

�x � 1

B y � �2x � 1

C y � ��13

�x � 1

D y � �2x � 1

16 A bank in Wilmington conducted a study to determine if it can predictthe number of mistakes tellers will make during their first month ofemployment from the number of hours of training they receive. Which isthe dependent variable in the study? 3.03A the number of tellersB the average number of mistakes madeC the number of mistakes a teller makesD the number of hours of training a teller receives

17 Which is an equation of the function that is graphed? 4.04A y � �3x � 5B y � 3�x � 5C y � 5�x � 3D y � 5x � 3

xO

y

xO

yB

A

S M LT-shirts 11 16 8

Sweatshirts 5 12 4 Shorts 8 10 7

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18 Hexagon ABCDEF models a gazebo. All six sides of the gazebo arecongruent. If the coordinates of the endpoints of two consecutivevertices of the hexagon are (3, 0) and (2, �2), which is the perimeter ofABCDEF? Round to the nearest tenth unit. 2.01A 11.2 units B 13.4 unitsC 25 units D 30 units

19 Which function describes the relationship between x and y in the graph? 4.01A y � �2 � 5xB y � 5x � 2C y � 2 � 5xD y � 2 � 5x

20 The cost of printing graduation programs includes a fixed amount plus anadditional charge for each program. If 1,000 programs cost $550 to printand 2,000 programs cost $800, what is the charge per program? 4.03A $0.25 B $0.75C $1.50 D $3.25

21 The formula for calculating the amount At after t years in a bank accountthat earns a compound annual interest rate r is At � A0(1 � r)t, where A0 is the initial amount in the account. How much money would you havein the account after 6 years if you initially deposited $800 in the accountand it earns 4.5% interest annually? 1.02A $996.95 B $1,041.81C $1,088.69 D $5,127.79

22 Hamid can join a ski club and pay a reduced fee for the ski lift or he canpay full price each time he takes the ski lift. The table shows the totalcost for each option for the first 6 lifts. At what point does it cost less tojoin the ski club? 4.03

A lift 8 B lift 9C lift 10 D lift 11

Number of Tickets 1 2 3 4 5 6Ski Club $140 $155 $170 $185 $200 $215Individual Tickets $29 $58 $87 $116 $145 $174

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23 Which is the coefficient of the function y � (8)2�3x � 1? 4.04A �3 B 1C 2 D 8

24 If Thomas is convicted for speeding in his city, he is fined $20 plus $5 foreach mile per hour that he exceeded the speed limit if he was speeding lessthan 15 miles per hour over the speed limit. If, however, he was driving 15or more miles per hour above the speed limit, his fine increases to $20plus $10 for each mile per hour that he was traveling above the speed limit.If Thomas received a ticket for $220, how far above the speed limit washe traveling? 1.02A 2 miles per hour B 20 miles per hourC 24 miles per hour D 40 miles per hour

25 The distance between S(6, �4) and Y(�2, y) is 8. Which is the value of y?A �4 B �2 2.01C �4 or 4 D 4

26 Factor 4u4 � 16v2 completely. 1.01A (2u � v)(2u � v)(u2 � v) B (2u2 � 4v)(2u2 � 4v)C 4(u2 � 2v)(u2 � 2v) D 4(u2 � 2v)(u2 � 2v)

27 Matrix A shows the education level of subjects in a 300-person surveywho said they had been convicted of a felony. Matrix B shows theeducation level of the respondents in the survey who said they had notbeen convicted of a felony. How many respondents with 16 or feweryears of education said they had not been convicted of a felony? 3.02

Convicted of a Felony? Yes Convicted of a Felony? No

A � B �

A 14 respondents B 62 respondentsC 194 respondents D 278 respondents

28 Which is a direct variation equation? 1.03

A C � �d B t � �dr�

C p � 500 � 1.8c D I � �dk2�

Educational LevelLess than 9 years 709 to 12 years 6212 to 16 years 62More than 16 years 84

Educational LevelLess than 9 years 49 to 12 years 812 to 16 years 2More than 16 years 8

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29 Archeologists have located an artifact midway between A and K. They have labeled this point M. Which are the coordinates of M? 2.01A (2, 18)B (0, �3)C (1, 9)D (0, 8)

30 The manager at a community swimming pool in Davie County insists thatthe average reading of three daily pH measurements of the pool water begreater than 7.2 and not greater than 7.8. If two pH readings are 7.48 and7.85, which is the maximum pH value for the third reading that willsatisfy the manager? 4.01A 8.55 B 8.07C 6.27 D 6.14

31 The temperature T of vegetable oil after n minutes of heating can be modeled by the function T � �0.04n � 1.6n � 18. Which point on the graph of the function represents the initial temperature of the oil? 4.02A the smaller zeroB the larger zeroC the maximumD the y-intercept

32 For which values of x is the function y � �x2 � 10x � 21 decreasing?A x � 5 4.02B x � 4C x � 7D x � 3

33 Which expression is equivalent to 3x2��16

�x3 � 5x2�? 1.01

A 2x6 � 15x4

B 2x5 � 15x4

C �12

�x6 � 2x4

D �12

�x5 � 15x4

Minutes

Tem

per

atu

re (

�C)

0 20 3010

40

30

20

10

n

T

xO

y

A

K

4 12�4

12

8

4

8

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34 The equation y � 3,900x � 65,283 models the change in average housingprices y over the last x years in a suburb. Which value does the slope ofthe line represent? 3.03A the increase in average price between two consecutive yearsB the decrease in average price between two consecutive yearsC the average price the first yearD the average price the last year


Mr. Panitsas owns 2 fleets of boats that he charters for fishing trips, whalewatching, and sail boating. The table shows his income from the two fleetsfor the past week.

35 Which matrix shows the total income from both fleets? 3.02

A

B

C

D

36 Mr. Panitsas wants to know how much more income Fleet 2 earned thanFleet 1. Which matrix shows the difference in income between the fleets?

A B

3.02

C D�$475 �$535�$106 �$80�$138 �$182

$475 �$106 $138$535 �$80 $182

$348 $408 $36 $62 $76 $120

$348 $36 $76$408 $72 $120

$1,515 $2,2710,$462 0,$560$1,302 $1,498

$1,388 $2,3980,$604 0,$418$1,240 $1,560

$1,515 $464 $1,302$2,271 $560 $1,498

$1,388 $604 $1,230$2,398 $418 $1,560

Fleet 1 Half Day Full Day Fleet 2 Half Day Full DayFishing $520 $995 Fishing $868 $1,403Whale watching $284 $178 Whale watching $320 $240Sailing $582 $720 Sailing $658 $840

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37 If A � , which matrix is the product of 3 and A? 3.02

A B

C D

38 Square WXYZ has vertices W(1, 7), X(5, 3), Y(1, �1), and Z(�3, 3).Which is the area of WXYZ? 2.01A 4 square units B 16 square unitsC 32 square units D 64 square units

39 If the area of the trapezoid is a2 � b2, what is the height of thetrapezoid? 4.02

A 2(a � b) B 2(a � b)

C �12

�(a � b) D �12

�(a � b)

40 U�Z� is an altitude of parallelogram UVWX. Which is an equation of the line that contains U�Z�? 2.02

A y � �2x � 3 B y � �12

�x � 3

C y � 2x � 3 D y � ��12

�x � 3

xO

y

U

V

WZ

X

b

a

h

2 3 7 111 8

�3 �12 24�0 �6 15

2 7 113 1 8

�3 �0 12 �6 24 15

�1 �4 8�0 �2 5

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41 If a linear regression line models a set of data very closely, which of theseis most likely the correlation coefficient for that regression line? 3.03A 10 B �0.95 or 0.95C �0.5 or 0.5 D �0.01 or 0.01

42 Which element is in row 1, column 3 of matrix M? 3.01

M �

A 5 B 1C �3 D �4

43 Triangle HJK has vertices H(4, 3), J(2, �1), and K(�1, 3). Which is theperimeter of �HJK? 2.01A 14.5 units B 15 unitsC 29 units D 30 units

44 Ahmad’s weekly gross income includes a salary plus a commission on his weekly sales. His weekly gross income is compared to his weekly sales in the graph. What does the y-intercept of the graphrepresent? 4.01A Ahmad’s commission rateB Ahmad’s weekly salesC Ahmad’s weekly salaryD Ahmad’s commission

45 One of Newton’s laws can be expressed by the formula F � . What

happens to the force of attraction F if m1 is doubled, m2 is tripled, andthe distance between the objects d is halved? 1.03A Force is 24 times greater than the original force.B Force is 12 times greater than the original force.C Force is 4 times greater than the original force.D Force is 3 times greater than the original force.

km1m2�

d2

Weekly Sales (thousands of $)

Ahmad’s Pay

Wee

kly

Gro

ss In

com

e ($

)

0 2 3 4 51

$1,000

800

600

400

200

�8 �2 �3 0 �1�6 �1 �1 3 �0�5 �4 �4 1 �7

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46 The expression g � (g � 2.9) � (2g � 2.8) � 3(g � 2.9) � 1 representsthe number of grams of carbohydrates Manuel ate during three mealsand one snack yesterday. Which is an equivalent expression? 1.01A 6g � 47 B 7g � 2C 7g � 13.4 D 7g � 7.8

47 Which is the completely factored form of 9x2 � 36a4? 1.01A (3x � 6a2)2 B 9(x � 2a2)( x � 2a2)C (3x � 6a2)(3x � 6a2) D 3(x2 � 4a4)

48 Which is an equation of a line that passes through (2, 8) and is parallel to G�H�? 2.02A y � �2x � 6B y � �2x � 8C y � �2x � 10D y � �2x � 12

49 The results of a survey comparing the cost of staying one night inmoderately priced hotels in four large cities are given in the table. Whichcity had the greatest range of prices? 3.01

A New York B San FranciscoC Dallas D Raleigh

50 Line m is parallel to line n and passes through (5, �4). If the equation of

n is y � ��25

�x � 6, which describes m? 2.02

A Line m has a slope of ��25

� and a y-intercept of �4.

B Line m has a slope of ��25


C Line m has a slope of �52

� and a y-intercept of 1.

D Line m has a slope of �52


New York San Francisco Dallas Raleigh$250 $150 $90 $95$200 $130 $96 $138$175 $148 $105 $148$220 $135 $100 $125$225 $140 $98 $128

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51 Aretha is stacking wood at her mountain cabin. She begins with a row of20 logs on the bottom layer. Each layer contains one log less than the layerbelow it. How many logs are in the pile? The formula for the sum of a

series of consecutive integers beginning with 1 is �n2

�(n � 1). 1.02

A 210 logs B 209 logsC 190 logs D 189 logs

52 Which statement best describes an arithmetic sequence? 1.02A Each term can be divided evenly by the previous term.B Each term after the first is the same multiple of the preceding term.C Each term after the first is the sum of the two previous terms.D Each term differs from the preceding term by a constant amount.

53 If y varies directly as x and the constant of proportionality is 2, which isthe constant of proportionality for x as a variation of y? 1.03A �2 B 0.5C 1 D 2

54 Which is the graph of the system of inequalities? 4.03

x � 5y � 53x � 2y � 8

A B

C D

55 Which term represents the values of the dependent variable in a function?A slope 3.03B domainC rangeD intercept

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56 Triangle PQR has vertices P(�8, 2), Q(�5, �2), and R(�3, 1). Whichtype of triangle is PQR? 2.01A equilateral B isoscelesC right D scalene

57 Students in a high school drama club wash cars to earn money for schooltrips. The table shows the number of students working a shift and theamount of money they collected for the shift. Which equation best fitsthe data? 3.03

A y � 5.8x � 33B y � 9.664x � 1.05C y � 5.8x � 33D y � 9.664x � 1.05

58 You invest a certain amount of money. Your investment doubles eachyear for ten years. If you have $102,400 at the end of 10 years, what wasyour initial investment? 4.04A $100B $200C $1,024D $5,120

59 Find a, b, and c so that the graph of y � ax2 � bx � c passes through(0, �3), (2, 1), and (�3, �24). 4.03A a � �1, b � 4, and c � �3B a � 1, b � 4, and c � 3C a � 2, b � 2, and c � �2D a � �3, b � 1, and c � 2

60 I�A� is an altitude of trapezoid GHIJ. Which is an equation of the line that includes I�A�? 2.02A y � �2x � 1

B y � ��12

�x � 1

C y � �12

�x � 1

D y � 2x � 1

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Number of Students 9 3 8 5 4Earnings ($) 85 25 75 54 36

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61 Which statement best describes a geometric sequence? 1.02A Each term can be divided evenly by the previous term.B Each term differs from the preceding term by a constant amount.C Each term after the first is the sum of the two previous terms.D Each term after the first is multiplied by the same number.

62 The length a spring will stretch varies directly as the weight attached tothe spring. If the spring stretches 1.6 inches when a 24-pound weight isattached, how far will it stretch when a 15-pound weight is attached?A 3.9 inches 1.03B 2.56 inchesC 2.25 inchesD 1 inch

63 Which is an equation of a line that includes an altitude of rhombus WXYZ? 2.02A y � 5x � 8B y � �5x � 2

C y � x

D y � �x

64 Which is an equation of a line that includes an altitude of parallelogram MNOP? 2.02

A y � �32

�x � 1

B y � x � 2

C y � �2x � 3D y � �x � 1

65 The table shows the price a seafood restaurant pays per pound of salmon.If the price per pound remains constant, how much would the restaurantpay for 85 pounds of salmon? 4.01

A $176.25 B $197.40C $199.75 D $211.50

Pounds 2 4 6 8 10 12Cost ($) 4.70 9.40 14.10 18.80 23.50 28.20

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66 Connie averages 5 miles per hour while power walking. Phillip walks at amore moderate pace, averaging 3 miles per hour. If Connie begins powerwalking 10 minutes after Phillip begins walking, after how many mileswill Connie be ahead of Phillip? 4.03A 0.5 miles B 0.8 milesC 1.2 miles D 1.25 miles

67 Which expression is equivalent to � ��23

�

1.01

A �y

x

2

6� B

C �y

x

3

9� D �xy

6

7�

Use the figure to answer

Questions 68–70.

68 Which best describes the growth in the world population from 1750 to 1900? 4.04A The population doubled each year.B The population grew by about the

same amount each year.C The population was constant.D The population grew most quickly during this period.

69 Why can the growth in world population from 1900 to the present becharacterized as exponential rather than linear? 4.04A The population increase each year is greater than the previous year’s

increase.B The population grew by about the same amount each year.C The population doubled each year.D The population grew by more than 1% each year.

70 If the world population y in billions can be modeled by the formula y � 1.52(1.014)x, where x is the number of years since 1900, which isthe most reasonable estimate of the world population in 2020? 4.04A 6.9 billion B 7.9 billionC 8.1 billion D 8.8 billion

Year

World Population Trends

Pop

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bill

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s)

1900 20001800 195018501750

8

6

4

2

0

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�

�x4

x3y�43

�

�x12y– �

53

�

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The table shows five used car prices for a luxury sedan taken from used cardealerships in North Carolina.

