Glencoe Algebra, chapter 2

Chapter 2Resource Masters

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CONSUMABLE WORKBOOKS Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.

Study Guide Workbook 0-07-869610-0Skills Practice Workbook 0-07-869311-XPractice Workbook 0-07-869609-7Spanish Study Guide and Assessment 0-07-869611-9

ANSWERS FOR WORKBOOKS The answers for Chapter 2 of these workbookscan be found in the back of this Chapter Resource Masters booklet.

StudentWorksTM This CD-ROM includes the entire Student Edition along with theEnglish workbooks listed above.

TeacherWorksTM All of the materials found in this booklet are included for viewingand printing in the Algebra: Concepts and Applications TeacherWorksCD-ROM.

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ISBN: 0-07-869254-7 Algebra: Concepts and Applications Chapter 2 Resource Masters

1 2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04

© Glencoe/McGraw-Hill iii Algebra: Concepts and Applications

Vocabulary Builder . . . . . . . . . . . . . . . . . vii-viii

Lesson 2-1Study Guide and Intervention . . . . . . . . . . . . . . . . 51Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Reading to Learn Mathematics . . . . . . . . . . . . . . . 54Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55




Lesson 2-5Study Guide and Intervention . . . . . . . . . . . . . . . . 71Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Reading to Learn Mathematics . . . . . . . . . . . . . . . 74Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Lesson 2-6Study Guide and Intervention . . . . . . . . . . . . . . . . 76Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Reading to Learn Mathematics . . . . . . . . . . . . . . . 79Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Chapter 2 AssessmentChapter 2 Test, Form 1A. . . . . . . . . . . . . . . . . . 81-82Chapter 2 Test, Form 1B . . . . . . . . . . . . . . . . . . 83-84Chapter 2 Test, Form 2A. . . . . . . . . . . . . . . . . . 85-86Chapter 2 Test, Form 2B . . . . . . . . . . . . . . . . . . 87-88Chapter 2 Extended Response Assessment . . . . . . 89Chapter 2 Mid-Chapter Test . . . . . . . . . . . . . . . . . . 90Chapter 2 Quizzes A & B. . . . . . . . . . . . . . . . . . . . 91Chapter 2 Cumulative Review . . . . . . . . . . . . . . . . 92Chapter 2 Standardized Test Practice . . . . . . . . 93-94

Standardized Test PracticeStudent Recording Sheet . . . . . . . . . . . . . . . . . . A1

ANSWERS . . . . . . . . . . . . . . . . . . . . . . . . . . A2-A23

Contents

© Glencoe/McGraw-Hill iv Algebra: Concepts and Applications

A Teacher’s Guide to Using theChapter 2 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file theresources you use most often. The Chapter 2 Resource Masters include the corematerials needed for Chapter 2. These materials include worksheets, extensions,and assessment options. The answers for these pages appear at the back of thisbooklet.

All of the materials found in this booklet are included for viewing and printing inthe Algebra: Concepts and Applications TeacherWorks CD-ROM.

Vocabulary Builder Pages vii-viii include a student study tool that presents the key vocabulary terms from the chapter. Students areto record definitions and/or examples for eachterm. You may suggest that students highlight orstar the terms with which they are not familiar.

When to Use Give these pages to studentsbefore beginning Lesson 2-1. Encourage them toadd these pages to their Algebra: Concepts andApplications Interactive Study Notebook.Remind them to add definitions and examples asthey complete each lesson.

Study Guide There is one Study Guide master for each lesson.

When to Use Use these masters as reteachingactivities for students who need additional reinforcement. These pages can also be used inconjunction with the Student Edition as aninstructional tool for those students who havebeen absent.

Skills Practice There is one master for eachlesson. These provide computational practice at a basic level.

When to Use These worksheets can be usedwith students who have weaker mathematicsbackgrounds or need additional reinforcement.

Practice There is one master for each lesson.These problems more closely follow the structure of the Practice section of the StudentEdition exercises. These exercises are of averagedifficulty.

When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson.

Reading to Learn Mathematics Onemaster is included for each lesson. The first section of each master presents key terms fromthe lesson. The second section contains questions that ask students to interpret the context of and relationships among terms in thelesson. Finally, students are asked to summarizewhat they have learned using various representation techniques.

When to Use This master can be used as astudy tool when presenting the lesson or as aninformal reading assessment after presenting thelesson. It is also a helpful tool for ELL (EnglishLanguage Learners) students.

Enrichment There is one master for each lesson. These activities may extend the conceptsin the lesson, offer a historical or multiculturallook at the concepts, or widen students’perspectives on the mathematics they are learning. These are not written exclusively forhonors students, but are accessible for use withall levels of students.

When to Use These may be used as extracredit, short term projects, or as activities fordays when class periods are shortened.

© Glencoe/McGraw-Hill v Algebra: Concepts and Applications

Assessment OptionsThe assessment section of the Chapter 2Resources Masters offers a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter AssessmentsChapter Tests• Forms 1A and 1B contain multiple-choice

questions and are intended for use with average-level and basic-level students,respectively. These tests are similar in format to offer comparable testing situations.

• Forms 2A and 2B are composed of free-response questions aimed at the average-level and basic-level student, respectively.These tests are similar in format to offercomparable testing situations.

All of the above tests include a challengingBonus question.

• The Extended Response Assessmentincludes performance assessment tasks thatare suitable for all students. A scoring rubricis included for evaluation guidelines. Sample answers are provided for assessment.

Intermediate Assessment• A Mid-Chapter Test provides an option to

assess the first half of the chapter. It is composed of free-response questions.

• Two free-response quizzes are included tooffer assessment at appropriate intervals inthe chapter.

Continuing Assessment• The Cumulative Review provides students

an opportunity to reinforce and retain skillsas they proceed through their study of algebra. It can also be used as a test. Themaster includes free-response questions.

• The Standardized Test Practice offers continuing review of algebra concepts inmultiple choice format.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questions thatappear in the Student Edition on page 89.This improves students’ familiarity with theanswer formats they may encounter in testtaking.

• The answers for the lesson-by-lesson masters are provided as reduced pages withanswers appearing in red.

• Full-size answer keys are provided for theassessment options in this booklet.

© Glencoe/McGraw-Hill vi Algebra: Concepts and Applications

Chapter 2 Leveled Worksheets

Glencoe’s leveled worksheets are helpful for meeting the needs of everystudent in a variety of ways. These worksheets, many of which are foundin the FAST FILE Chapter Resource Masters, are shown in the chartbelow.

• The Prerequisite Skills Workbook provides extra practice on the basicskills students need for success in algebra.

• Study Guide and Intervention masters provide worked-out examplesas well as practice problems.

• Reading to Learn Mathematics masters help students improve readingskills by examining lesson concepts more closely.

• Noteables™: Interactive Study Notebook with Foldables™ helps students improve note-taking and study skills.

• Skills Practice masters allow students who are progressing at a slowerpace to practice concepts using easier problems. Practice masters provide average-level problems for students who are moving at a regular pace.

• Each chapter’s Vocabulary Builder master provides students the opportunity to write out key concepts and definitions in their own words.

• Enrichment masters offer students the opportunity to extend theirlearning.

Nine Different Options to Meet the Needs ofEvery Student in a Variety of Ways

primarily skillsprimarily conceptsprimarily applications

BASIC AVERAGE ADVANCED

1

2

Prerequisite Skills Workbook

Study Guide and Intervention

3 Reading to Learn Mathematics

4 NoteablesTM: Interactive Study Notebook with FoldablesTM

5 Skills Practice

6 Vocabulary Builder

7 Parent and Student Study Guide (online)

8 Practice

9 Enrichment

Reading to Learn MathematicsVocabulary Builder

This is an alphabetical list of the key vocabulary terms you will learn in Chapter 2.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term.

© Glencoe/McGraw-Hill vii Algebra: Concepts and Applications

Vocabulary Term Foundon Page Definition/Description/Example

absolute value

additive inverseA•duh•tiv

coordinateco•OR•duh•net

coordinate plane

coordinate system

dimensions

element

graph

integersIN•tah•jerz

matrixMAY•triks

natural numbers

negative numbers

(continued on the next page)

22NAME DATE PERIOD

© Glencoe/McGraw-Hill viii Algebra: Concepts and Applications

NAME DATE PERIOD

22 Reading to Learn MathematicsVocabulary Builder (continued)

Vocabulary Term Foundon Page Definition/Description/Example

number line

opposites

ordered array

ordered pair

originOR•a•jin

quadrantsKWA•druntz

scalar multiplicationSKAY•ler

Venn diagram

x-axis

x-coordinate

y-axis

y-coordinate

zero pair

© Glencoe/McGraw-Hill 51 Algebra: Concepts and Applications

NAME DATE PERIOD

Study Guide2–12–1

Graphing Integers on a Number Line

The numbers displayed on the number line below belong to the setof integers. The arrows at both ends of the number line indicatethat the numbers continue indefinitely in both directions. Noticethat the integers are equally spaced.

Use dots to graph numbers on a number line. You can label the dotswith capital letters.

The coordinate of B is �3 and the coordinate of D is 0.

Because 3 is to the right of �3 on the number line, 3 � �3. Andbecause �5 is to the left of 1, �5 � 1. Because 3 and �3 are thesame distance from 0, they have the same absolute value, 3. Usetwo vertical lines to represent absolute value.

|3| � 3 The absolute value of 3 is 3.

|�3| � 3 The absolute value of �3 is 3.

Example: Evaluate |�12| � |10|.|�12| � |10| � 12 � 10 |�12| � 12 and |10| � 10

� 22

Name the coordinate of each point.

1. B �4 2. D �3 3. G 5

Graph each set of numbers on a number line.

4. {�3, 2, 4} 5. {�1, 0, 3}

Write � or � in each blank to make a true sentence.

6. �7 5 7. �3 �8 8. |�1| 0

Evaluate each expression.

9. |9| 9 10. |�15| 15 11. |�20| � |10| 10

��

4–2 –1 0 1 2 34–3 –2 –1 0 1 2 3–4

4–3 –2 –1 0 1 2 3 5 6–5 –4

B D FE G

4–3 –2 –1 0

3 units 3 units

1 2 3–4

4–3 –2 –1 0 1 2 3 5–5 –4

A B C D E F

4–3 –2 –1 0

integers

negative integers positive integers

1 2 3 5–5 –4


Graphing Integers on a Number LineName the coordinate of each point.

1. S �3 2. U 0 3. T �2

4. R �5 5. W 4 6. V 1


7. {�2, 0, 3} 8. {�5, �3, �1}

9. {2, 4, �4} 10. {�1, 3, 5}

11. {�4, �2, 2} 12. {�3, �1, 1, 3}


13. 2 7 14. 4 �2 15. �3 0

16. �5 �2 17. �1 2 18. �5 �8

19. �4 3 20. 0 �9 21. �6 �3


22. |4| 4 23. |�5| 5

24. |�8| 8 25. |10| 10

26. |3| � |�2| 5 27. |�7| � |�12| 19

��

� ��

��

�5 �4 �3 �2 �1 0 1 2 3 4 5

R S T U V W

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Skills Practice2–12–1


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Practice2–12–1

Graphing Integers on a Number LineName the coordinate of each point.

1. A �4 2. B 3 3. C �1

4. D 5 5. E �2 6. F 1


7. {�5, 0, 2} 8. {4, �1, �2}

9. {3, �4, �3} 10. {�2, 5, 1}

11. {2, �5, 0} 12. {�4, 3, �2, 4}


13. 7 9 14. 0 �1 15. �2 2

16. 6 �3 17. �4 �5 18. �7 �3

19. �8 0 20. �11 2 21. �5 �6


22. |�4| 4 23. |6| 6

24. |�3| � |1| 4 25. |9| � |�8| 1

26. |�7| � |�2| 5 27. |�8| � |11| 19

��

��

��

4–3 –2 –1 0 1 2 3 5–5 –44–3 –2 –1 0 1 2 3 5–5 –4

4–3 –2 –1 0 1 2 3 5–5 –44–3 –2 –1 0 1 2 3 5–5 –4

4–3 –2 –1 0 1 2 3 5–5 –44–3 –2 –1 0 1 2 3 5–5 –4

4–3 –2 –1 0 1 2 3 5–5 –4

A E C F B D


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Reading to Learn MathematicsGraphing Integers on a Number Line

2–12–1

Key Termsabsolute value the distance a number is from 0 on a

number linecoordinate (co OR di net) the number that corresponds to a

point on a number linegraph to plot points named by numbers on a number linenumber line a line with equal distances marked off to

represent numbers

Reading the Lesson1. Refer to the number line.

a. What do the arrowheads on each end of the number line mean?The line and the set of numbers continueinfinitely in each direction.

b. What is the absolute value of �3? What is the absolute value of 3? Explain.3, 3; �3 and 3 are both 3 units away from zero on the numberline.

2. Refer to the Venn diagram shown at the right. Write true or false for each of the following statements. a. All whole numbers are integers. true

b. All natural numbers are integers. true

c. All whole numbers are natural numbers. false

d. All natural numbers are whole numbers. true

e. All whole numbers are positive numbers. false

f. All integers are natural numbers. false

g. Whole numbers are a subset of natural numbers. false

h. Natural numbers are a subset of integers. true

Natural Numbers

WholeNumbers

Integers

�5 543210�4 �1�2�3

Helping You Remember3. One way to remember a mathematical concept is to connect it to something you have

seen or heard in everyday life. Describe a situation that illustrates the concept ofabsolute value.

Sample answer: On a football field, the distance from each goal lineto the 50-yard line is 50 yards.


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Enrichment2–12–1

Venn DiagramsA type of drawing called a Venn diagram can be useful in explaining conditionalstatements. A Venn diagram uses circles to represent sets of objects.