71 Based on a regression line for these data, which price might you expectfor this model sedan if it were 54 months old? 3.03A $18,600 B $16,537C $14,545 D $10,450

72 Based on a regression line for these data, approximately what pricemight you expect for this model sedan if it were 8 years old? 3.03A $10,000 B $7,500C $6,500 D $2,100

73 If Q � �9 , which element is in row 4, column 3 of Q?

A �108 B 72

3.02

C �63 D 12

74 At which point do the graphs of 2x � y � 5 and 6x � 2y � �5intersect? 4.03A (2, �4) B (�4, 1)

C ��12

�, �4� D ��32

�, �8�

75 The table shows the number of hours Gina thinks it will take to drive acertain number of miles on a car trip she plans to take from Fayettevilleto Tulsa, Oklahoma. If the table corresponds to Gina’s actual trip, how

many miles will she have driven after 14�12

� hours? 4.01

A 806 miles B 837 milesC 868 miles D 899 miles

Time (hours) 3 6 9 12 15 18Distance (miles) 186 372 558 744 930 1,116

�2 5 3 �1 6 �4 8 �3 12 �6 4 �8 7 9 12 �0

Age (years) 2.0 2.5 3.5 1.0 0.5Price $25,935 $27,775 $19,250 $30,265 $33,100

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76 A 12% solution and a 20% solution of sulfuric acid are mixed to produce8 liters of a 16% solution. How many liters of the 20% solution arerequired? 4.03A 4 liters B 3.5 litersC 3 liters D 2 liters

77 A human resources director at a golf resort finds that the average salary of25-year old employees is $21,951 and the average salary of 60-year oldemployees is $71,882. Which linear model is based on these data? 4.01A y � 1,426.4x � 10,253 B y � 0.0007x � 71,882C y � 7x � 71,942 D y � 1,426.6x � 13,714

78 Which inequality describes the graph? 4.01

A �12

�y � x � 1

B 2y � 1 � x

C y � 2x � �12

�

D y � �12

�x � 1

79 Which statement is true? 1.01A am an � am � n B am an � amn

C am an � (am)n D (mn)a � ��m1n��a

80 Aida uses the declining balance method on her income tax to depreciatea plotter that her surveying firm in Greensboro uses. If her plotter has a

five-year useful life, it depreciates �15

� of its value at the end of the first

year. At the end of the second year it is depreciated �15

� of the value that

remained after the first year, and so forth. After 5 years the plotter stillwill retain a positive “salvage” value. Aida uses this method to depreciateher plotter over the course of five years. If the initial cost of the plotterwas $9,800 and an represents the value of the plotter after n years, whichexpression can be used to calculate an? 1.02

A 7,840��45

��nB 7,840��

15

��n � 1

C 9,800��45

��nD 9,800��

15

��n � 1

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OBJECTIVE 1.01 Write equivalent forms of algebraic expressions tosolve problems.

1 Which expression represents the area of the rectangle?

A 2x2 � 5xB 2x3 � 5x2

C 2x2 � 4x � 10D 2x3 � 5

2 If the expressions �x �

25

� and �x(x

a� 5)� are equivalent, what is the value of a?

A 2 B 2xC x D x � 5

3 The cost of a DVD player that was first marked up 30% above thewholesale price and then later put on sale for 30% off the retail price canbe represented by (c � 0.3c) � 0.3(c � 0.3c), where c is the wholesaleprice of the DVD player. Which is an equivalent expression?A 0.1c B 0.7cC 0.91c D c

4 Which property of real numbers guarantees that for all real values of x,(2x � 4) � 1 � 2x � (4 � 1)?A Distributive PropertyB Commutative Property of AdditionC Identity Property of MultiplicationD Associative Property of Addition

5 If Anchara borrows P dollars from her credit union for t months, and thecredit union charges her a simple interest rate r, then the amount shemust repay at the end of her loan can be represented by P(1 � rt).Which expression is equivalent to P(1 � rt)?A Prt B P � PrtC 1 � Prt D P � rt

2x � 5

x2


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OBJECTIVE 1.01 (continued)

6 One factor of 4x3 � 8x2 � 2x is 2x. Which is another factor?A 2x2 � 4x � 1 B 2x2 � 4xC 2x3 � 4x2 � x D 8x4 � 16x3 � 4x2

7 Esther is making a quilt. Each quilt square is divided into two smaller squares and two rectangles as shown. Which expression represents the sum of the areas of the four parts of the quilt square?A x2 � 16B x2 � 4x � 16C x2 � 8x � 16D 16x2

8 What is the coefficient of k when �8p � k (33 � 5 2) � 6k � 3(4k � 9)is written in simplest form?A �27 B 23C 31 D 58

9 A rectangle has a width of 2x and a length of x3 � 4x2. Into how manysquares each with a side length of x can the rectangle be divided?A 2x2 � 8x B x2 � 4xC 2x3 � 8x2 D x3 � 4x2

10 The area of a trapezoid is half the sum of the lengths of the parallel sidestimes the height. Which expression represents the area of the trapezoid?

A 2x2 � 10.5x � 13.5 B 2x2 � 6.5x � 13.5C 2x2 � 9.5x � 12.5 D 4x2 � 21x � 27

11 What value of c makes 25m2 � 20m � c a perfect square trinomial?A 100 B 16C 4 D 1

3x � 4

x � 5

x � 3

4

4

x

x


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12 What is the greatest common factor of the terms of 24p5q3z2 � 18p4qz3?A 6p4qz2 B 9p4q3z2

C 6p5q3z3 D 72p5q3z3

13 Which is equivalent to a if a(2p � q) � 10p2 � pq � 2q2?A 5p B 5pq � 2C 5p � 2q D 5p � 2q

14 A rectangular commercial real estate parcel has an area of x2 � 64 squareunits and a length of x � 8 units. Which expression represents theperimeter of the parcel?A x � 8 B 4x � 64C 4x � 64 D 4x

15 Which is equivalent to �237a

a3

1

b

5b4

8� for a 0, b 0?

A 9a5b2 B 9a17b12

C 9a12b4 D �a1

92b4�

16 Which demonstrates the Commutative Property of Addition?A 3x � 4(x � 3) � 10x � 3x � 4x � 12 � 10xB 3x � 4(x � 3) � 10x � �4(x � 3) � 3x � 10xC 3x � 4(x � 3) � 10x � 3x � 4(3x) � 10xD 3x � 4(x � 3) � 10x � 3x � (x � 3)(4) � 10x

17 A city planner in Gastonia wants to build a rectangular playground at apark. If 2x2 � 5x � 2 represents the area of the playground and 2x � 1represents the length, which represents the width of the playground?A x � 1 B x � 2C 4x3 � 12x2 � 9x � 2 D 2x � 1

18 Simplify 5y � 8z � (z � 3y) � 5(y � 2z).A 7y � 19z B 13y � 19zC 7y � 11z D 13y � 11z


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19 Mrs. Ha sent a package with the dimensions shown to her nephew in Mt.Airy. If 4x3 � 13x2 � 11x � 2 represents the volume of the package,which represents the length of the package?

A 4x � 1 B 4x � 1C 2x � 1 D 4x

20 Which is equivalent to �x2 �

x27�x

1�6

12� for x �4?

A �xx

��

34

� B �xx

��

44

�

C �xx

��

34

� D �xx

��

34

�

21 What is the completely factored form of 36s4t2 � 9s2t4?A 9st(4s3t � st3) B 9s2t2(4s2 � t2)C 9s2t2(2s � t)2 D 9s2t2(2s � t)(2s � t)


Mr. Whitford owns a farm in Beaufort County. The figure shows the dimensions of a rectangularcorn field on his farm. Mr. Whitford plans toexpand the length and width of the corn field by x on all four sides.

22 Which represents the area of the field after the expansion?A 6x2 � 23x � 20B 10x2 � 33x � 20C 12x2 � 32x � 20D 20x2 � 41x � 20

23 Which represents the perimeter of the field after the expansion?A 9x � 9 B 18x � 18C 10x � 18 D 12x � 18

3x � 4

x

x

2x � 5

?

x � 2

x � 1


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OBJECTIVE 1.02 Use formulas and algebraic expressions, includingiterative and recursive forms, to model and solve problems.

1 The approximate time T in seconds that it takes a pendulum to complete one swing back and forth

can be found using the formula T � 2��3�2�, where

� is the length of the pendulum in feet. About howmany swings back and forth will the pendulum make in 1 minute?A 2 B 19C 38 D 94

2 To enter 6x � 3y � 9 in his graphing calculator, Alaysia must first solvethe equation for y. Which equation should Alaysia enter?A y � �2x � 3 B y � 2x � 3

C y � �2x � 3 D y � ��12

�x � 3

3 Vanessa is offered a job with a high-technology company in Durham, andpromised that if her work is good, her salary for year n, with 2 � n � 5,will be given by the formula Sn � 1.1Sn�1. If S1 � $30,000, what willVanessa’s salary be for her fifth year at the job?A $36,300 B $39,930C $42,000 D $43,923

4 The price of a lawn mower was marked up 20% above wholesale. Thenthe price was reduced by 25% for a sale. If the wholesale price was$300, by how much was the sale price below the wholesale price?A $15 B $30C $60 D $75

5 Martina works as a server at a restaurant part-time while attending WakeForest University. She earns $3 per hour plus tips. If Martina made $260for a week in which she worked 20 hours, how much did Martinaaverage per hour in tips?A $15.29 B $13C $10 D $4.33

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6 The width of a rectangular banquet room is 21 feet. The length of theroom is 3 feet more than twice the width. What is the cost of carpetingthe room with carpet that costs $24.50 per square yard?A $945 B $2,572.50C $3,234.00 D $23,152.50

7 A display of soup cans has 3 cans on the top row, 4 on the second row,

5 on the third row, and so on. The formula Sn � �n(a1

2� an)�, where a1 is

the number of cans in the top row, an is the number of cans in the nthrow, and n is the number of rows, can be used to determine the totalnumber of cans Sn that can be displayed in n rows. How many canscould be displayed in 20 rows?A 200 B 210C 240 D 250

8 The formula an � �n

n

�

2

4� is used to generate each number an in a

sequence, where n 1 is the position of the number in the sequence.What are the first four terms of the sequence?

A �15

�, �23

�, �97

�, 2 B �15

�, �45

�, �75

�, 2

C 0, �15

�, �23

�, �97

� D �15

�, �12

�, �97

�, 2

9 Chandra has $250 more invested at 4% annual interest than she does at6% interest. If she has a total of $1250 invested, how much interest willshe earn on both accounts in one year?A $60 B $62.50C $65 D $85

10 Aaron performs an experiment to see how quickly a rumor can spread.He tells 5 friends a secret and instructs each of these friends to tell thesecret to 5 more friends, who in turn are instructed to tell the secret to 5 other friends. If no friend hears the secret more than once, whichexpression can Aaron use to determine how many people, includinghimself, will know his secret?A 51 � 52 � 53 B 1 � 51 � 52 � 53

C 1 � 53 D 56


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11 The formula A � P(1 � rt) gives the amount A that a borrower mustrepay a bank for a loan of P dollars that are borrowed at a simple interestrate r for a time t in years. Which can be used to find t?

A t � �A

r�P

P� B t � P��A �

rP

��C t � �

rPA� � 1 D t � r ��A �

PP

��

12 A company that manufactures digital cameras uses the function p � 35c � 525,000 to estimate its profit p on the sale of c cameras.How many cameras must the company sell in order to break even?A 1,500 B 15,000C 30,000 D 525,000

13 A golf tournament uses the formula Z � �X �

��

� to compare this year’s

attendance to the average attendance over the previous five years. Whichformula can be used to find X?A Z� � � � X B Z� � � � X

C ��Z

� � � � X D � � ��Z

� � X

14 An electrical engineer uses the formula P � I2R to calculate the power P,in watts, of a current of I amperes at a resistance of R ohms. What is thevalue of R if the power is 750 watts and the current is 15 amperes?A 168,750 ohms B 50 ohms

C 25 ohms D 3�13

� ohms

15 In the formula an � a1 � (n � 1)d, an represents the nth term of anarithmetic sequence, n represents the number of terms in the sequence,and d represents the constant difference between any two consecutiveterms. If d � 3 and an � 152 in the sequence 5, 8, 11, 14, 17, … an,how many terms are in the sequence?A 47 B 48C 49 D 50


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16 Katrina hits a nail with a hammer and drives it 9 millimeters into a stud.

Each additional hit of the nail drives it �23

� of the distance of the previous

hit. How many millimeters into the wall does Katrina drive the nail onher fourth hit?

A 1�13

� millimeters B 1�79

� millimeters

C 2�23

� millimeters D 7 millimeters

17 Juan paid $36 plus tax for admission to an amusement park. If the totalcost was $38, what was the approximate tax rate?A 0.0526% B 0.0556%C 5.26% D 5.56%

18 In a twenty-year period, the U.S. Bureau of Labor Statistics reported a65% increase in the number of employed mothers. If 16.8 million motherswere employed at the end of the 20-year period, about how many millionwere employed at the beginning of the period?A 5.9 million B 10.2 millionC 10.9 million D 27.7 million

19 Each millimeter of a filter screens out 20% of the incoming light. What percent of incoming light remains after passing through a 4-millimeter-thick filter?A 0.16% B 20%C 32% D 40.96%

20 Leon and Sadie both have sales positions. Leon earns an 8% commissionon sales each week. Sadie earns $200 plus a 4% commission on saleseach week. For which sales amount do Leon and Sadie earn the sameamount in 1 week?A $3,000 B $4,000C $5,000 D $6,000

21 The distance in feet traveled by a falling object in t seconds isapproximately equal to 16t2. About how long does it take an object tofall 1,024 feet?A 64 seconds B 32 secondsC 16 seconds D 8 seconds


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OBJECTIVE 1.03 Model and solve problems using direct variation.

1 Which is a direct variation equation?

A t � �dr� B C � �d

C A � �r2 D y � 5

2 A jogger on the beach at Cape Hatteras covered 8 miles at a constantspeed. Given that distance run varies directly as time, what is the constantof variation in miles per hour if it took the jogger 54 minutes to coverthe 8 miles?

A 8�89

� miles per hour B 8�34

� miles per hour

C 8�35

� miles per hour D 7�15

� miles per hour

3 The cooks in a school cafeteria use 1�14

� cups of sugar to make 3 dozen

cookies. Given that the amount of sugar used varies directly as the numberof cookies made, how many cups of sugar do the cooks need to make 5 dozen cookies?

A 1�13

� cups B 1�78

� cups

C 1�11

12� cups D 2�

112� cups

4 The gravitational force of attraction F between an object and Earth isdirectly proportional to the mass m of the object. If the force of theattraction is 640 when the object’s mass is 20, what is the constant ofvariation?A 0.03125 B 32C 660 D 12,800

5 Which statement about direct variation is true?A The constant of variation is always positive.

B If y varies directly as x, then y � �kx� for some constant k.

C The graph of every direct variation equation passes through the origin.D The graph of a direct variation equation always rises from left to right.