Consider the statement “All rabbits have long ears.” To make a Venn diagram forthis statement, a large circle is drawn to represent all animals with long ears. Thena smaller circle is drawn inside the first to represent all rabbits. The Venn diagramshows that every rabbit is included in the group of long-eared animals.

The set of rabbits is called a subset of the set of long-eared animals.

The Venn diagram can also explain how to write the statement, “All rabbits havelong ears,” in if-then form. Every rabbit is in the group of long-eared animals, so ifan animal is a rabbit, then it has long ears.

For each statement, draw a Venn diagram. The write the sentence in if-then form.

1. Every dog has long hair. 2. All rational numbers are real.

If an animal is a dog, then it If a number is rational, thenhas long hair. it is real.

3. People who live in Iowa like corn. 4. Staff members are allowed in the faculty lounge.

If a person lives in Iowa,then the person likes corn. If a person is a staff member,

then the person is allowed inthe faculty lounge.

animals withlong ears

rabbits


NAME DATE PERIOD


The Coordinate Plane

The two intersecting lines and the grid at the right form a coordinate system. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis. The x- and y-axes divide the coordinate plane into fourquadrants. Point S in Quadrant I is the graph of the ordered pair (3, 2). The x-coordinate of point S is 3, and the y-coordinate of point S is 2.

The point at which the axes meet has coordinates (0, 0) and is called the origin.

Example 1: What is the ordered pair for point J? In what quadrant is point J located?

You move 4 units to the left of the origin and then 1 unit up to get to J. So the ordered pair for J is (�4, 1). Point J is located in Quadrant II.

Example 2: Graph M(�2, � 4) on the coordinate plane. Start at the origin. Move left on the x-axis to �2 and then down 4 units. Draw a dot here and label it M.

Write the ordered pair that names each point.

1. P (1, 3) 2. Q (�4, �3)

3. R (0, 2) 4. T (�4, 0)

Graph each point on the coordinate plane. Name the quadrant, if any, in which each point is located.

5. A(5, �1) IV 6. B(�3, 0) none

7. C(�3, 1) II 8. D(0, 1) none

9. E(3, 3) I 10. F(�1, �2) III

O x

y

O x

y

1 2 3 4

4321

–1–2–3–4

–1–2–3–4T

R

P

Q

O x

y

1

Quadrant I

Quadrant IV

Quadrant II

Quadrant III

2 3 4

4321

–1–2–3–4

–1–2–3–4

J

M

O x

y

1

Quadrant I

Quadrant IV

Quadrant II

Quadrant III

2 3 4

4321

–1–2–3–4

–1–2–3–4

S

The Coordinate PlaneWrite the ordered pair that names each point.

1. L (�4, 0) 2. M (�3, �1)

3. N (�1, �3) 4. P (0, 0)

5. Q (�2, 4) 6. R (2, 1)

7. S (2, �1) 8. T (5, 0)

9. U (0, �2) 10. V (0, 3)

Graph each point on the coordinate plane.

11. A(�2, 4) 12. B(0, �4)

13. C(5, �3) 14. D(�2, �1)

15. E(1, 4) 16. F(4, 0)

17. G(�4, �1) 18. H(3, 3)

19. I(�4, 3) 20. J(�5, 0)

Name the quadrant in which each point is located.

21. (�2, �2) III 22. (3, 4) I

23. (�4, 3) II 24. (4, �3) IV

25. (0, �2) none 26. (�1, �1) III

27. (4, �1) IV 28. (�3, 5) II

29. (�3, 0) none 30. (8, �4) IV

y

x�4 �2 2 4

�4

�2

2

4

y

x�4 �2 2 4

�4

�2

2

4

L

M

N

P

Q

R

S

T

U

V


NAME DATE PERIOD



NAME DATE PERIOD

Practice2–22–2

The Coordinate PlaneWrite the ordered pair that names each point.

1. A (�3, 4) 2. B (5, 2)

3. C (�4, �3) 4. D (2, �4)

5. E (�1, 1) 6. F (1, 0)

7. G (0, �2) 8. H (�2, 5)

9. J (�2, �4) 10. K (5, �1)

Graph each point on the coordinate plane.

11. K(0, �3) 12. L(�2, 3)

13. M(4, 4) 14. N(�3, 0)

15. P(�4, �1) 16. Q(1, �2)

17. R(�5, 5) 18. S(3, 2)

19. T(2, 1) 20. W(�1, �4)

Name the quadrant in which each point is located.

21. (1, 9) I 22. (�2, �7) III

23. (0, �1) none 24. (�4, 6) II

25. (5, �3) IV 26. (�3, 0) none

27. (�1, �1) III 28. (6, �5) IV

29. (�8, 4) II 30. (�9, �2) III

O x

y

O x

yA

H

E

F

B

K

DJ

C G


NAME DATE PERIOD

Reading to Learn MathematicsThe Coordinate plane

2–22–2

Key Termscoordinate plane the plane containing the x- and y-axescoordinate system the grid formed by the intersection of two

perpendicular number lines that meet at their zero pointsordered pair a pair of numbers used to locate any point on a

coordinate planequadrant one of the four regions into which the x- and y-axes

separate the coordinate planex-axis the horizontal number line on a coordinate planey-axis the vertical number line on a coordinate planex-coordinate the first number in a coordinate pairy-coordinate the second number in a coordinate pair

Reading the Lesson1. Identify each part of the coordinate system.

2. Use the ordered pair (�2, 3). a. Explain how to identify the x- and y-coordinates.

The x-coordinate is the first number; the y-coordinate is thesecond number.

b. Name the x-and y-coordinates. The x-coordinate is �2 and the y-coordinate 3.

c. Describe the steps you would use to locate the point at (�2, 3) on the coordinateplane.Start at the origin, move two units to the left and then move upthree units.

3. What does the term quadrant mean? Sample answer: It is one of four regions in the coordinate plane.

x

y

O

Helping You Remember4. Describe a method to remember how to write an ordered pair.

Sample answer: Since x comes before y in the alphabet, the x-coordinate is written first in an ordered pair.

y axis

x axisorigin


NAME DATE PERIOD


Points and Lines on a MatrixA matrix is a rectangular array of rows and columns. Pointsand lines on a matrix are not defined in the same way as inEuclidean geometry. A point on a matrix is a dot, which can besmall or large. A line on a matrix is a path of dots that “line up.”Between two points on a line there may or may not be otherpoints. Three examples of lines are shown at the upper right.The broad line can be thought of as a single line or as two nar-row lines side by side.

A dot-matrix printer for a computer uses dots to form characters.The dots are often called pixels. The matrix at the right showshow a dot-matrix printer might print the letter P.

Sample answers are given.Draw points on each matrix to create the given figures.

1. Draw two intersecting lines that have 2. Draw two lines that cross but have four points in common. no common points.

3. Make the number 0 (zero) so that it 4. Make the capital letter O so that itextends to the top and bottom sides extends to each side of the matrix.of the matrix.