6 Michael earns $123.75 for working 15 hours at a daycare center. Howmuch will Michael earn for working 40 hours?A $309.38 B $330C $352.25 D $453.75


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7 The size of a building will vary directly as its size on an architect’ssketch. If a balcony that will be 25 feet long is 2 inches long on thesketch, how long will a wall be that measures 4.5 inches on the sketch?A 11.11 feet B 45 feet C 56.25 feet D 62.5 feet

8 Which graph corresponds to a direct variation equation?A B

C D

9 If p varies directly as the square of q, and the constant of variation is 6,what is the value of p when q equals 12?A 2 B 18 C 72 D 864

10 The total mass of an alloy made of tin and lead varies directly as themass of lead in the alloy. If 29.4 kilograms of the alloy contain about 8.4 kilograms of lead, about how many kilograms of lead are in 8 kilograms of the alloy?A 2.3 kilograms B 2.4 kilogramsC 5.7 kilograms D 28 kilograms

11 The volume of a rectangular solid of a given length varies directly as theproduct of the width and the height of the solid. When the volume of therectangular solid is 80 cubic inches, the width is 4 inches and the heightis 8 inches. What is the volume of the rectangular solid when the widthis 8 inches and the height is 16 inches?A 240 cubic inches B 320 cubic inchesC 384 cubic inches D 512 cubic inches

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12 The property taxes on a warehouse are $21,670. If the taxes vary directlyas the value, and the constant of variation is 0.022, what is the value ofthe warehouse?A $46,674 B $98,500C $985,000 D $1,083,500

13 North Carolina is 560 miles wide. If the scale on a map of North Carolinais 2 inches � 25 miles, what is the approximate map width?A 11.2 inches B 22.4 inchesC 28 D 44.8 inches

14 If w varies directly as the square root of T, what is the value of theconstant of variation when w � 562.5 and T � 225?A 0.027 B 2.5C 22.5 D 37.5

15 Which situation can best be modeled using a direct variation equation?A A clinic in Wilmington calculates the caloric needs of its patients in

the 20- to 50-year-old age group by adding 2900 to �20 times thepatient’s age.

B The Bridgewater reservoir on the Catawba River is releasing water tolower the surface level from its current elevation of 1198 feet by 0.75 inch per day.

C The yearly profit of a concession at the Raleigh/Durham airport canbe estimated by subtracting 5,000 from one tenth the number of itemssold each year.

D The owner of a natural foods store is labeling the total amount of faton bags of different sizes containing the same granola mix.

16 An environmental testing agency found that the amount of carbonmonoxide m produced by the idling engine of an older-model car wasproportional to the time t the engine was idling. If the engine produced60,000 cubic centimeters of carbon monoxide when it idled for 2 minutes,which equation relates m and t?

A t � 60,000m B t � �60,

m000�

C m � 30,000t D m � �30,

t000�


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17 The resistance R of a wire varies directly as its length L. Which equationmodels this relationship?A L � k � R B R � kL

C R � �Lk

� D �Rk

� � �Lk

�

18 The force required to accelerate an object a given amount varies directly asthe mass of the object. If it takes jet engines producing 6,300 kilogramsper second squared of thrust to accelerate an 1,800-kilogram jet a givenamount, about how much thrust would it require to accelerate a 4,500-kilogram jet by the same amount?A 1,286 kilograms per second squaredB 2,520 kilograms per second squaredC 15,750 kilograms per second squaredD 22,050 kilograms per second squared

19 Jeri owns an Italian restaurant in Fuquay-Varina. She buys spices in bulkfrom a local organic farmer. The cost of fresh rosemary varies directlywith the number of pounds of rosemary she purchases. Fresh rosemarycosts $11.28 when Jeri buys 4 pounds. What is the cost when she buys6.5 pounds?A $13.78 B $18.33C $26.00 D $29.61

20 Rami sells shoes on commission at a department store. The commissionhe makes is directly proportional to the total amount of his sales. Ramiearns $120 in commission when his total sales are $800. What doesRami earn in commission if his sales are $1,250?A $187.50 B $288.00C $435.20 D $570.00

21 Hooke’s Law states that the force applied to a spring is directlyproportional to the length that the spring is stretched. When Caitlinapplied a force of 25 pounds to a spring, the spring stretched 4 inches.What is the constant of variation?A 6.25 pounds per inch B 10.25 pounds per inchC 21 pounds per inch D 100 pounds per inch


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OBJECTIVE 2.01 Find the lengths and midpoints of segments to solveproblems.

1 What is the midpoint of A�B� if the coordinates of the endpoints areA(�14, 5) and B(10, 6)?

A (�24, 11) B ��12, �121��

C ��2, �121�� D �2, �

121��

2 Square CDEF has vertices C(�1, 1), D(2, 6), E(7, 3), and F(4, �2).What is the area of CDEF?A 16 square units B 4�34� square unitsC 25 square units D 34 square units

3 Marc bought a small lot on the North Carolina coast, and plans to builda cottage on the lot. The lot is shown on the coordinate grid, with one ofthe corners of the lot as the origin. The grid uses units of feet. What isthe perimeter of Marc’s lot to the nearest foot?

A 224 feet B 264 feetC 314 feet D 321 feet

4 In parallelogram MNOP, Z is the midpoint of side N�O�. If the coordinatesof Z are (5.5, �1.1) and the coordinates of O are (8.4, 2.5), what are thecoordinates of N?A (6.95, 0.7) B (�5.8, �7.2)C (2.6, �4.7) D (11.3, 6.1)

5 The coordinates of the vertices of a triangle are I(3, 4), J(2, 2), and K(5, 5). What kind of triangle is triangle IJK?A right B isoscelesC equilateral D scalene

x

y

(0, 0)20 40 60 80

80

60

40

20

(90, 50)

(90, 0)

(0, 60)

(40, 90)


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6 The distance between B(0, y) and Z(12, 0) is 13. What is the value of y?A �5 B 5C �1 or 1 D �5 or 5

7 Pentagon ABCDE is sketched on a coordinate grid to model a deck beingbuilt at a cabin near the Smoky Mountains. All sides of the deck arecongruent. If the coordinates of two consecutive vertices of the pentagonare (�2, 3) and (5, �3), what is the perimeter of pentagon ABCDE?

A 5�13� units B 35 units

C 5�85� units D 65 units

8 A median of a triangle is a segment from a vertex to the midpoint of theopposite side. Triangle ABC has vertices A(�1, �5), B(2, �4), and C(3, �1). What is the equation of the line that contains the median from B to A�C�?A y � �7x � 10 B y � �x � 2C y � 2x � 4 D y � x � 4

9 What is the perimeter of STYX? Round your answer to the nearest wholenumber.

A 18 units B 19 unitsC 20 units D 21 units

10 Points P(5, 7) and Q(�4, �5) are the endpoints of a diameter of a circle.What are the coordinates of point O, the center of the circle?A (�4.5, �6) B (1, 2)C (0.5, 1) D (0.5, �1)

xO

y

V

W

S

T


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Use parallelogram PQRT to answer

Questions 11–13.

11 What is the length of diagonal P�R�?

A 2�10�B 8

C 4�17�D 10

12 Which type of triangle is XRT ?A scalene B rightC isosceles D equilateral

13 The formula for the area A of a parallelogram is A � bh, where b is the base and h is the height. If Q�R� is the base of parallelogram PQRT, thenthe height is about 3.4 units. Which is the best estimate of the area ofPQRT ?A 6 square units B 18 square unitsC 22 square units D 31 square units

14 Triangle RST has vertices R(�2, 4), S(2, �6), and T(6, 6). What is the length of the segment that connects the midpoints of R�T� and S�T�?

A 5 units B �29� units

C �34� units D 7 units

15 In triangle ABC, point M is the midpoint of A�C�. What is the length of B�M� ?

A �18.5� units

B �24.5� units

C �26.5� units

D �32.5� units

xO

y

A

BC

M

xO

y

R

T

P

QX


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16 The distance between the points S(x, 5) and U(�4, 13) is 10. What is thevalue of x?A �10 B �8C �10 or 2 D 2

17 Emma sketched rectangle BYRD on a coordinate grid. She wants to draw a line segment from the midpoint of B�Y� to the midpoint of R�D�. If A is the midpoint of B�Y�and I is the midpoint of R�D�, which are the endpoints of A�I�?A A(�0.5, 2.5), I(1.5, 0.5)B A(0.5, 1.5), I(2.5, �0.5)C A(2, 3), I(�1, 0)D A(3, 2), I(0, �1)

18 What is the midpoint of X�Y� if the coordinates of the endpoints are X(8, �3) and Y(�6, �11)?A (2, �14) B (�1, �7)C (1, �8) D (1, �7)


The coordinates of the vertices of parallelogram STUV are S(�1, 4), T(3, 0),U(4, �3), and V(0, 1).

19 Given that the diagonals meet at each other’s midpoints, what are thecoordinates of the intersection of the diagonals of STUV?A (0.5, 1.5) B (�0.5, 2.5)C (1.5, 0.5) D (0.5, 0.5)

20 What is the perimeter of parallelogram STUV? Round your answer to thenearest whole number.A 17 units B 18 unitsC 19 units D 24 units

xO

y

D

Y

R

B


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OBJECTIVE 2.02 Use the parallelism or perpendicularity of lines andsegments to solve problems.

1 The equation of the graph of line n is 3x � y � 4. Which could be theequation of a line m that is parallel to line n?A y � 3x � 1.6 B y � �3x � 4

C y � �13

�x � 4 D y � �13

�x � 4

2 J�E� is an altitude of trapezoid GHIJ.

Which is an equation of JE��?

A y � ��32

�x � 12

B y � ��23

�x � 7

C y � ��43

�x � 11

D y � ��34

�x � 7.5

3 What is the slope of a line parallel to a line that passes through thepoints at (�3, 5) and (2, 8)?

A �13

� B �35

�

C �53

� D 3

4 Line m is the perpendicular bisector of G�H�. What is the equation of line m?

A y � ��74

�x � �12

�

B y � �74

�x � �12

�

C y � �47

�x

D y � �47

�x � �12

�

5 What is the slope of a line perpendicular to the line that passes through(�5, 4) and (0, 2)?

A ��52

� B ��25

�

C �25

� D �52

�

xO

yG

H

xO

y

J(�6, �3)

I(�3, �1)

H(0, �2)

EG(�6, �6)


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6 Line a is parallel to line b and passes through (�3, 2). If the equation ofthe graph of line b is y � 3x � 2, which is an equation of line a?A y � �3x � 7

B y � ��13

�x � 1

C y � 3x � 7D y � 3x � 11

7 Three of the vertices of parallelogram ABCD are A(2, 7), B(4, 4), andC(�2, �1). Given that opposite sides of a parallelogram are parallel, which is an equation of the line containing C�D�?

A y � ��32

�x � 4 B y � ��32

�x � 2

C y � �32

�x � 2 D y � �23

�x � �13

�

8 What is the slope of any line parallel to line m?A �2

B ��12

�

C �12

�

D 2

9 Which is an equation for the line that passes through (1, 3) and is parallel to R�S�?A y � 2x � 1B y � 2x � 2C y � 2x � 3

D y � ��12

�x � �52

�

10 Which point lies on the line that passes through (6, �3) and is parallel to

the graph of the line y � ��13

�x � 9?

A (9, �2) B ��13

�, 3�C (3, �2) D (3, �12)

xO

yS

R

xO

ym


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11 Which is an equation of the line that passes through (�3, 2) and isperpendicular to the graph of y � 3x � 2?

A y � �3x � 7 B y � ��13

�x � 1

C y � ��13

�x � 3 D y � �13

�x � 3

12 Which is an equation of a line perpendicular to M�N�?A 2x � y � 3B x � 2y � 2C x � 2y � 17D �2x � y � �3

13 A quadrilateral has vertices R(�4, 2), S(1, �3), T(3, 1), and U(�1, 5).Which is the most specific classification of quadrilateral RSTU?A rectangle B rhombusC square D trapezoid

14 Which point lies on the line that has a y-intercept of 1 and is perpendicular to line k ?A (�2, �8)B (�1, �4)C (1, 5)D (2, 10)

15 Which is an equation of a line that contains a vertex of trapezoid FGHI and is perpendicular to the parallel sides of the trapezoid?A y � 2x � 4B y � 2x � 4

C y � ��12

�x � 1

D y � �12

�x � 3

xO

y

F

G

H

I

xO

y

k

xO

y N

M


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16 Line c is perpendicular to line d and passes through (5, �1). If theequation of the graph of d is y � 5x � 3, which describes line c ?A Line c has a slope of 5 and a y-intercept of �1.B Line c has a slope of 5 and a y-intercept of �26.

C Line c has a slope of ��15


D Line c has a slope of ��15


17 A�E� is an altitude of parallelogram ABCD. Which is an equation of the line that contains A�E�?A x � y � �4B x � y � 4C x � y � �4D x � y � 4

18 Line q passes through (6, 4) and is perpendicular to the graph of the line

y � ��23

�x � 8. Which is an equation of line q ?

A y � ��23

�x � 8 B y � �23

�x

C y � �32

�x � 5 D y � �32

�x � 5

Saraj has started drawing rectangle PQRS

on a coordinate grid as shown. Use the

figure to answer Questions 19 and 20.

19 Saraj will next draw R�S�. Which is an equation of the line containing R�S�?A y � �2x � 4B y � �2x � 8C y � 2x � 8D y � 2x � 4

20 Saraj will draw P�S� last. Which is an equation of the line containing P�S�?

A y � ��12

�x � �92

� B y � ��12

�x � �92

�

C y � �12

�x � �92

� D y � �12

�x � 4

xO

y

Q

R

P

xO

y B

C

D

A

E


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OBJECTIVE 3.01 Use matrices to display and interpret data.

1 The matrix below shows how a corporation distributed its income dollars(in millions) in 2002 and 2003. Which category shows the greatestpercent decrease from 2002 to 2003?

A salariesB researchC equipmentD buildings

2 The element in which position in matrix M is greatest?

M �

A row 3, column 4B row 3, column 1C row 2, column 3D row 3, column 2

3 Three sisters, Maria, Julia, and Flavia, are being treated for highcholesterol. Each sister is on a different low-fat diet as part of hertreatment. The matrix shows each sister’s cholesterol level at differenttimes during her treatment. Which sister(s) had the largest total drop incholesterol level over the time recorded?

A MariaB JuliaC FlaviaD Maria and Flavia

Jan Mar May JulyMaria 220 210 200 195 Julia 220 215 210 205

Flavia 215 205 195 190

�1 �6 �3 �4�0 �2 �7 �1�8 �9 �2 �15

Salaries Research Equipment Buildings Other2002 55 30 10 10 5 2003 45 23 8 15 10


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4 Anya called animal shelters in Greensboro, Asheville, and Charlotte and asked how many cats, dogs, and other animals were at the shelters.Greensboro reported 9 dogs, 15 cats, and 3 others. Asheville reported 2 ferrets, 4 birds, 2 rabbits, 8 dogs, and 7 cats. Charlotte reported 9 others, 26 cats, and 19 dogs. Which matrix displays the data so that the respective rows are Greensboro, Asheville, and Charlotte, and therespective columns are cats, dogs, and others?

A B

C D


The matrix shown gives the numbers of high school students enrolled inphysical education courses by grade in some Wake County high schools forthe school years beginning in 2001, 2002, and 2003.

5 Which grade(s) had the greatest enrollment increase from 2001 to 2002?A 10thB 10th and 11thC 11thD 12th

6 Which best describes the data shown in the matrix?A Students in the 9th grade are the most physically fit.B Overall, the 12th grade showed the greatest rate of increase.C Enrollment increased at all grade levels each year.D Enrollment decreased steadily from grade to grade.

9th 10th 11th 12th2001 76 48 51 31 2002 74 59 62 43 2003 82 62 70 54

15 8 26 9 7 19 3 8 9

15 9 3 7 8 826 19 9

15 9 3 2 1 3 2 8 7 9 26 19

9 15 38 7 89 26 19


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7 The matrix shows the predicted height of a person based on the length ofthe person’s tibia, or “shinbone.” Which is the best estimate of the heightof a person if the length of that person’s tibia is 16 inches?

A 62.8 in. B 67.1 in.C 69.5 in. D 70.1 in.

Use the following information to answer Questions 8–10.

A company owns and operates 4 fitness gyms in the Raleigh-DurhamTriangle area. For the past 5 months, January through May, the company hasoffered cruises and reduced fees as incentives to join the gym. The matrixshows the numbers of memberships each of the 4 gyms sold during themembership drive.

8 Which gym sold the fewest memberships in the month indicated?A Chapel Hill in AprilB Carrboro in MarchC Durham in MayD Cary in May

9 Employees at any gym that sold the greatest number of memberships (ortied for the greatest number) for at least two months received bonuses.Employees at which location(s) received bonuses?A Cary, Durham, and CarrboroB Cary and DurhamC Durham onlyD Cary only

10 The gym in which city sold the greatest total number of membershipsduring the drive?A Cary B Chapel HillC Durham D Carrboro

Jan Feb Mar April MayCary 64 71 53 28 21

Chapel Hill 58 43 38 22 33 Durham 72 64 53 37 32

Carrboro 47 52 23 37 40

Tibia (in.) 11 13 18 20 22 Height (in.) 54.1 59.3 72.3 77.5 82.7


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A small library in Wayne County has an annual book sale each February anduses the proceeds to buy new books. The matrix shows the dollar amount ofsales from 2002 to 2004.

11 Which category shows the greatest increase from 2002 to 2003?A adult fiction B adult nonfictionC children’s fiction D children’s nonfiction

12 Which describes the location of children’s fiction in 2003?A row 3, column 2 B row 3, column 3C row 2, column 2 D row 2, column 3

13 If the trends in the data shown in the matrix continue, which bestpredicts the dollar amount of book sales of adult nonfiction in 2005?A $98 B $101 C $110 D $122


Jillian collects antique bottles. The matrix shown organizes her collectionaccording to color and type.

14 Jillian’s single favorite bottle is in the category that ranks third accordingto the number of bottles. Which describes her favorite?A amethyst flask B aqua flaskC amethyst apothecary D amber apothecary

15 Of which color or type of bottle does Jillian have the fewest?A amber B aquaC apothecary D soda

Amber Aqua AmethystApothecary 6 2 11

Flask 7 12 9 Soda 2 7 8

Adult Adult Children’s Children’sFiction Nonfiction Fiction Nonfiction

2002 $75 $50 $85 $68 2003 $88 $68 $96 $37 2004 $94 $88 $52 $64


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OBJECTIVE 3.02 Operate (addition, subtraction, scalar multiplication)with matrices to solve problems.

1 A company makes three models of office chairs at two different plants.The first matrix summarizes the June production of these chairs and thesecond matrix summarizes the July production. Which information canthe company gain directly from the sum of the two matrices?

June:

July:

A the total number of chairs produced at each locationB the model with the greatest production rateC the total number of each model producedD the total production of each model at each plant in June and July

2 If A � , which is equivalent to 3A?

A B

C D

3 If R � and V � , which is equivalent to 2V � R?

A B

C D�3 6�3 2

3 83 2

3 01 2

3 03 2

3 21 2

�3 4�1 2

6 �3 60 �3 9

9 �3 60 �3 12

6 2 53 4 7

�9 0�3 3�6 12

3 �1 20 �1 4

Model A Model B Model CPlant X 180 210 330 Plant Y 420 180 280

Model A Model B Model CPlant X 420 880 540 Plant Y 280 280 460


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4 If � � , what is the value of y?

A �7 B �1C 1 D 2

5 If C � and D � , which is true?

A C � D � B C � D �

C C � D � D C � D does not exist.

6 If N � �4 , which element is N21?

A �28 B �20C 20 D 32

7 Lamont is trying to sell 6 baseball cards online. He is asking 3 times hispurchase price for each. The matrix shows the issue year of each cardand the original price Lamont paid for each card in dollars. Whichmatrix shows the asking prices?

A B

C D36 16 1054 11 9

72 96 60108 66 54

15 19 1321 14 12

36 48 3054 33 27

1974 1975 1975Player A 12 16 10 Player B 18 11 9

�3 �7�5 �8

�3 0 3�0 8 0

�2 2 4�2 6 3

�2 2 4�2 6 3�4 3 0

�3 �0 1�0 �2 3�2 �1 0

�1 2 3�2 4 0

3 72 0

2 � y z2 � z �x

x 3z 2


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The King High seniors sponsor school-wide fall and spring dances. Thematrices show the numbers of students by grade who attended the dances intwo consecutive school years.

2002–2003:

2003–2004:

8 Which matrix gives total attendance by season and grade for both years?

A B

C D [85 115 188 287]

9 The seniors want to know how the attendance changed by season andgrade from the 2002–2003 dances to the 2003–2004 dances. Whichmatrix gives them this information?

A B

C D

10 The cost per ticket for the 2003–2004 dances was $8. Which matrixshows the revenue by season and grade from ticket sales that year?

A B

C D144 216 368 592224 280 344 576

26 35 54 8136 43 51 80

264 388 696 1,136416 528 808 1,160

120 172 328 544192 248 464 584

�3 �5 �5 �6�4 �4 �15 �1

3 5 �5 �64 4 �15 �1

3 5 5 64 4 15 1

9 9 17 510 8 3 2

33 49 87 13252 66 91 111

33 49 87 14252 66 101 145

39 53 99 14146 62 89 146

9th 10th 11th 12thFall 18 27 46 74 Spring 28 35 43 72

9th 10th 11th 12thFall 15 22 41 68 Spring 24 31 58 73


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11 If T � and W � , which is 3T � 2W?

A B

C D

12 Given A � and B � , which is B � 2A?

A B

C D

13 The matrix shows profits in millions of dollars last year at two toycompanies. If both companies increase profits by 15% next year in eachcategory, which matrix shows how much additional profit in millions ofdollars the companies will earn for each type of toy next year?

A B

C D

14 If P � �3 , which element is P23?

A 6 B 5C �15 D �18

�2 �1 �4 �5 �0�3 �12 �6 �8 �2�1 �5 �4 �7 �6

48.3 13.843.7 18.4

6.3 1.85.7 2.4

63 1857 24

57 2753 31

Action Figures Board Games

Company A 42 12 Company B 38 16

�11 �7 �3 �4 �2 �7

�16 �8 �3 �1 �7 �2

16 �8 3�1 �7 2

�12 �8 �1 �1 �9 �6

2 �2 13 �1 4

�7 �3 �1�2 �4 �1

2 226 �1

�15 12 �2 �5

7 184 �8

�7 18�4 �4

4 62 1

�5 �2�0 �2


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OBJECTIVE 3.03 Create linear models for sets of data to solveproblems.

1 The scatter plot shows eight data points and a linear regression line for the data. Point T, which has coordinates (5, 64), is called an observed point. The point T � lies on the regression line. The y-coordinate of T� is the predicted value for y on the regression line when x � 5.Which is the term for the distance �ybetween T and T�?A intercept B interpolationC residual D slope

2 The table gives data for the number of hours x several students studiedand the grade y received. Which equation best fits the data?

A y � 5.57x � 54.54 B y � 5.57x � 54.54C y � 54.54x � 5.57 D y � 54.54x � 5.57

3 The scatter plot shows the energy efficiency ratings and prices of six airconditioners that will cool the same volume of air. Using these data anda linear model, which is the most reasonable prediction of the price of amodel that has an 8.0 energy efficiency rating?

A $200 B $280C $320 D $350

10Energy Efficiency Rating

Energy Efficiency ofAir Conditioners vs. Cost

Cost

($)

8 9 10.58.5 9.5

500400300200100

Student Hours Studied x Grade y (%)A 6 82B 2 63C 3 75D 5 88E 1 57F 2 68

6 1020 84

70

60

50

40

30

x

y

S U

VT

T�R

X

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4 Which best describes the correlation shown by the data graphed in the scatter plot?A positive correlationB negative correlationC zero correlationD undefined correlation

5 For which data set is y � �0.32x � 21 the best prediction equation?A (18, 16), (26, 12), (39, 9), (48, 5), (53, 6), (58, 2)B (1, 500), (5, 100), (3, 300), (10, 50), (7, 75), (6, 80)C (97, 2.1), (107, 2.2), (100, 3.2), (100, 2.7), (106, 2.2), (98, 2.1)D (83, 78), (91, 90), (86, 80), (97, 97), (95, 97), (80, 82)

6 A study investigated the relationship between the dose of a new drug anddiastolic blood pressure. The scatter plot shows the average diastolic bloodpressure of eight large groups of patients at different dosage levels (in milligrams). For which data point is the residual the greatest?A (0.45, 81)B (0.3, 92)C (0.25, 93)D (0.1, 95)

7 A Brunswick County service station made the scatter plot shown of the hightemperature for seven consecutive July days and the number of emergency roadservice calls received each day. Using these data and a linear model, which is the best prediction for how many calls the service station will receive if the high temperature is 94º?A 4 B 5C 6 D 7

100Temperature (�F)

Calls vs. Temperature

Num

ber

of C

alls

84 9288 96

1086420

0.3Dose (mg)

Dia

stol

ic P

ress

ure

(mm

Hg)

0.50.10 0.40.2

96

92

88

84

80

x

y

(0.1, 95)

(0.2, 91)(0.3, 92)

(0.5, 82)

(0.25, 93)

(0.35, 88)

(0.45, 81)

(0.2, 92)

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The table shows the height at 1-year intervals of a sapling Chris bought at an Asheville nursery.

8 If x represents the number of years since 1999, which linear model best fits the data?A y � 0.25x � 1.25B y � �0.25x � 1.25C y � 0.62x � 1.1D y � 1.1x � 0.62

9 The nursery claimed that the tree would grow an average of 18 inchesannually. Which conclusion most accurately compares the actual growthrate to the nursery’s predicted growth rate?A The actual growth rate is about the same as the predicted rate.B The actual growth rate is about 40% of the predicted rate.C The actual growth rate is about 10% of the predicted rate.D The actual growth rate is about 3.4% of the predicted rate.

10 Shondra is investigating whether there is a linear relationship between the heights of the players on her basketball team and the average number of points scored per game last season. Her data are shown in the table.Which conclusion best describes the data?A A linear model predicts about 3 additional

points scored for each centimeter gain inheight.

B There is a strong positive correlation between height and points scored.

C There is a strong negative correlation between height and pointsscored.

D There is little correlation between height and points scored.

Height (cm) Points178 09180 15179 12185 03177 06181 09173 06175 06

Year Height (ft)1999 1.252000 1.502001 2.332002 2.752003 3.502004 4.33


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The spreadsheet shows Cumberland County population data.

11 Which is the equation for the best line of fit for the data? Let x � 0 for 1950, x � 10 for 1960, and so on.A y � 4.14x � 110B y � 41.4x � 68.7C y � 41.4x � 110D y � 414x � 68.7

12 Which most accurately describes the data?A From 1950 to 2000, the population increased steadily by 41,400 people

per decade.B The population growth decreased each decade.C A linear model is not helpful for prediction with this data.D From 1950 to 2000, there was an overall growth in population of

about 4,140 people per year.

13 Which is the best estimate of the population in the 2010 census year?A about 315,000 B about 360,000C about 400,000 D about 500,000

14 A swim team is selling posters of rhododendron and other Appalachianwildflowers to raise funds. The scatter plot shows sales for the past 10 days. Which conclusion most accurately reflects the data?A The data show a strong negative

correlation, which means sales are rapidly declining at a predictable rate the longer the sale.

B A modest negative correlation indicates that fewer posters are beingsold as the sale continues, but it is difficult to predict the sales forany particular day.

C The line of best fit shows a decrease in sales of about 2.5 posters per day.

D The correlation is too low to identify any trends.

10Day

Poster Sales

Post

ers

Sold

20 64 8

5040302010

x

y

U.S. Census Data

Year Population(thousands)

1950 096.01960 148.41970 212.01980 247.21990 274.62000 303.0


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OBJECTIVE 4.01 Use linear functions or inequalities to model andsolve problems; justify results.


Manuel has $1500 saved for a motorcycle. He plans to make deposits to his savings account for the motorcycle each month. The graphillustrates how his savings will increase.

1 What is the slope of the line that contains the points on the graph?A �750 B 150C 750 D 1,500

2 What does the slope of the line represent?A the increase in price of the motorcycleB the number of months Manuel will save for the motorcycleC the difference between the cost of the motorcycle and the amount

Manuel has savedD the amount Manuel will save each month

3 Which describes the domain and range of the function y � 5x � 3?A domain: all real numbers; range: all real numbersB domain: positive real numbers; range: real numbers greater than 2C domain: nonnegative real numbers; range: positive real numbers

D domain: all real numbers; range: real numbers greater than �35

�

4 Which equation describes the relationship shown by the set of orderedpairs {(�3, 17), (�2, 12), (1, �3), (4, �18), (5, �23)}?A y � 5x � 2 B y � 2 � 5xC y � �5x � 2 D y � 5x � 2

5 Which properties justify the statement �34

�(1 � 5m) � �43

� � 1 � 5m?

I. Multiplicative Inverse PropertyII. Multiplicative Identity PropertyII. Commutative Property of MultiplicationIV. Distributive Property

A I only B III onlyC I, II, and III D I, II, III, and IV

Number of Months

Am

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Sol

d ($

)

100 3020 40

8,0006,0004,0002,000

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6 Carl has budgeted $60 to buy pork ribs and chicken legs for a facultybarbecue. Ribs cost $3.75 per pound, and chicken legs cost $3.00 perpound. If Carl buys x pounds of chicken, which represents the number ofpounds y of ribs he can buy and not exceed his budget?A y � �3x � 60 B y � �0.8x � 16C 3.75y � 60 � 3x D 3x � 3.75y 60

7 Aly and Elsa went rafting with their parents on the Tuckaseigee River.The cost was $29 each for the girls and $39 for each parent. Below arethe methods each girl used to find the total cost of the trip. Elsa claimsthe methods are equivalent. Which supports her claim?

Aly: 2 � $29 � 2 � $39 Elsa: 2($29 � $39)

A Multiplicative Identity PropertyB Distributive PropertyC Associative Property of MultiplicationD Commutative Property of Multiplication

8 A Raleigh company has monthly expenses represented by the functionC(x) � 16x � 4,200, where x represents the number of items produced.For how many items produced is the monthly cost $81,000?A 1,300,200 B 5,325C 5,063 D 4,800

9 While solving an equation, Kaitlin rewrites �4 � (1 � m) as (�4 � 1) � m. Which property justifies Kaitlin ’s work?A Additive Identity PropertyB Associative Property of AdditionC Commutative Property of AdditionD Distributive Property

10 Annamarie earns a weekly salary of $150 plus an average of $15 perhour in tips at her job as a parking valet at a Nags Head beach resort.This relationship is expressed by the function f(x) � 15x � 150. What isthe dependent quantity in f(x)?A the number of hours worked each weekB the hourly rateC the total weekly incomeD the weekly salary


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11 Justin must average at least 90% on five tests to receive a grade of A.His grades on the first four tests were 85%, 93%, 88%, and 94%. Whichinequality can Justin use to find the minimum percent score he mustmake on the fifth test to receive an A?