5. Using separate grid paper, make dot designs for severalother letters. Which were the easiest and which were themost difficult? See students’ work.


NAME DATE PERIOD


Adding Integers

You can use a number line to add integers. Start at 0. Then move to the right for positive integers and move to the left for negative integers.

Both integers are positive. Both integers are negative. First move 2 units right from 0. First move 2 units left from 0. Then move 1 more unit right. Then move 1 more unit left.

When you add one positive integer and one negative integer on the number line, you change directions, which results in one move being subtracted from the other move.

Move 2 units left, then 1 unit right. Move 2 units right, then 1 unit left.

Use the following rules to add two integers and to simplify expressions.

Rule Examples

To add integers with the same sign, add 7 � 4 � 11their absolute values. Give the result the �8 � (�2) � �10same sign as the integers. �5x � (�3x) � �8x

To add integers with different signs, 9 � (�6) � 3subtract their absolute values. Give the 1 � (�5) � �4result the same sign as the integer with �2x � 9x � 7xthe greater absolute value. 3y � (�4y) � �y

Find each sum.

1. 5 � 8 13 2. �8 � (�9) �17 3. 12 � (�8) 4 4. �16 � 5 �11

5. 5 � (�8) � (�5) �8 6. �8 � (�8) � 20 4 7. 12 � 5 � (�1) 16

Simplify each expression.

8. 3x � (�6x) �3x 9. �5y � (�7y) �12y 10. 2m � (�4m) � (�2m) �4m

4�1 0 12 � (�1) � 1

2 3�2

�1

�2

�3 �1 0 1

�2

�2 � 1 � �1

�1

2�4 �2

�3 �1 0 1

�2

�2 � (�1) � �3

�1

2�4 �24�1 0 1

�2

2 � 1 � 3

�1

2 3 5


Adding IntegersFind each sum.

1. 2 � 7 2. �3 � (�2) 3. �4 � 1

9 �5 �3

4. 3 � (�9) 5. �2 � 12 6. �1 � (�6)

�6 10 �7

7. 10 � (�8) 8. �9 � 4 9. 3 � (�3)

2 �5 0

10. �5 � (�5) 11. 8 � (�9) 12. �7 � 4

�10 �1 �3

13. �2 � 2 14. �12 � 10 15. �8 � (�5)

0 �2 �13

16. �14 � 8 17. 15 � (�8) 18. 3 � (�11)

�6 7 �8

19. �9 � (�7) 20. 6 � (�9) 21. �14 � 15

�16 �3 1

22. �10 � 6 � (�4) 23. 13 � (�14) � 1 24. �4 � (�8) � 5

�8 0 �7


25. �4c � 8c 26. �5a � (�9a) 27. �8d � 3d

4c �14a �5d

28. 7x � 3x 29. 6y � (�3y) 30. �7t � 4t

10x 3y �3t

31. �12s � (�4s) 32. 5t � (�13t) 33. 15h � (�4h)

�16s �8t 11h

34. 7b � 6b � (�8b) 35. �9w � 4w � (�5w) 36. 12t � 3t � (�6t)

5b �10w 9t

NAME DATE PERIOD



NAME DATE PERIOD

Practice2–32–3

Adding IntegersFind each sum.

1. 8 � 4 2. �3 � 5 3. 9 � (�2)

12 2 7

4. �5 � 11 5. �7 � (�4) 6. 12 � (�4)

6 �11 8

7. �9 � 10 8. �4 � 4 9. 2 � (�8)

1 0 �6

10. 17 � (�4) 11. �13 � 3 12. 6 � (�7)

13 �10 �1

13. �8 � (�9) 14. �2 � 11 15. �9 � (�2)

�17 9 �11

16. �1 � 3 17. 6 � (�5) 18. �11 � 7

2 1 �4

19. �8 � (�8) 20. �6 � 3 21. 2 � (�2)

�16 �3 0

22. 7 � (�5) � 2 23. �4 � 8 � (�3) 24. �5 � (�5) � 5

4 1 �5


25. 5a � (�3a) 26. �7y � 2y 27. �9m � (�4m)

2a �5y �13m

28. �2z � (�4z) 29. 8x � (�4x) 30. �10p � 5p

�6z 4x �5p

31. 5b � (�2b) 32. �4s � 7s 33. 2n � (�4n)

3b 3s �2n

34. 5a � (�6a) � 4a 35. �6x � 3x � (�5x) 36. 7z � 2z � (�3z)

3a �8x 6z


NAME DATE PERIOD

Reading to Learn MathematicsAdding Integers

2–32–3

Key Termsadditive inverses two numbers are additive inverses if their

sum is 0opposite additive inversezero pair the result of positive algebra tiles paired with negative

algebra tiles

Reading the Lesson1. Explain how to add integers with the same sign.

Add their absolute values. The result has the same sign as theintegers.

2. Explain how to add integers with opposite signs.Find the difference of their absolute values. The result has thesame sign as the integer with the greater absolute value.

3. If two numbers are additive inverses, what must be true about their absolute values?The absolute values must be equal.

4. Use the number line to find each sum.

a. � 3 � 5 2

b. 4 � (�6) �2

c. How do the arrows show which number has the greater absolute value?The longer arrow represents the number with the greaterabsolute value.

d. Explain how the arrows can help you determine the sign of the answer.The direction of the longer arrow determines the sign of theanswer.

Write an equation for each situation.5. a five-yard penalty and a 13-yard pass �5 � 13 � 86. gained 11 points and lost 18 points 11 � (�18) � �77. a deposit of $25 and a withdrawal of $15 25 � (�15) � 10

�5�4�3�2�1 0 1 4 532

�4

�6

�5�4�3�2�1 0 1 4 532

�3

�5

Helping You Remember8. Explain how you can remember the meaning of “zero pair.”

Sample answer: Since the sum of a number and its opposite iszero, when a positive tile is paired with a negative tile, the sum iszero.


NAME DATE PERIOD


Integer Magic

A magic triangle is a triangular arrangement of numbers in which the sum of the numbers along each side is the samenumber. For example, in the magic triangle shown at theright, the sum of the numbers along each side is 0.

In each triangle, each of the integers from �4 to 4 appearsexactly once. Complete the triangle so that the sum of theintegers along each side is �3.

1. 2.

3. 4.

In these magic stars, the sum of the integers along each line ofthe star is �2. Complete each magic star using the integers from�6 to 5 exactly once.

5. 6.

1

0

–2

2

54–6

4

–4

2

–2

–3

–5

–2

–3

–4

0

4

–1

3

–3 –2

4

–1

–4

–3

–2

4

1

3 –2 2

0

–3

41

–4 –1

Sample answersare given.


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Subtracting Integers

If the sum of two integers is 0, the numbers are opposites oradditive inverses.