A �x �

5360� � 90 B �

x �5360� 90

C �360

5� x� � 90 D �

3605� x� 90

12 What is the slope of the graph of 3x � 4y � 20?

A �5 B �4 C �34

� D �43

�

13 An Internet wholesaler charges vendors $5.10 for each bottle of herbalhand lotion plus $27.50 per order for shipping. What is the total cost to avendor for ordering 72 bottles of the hand lotion?A $367.20 B $387.50 C $394.70 D $2,347.20

14 A company that manufactures and sells surfboards uses the function P � 40s � 200,000 to estimate its profit P on the sale of s surfboards.How many boards must the company sell to make $1,200,000 in profit?A 35,000 B 45,000 C 350,000 D 450,000

15 Which is the graph of the solution set of 2x � y 3?A B

C D

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16 As Jasmine hikes near Clingman’s Dome, the temperature drops about4.5°F for each 1,000 feet climbed. At the start of her hike, at 3,000 feet inelevation, the temperature is 72°F. Which equation gives the temperaturet in degrees Fahrenheit as a function of elevation h in feet?A t(h) � �4.5h � 72 B t(h) � �0.0045h � 72C t(h) � �0.0045h � 85.5 D t(h) � 4.5h � 72


Ahmad begins driving east from Waynesville en route to Kill Devil Hills witha full tank of fuel. His car has a 15-gallon tank that gets 30 miles per gallonon the highway.

17 Which gives the relationship between how many miles m Ahmad hasdriven and the number of gallons of gas g remaining in his tank?A g � 15 � 30m B m � 30g � 15

C g � 15 � �3m0� D m � �

3g0� � 15

18 How far can Ahmad drive until only two gallons of gas remain?A 390 miles B 420 milesC 450 miles D 480 miles

19 Which inequality describes the graph?A �2y � 3 � 3xB 2y � 3 � 3xC 2y � 3 � �3x

D y ��32

�x � �32

�

20 Ione has no more than $80 to buy tickets to a football game for herfriends and family. Student tickets cost $3 each and non-student ticketscost $5 each. Ione graphed 3x � 5y � 80 to determine how many ofeach kind of ticket she can buy. Which describes the point (5, 13)?A Ione has $5 left after buying 13 non-student tickets.B Ione has $13 left after she buys 5 student tickets.C Ione can buy 5 non-student tickets and 13 student tickets.D Ione can buy 5 student tickets and 13 non-student tickets.

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OBJECTIVE 4.02 Graph, factor, and evaluate quadratic functions tosolve problems.

1 For which values of x is f(x) � �x2 � 6x � 7 increasing?A x � 3 B x � 3C �1 � x � 7 D x � �1 and x � 7

2 Which is the graph of y � x2 � 2x � 4?A B

C D

3 At a festival, pumpkins are launched with large catapults and aircannons. On one launch, the height of a pumpkin in feet above theground after t seconds is modeled by f(t) � �16t2 � 100t � 12. Howcan you use f(t) to find the height from which the pumpkin is launched?A Find the value of t when f(t) � 0.B Find the greatest value of f(t).C Find the value of f(t) when t � 0.D Graph the function for t � 0 and find the value of f(t) where the

graph crosses the horizontal axis.

4 For which function(s) is the vertex at the maximum point?

I. y � 7 � 3x � 2x2 II. y � 4x2 � x � 3III. y � 0.01x2 � 4x � 1 IV. y � �(x � 5)(x � 2)

A I only B III only C I and II D I and IV

5 What are the solutions of 18x2 � 27x � 4 � 0?

A ��16

� and ��43

� B �16

� and �43

� C �6 and ��34

� D 6 and �34

�

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6 A rectangular garden and surrounding path have the dimensions shown.

If the area of the garden is �23

� that of the rectangle enclosing the garden

and path, how wide is the path along the south side of the garden?

A 0.5 meter B 0.8 meterC 1 meter D 2 meters

7 Leo throws a rock upward from the top of an 80-foot cliff. The rock landsat the base of the cliff. The rock’s height above the base of the cliff aftert seconds is represented by �16t2 � 64t � 80. Which is true?A After 5 seconds, the rock is even with the top of the cliff.B The rock rises and falls for equal amounts of time.C The rock reaches its maximum height after 2.5 seconds.D It takes the rock 5 seconds to hit the ground.

8 If f(x) � 2x2 � 8x � 5, what is the minimum value of f ?A �13 B �8C �5 D no minimum value

9 The graph of y � a(x � h)2 � k, a 0, is a parabola with axis ofsymmetry x � h and vertex (h, k). If the domain of the function is theset of real numbers, which is true?A If a � 0, (h, k) is a minimum and the parabola opens downward.B If a � 0, (h, k) is a maximum and the parabola opens upward.C If a � 0, (h, k) is a maximum and the parabola opens downward.D If a � 0, (h, k) is a minimum and the parabola opens upward.

10 A developer planning to construct an office building in Charlotte isusing the model p � �8x2 � 1,400x � 30,000 to estimate the monthlyprofit p in dollars from a building with x offices. For which number ofoffices is a profit predicted?A at least 88 B more than 25C between 25 and 150 D more than 150

x

x

2x 2x

x24 m

10 m

N


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11 Yukari is fencing in a pen along an outside wall of her house for her dog. Yukari has 60 meters of fencing and wants to give her dog the greatest possible area. What should x be?A 7.5 meters B 15 metersC 20 meters D 30 meters

12 If the graph of y � ax2 � 1 is wider than the graph of y � 2x2 � 1,which is a possible value for a?A �2 B �4

C �12

� D 4

13 If a function f(x) is quadratic, with the characteristics shown below,which is the solution set of f(x) � 0?

vertex: (4, �1) y-intercept: 15 x-intercepts: 3, 5

A {1, �4} B {�1, 4}C {3, 5} D {15}

14 An art museum charges $10 for an adult admission. The museumestimates they will lose 15 adult visitors per day for each one dollarincrease in price. If the museum averages 300 adult visitors a day, whichis the most profitable adult admission price?A $10 B $12.50C $15 D $16.50

15 For which pair of functions are the domain values the same and therange values opposite?

A f : y � 8x2; g: y � x2 B f : y � 8x2; g: y � �18

�x2

C f : y � 8x2; g: y � 8 � x2 D f : y � 8x2; g: y � �8x2

16 Nick’s height in meters above the water t seconds after diving from adiving board into a pool can be modeled by f(t) � �4.9t2 � 4.9t � 5.What is Nick’s maximum height above the water?A 9.9 meters B 6.225 metersC 5.5 meters D 5 meters

x x

House


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The function y � �2x2 � 32x � 150 models the monthly flour expense lastyear at Antonio’s bakery, where x � 1 represents January.

17 During which month was the expense the highest?A February B JuneC July D August

18 What was the maximum flour expense?A $150 B $270C $278 D $406

19 The function y � �x2 � 24x � 120 models the number of T-shirts ashop in the Outer Banks sold each day of a two-week festival, where x � 1 represents the first day. On which day does the model say 200 T-shirts were sold?A day 4 B day 6C day 12 D day 14

20 Alexis tracks the value of the coins in her collection. The function y � �0.45x2 � 8.6x � 16.8 represents the value of one of her coins,where x � 0 represents January 1, x � 1 represents February 1, and soon. If Alexis had wanted to sell the coin, when would she have receivedthe highest price?A January 1B about the middle of SeptemberC about the middle of OctoberD December 31

21 The function y � 2.6x2 � 15.6x � 73.4 models the number ofinternational long distance minutes on the Tonwe family phone bill forthe past 12 months, where x � 1 represents January. What was theminimum monthly cost for international calls to the nearest dollaraccording to the model?A $3 B $13C $19 D $50


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OBJECTIVE 4.03 Use systems of linear equations or inequalities intwo variables to model and solve problems. Solve using tables, graphs,and algebraic properties; justify results.

1 Which is the graph of the solution set of the system of inequalities?

x � 2y � 102x � y � 0

A B

C D

2 Which ordered pair is the solution of the system of equations?

3x � 2y � 15x � 3y � 4

A (�5, �8) B ��11

19�, ��

179�� C (5, 7) D (11, 16)

3 A restaurant is able to seat 62 people at 23 tables, with no empty seatsremaining. Each table seats either two people or four people. How manyof the tables seat four people?A 15 B 12 C 9 D 8

4 Which system of equations has no solution?A 2x � 3y � 12 B x � 6y � 24

6x � 5y � �4 2x � 12y � 48C 5x � 2y � �4 D x � 4y � 5

�10x � 4y � 8 7x � 28y � 42

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5 Admission to the senior class variety show was $3.75 for students and$4.50 for adults. The senior class collected $1,680 from the sale of 400 tickets. How many student tickets were sold?A 240 B 200C 185 D 160

6 The solution of which system of inequalities is graphed?

A y � 3x � 1 B y � 3x � 1y � �2x � 3 y � �2x � 3

C y � 3x � 1 D y � 3x � 1y � �2x � 3 y � �2x � 3

7 Which point is not a solution of the system of inequalities?

y � x � 3y � 3x � 1

A (3, 7) B (0, 4)C (9, 15) D (16, 45)

8 A tennis instructor charges $40 for each one-hour lesson and $25 foreach half-hour lesson. If the instructor’s income from 35 lessons was$1,115, how many one-hour lessons did she give?A 22 B 19 C 16 D 15

9 Which equation is formed by using substitution to solve this system oflinear equations?

7x � 3y � 6�y � �11 � 2x

A 7x � 3y � 11 � 2x � 6 � y B 7x � 3(11 � 2x) � 6C 7x � 3(�11 � 2x) � 6 D 7(�y � 11) � 3y � 6

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10 Last season the sales of pennants costing $5 and mugs costing $6 at abaseball stadium totaled $4,540. This season the same numbers of mugsand pennants were sold, but at a cost of $7 each for the new mugs and$9 each for the new pennants. Which system of equations models thissituation if x represents pennants sold, y represents mugs sold, and totalsales this season were $6,560?A 5x � 6y � 4,540; 7x � 9y � 6,560B 5x � 6y � 4,540; 9x � 7y � 6,560C 11xy � 4,540; 16xy � 6,560D 11(x � y) � 4,540; 16(x � y) � 6,560

11 Which system of equations has exactly one solution?A 3x � 5y � 10 B 4x � 6y � 9

�6x � 10y � 20 2x � 3y � 8C y � 3x � 2 D x � 2y � 3

2y � 6x � 2 y � �12

�x � �23

�

12 A large Fayetteville corporation is hiring two consultants to streamlineaccounting practices. They have contracted for a total of 640 hours ofwork from the two consultants at rates of $80 per hour and $100 perhour. If the total cost of the consultants is $55,600, for how many hoursof work was the consultant who charges $100 per hour hired?A 420 hours B 360 hoursC 320 hours D 220 hours

13 A parking meter on Hillsborough Street in Raleigh has 106 coins removedfrom it, all dimes and quarters. The value of the coins is $17.35. Howmany of each coin were in the meter?A 45 dimes, 61 quarters B 87 dimes, 19 quartersC 61 dimes, 45 quarters D 55 dimes, 51 quarters

14 Which is a solution of the system of inequalities?

y � �7x � 4�2x � 6y 3

I. (0, 0) II. (0, �2) III. (�2, 0) IV. (�5, 5)

A I only B II onlyC II and III D III and IV


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15 The solution of which system of inequalities is graphed?

A �25

�x � y 2 B ��25

�x � y � �2

�3x � y � �2 �3x � y � �2

C ��25

�x � y �2 D ��25

�x � y �2

�3x � y � �2 �3x � y � �2

16 Emily flew 1,800 miles from Dallas to attend her son’s graduation from

Meredith College. With a tailwind, the trip took 2�34

� hours. With a

headwind, the return trip took 3�12

� hours. From which system of equations

can you determine the airplane’s speed in still air?A 3.5(x � y) � 1,800; 2.75(x � y) � 1,800B 3.5(x � y) � 2.75(x � y); 1,800x � 1,800yC 3.5x � y � 1,800; 2.75x � y � 1,800D 3.5(x � y) � 2.75(x � y) � 1,800; x � y � 6.25

17 The points A(�5, 20) and B(1, 2) both lie on the graph of the linearfunction f. The points C(�3, �11) and D(3, 1) both lie on the graph ofthe linear function g. Which point lies on both graphs?A (0, 0) B (8, 3)C (�2, �1) D (2, �1)

18 A gas dryer will cost Mr. Japlenko $480. Operating costs are about$7.20 per month. A comparable electric dryer costs $420, with monthlyoperating costs about $13.20. After how many months will Mr. Japlenkorealize a savings if he purchases a gas dryer?

A 8�12

� months B 9 months

C 9 �12

� months D 10 months

19 An inkjet printer costs $125 and 6 cents per page to operate. A laser jetprinter costs $250 and 2 cents per page to operate. At how many pageswill the cost of the two printers be the same?A 9,375 pages B 3,125 pagesC 1,875 pages D 1,563 pages

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OBJECTIVE 4.04 Graph and evaluate exponential functions to solveproblems.

1 Consuelo and Jorge paid $215,000 for their house overlooking PamlicoSound. If the house appreciates at a rate of 3% each year, the value V ofthe house after n years can be represented by V � 215,000(1.03)n.Which is the closest estimate of the value of the house after 5 years?A $249,244 B $247,250C $241,984 D $240,493

2 In the last ten years, a company’s gross income has risen at an annualrate of 40%. If the gross income at the beginning of the period was 0.2 million dollars, which formula can be used to estimate the income Iin millions of dollars during the period, where t is the number of yearssince the beginning of the period?A I � 0.2(0.4)t B I � 0.2(40)t

C I � (0.2 1.4)t D I � 0.2(1.4)t

3 Which is true of the graph of y � 2x?

I. The y-value doubles whenever the x-value doubles.II. The graph has no x-intercept.III. The graph has no y-intercept.IV. The y-intercept is 1.

A IV only B I and IIIC II and IV only D I, II, and IV

4 If y � a�1 � �mn

��mt, what is the value of y when a � 500, n � 0.065,

m � 12, and t � 8? Round your answer to the nearest hundredth.A 0 B 9.55C 839.83 D 4,267.89

5 The function P(t) � 100(1.05)x models the population P in thousands ofa city from 1992 to 2004, where t � 0 represents the year 1992. If thegrowth rate remains the same, about how many people does the modelpredict will live in the city in 2010?A 265,000 B 241,000C 200,000 D 190,000


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6 Which is the graph of y � ��13

��x� 1?

A B

C D

7 A medicine is injected into a patient at the Duke University MedicalSchool. After each hour, five-eighths of the previous hour’s medicineremains in the patient’s system. Approximately what percent of themedicine remains in the patient’s system after 10 hours?A 9.1% B 6.25% C 0.9% D 0.5%

8 Scientists use carbon 14 dating to find the age of fossils. The formula

used is A(t) � A0�2��

56t00��, where A0 represents the amount of carbon

14 present when the fossil was formed and A(t) represents the amount ofcarbon 14 present after t years. If 400 grams of carbon 14 were presentwhen an organism died, about how many grams will remain in its fossil1,000 years later?A 303 grams B 353 grams C 453 grams D 512 grams

9 How does the graph of y � 4�x compare to the graph of y � ��14

��x?

A The graph of y � 4�x is increasing and the graph of y � ��14

��xis

decreasing.B The graphs are the same.C The graphs are reflections of each other in the x-axis.D The graphs are reflections of each other in the y-axis.

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y

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y

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Standards Practice


10 The graph of which equation represents exponential decay?

A y � ��43

��xB y � ��

43

��x

C y � ��34

��xD y � ��

43

��x

11 The change of a quantity after x years can be modeled by the function y � 200(0.96)x. Which describes how the quantity changes each year?A It is growing at an annual rate of 96%.B It is growing at an annual rate of 0.96%.C It is decreasing by 8 each year.D It is decreasing at an annual rate of 4%.

12 The number N of bacteria in a culture increases by 50% each hour. If1,000 bacteria were originally present in the culture, which formulagives the number of bacteria present in the culture after t hours?A N � 0.51,000t B N � 1,000(0.5)t

C N � 1.5t D N � 1,000(1.5)t

13 A small town had a population of 400 in 2000. For the next 4 years, thetown had a boom in population, growing at an average annual rate of120%. What was the approximate 2004 population?A 720 B 830C 3,520 D 9,370

14 The graph of which equation is shown?A y � 2x

B y � 2x � 1C y � 2(1.5)x

D y � 1.5x � 1

15 A chemical decomposes 20% by mass each hour. If the initial mass ofthe chemical is 700 grams, about how much of the chemical remainsafter 4 hours?A 1 gram B 41 gramsC 140 grams D 287 grams

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The graph compares linear growth of $1,500 invested at 5% simple interest to exponentialgrowth of the same amount invested at 5%compounded annually. For each function, A(t) represents the amount in dollars of theinvestment after t years.

16 Which is the best estimate of the amount of time it takes $1,000 to double in valuewhen invested at 5% simple interest?A 6 years B 10 yearsC 15 years D 20 years

17 Which is the best estimate of the amount of time it takes $1,000 todouble in value when invested at 5% compounded annually?A 6 years B 10 yearsC 15 years D 20 years

18 Which is the best estimate of the difference in value after 24 years for$1,500 invested by each method?A $1,000 B $1,500C $2,000 D $3,000

19 What is the y-intercept of the graph of y � 50��23

��x?

A 50 B 33�13

�

C 1 D 0

20 The decline in dollar value y in t years of a tractor-trailer truck ismodeled by y � 160,000(0.88)t. What is the truck’s initial value?A $160,000 B $148,000C $140,800 D $88,000

21 Which function is decreasing?A y � 5�x B y � 5x

C y � 5x � 2 D y � �5��12

��x

YearsA

mou

nt ($

)60 1812 24

4,000

3,000

2,000

1,000

t

A(t)

Linear growth

Exponential growth


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Sample Test 1

1 Computer cables sell for p dollars each. The income I from their weekly sales can be modeled as a function of p by the equation I � �148p2 � 21,165p. How does the value of p affect the value of I?A I increases as p increases.B I decreases as p increases.C I increases to its maximum as p increases, then decreases as p

continues to increase.D I increases to a maximum as p increases, then levels off as p continues

to increase.

2 If A is a 3 � 5 matrix and B is a 5 � 2 matrix, which are the dimensionsof A B?A 3 � 2 B 2 � 3 C 5 � 5 D 5 � 6

3 Which are the roots of y � 15x2 � 14x � 8?

A ��43

�, �52

� B �43

�, ��25

� C �34

�, �25

� D �43

�, �52

�

4 Which expression is equivalent to �5v2 � 305vv

3

2� 15v4�?

A 6v � 3v2 B 3vC 4v D 1 � 6v � 3v2

5 Under controlled conditions in a laboratory, a substance that initiallyweighs 450 grams is observed to lose 15% of its mass each hour.Approximately how much of the substance remains after 8 hours?A 115.33 grams B 104.23 gramsC 122.62 grams D 144.26 grams

6 If the graph of y � 3x2 � c is translated 5 units up from the graph of y � 3x2 � 4, what is the vertex of y � 3x2 � c?A (0, 0) B (4, 5)C (5, 4) D (0, 9)

7 A coordinate grid is placed over a map of Henderson. The policedepartment is located at (�12, 7) and the fire department is located at(�6, 6). Which are the coordinates of the point halfway between thepolice department and the fire department?A (�11, 15) B (�9, 6.5)C (�7, 8) D (�5, 4) Go on


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Sample Test 1 (continued)

8 Which shows the factors of x3 � 3x2 � 4x � 12?A (x2 � 4)(x � 3)B (x2 � 4)(x � 3)C (x2 � 2)(x � 6)D (x2 � 2)(x � 6)

9 The table describes the graphs that model the growth in the number ofpilots employed by two airlines during a 5-year period. Which statementdescribes the relationship between the graphs?

A The number of pilots in Airline B grew at a faster rate.B While the number of pilots in Airline A decreased, the number of

pilots in Airline B increased.C The total number of pilots in both airlines at the end of the period

was 263.D The number of pilots in both airlines increased at the same rate, but

Airline B had more pilots at the beginning of the period.

10 A community task force is studying plans to build a circular gazebo in thetown common. Alternate plans call for the diameter of the floor to be

�23

� the length of the diameter in the original plan. The floor area in the

alternate plan is which fractional part of the floor area in the original plan?

A �29

� B �49

�

C �23

� D �89

�

11 If N � and G � , which is �2N � 3G?

A B

C D�10 �8�22 � 3�18 �12

�15 �5�16 �26� 5 �20

�15 16� 5 5�26 20

�2 �8 6 3 18 �12

�3 4�1 5�6 2

�3 �2�1 �5�4 �7

Airline Slope y-intercept

Airline A 8 121Airline B 8 142

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12 If K � and T � , which is 2K � 4T ?

A B

C D

13 Given R � and S � , which is S � 3R?

A B

C D


Matrix A displays the average distribution of eligible voters by age and partyaffiliation in the last 10 years in several of North Carolina’s voting districts.

A �

14 Which is the element in row 3 column 2 of the matrix?A 0.48 B 0.40C 0.30 D 0.10

15 The average population of registered voters in these districts who wereyounger than 30 was 35,000 during the last ten years. Approximatelyhow many of these voters were either Democrat or Republican?A 4,725 B 24,500C 26,250 D 29,750

16 The average population of voters younger than 30 in these districts isexpected to be 4% greater during the next ten years. Using Matrix A as amodel, about how many independents younger than 30 will become votersduring the next 10 years?A 280 B 728C 1,456 D 7,280

Age Democrat Republican Independent Other� 30 0.45 0.30 0.20 0.05

30–50 0.40 0.30 0.20 0.10 � 50 0.40 0.48 0.10 0.02

�0 11 �15�7 5 � 8

10 11 22�5 0 11

�0 �23 �11�5 �15 �8

0 �23 115 �15 8

�6 8 11�4 3 5

�2 �5 �0�3 �6 �1

�6 �6�2 �4

6 �26 �4

�16 2�12 0

8 �410 �16

�2 �3�1 �3

7 �31 �4

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17 In a set of data points the observed value for y is 2.8 when x � 3. If thelinear regression line y � �3.5x � 10 is used to model the data, whichis the difference between the observed value for x � 3 and its predictedvalue on the regression line?A 3.3 B 2.3C �2.3 D �3.3

18 Which formula is equivalent to E � 0.238I2Rt?

A I � ��151090REt� B R � �

510109IE2t

�

C �t� � �90.2

E38IR� D t � �

0.I2

23R8E�

19 Which is an expression for the area of the rectangle in square units?A 2x2 � 6x � 10B x2 � x � 11C 2x3 � 5x2 � 17x � 10D 3x3 � 5x2 � 17x � 10

20 The solution set of which inequality is graphed?A y � 2x � 4B y � 2x � 4C y � 4 � 2xD y � �2x � 4

21 Which is the equation of the graph of a line that passes through (1, 3) and is perpendicular to line m?A x � 2y � 5B 2x � y � �5C y � 2x � 5D 2y � x � 5

x

m

O

y(1, 3)

(4, �3)

xO

y

2x � 1

x2 � 3x � 10

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22 Which ordered pair is a solution of the system of equations representedby the two tables?

A (3, 1) B �3, �5�12

��C (4, �3) D (4, �5)

23 Which is an example of a direct variation equation?A y � 6x � 4 B s � a � cp

C s � hm D T � �mk�

24 A computer security company with customers in North and SouthCarolina had sales of $1,000,000 in its first year of operation. If its salesincreased by 10% each successive year, what were the company’s salesin its fifth year of operation?A $1,464,100 B $1,610,510C $4,400,000 D $5,500,000

25 Which expression is equivalent to p � (3q � p) � (4p � q) � q?A 2p � 3q B 2p � qC 4p � 3q D 5p � q

26 During a collision, the force F that acts on an object can be modeled bythe function F � 87t � 21t2, where t is the time in seconds after thecollision. Which is the most reasonable domain for this situation?A 0 t 2 B 0 t 4C 0 � t � 4 D 0 � t � 90

27 Participants in an outdoor leadership school are planning a sailing trip offthe North Carolina coast. They will combine one brand of energy mix thatis 30% carbohydrate with a brand that is 60% carbohydrate. Which systemof equations can be solved to determine how many grams of each mixshould be used to obtain a mix with 600 grams that is 45% carbohydrate?A x � y � 600; 0.30x � 0.60y � 0.45(600)B x � y � 600; 0.30(x � y) � 0.60(x � y) � 1.8C 600 � x � y; 0.30x � 0.60y � 0.45(600)D 0.30x � 0.60y � (0.45)600; 0.30x � 0.60y � 600

x �2 �1 �0 �1 �2

y �8 �7�12

� �7 �6�12

� �6

x �2 �1 0 1 �2y �7 �5 3 1 �1

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28 Which expression can be substituted for y in Equation 2?

Equation 1: x � �13

�y � 2

Equation 2: �23

�x � 2y � 4

A �13

�y � 2 B 2 � �13

�y

C 3x � 6 D 6 � 3x

29 Tess tells a joke to 3 friends on Monday. Each of those friends tells 3 other friends the joke on Tuesday. The joke continues to be retold in thesame way. Which expression can Tess use to determine how many peoplebesides herself have heard her joke n days after she first told it?A 1 � 3n

B 3n

C 1 � 3 � 32 � 33 � 34 � … � 3n

D 3 � 32 � 33 � 34 � … � 3n


A tree farmer depreciates the cost of a $60,000 truck over ten years using adepreciation method called the double declining balance method. Under thismethod, the book value of the truck Vn after n years can be calculated using

the formula Vn � C�1 � �N2

��n, where C is the original cost of the truck, and

N is the length of the depreciation period in years.

30 Which is the book value of the truck at the end of five years?A $4,665.60 B $19,660.80C $25,480.40 D $36,279.71

31 By how much has the truck depreciated at the end of the fifth year?A $23,720.29 B $34,519.60C $40,339.20 D $55,334.40

32 If M � , which element is in row 2, column 4

of ��25

�M?

A �0.6 B �1.2C 0.8 D 7.5

�6 �5 10 �8 �3�1 �1 2 �3 �4�5 �8 7 �6 �6

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33 The monthly profit for a new business in Pitt County increased from$6,000 in March to $7,200 the following month. If the profit continuesto increase at the same rate, what will be the profit in May of the sameyear?A $8,200 B $8,400C $8,640 D $8,820

34 Which are the coordinates of the midpoint of A�B� after it is rotated 180degrees about the origin?

A ��3, �52

�� B ��52

�, �3�C ��3, ��

32

�� D ��52

�, �4�

35 Kyra makes and sells three sizes of picture frames that she decorateswith shells, ceramic beads, or quartz stones. The matrix shows Kyra’scost to make the frames. She sells them for 7 times their cost. Whichmatrix shows the selling price of the frames?

A � 4 � 6 inches, B � 5 � 8 inches, C � 8 � 10 inches

A B

C D28 63 7742 91 10556 98 119

28 42 5663 91 9877 105 119

11 16 1813 20 2215 21 24

11 13 1516 20 2118 22 24

A B Cshells 4 6 8 beads 9 13 14 stones 11 15 17

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B

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36 For which value of x does �10x

7� 9� � �

3x2� 2�?

A 4 B �25

�

C ��190� D �4

37 In the communication matrix, only receivers 2 and 4 receive a signalfrom sender 1. Which receivers receive a signal from sender 3?

A receiver 1 B receiver 2C receiver 1 and receiver 2 D receiver 4 and receiver 2

38 Which mathematical model represents a rate of change?A zeros of a quadratic functionB shaded region in the graph of a linear inequalityC slope of a lineD increase in an exponential function

39 The volume V of a cone with radius r and height h is equal to �13

��r2h.

How much ice cream can be packed into a super-size ice cream cone

with a diameter of 3�12

� inches and a height of 4 inches? Round your

answer to the nearest cubic inch.A 13 cubic inches B 22 cubic inchesC 51 cubic inches D 180 cubic inches

40 What is the perimeter of pentagon PQRST? Round to the nearest tenth.A 18.2 unitsB 20.0 unitsC 20.4 unitsD 25.0 units

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y

QP R

ST

Possible ReceiversSender 1 2 3 4

1 0 1 0 1 2 1 0 0 1 3 1 1 0 0 4 1 1 1 0

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41 Which is the base of y � (�0.2)(5)2x?A �0.2 B �1.0C 2 D 5

42 Which set of ordered pairs (x, y) is a direct variation?A B

C D

43 The scatter plot shows how the number of donors at a blood bank withblood type A positive compares to the total number of donors. Whichequation best fits the data?

A y � 0.5x � 8.9 B y � �0.6x � 0.4C y � �0.36x � 5.2 D y � 0.4x � 21.4

44 Quadrilateral LMNO has vertices L(4, 1), M(6, �1), N(6, �4), and O(1, �4). Which is the perimeter of LMNO if each grid unit is 2 centimeters? Round your answer to the nearest tenth centimeter.A 35.3 centimeters B 33.3 centimetersC 31.7 centimeters D 16.7 centimeters

45 The quarterly profit p of a company for the sale of its frozen yogurt barscan be modeled by the equation p � 0.12x � 4,500, where x is the numberof yogurt bars sold. If the company expects to sell at most 300,000 barsin a quarter, which is the most reasonable range for this model?A p � 31,500 B �4,500 � p � 31,500C p � 300,000 D �4,500 � p � 300,000

Number of Donors

Blood Donors

Don

ors

wit

h A

Pos

itiv

e

300 500400200

200

150

100

50

(200, 60) (275, 78)

(316, 107)

(427, 160)

(482, 160)

x 1 2 3 4

y �12

� �14

� �16

� �18

�

x 1 2 4 8y 1 0.5 0.25 0.125

x 0 �1 �1 �2y 0 �3 �3 �6

x 1 2 4 8

y 4 2 1 �12

�

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46 Line a is the perpendicular bisector of S�T�. Which point does not lie on a ?