Example 1: a. �3 is the opposite of 3 because �3 � 3 � 0

b. 17 is the opposite of �17 because 17 � (�17) � 0

Use this rule to subtract integers.

Example 2: Find each difference.

a. 5 � 25 � 2 � 5 � (�2) Subtracting 2 is the same as adding its

� 3 opposite, �2.

b. �7 � (�1)�7 � (�1) � �7 � 1 Subtracting �1 is the same as adding its

� �6 opposite, 1.

Example 3: Evaluate c � d � e if c � �1, d � 7, and e � �3.

c � d � e � �1 � 7 � (�3) Replace c with �1, d with 7, and e with �3. � �1 � 7 � 3 Write 7 � (�3) as 7 � 3. � 6 � 3 �1 � 7 � 6 � 9 6 � 3 � 9

Find each difference.

1. 5 � 8 �3 2. �8 � (�9) 1 3. �2 � 8 �10 4. �4 � (�5) 1

5. 16 � 8 8 6. 10 � (�10) 20 7. 0 � 10 �10 8. 0 � (�18) 18


9. 3x � 9x �6x 10. �4y � (�6y) 2y 11. 2m � 8m � (�2m) �4m

Evaluate each expression if x � �1, y � 2, and z � �4.

12. x � y �3 13. y � z � 5 1 14. z � y � (�2) �4

15. 9 � x 10 16. x � z � z 7 17. 0 � y �2

To subtract an integer, add its oppositeor additive inverse.


NAME DATE PERIOD


Subtracting IntegersFind each difference.

1. 8 � 2 2. 12 � 4 3. �7 � (�2)

6 8 �5

4. �9 � 4 5. 4 � 12 6. �4 � (�10)

�13 �8 6

7. �6 � 1 8. �5 � 8 9. �5 � (�5)

�7 �13 0

10. �8 � 8 11. �11 � 7 12. 8 � (�7)

�16 �18 15

13. 9 � 14 14. �3 � (�15) 15. �14 � 6

�5 12 �20

16. �3 � 9 17. �7 � 7 18. 13 � 14

�11 �14 �1

Evaluate each expression if a � 2, b � �3, c � �1, and d � 1.

19. a � b 20. b � c 21. a � c

5 �2 3

22. c � d 23. a � b � c 24. b � d � c

�2 0 �3

25. d � b � a 26. c � a � b 27. a � d � b

�4 0 �2


NAME DATE PERIOD

Practice2–42–4

Subtracting IntegersFind each difference.

1. 9 � 3 2. �1 � 2 3. 4 � (�5)

6 �3 9

4. 6 � (�1) 5. �7 � (�4) 6. 8 � 10

7 �3 �2

7. �2 � 5 8. �6 � (�7) 9. 2 � 8

�7 1 �6

10. �10 � (�2) 11. �4 � 6 12. 5 � 3

�8 �10 2

13. �8 � (�4) 14. 7 � 9 15. �9 � (�11)

�4 �2 2

16. �3 � 4 17. 6 � (�5) 18. 6 � 5

�7 11 1

Evaluate each expression if a � �1, b � 5, c � �2, and d � �4.

19. b � c 20. a � b 21. c � d

7 �6 2

22. a � c � d 23. a � b � c 24. a � c � d

1 �8 �3

25. b � c � d 26. b � c � d 27. a � b � c

3 11 �4


NAME DATE PERIOD

Reading to Learn MathematicsSubtracting Integers

2–42–4

Key Termsadditive inverses two numbers are additive inverses if their sum

is 0opposite additive inversezero pair the result of positive algebra tiles paired with negative

algebra tiles

Reading the Lesson1. Write each subtraction problem as an addition problem.

a. 12 � 4 12 � (�4)

b. �15 � 7 �15 � (�7)

c. 0 � 11 0 � (�11)

d. �20 � 34 �20 � (�34)

e. �15 � (�4)�15 � 4

f. 16 � (�18) 16 � 18

2. Describe how to find each difference. Then find each difference.

a. 8 � 11 Add the opposite of 11 to 8; �3

b. 5 � (�8) Add the opposite of �8 to 5; 13

c. 17 � 14 Add the opposite of 14 to 17; 3

d. �8 � 19 Add the opposite of 19 to �8; �27

3. Explain how zero pairs are used to subtract with algebra tiles. Zero pairs are not needed to subtract negative tiles. If a positive tileis to be subtracted from negative tiles, first add a zero pair. Thenyou can subtract one positive tile.

Helping You Remember4. Explain why knowing the rules for adding integers can help you to subtract integers.

Sample answer: Since subtraction is really adding the number’sadditive inverse, the rules for addition also apply to subtraction.


NAME DATE PERIOD


ClosureA binary operation matches two numbers in a set to just onenumber. Addition is a binary operation on the set of wholenumbers. It matches two numbers such as 4 and 5 to a singlenumber, their sum.

If the result of a binary operation is always a member of theoriginal set, the set is said to be closed under the operation. For example, the set of whole numbers is not closed undersubtraction because 3 � 6 is not a whole number.

Is each operation binary? Write yes or no.

Is each set closed under addition? Write yes or no. If youranswer is no, give an example.

Is the set of whole numbers closed under each operation?Write yes or no. If your answer is no, give an example.

13. multiplication: a � b yes

15. exponentation: ab yes

14. division: a � b no; 4 � 3 is not awhole number

16. squaring the sum: (a � b)2 yes

7. even numbers yes

9. multiples of 3 yes

11. prime numbers no; 3 � 5 � 8

8. odd numbers no; 3 � 7 � 10

10. multiples of 5 yes

12. nonprime numbersno; 22 � 9 � 31

1. the operation ←, where a ← b meansto choose the lesser number from aand b yes

3. the operation sq, where sq(a) meansto square the number a no

5. the operation ⇑ , where a ⇑ b meansto match a and b to any numbergreater than either number no

2. the operation ©, where a © b meansto cube the sum of a and b yes

4. the operation exp, where exp(a, b)means to find the value of ab yes

6. the operation ⇒ , where a ⇒ b meansto round the product of a and b up tothe nearest 10 yes


NAME DATE PERIOD


Multiplying Integers

Use these rules to multiply integers and to simplify expressions.

Example 1: Find each product.a. 7(12)

7(12) � 84 Both factors are positive, so the product is positive.

b. �5(�9)�5(�9) � 45 Both factors are negative, so the

product is positive.

c. �4(8)�4(8) � �32 The factors have different signs,

so the product is negative.

Example 2: Evaluate �3ab if a � 3 and b � �5.�3ab � �3(3)(�5) Replace a with 3 and b with �5.

� �9(�5) �3 � 3 � �9� 45 Both factors are negative.

Example 3: Simplify �12(4x).�12(4x) � (�12 � 4)(x) Associative Property

� �48x �12 � 4 � �48

Find each product.

1. 3(8) 24 2. (�7)(�9) 63 3. 12(�1) �12 4. �6(5) �30

5. 4(�1)(�5) 20 6. (�8)(�8)(�2) �128 7. 2(�5)(10) �100

Evaluate each expression if a � 3, b � �2, and c � �3.