A (�4, �4) B (�1, 0)C (2, 5) D (4, 8)

47 A culture of bacteria doubles in population every three hours. If thepopulation of a culture was 20 at 3:00 P.M., which expression representsits population after 24 hours?A 20(2)6 B 20(2)8

C 20 � (20)7 D 20 � (2)24

48 Which is the slope of a line parallel to a line that passes through (�3, 6)and (0, 8)?

A ��32

� B ��23

�

C �13

� D �23

�

49 Shane enlarges the floor plan of his square garage by increasing eachside by a factor of k. Which statement is true?A The area of the enlarged floor is increased by a factor of k.B The area of the enlarged floor is increased by a factor of 2k.C The area of the enlarged floor is increased by a factor of k2.D The area of the enlarged floor is increased by k units.

50 The formula P � 20,000(1.005)�n gives the amount of money P thatshould be deposited in an account paying an interest rate of 6% per yearcompounded monthly, so that at the end of n months, the accumulatedamount will be $20,000. Which is the y intercept of the graph of P � 20,000(1.005)�n?A 0 B �20,100C 20,000 D 20,100

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51 The coordinates of the vertices of parallelogram ABCD are A(�3, 7),B(1, 3), C(2, 0), and D(�2, 4). What are the coordinates of theintersection of the diagonals of ABCD?A (�1, 5)B (�0.5, 3.5)C (0, 2)D (0.5, 3.5)

52 What is the value of the dependent variable when the independentvariable is �5 for the function f(x) � �x2 � 2x � 15?A �20B �5C 15D 30

53 A concrete sphere with diameter 8 centimeters is completely submerged in

a fish tank. If the formula for the volume V of a sphere is V � �43

��r3 where

r is the radius of the sphere, how much water is displaced in the tank bythe sphere? Round your answer to the nearest cubic centimeter.A 50 cubic centimetersB 268 cubic centimetersC 1,609 cubic centimetersD 2,164 cubic centimeters

54 Which situation can be modeled by the slope of a linear function?A area of a square with side x units longB amount of increase in tuition cost this year at Duke UniversityC constant rate of annual depreciation of a piece of surveying equipmentD difference in germination rate of two types of tomato seeds

55 The ordered pairs (x1, y1) and (x2, y2) both satisfy the direct variationequation y � kx. If (x1, y1) (0, 0) and (x2, y2) (0, 0), whichstatements are always true?

I. y1 � �x

k1� II. �

yx

2

2� � k III. �

yx

1

1� � �

yx

2

2� IV. y2 � kx1

A I and III onlyB III onlyC II and III onlyD II, III, and IV only

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56 Rectangle DEFG has vertices D(0, �2), E(�6, 4), F(�2, 8), and G(4, 2).What are the coordinates of the intersection of the diagonals of DEFG?A (�1, 3) B (�3, 1)C (�4, 6) D (1, 0)

57 Which correlation coefficient indicates a moderate negative correlationbetween an independent variable x and the dependent variable y?A �0.05 B �0.40C �0.83 D �0.99

58 How does the graph of y1 � �3x � 1 differ from the graph of y2 � 3x � 1?A One line is vertical and the other line is horizontal.B The graphs have different y-intercepts.C The rate of change for y2 is greater than the rate of change for y1.D As x increases, y1 decreases, while y2 increases.

59 Which is the graph of y � 3(0.4)x � 2?A B

C D

60 Which is the slope of a line perpendicular to a line that passes through(0, �3) and (5, 0)?

A ��53

� B ��35

�

C �35

� D �53

�

xO

y

xO

y

xO

y

xO

y

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Matrix A displays the expected demographic distribution for the incomingfreshmen students at a university. Matrix B shows their expected enrollmentin the university’s four colleges.

Demographic Distribution:

A �

Percent of College Enrollment:

B �

61 Approximately what percentage of the freshmen are expected to be in-state or out-of-state students?A 42% B 48% C 72% D 90%

62 How much greater is the expected enrollment of in-state freshmen in theCollege of Engineering than the enrollment of foreign freshmen in theCollege of Fine Arts?A 105 freshmen B 495 freshmenC 670 freshmen D 900 freshmen

63 How many freshmen are expected to enroll in the university?A 3,400 students B 3,700 studentsC 6,400 students D 7,100 students

64 Cans collected in a recycling project are displayed against a wall and arearranged in a pyramid with 2 cans in the top row, 4 cans in the secondrow, six cans in the third row, and so on. How many rows are in thepyramid if it contains 1,190 cans?A 17 rows B 34 rows C 68 rows D 70 rows

65 At which point do the graphs of 2x � y � 1 and 3x � 2y � 12 intersect?

A ��170�, �

173�� B ��

1132�, �

76

��C (2, 3) D ��

171�, �

175��

Arts and Fine Business EngineeringSciences Arts

Male 0.25 0.20 0.30 0.25 Female 0.30 0.35 0.25 0.10

Male FemaleIn-State 2,300 2,800

Out-of-State 700 600 Foreign 400 300

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66 The line y � 0.42x � 0.12 models the number of tourists x who visit astore compared to the number of those visitors y who make purchases.What is the significance of the slope of the line?A More than half of the tourists who visit the store make purchases.B About 40% of the tourists who visit the store make purchases.C There is a negative correlation between the variables.D A linear equation is not a good model for the data.

67 The value of f(50) for the function f(x) � 240x2 � �500 �� 503� is anapproximation of the number of households in North Carolina in 2000where a language other than English was spoken at home. Inapproximately how many North Carolina households was a languageother than English spoken in 2000?A 24,000 B 144,000C 600,000 D 144,000,000

68 On a tax map, a parcel of land in Cumberland County is represented bya rectangle measuring 2.9 inches by 3.5 inches. If the scale of the map is1:5,000 and there are 43,560 square feet in one acre, how many acres arein the parcel, to the nearest acre?A 14 acres B 40 acresC 485 acres D 583 acres

69 Line c passes through (�2, �3) and is parallel to line d. If the equation of

the graph of line d is y � ��12

�x � 2, which is the equation of line c ?

A y � ��12

�x � 4 B y � ��12

�x � 3

C y � �12

�x � 3 D y � �2x � 4

70 Which is the solution of the system of equations?

Equation 1: y � 2x � 1 Equation 2: 2x � y � 3 � 0

A ��76

�, ��130�� B 0

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71 Which expression is equivalent to ?

A �y2

14

xz2

3� B 8x2y14z3

C 2x�2y�3z�5 D 2x3y�48z4

72 The table below shows the rates charged at a parking garage in Raleigh.Which equation models the maximum amount of time t you can park inthe garage if you want to pay no more than $7.50?

A t � 1.5 � 7.5 B t � 1.5 7.5C 100t � 250 � 7.5 D 3.5t � 7.5

73 The equation of the graph of one diagonal of a square is 4x � 5y � 10.The square has a vertex at (�5, 6). A square’s diagonals are perpendicularbisectors of each other. Which could be an equation of the square’s otherdiagonal?

A y � �54

�x � 2 B y � ��45

�x � 2

C y � ��54

�x � 2 D y � �45

�x � 2

74 Which are the factors of 6x2 � 28x � 16?A (2x � 4)(3x � 4) B (2x � 8)(3x � 2)C 2(3x � 4)(x � 2) D 2(3x � 2)(x � 4)

75 If B � , which is equivalent to �5B?

A B

C D�10 �5 �20�25 �15 �10�30 �0 �20

�7 �4 �1�0 �8 �3�1 �5 �9

�10 �25 �30 �5 �15 � 0�20 �10 �20

�10 �5 �20�25 �15 �10�30 �0 �20

�2 �1 �4�5 �3 �2�6 �0 �4

1st Hour Each Additional Hour$2.50 $1.00

2x(2y3)2z�1��16x3(y2z)�4

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76 Which point is a solution of the system of inequalities?

y � �2x � 3y � 3x � 1

A (�1, 4) B (0, 5)C (1, �4) D (2, 0)

77 Consider the graphs of y � 6x2 and y � �6x2. Which statement is true?A The vertex of y � 6x2 is two units above the vertex of y � �6x2.B The graph of y � 6x2 is wider than the graph of y � �6x2.C The graphs are mirror reflections of each other in the x-axis.D The graphs are mirror reflections of each other in the y-axis.

78 The gravitational force of attraction F between an object and the earth isdirectly proportional to the mass m of the object. If the force ofattraction is 640 on an object with mass 20, which is the force ofattraction on an object with mass 32?A 400 B 640C 896 D 1,024

79 The table shows the profits of Karyn’s newsletter business for the past 6 months. Create a model of the data. If you use the line of best fit,which is the best prediction of Karyn’s income at 18 months?

A $1,900 B $2,000C $2,100 D $2,200

80 The coordinates of the vertices of parallelogram RSTW are R(�2, 2),S(1, 1), T(2, �3), and W(�1, �2). What are the coordinates of theintersection of the diagonals of RSTW?A (0, �0.5) B (0.5, 1.5)C (0.5, �2.5) D (1.5, �1)

Month 1 2 3 4 5 6Profit ($) 260 340 480 565 694 836


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Sample Test 2

1 The ordered pairs ��4, �116��, ��3, ��

18

��, (0, 1), (5, �32), and (8, 256) are

solutions of which function?

A f(x)� �2x B f(x) � ��22

1x� C f(x) � 22x D f(x) � (�2)x

2 Which product is equal to �1?

A [1 �2 3] B [3 2]

C [1 2 3] D [2 3 �1]

3 Which is the solution of the system of equations graphed?

A ��23

�, ��43

�� B ��12

�, ��12

��C ��

23

�, ��23

�� D ��58

�, ��12

��

4 What is the perimeter of trapezoid BRTY?A 19.1 unitsB 18.6 unitsC 15.1 unitsD 14.3 units

5 The center of circle P is at (8, 6) and Q(13, 6 � �39� ) is a point on thecircle. If circle P is inscribed in square ABCD, what is the area of ABCD?A 49 square units B 156 square unitsC 256 square units D 4,096 square units

6 The vertices of parallelogram IJKL are I(�2, 1), J(2, 4), K(2, �1), andL(�2, �4). Which statement is true?A The diagonals form four right angles.B The diagonals form exactly two congruent angles.C Exactly two sides of IJKL are congruent.D IJKL is a square.

xO

yT

R

B

Y

xO

y

(�1, 1)

(�1, �2)

(�6, �4)

(1, �1.8)

528

�2�1�1

�1�1

�2�1�1

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The table shows the attendance rates at a tourist attraction from 1999 through 2003.

7 Which is the least squares regression line for the data, where x is thenumber of years since 1999 and y is the attendance for that year?A y � �811x � 24,404B y � �811x � 24,404C y � 811x � 24,404D y � 811x � 24,404

8 Which does the y-intercept represent?A rate of increase B attendance in 1999C amount of increase D attendance in 2003

9 Using the least squares regression line, which is a prediction of thenumber of tourists who will visit the attraction in 2005?A 28,713 B 29,270C 30,217 D 30,498

10 A boat is traveling on the Roanoke River near its terminus in AlbemarleSound. The boat travels at 18.2 miles per hour with the current and 16.5 miles per hour against the current. Which system of equations canyou solve to determine the speed of the current?A x � y � 16.5 B x � y � 34.7

x � y � 18.2 x � y � 1.7C x � y � 18.2 D x � 18.2

x � y � 16.5 y � 16.5

11 The graph models the height h of an object t seconds after it is projected upward from a rooftop 100 feet above the ground at a velocity of 64 feet per second. How long does it take the object to reach its maximum height?A 0 secondsB 2 secondsC 5.2 secondsD 100 seconds

0 4 62

150

100

50

t

h

Year 1999 2000 2001 2002 2003Attendance 24,800 25,900 24,700 25,850 28,880

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12 Which expression describes a linear function that always passes through(0, 0)?A positive function B negative functionC inverse variation D direct variation

13 Which statement is always true for matrix A and matrix B?

I. A � B � B � A II. AB � BA III. A � B � B � A

A I B I and II C I and III D II and III

14 Which ordered pair is a solution for the system of equations representedby the tables?

A (6, 13) B (5, 10) C (5, 11) D (4, 7)

15 Which system of inequalities is graphed?

A 3x � 2y 0 B 3x 2y4x � y � 0 �x � 4y � 0

C 3x � 2y � 0 D 2y 3x4y x 4x y

16 The table displays the growth of new houses in a suburb of Raleigh. If the number of new houses grew at a constantrate in the 10-year period, which statement about the growth rate of new houses is true?A The number of houses grew by the same amount each year.B You can divide the total growth by 8 to find the rate of growth.C Since the rate of growth is constant, you can use a linear function to

model the growth.D The number of new houses leveled off after 2000.

Year 1994 2003New Houses 34 52

xO

y

(4, 1)

(2, 3)

x �2 �1 0 1 2y �3 �1 1 3 5

x �2 �1 �0 �1 2y �11 �8 �5 �2 1

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17 A vineyard owner in Bladen County uses the equation y � 1�78

�x � �14

� to

predict the yield of grapes in tons y on a one-acre plot when he applies x tons of fertilizer to the plot. Which yield can he expect if he applies0.8 tons of fertilizer to a one-acre plot?A 0.65 tons B 0.8 tons C 1.25 tons D 1.75 tons

18 Point A is the midpoint of S�T�. What is the length of A�U�? Round to the nearest tenth.A 1.5B 2.5C 4.3D 4.7

19 A salamander scurries 10 inches along a straight path, then stops and rests.

After catching its breath, it scurries �13

� of its previous distance, continuing

along its straight path before stopping to rest again. The salamander

continues this pattern of travel along a straight path, moving �13

� of the

previous distance each time. Which expression will give the totaldistance the salamander has traveled after n moves?

A 10 � ��13

��(10) � ��13

��2(10) � … � ��

13

��n � 1(10)

B 10 � ��13

��(10) � ��13

��2(10) � … � ��

13

��n(10)

C 10��13

��n

D 10��13

��n � 1


The formula N � 1,000��32

��trepresents the number of bacteria N in a culture

after t hours.

20 How many bacteria were in the culture initially?A 0 B 1.5 C 1,000 D 1,500

21 What is the percent increase in the number of bacteria from one hour tothe next?A 50% B 66.7%C 150% D 1,500%

xO

y

AT

U

S

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22 The vertices of �DEF are D(�2, �1), E(�6, �1), and F(�2, �5). Themidpoints of sides DE and DF are M(�4, �1) and N(�2, �3). Whichstatement is true?

A MN � �13

�EF

B M�N� is parallel to D�E�.

C M�N� is parallel to D�F�.

D M�N� is parallel to E�F�.

23 Which describes the graph of y � �2x2?A two rays that form a V with vertex at (0, 0)B a parabola symmetric to the y-axis with vertex at the origin, and

opening downwardC a line through (0, 0) with a slope of �2D a line through (0, 0), with y decreasing at the same rate that x increases

24 The graph shows that the amount of time for which a North Carolina bank will lend$100,000 to a homeowner depends on his or her annual income. Which is theindependent variable in this relationship?A $100,000 loanB term of loanC amount of loanD annual income

25 A seamstress used 27 inches of elastic to sew x costumes. She also usedan additional y inches of elastic on each costume. Which expressionrepresents the average amount of elastic needed for each costume?