8. 5c �15 9. 2ab �12 10. abc 18 11. 3b � c �3


12. 3(�6x) �18x 13. �5(�7y) 35y 14. (2p)(�4q) �8pq

The product of two positive integers is positive.The product of two negative integers is positive.The product of a positive integer and a negative integer is negative.


Multiplying IntegersFind each product.

1. 3(12) 2. �4(7) 3. �8(�8)

36 �28 64

4. 5(�9) 5. �2(�9) 6. �3(�10)

�45 18 30

7. 0(�5) 8. �13(�4) 9. 4(�11)

0 52 �44

10. �5(12) 11. 14(0) 12. �8(7)

�60 0 �56

13. �15(�4) 14. 9(�3) 15. �8(11)

60 �27 �88

16. (�2)(4)(�3) 17. (�4)(�5)(�1) 18. (3)(5)(�5)

24 �20 �75

Evaluate each expression if x � �2 and y � �4.

19. �3xy 20. �2xy 21. �5x

24 �16 10

22. �7y 23. 8xy 24. �6xy

28 64 �48


25. 3(2a) 26. �4(�3c) 27. �5(�8b)

6a 12c 40b

28. (5c)(�7d) 29. (�8m)(�2n) 30. (�9s)(7t)

�35cd 16mn �63st

NAME DATE PERIOD



NAME DATE PERIOD

Practice2–52–5

Multiplying IntegersFind each product.

1. 3(�7) 2. �2(8) 3. 4(5)

�21 �16 20

4. �7(�7) 5. �9(3) 6. 8(�6)

49 �27 �48

7. 6(2) 8. �5(�7) 9. 2(�8)

12 35 �16

10. �10(�2) 11. 9(�8) 12. 12(0)

20 �72 0

13. �4(�4)(2) 14. 7(�9)(�1) 15. �3(5)(2)

32 63 �30

16. 3(�4)(�2)(2) 17. 6(�1)(2)(1) 18. �5(�3)(�2)(�1)

48 �12 30

Evaluate each expression if a � �3 and b � �5.

19. �6b 20. 8a 21. 4ab

30 �24 60

22. �3ab 23. �9a 24. �2ab

�45 27 �30


25. 5(�5y) 26. �7(�3b) 27. �3(6n)

�25y 21b �18n

28. (6a)(�2b) 29. (�4m)(�9n) 30. (�8x)(7y)

�12ab 36mn �56xy


NAME DATE PERIOD

Reading to Learn MathematicsMultiplying Integers

2–52–5

Key Termsfactors the numbers being multipliedproduct the result when two or more factors are multiplied

together

Reading the Lesson1. Complete: If two numbers have different signs, the one number is positive and the other

number is .

2. Complete the table.

a.

b.

c.

d.

3. Explain what the term “additive inverse” means. Then give an example.

The product of any number and �1 is its additive inverse; � �

(�1) � .2 3

2 3

neg

Helping You Remember4. Describe how you know that the product of �3 and �5 is positive. Then describe how

you know that the product of 3 and �5 is negative.Sample answer: The signs are the same; the signs are different.

Multiplication Are the signs of the numbers Is the product positiveExample the same or different? or negative?

(�4)(9) different neg(�2)(�13) same pos5(�8) different neg6(3) same pos


NAME DATE PERIOD


The Binary Number System

Our standard number system in base ten has ten digits, 0 through 9. In base ten, the values of the places are powers of 10.

A system of numeration that is used in computer technology is the binary number system. In a binary number, the place value of each digit is two times the place value of the digit to its right. There are only two digits in the binary system: 0 and 1.

The binary number 10111 is written 10111two. You can use a place-value chart like the one at the right to find the standard number that is equivalent to this number.

10111two � 1 � 16 � 0 � 8 � 1 � 4 � 1 � 2 � 1 � 1� 16 � 0 � 4 � 2 � 1� 23

Write each binary number as a standard number.

1. 11two 3 2. 111two 7 3. 100two 4

4. 1001two 9 5. 11001two 25 6. 100101two 37

Write each standard number as a binary number.

7. 8 1000two 8. 10 1010two 9. 15 1111two

10. 17 10001two 11. 28 11100two 12. 34 100010two

Write each answer as a binary number.

13. 1two � 10two 11two 14. 101two � 10two 11two

15. 10two � 11two 110two 16. 10000two � 10two 1000two

17. What standard number is equivalent to 12021three? 142

8 �

2 �

164

�2

�8

2 �

2 �

41

�2

�2

1

1 0 1 1 1


NAME DATE PERIOD


Dividing Integers

Example 1: Use the multiplication problems at the rightto find each quotient.

a. 15 � 5Since 3 � 5 � 15, 15 � 5 � 3.

b. 15 � (�5)Since �3 � (�5) � 15, 15 � (�5) � �3.

c. �15 � 5Since �3 � 5 � �15, �15 � 5 � �3.

d. �15 � (�5)Since 3 � (�5) � �15, �15 � (�5) � 3.

Use these rules to divide integers.

Example 2: Evaluate if r � 8 and s � �2.

� Replace r with 8 and s with �2.

� �3 � 8 � �24

� 12 �24 � (�2) � 12

Find each quotient.

1. 36 � 9 4 2. �63 � (�7) 9 3. 25 � (�1) �25 4. �60 � 5 �12

5. �4 6. 6 7. 1 8. �7

Evaluate each expression if k � �1, m � 3, and n � �2.

9. �21 � m �7 10. 4 11. m � k �3 12. �4m � 5

n2nk

�56

8�1�1

�18�3

20�5

�24�2

�3 � 8

�2�3r

s

�3r

s

The quotient of two positive integers is positive.The quotient of two negative integers is positive.The quotient of a positive integer and a negative integer is negative.

3 � 5 � 15

�3(�5) � 15

�3 � 5 � �15

3(�5) � �15


NAME DATE PERIOD


Dividing IntegersFind each quotient.

1. 36 � 3 2. �15 � 5 3. 24 � (�8)

12 �3 �3

4. �45 � (�3) 5. 81 � (�9) 6. �28 � 4

15 �9 �7

7. �121 � 11 8. �144 � (�12) 9. 32 � (�4)

�11 12 �8

10. �64 � (�8) 11. �80 � 10 12. 48 � (�6)

8 �8 �8

13. 100 � (�25) 14. �20 � 5 15. 36 � (�9)

4 �4 �4

16. 56 � (�7) 17. �63 � (�9) 18. �32 � (�16)

�8 7 2

19. �21 � 3 20. �18 � 2 21. 72 � (�8)

�7 �9 �9

22. 23. 24.

�5 �3 25

Evaluate each expression if d � �3, f � 8, and g � �4.

25. f � g 26. 8d � g 27. 4g � f

�2 6 �2

28. 29. 30.

�16 2 �10

31. 32. 33.

12 4 �8

4fg

�2f

g9g

d

5fg

df�12

gf2

�125

�539�13

�35

7


NAME DATE PERIOD

Practice2–62–6

Dividing IntegersFind each quotient.

1. 28 � 7 2. �33 � 3 3. 42 � (�6)

4 �11 �7

4. �81 � (�9) 5. 12 � 4 6. 72 � (�9)

9 3 �8

7. 15 � 15 8. �30 � 5 9. �40 � (�8)

1 �6 5

10. 56 � (�7) 11. �21 � (�3) 12. �64 � 8

�8 7 �8

13. �8 � 8 14. �22 � (�2) 15. 32 � (�8)

�1 11 �4

16. �54 � (� 9) 17. 60 � (�6) 18. 63 � 9

6 �10 7

19. �45 � (�9) 20. �60 � 5 21. 24 � (�3)

5 �12 �8

22. 23. 24.

�2 �4 5

Evaluate each expression if a � 4, b � �9, and c � �6.

25. �48 � a 26. b � 3 27. 9c � b

�12 �3 6

28. 29. 30.

6 �9 2

31. 32. 33.

�8 9 �4

ac6

�4b

a12a

c

3cb

bc�6

abc

�45�9

40�10

�12

6


NAME DATE PERIOD

Reading to Learn MathematicsDividing Integers

2–62–6

Key Termsadditive inverses two numbers are additive inverses if their

sum is 0opposite additive inversezero pair the result of positive algebra tiles paired with negative

algebra tiles

Reading the Lesson1. Write the math sentence 18 divided by 6 two different ways. Then find the quotient.

18 � 6 � 3; � 3

2. Write negative or positive to describe each quotient. Explain your answer.

a.

b.

c.

d.

e.

f.

18 6

Helping You Remember3. Explain how knowing the rules for multiplying integers can help you to divide integers.

Sample answer: The rules to find the sign of the answer are thesame for multiplication and division. If the signs of the factors arethe same, the answer will be positive. If the signs of the factors aredifferent, the answer will be negative.

Expression Negative or Positive? Explanation

15 � 12 pos The signs of two numbers are the same.

9 � �10 neg The signs of the two numbers are different.

�35

7 neg The signs of the two numbers are different.

��

7183

pos The signs of two numbers are the same.

�1

23x neg The signs of the two numbers are different.

466y pos The signs of two numbers are the same.


NAME DATE PERIOD


Day of the Week Formula

The following formula can be used to determine the specific day of the week on which a date occurred.

s � d � 2m � [(3m � 3) � 5] � y � �4y

� � �10y

0� � �

40y

0� � 2

s � sumd � day of the month, using numbers from 1–31m� month, beginning with March is 3, April is 4, and so on,

up to December is 12, January is 13, and February is 14y � year except for dates in January or February when the

previous year is used

For example, for February 13, 1985, d � 13, m � 14, and y � 1984;and for July 4, 1776, d � 4, m � 7, and y � 1776

The brackets, [ ], mean you are to do the division inside them,discard the remainder, and use only the whole number part of thequotient. The next step is to divide s by 7 and note the remainder.The remainder 0 is Saturday, 1 is Sunday, 2 is Monday, and so on,up to 6 is Friday.

Example: What day of the week was October 3, 1854?

For October 3, 1854, d � 3, m � 10, and y � 1854.

s � 3 � [ 2(10) ] � [ (3 � 10 � 3) � 5 ] � 1854 � � � � � � � � � � 2

� 3 � 20 � 6 � 1854 � 463 � 18 � 4 � 2� 2334

s � 7 � 2334 � 7� 333 R3

Since the remainder is 3, the day of the week was Tuesday.

Solve.

1. See if the formula works for today’s date. Answers will vary.

2. On what day of the week were you born? Answers will vary.

3. What will be the day of the week on April 13, 2006?s � 13 � 2(4) � [(3 � 4 � 3) � 5] � 2006 � ��20

406�� 2100006�� 2400006�� 2

� 13 � 8 � 3 � 2006 � 501 � 20 � 4 � 2 � 2518; 2518 � 7 � 359 R5 Thursday4. On what day of the week was July 4, 1776?

s � 4 � 2(7) � [(3 � 7 � 3) � 5] � 1776 � ��17476�� 1170706�� 1470706�� 2

� 4 � 14 � 4 � 1776 � 444 � 17 � 4 � 2 � 2231; 2231 � 7 � 318 R5 Thursday

1854400

1854100

1854

4��

2NAME DATE PERIOD

Chapter 2 Test, Form 1A2


Write the letter for the correct answer in the blank at the right of eachproblem.

1. Which of the following sentences is true?A. |�3| � �|�3| B. 2 � |�2|C. |�5| � |�3| D. �5 � �3

2. Name the coordinate of C on the numberline at the right.A. �4 B. �2C. 2 D. 3

3. Order �8, 6, �7, 7, and 0 from greatest to least.A. �8, �7, 0, 6, 7 B. �8, 7, �7, 6, 0C. 7, 6, 0, �7, �8 D. 7, 6, 0, �8, �7

4. Evaluate �|14| � |�7|.A. �21 B. �7 C. 7 D. 21

For Questions 5–6, refer to the coordinate plane at the right.

5. Which ordered pair names point A?A. (�3, 4) B. (�4, �3)C. (3, �4) D. (4, �3)

6. In which quadrant is point C located?A. IB. IIC. No quadrant; it lies on the y-axis.D. No quadrant; it lies on the x-axis.

7. Which of the following points is located in Quadrant III?A. (�2, �4) B. (�6, 0) C. (�5, 3) D. (1, �2)

8. The graph of P (x, y) satisfies the condition that y � 0. In whichquadrant(s) could point P be located?A. III only B. IV only C. II or III D. III or IV

9. Which ordered pair names a point that lies on the y-axis and below the x-axis?A. (�1, �4) B. (�6, 0) C. (0, �3) D. (0, 2)

10. Find the sum: �18 � (�24).A. �42 B. �32 C. �6 D. 6

11. What is the value of k if 40 � (�58) � 32 � k?A. 130 B. 50 C. 16 D. 14

12. Simplify 15z � (�23z) � 25z.A. 27z B. 17z C. 63z D. �7z

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2NAME DATE PERIOD

Chapter 2 Test, Form 1A (continued)2


13. A basketball player averages 24 points per game. In her next four games,she scores 5 points above her average, 4 points below her average, 6 points below her average, and 11 points above her average. How manypoints total is she above or below average for the four games?A. 6 below B. 4 below C. 4 above D. 6 above

14. Find the difference: �12 � (�5).A. �17 B. �7 C. 7 D. 17

15. Evaluate 20 � a � b if a � 18 and b � �5.A. 43 B. 33 C. �3 D. �7

16. Simplify �14d � 8d � (�21d ). A. �d B. �43d C. �15d D. d

17. The week that your rent is due your paycheck is $462. If your rent is$275, how much money do you have left for the week after paying yourrent?A. $87 B. $177 C. $187 D. $737