A �27 �

yxy

� B �x

2�

7y

�

C �27

x� y� D �

27 �x

xy�

26 The area of a rectangle is represented by the expression 8x2 � 2x � 3.Which expression could represent the length and width of the rectangle?A (8x � 3)(x � 1)B (2x � 3)(4x � 1)C (4x � 3)(2x � 1)D 2(2x � 3)(2x � 1)

0 40Annual Income (1,000s of $)

$100,000 Loan

Term

of

Loan

(ye

ars)

60 8020

30

20

10

x

y

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27 For which values of x is f(x) � 1 � x � 2x2 decreasing?A x � �0.25 B x � 1.125 C x � 0.5 D x � �1

28 How do the graphs of Equation 1 and Equation 2 compare?

Equation 1: y � 5x2 Equation 2: y � �15

�x2

A Equation 1’s graph is wider than Equation 2’s graph.B The vertex of Equation 1’s graph is 5 units above the vertex of

Equation 2’s graph.C Every point (x, y) on Equation 1’s graph corresponds to the point

�x, �15

�y� on Equation 2’s graph.

D Every point (x, y) on Equation 1’s graph corresponds to the point

�x, �215�y� on Equation 2’s graph.

29 Conchita stopped at a scenic outlook on the Blue Ridge Parkway to takea photograph. When she did, she saw a flash of lightning. She heard thethunder that was associated with it at least x seconds later. If the averagespeed of sound is 1,100 feet per second, which function represents therelationship between Conchita’s distance from the storm and x?

A d 1,100x B d � 1,100x C d � �1,1

x00� D d �

1,1x00�

30 Which is an increasing function?A y � 3�x � 3 B y � �3x � 3C y � 3x � 3 D y � �3x � 3

31 The table shows how many moves can be made in the first three steps of a video game. Which expressioncan be used to determine the number of moves that can be made in the nth step of the game?A 2n B 2(n � 1) C n(n � 1) D n(n � 2)

32 The function i � 8,000r models the amount of simple interest earned ina year on an investment of $8,000. If interest rates higher than 12% areunlikely, which is the most reasonable range of the function?A 0 � i � 960 B i � 960C 0 � i � 960 D i � 960

Step 1 2 3Number of Moves 2 6 12

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33 This summer a merchant sold souvenir pens for $7 and jackknives for$9. Sales for the two items were $6,560. Last summer the sales for thetwo items were $4,540. Pens sold then for $5 and jackknives sold for $6.If the same number of each souvenir was sold both years, which systemof linear equations models this situation?A 5x � 6y � 4,540 B 11xy � 4,540

7x � 9y � 6,560 17xy � 6,560

C x � y � z D 11(x � y) � 4,54012x � 15y � 11,100 16(x � y) � 6,560


If P dollars are deposited in a savings account that compounds interestannually, the value V of the account after t years is given by the function V � P(1 � r) t, where r is the interest rate expressed as a decimal.

34 What is the base of the function?A P B rC t D 1 � r

35 What is the value of the account if $500 is deposited for 7 years at a4.5% interest rate?A $6,738.23 B $761.22C $673.82 D $680.43

36 Which is the equation of a line that passes through (�3, 7) and isparallel to the line 2x � y � 6?A y � 2x � �1 B y � 2x � 1C 2x � 1 � y D y � �2x � 1

37 Which element is in row 4, column 2 of �2A?

A �

A �12 B �6C �5 D 4

�4 2 �1 �8�0 4 �3 �2�8 1 �5 �1�2 6 �3 �7

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38 A contractor is preparing two sketches at different scales of the additionhe will build for a client’s house in New Bern. The length of the kitchenis 45 centimeters in one sketch and 54 centimeters in the other sketch. Ifthe length of the bath in the smaller sketch is 38 centimeters, whatshould this measurement be on the larger sketch?A 31.7 centimetersB 38 centimetersC 45.6 centimetersD 69 centimeters

39 The formula P � R�1 � (1i� i)�n� shows the monthly payment R needed

to pay off a debt P in n months with an interest rate i, which is expressedas a decimal and compounded monthly. What is the monthly payment fora $1,000 debt if i � 0.01 compounded monthly and the debt will be paidoff in a year?A $23.10B $52.98C $88.85D $112.68

40 Line a passes through (�3, 6) and is perpendicular to the graph of y � 3x � 4. Which is the equation of line a?

A y � ��13

�x � 5 B y � ��13

�x � 6

C y � �13

�x � 3 D y � �13

�x � 3

41 Which is the slope of the line that passes through (3, 7) and (5, 11)?A 2 B 1C �1 D �2

42 Which are the roots of y � �8x2 �10x � 3?

A ��14

�, �32

� B ��14

�, ��32

�

C ��14

�, �23

� D �14

�, �32

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43 The perimeter of the isosceles triangle shown is 50 feet, and the base bdoubled is 9 feet more than 3 times the length r. What is r?

A 13 feet B 18.2 feetC 21.8 feet D 24 feet

44 The expression for the area of a rectangle is 40a4 � 11a2b3 � 63b6. Theexpression of the length of the rectangle is 5a2 � 7b3. Which is theexpression for the width of the rectangle?A 45a2 � 56b3 B 35a2 � 4b2

C 8a2 � 9b3 D 8a2 � 5ab � 9b3

45 Which is a solution of the system of inequalities?

Equation 1: 2x � 3y � 6 Equation 2: 4x � 2y 8

A (�2, 1) B (4, �1)C (5, 2) D (0, 0)

Use the inventory and shipment matrices for Warehouses A, B,

and C to answer Questions 46 and 47.

Inventory Matrix June 3, 2003 Shipment Matrix, June 4, 2003

46 How much greater was the inventory of DVD drives than hard drives inall three warehouses?A 60 B 180C 200 D 260

47 How many CPUs remain in warehouses A and C after the orders areshipped on June 4?A 190 CPUsB 230 CPUsC 250 CPUsD 340 CPUs

A B CMonitors 20 10 30

CPUs 40 0 20 DVD Drives 50 10 10 Hard Drives 10 0 0

A B CMonitors 100 120 200

CPUs 170 110 120 DVD Drives 110 150 320 Hard Drives 50 70 200

r r

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48 What is the length of diagonal N�P�?A 4B 6

C 2�10�D 6�2�

49 A bed and breakfast on Ocracoke Island logs requests for information onisland attractions to provide background on writing a pamphlet on the mostrequested attractions. In June, they had 43 requests for information on thelighthouse, 32 on pony pens, and 18 on Portsmouth Village. In July, therewere 27 for Portsmouth Village, 34 for the lighthouse, and 51 for the ponypens. Which matrix organizes the data so that the rows are June and Julyand the columns are lighthouses, pony pens, and Portsmouth Village,respectively?

A B

C D

50 Which are the roots of �x2 � 8x � 12 � 0?A There are no roots.B (4, 4)C (0, 4) and (4, 4)D (2, 0) and (6, 0)

51 Which parabola has a maximum point?A y � (3x � 1)(2x � 2) B y � 8x2 � 5x � 1C y � (2 � x)(6 � 5x) D y � (7 � 3x)(1 � 2x)

52 The formula 0.85x � 0.50(a � x) � 0.70a expresses the number ofgallons x of a fungicide that is 85% detergent and will be mixed with a50% detergent solution to achieve a 70% detergent solution. The 70%solution will fill a 10-gallon tank. What is the value of a in the equation?A 0.7 B 0.35C 1.40 D 10

xO

y

(2, 0) (6, 0)

(4, 4)

43 32 1834 51 27

43 32 1827 34 51

43 3432 5118 27

43 2732 3418 51

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The graph shows the average amount of dividends d earned on an initial investment of x dollars in a particular stock over a period of ten years.

53 At this rate, how much in dividends wasearned on a $390 investment?A $1,798 B $2,170C $2,387 D $2,418

54 What was the rate of return on the investment?A 1.6% B 6.2% C 62% D 620%

55 For her health class, Maya analyzed the relationship between the numberof calories y and grams of fiber x in selected foods. The line of best fitfor the data is y � �1.62556x � 137.6, with a correlation coefficientclose to zero. Which conclusion best describes the data?

A There is essentially no correlation between calories and fiber.B There is a positive but weak correlation between calories and fiber.C There is a strong correlation between calories and fiber.D The line of best fit shows a strong negative correlation between

calories and fiber.

56 In each successive stage of the sequence of figures shown, one moresquare is inscribed in the previous square. Which will be the area of thenext square to be drawn?

A �14

� square centimeter B �18

� square centimeter

C �116� square centimeter D �

312� square centimeter

1 cm

1 cm

Food Bananas Apples Straw- Bran Sweet Black (1 serving) berries muffin potato beansCalories 200 190 43 130 117 110Fiber (grams) 3 3 2.2 3.2 3.5 7

0 200Initial Investment ($)

Div

iden

ds

($)

300 400100

2,000

1,500

1,000

500

x

y

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57 Which expression is equivalent to (8de5)(3d2e�3)?A 5d2e�15 B 24deC �11d2e�15 D 24d3e2

58 A quadrilateral has vertices P(1, 7), R(5, 3), U(1, �1), W(�3, 3). Whichkind of quadrilateral is PRUW?A parallelogram B rhombusC trapezoid D square

59 If square RSTV is constructed with side length equal to the length of the diagonal in square ABCD, what will be the ratio of the area of RSTV to the area of ABCD?

A 2:1 B �2�:2

C �2�:1 D 5:1

60 Jacob needs to rent a floor waxer to polish the floors in his beach houseat Yaupon Beach. The cost f(x) of renting a floor waxer for x hours canbe modeled by the function f(x) � 25 � 2.5x. Which is the independentquantity in this relationship?A number of floors Jacob will waxB number of hours Jacob will rent the floor waxerC total number of floors in the beach houseD fixed cost of renting the waxer

61 Six grapefruit are displayed as shown in the produce section of a grocery store in Greensboro.How many oranges could be similarly displayed in a triangle with 25 rows?A 278 orangesB 301 orangesC 325 orangesD 351 oranges

62 It takes 150 square feet of wood flooring to cover a 13 by 11-foot room,counting waste. At this rate, how much flooring, to the nearest foot,would it take to cover a 15 by 20-foot room?A 315 square feet B 318 square feetC 307 square feet D 286 square feet

xO

y

A(0, 7)

B(4, 10)

C(7, 6)

D(3, 3)

4 8

8

4

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63 Right triangle RST has vertices R(�2, �1) and S(0, 1). If the measure of

�R is 90 degrees, which is the equation of RT��?A y � �5x � 2 B y � �x � 3C y � �x � 1 D y � 5x � 3

64 If � � and x � y � z, which is the value of z?

A �12 B �11 C �4 D �3

65 How many times as great is the volume of the shaded box as the volumeof the unshaded box?

A 6 B 8 C 9 D 24

66 A new hotel design includes a glass-enclosed cylindrical elevator. A scalemodel of the elevator is 1 foot high. The actual elevator will be 100 feettall and 10 feet in diameter. What is the approximate area of a base ofthe model elevator? Round your answer to the nearest tenth inch.A 1.1 square inches B 4.5 square inchesC 7.5 square inches D 113.1 square inches

67 The matrix shows the number and the class level of students who signedup for elective courses at a high school. Which best describes any trendsin the data as students rise from freshmen to seniors?

A All electives show about the same rate of increase in enrollment.B Enrollment in interior design increases at a faster rate than

broadcasting or electronics.C Enrollment in electronics increases at a faster rate than broadcasting

or interior design.D Broadcasting shows the least change in enrollment.

Courses Freshman Sophomore Junior SeniorBroadcasting 18 22 25 27Interior design 25 24 26 29Electronics 15 19 23 28

x � 1

x � 2x

2x � 2

3x � 6

4x

� 6�10

xy

34

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68 Which are the coordinates of the center of a circle whose diameter hasendpoints with coordinates (�4, �5) and (5, 7)?

A �1, �12

�� B ��12

�, 1�C ��4�

12

�, �6� D ��6, �4�12

��

69 North Carolina has 78,000 miles of paved road. Which equation can beused to convert the number of miles x to the number of kilometers y?One mile is equal to approximately 0.6214 kilometers.

A y � �1.6

x09� B y � 1.609x

C y � 0.622x D y � �0.6

x22�

70 The matrix shows the mean test scores for each of Mr. Gregory’s fourgeometry classes. Which class shows the greatest overall improvement inthe mean test score?

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

71 If the trend in the matrix in Question 70 continues, which best predictsthe mean test score for class 3 on test 4?A 83.3 B 84.8C 85.1 D 85.4

72 H�J� of parallelogram HJKL passes through (�1, 4) and (2, 1). If K�L� passes through (1, �3), which is the equation of the line which includes K�L�?A y � �x � 2 B y � �x � 3C y � x � 2 D y � x � 3

73 Which is the y-intercept of the line that has slope �1 and passes through(5, �3)?A �8 B �2C 2 D 8

Average Test ScoresTest Class 1 Class 2 Class 3 Class 4

1 78.4 72.0 82.4 82.1 2 79.8 75.6 84.1 83.1 3 84.6 82.5 85.0 84.5

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74 The formula � � �9.461

d� 1012� calculates how many light years � a star is

from Earth, given the star’s distance d in kilometers from earth. A star is2.649 � 1013 kilometers from Earth. How many light years is it fromEarth? Round your answer to the nearest tenth of a light year.A 0.3 light yearsB 2.8 light yearsC 3.6 light yearsD 29.0 light years


The table below shows the number of horses boarded last year at a stable in Apex.

75 Which matrix shows the total number of horses boarded at the stable?

A B

C D

76 The owners want to know how many more horses are partial boardedthan full boarded. Which is the difference?

A B

C D28 �2 1075 �15 3

28 75�2 15 10 3

6 �136 �114 �11

6 � 6 613 �11 11

90 4138 2572 59

90 38 6241 25 59

56 34 5875 29 73

56 7534 2958 73

Full Board Regular Special Partial Board Regular Special Needs Needs Needs Needs

Short Term 42 14 Short Term 48 27Long Term 16 18 Long Term 22 7Overnight 34 24 Overnight 38 35

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77 Joaquin owns a small publishing company. The matrix shows his expensesfor the past two years in thousands of dollars. Which category ofexpenses shows the greatest percent increase from 2002 to 2003?

Categories: Salaries (S), Supplies (Sp), Development (D), Postage (P), Other (O)

A development B salariesC postage D supplies

78 The characteristics of an inherited trait are displayed in the matrix. BothR parents have a recessive gene for the trait, both D parents have adominant gene for the trait, and in a pair of H parents, only one parenthas the dominant gene for the trait. Which percent of the offspring willbe dominant for the trait if the parents are both dominant for it?

A 0% B 25%C 50% D 75%

79 Which statement is true for real numbers a, b, m, and n, b 0?

A ��ab

��m� am � bm B ��

ab

��m� �

ab

m

m�

C ��ab

��m� abm D ��

ab

��m� �

ba

m

m�

80 The linear regression model for a set of data compares the number of highdefinition television screens a company manufactures daily to its profit.Which correlation coefficient would suggest that the company’s profitsdecrease linearly as it manufactures more than 50 screens per day?A 0.93 B 0C �0.88 D �0.4

OffpringParents R H D

R 0.75 0.25 0.00 H 0.25 0.50 0.25 D 0.00 0.75 0.25

S Sp D P O2002 56 32 45 9 14 2003 72 28 58 12 16


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