18. Find the product: �2(3)(�1)(5)(�2).A. �60 B. �30 C. 30 D. 60

19. Evaluate �2xy � 3z if x � 8, y � �1, and z � �5.A. 31 B. 1 C. �1 D. �31

20. What is the product of �5, �6, and �2?A. �70 B. �60 C. 60 D. 70

21. Simplify �2(�3r)(5s).A. 6r � 5s B. 11r � s C. 25rs D. 30rs

22. Find the quotient: �125 � (�5).A. �120 B. �24 C. 24 D. 25

23. Find the value of s if �84 � 12 � s.A. 72 B. 7 C. �7 D. �8

24. Evaluate if m � �5, n � 6, and p � �3.

A. �7 B. �3 C. 3 D. 7

25. Over a six-year period, the enrollment of a school decreased from 812 to 482. What was the average change in enrollment for each of those six years?A. �330 B. �55 C. �45 D. �38

Bonus Simplify � (�2)(�9).

A. �2 B. 0 C. 2 D. 34

�96��6

mp � n�

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2NAME DATE PERIOD

Chapter 2 Test, Form 1B2


Write the letter for the correct answer in the blank at the right of eachproblem.

1. Name the coordinate of Z on the number line at the right.A. 3 B. 2C. 1 D. �3

2. Order �4, 2, �1, �3, and �2 from least to greatest.A. �1, �2, �3, �4, 2 B. �2, �1, 2, �3, �4C. �4, �3, �2, �1, 2 D. 2, �1, �2, �3, �4

3. Which of the following sentences is true?A. �|2| � |�2| B. �4 � �3C. 6 � |�7| D. |�1| � 1

4. Evaluate |5| � |�2|.A. 7 B. 3 C. �3 D. �7

5. Which of the following points is located in Quadrant II?A. (�4, 0) B. (�2, 7) C. (5, �1) D. (�3, �4)

For Questions 6–7, refer to the coordinate plane at the right.

6. Which ordered pair names point P?A. (0, 4) B. (4, 0)C. (�4, 0) D. (0, �4)

7. In which quadrant is point Q located?A. I B. IIC. III D. IV

8. The graph of P (x, y) satisfies the conditions that x � 0 and y � 0. Inwhich quadrant is point P located?A. I B. II C. III D. IV

9. Which ordered pair names a point that lies on the x-axis and to the left ofthe y-axis?A. (0, �3) B. (4, 0) C. (0, 0) D. (�1, 0)

10. What is the value of m if m � 13 � (�27)?A. �40 B. �24 C. �14 D. 40

11. Simplify �4k � (�2k) � 8k.A. �2k B. 2k C. 14k D. 6k

12. Find the sum: �50 � 28.A. �78 B. �32 C. �22 D. 78

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2NAME DATE PERIOD

Chapter 2 Test, Form 1B (continued)2


13. In four days, a golfer has rounds of four over par (�4), 1 under par (�1), 2 over par (�2) and 3 under par (�3). What is the golfer’s overall score forthe four days?A. �1 B. �1 C. �2 D. �4

14. Evaluate y � x if x � 12 and y � �8.A. �20 B. �4 C. 4 D. 20

15. On January 13, the low temperature was 12°F. The next day, the lowtemperature dropped by 25°. What was the low temperature on January 14?A. �37°F B. �25°F C. �13°F D. 37°F

16. Find the difference: �9 � 5.A. 45 B. 14 C. �4 D. �14

17. Simplify �6p � (�9p).A. �3p B. 3p C. �15p D. 15p

18. Evaluate �2�m � n if � � �1, m � 2, and n � �3.A. �7 B. �4 C. 1 D. 7

19. Simplify �5(�4t).A. 20t B. �9t C. �t D. �20t

20. Find the product: �8(�6).A. �56 B. �48 C. 14 D. 48

21. What is the value of n if n � (�6)(3)(�3)?A. �54 B. �36 C. 36 D. 54

22. Evaluate if f � �4 and g � 2.

A. 4 B. 3 C. 1 D. �4

23. Find the quotient: 54 � (�3).A. �18 B. �16 C. 16 D. 18

24. Find the value of b if b � �72 � (�18).A. �6 B. �4 C. 4 D. 6

25. Over eight years, the population of a town decreased from 1000 to 800.What was the average change in population for each of the eight years?A. �200 B. �25 C. 25 D. 200

Bonus Simplify � (�4)(2).

A. �11 B. �5 C. 5 D. 11

9��3

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2NAME DATE PERIOD

Chapter 2 Test, Form 2A2


1. Graph the set of numbers {3, �1, 0} on a number line.

For Questions 2–4, replace each ● with � or � to make a truesentence.

2. |�10| ● 11

3. �6 ● �8

4. �3 ● �|�2|

5. Evaluate �|�6| � |0|.

For Questions 6–9, use the coordinate plane at the right.

6. What ordered pair names point P?

7. What ordered pair names point R?

8. In what quadrant is point S located?

9. In what quadrant is point T located?

10. In what quadrant is the point D(�4, 8) located?

For Questions 11–13, find each sum.

11. 18 � (�27) � 46

12. �36 � (�8) � 20

13. 50 � (�36) � (�12)

14. During one week the Dow Jones Industrial average, the mostcommonly used measure of the stock market, rises 43 points,falls 11 points, rises 38 points, rises 69 points, and falls 148 points. By how many points is it up or down overall for the week?

15. Evaluate �26 � |z| � y if y � �8 and z � �15.

Find each difference.

16. 22 � (�9)

17. �8 � (�12)

18. �30 � (�8) � (�25)

19. 45 � (�18) � 75

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2NAME DATE PERIOD

Chapter 2 Test, Form 2A (continued)2


20. Simplify �28k � (�18k) � 14k.

21. What is the difference in elevation between the highest pointin California, Mount Whitney, which towers 4421 metersabove sea level, and the lowest point in California, DeathValley, which lies 86 meters below sea level?

For Questions 22–24, find each product.

22. �2(�3)(�3)

23. 4(�2)(�1)(5)(�2)

24. �12(�2)(�1)

25. A small company buys 8 chairs, each at a price of $40 lessthan the regular price, and 6 lamps, each at a price of $15 lessthan the regular price. What number describes the price thecompany pays in all compared to the regular price?

26. Evaluate 3xz � 8y if x � 4, y � �1, and z � �2.

27. Find the next term in the pattern 2, �8, 32, �128, ….

For Questions 28–30, find each quotient.

28.

29. �120 � (�15)

30.

31. The acceleration a of an object (in feet per second squared) is

given by a � , where t is the time in seconds, s1 is the

speed at the beginning of the time, and s2 is the speed at theend of the time. What is the acceleration of a car that brakesfrom a speed of 114 feet per second to a speed of 18 feet persecond in 6 seconds?

32. Evaluate if x � �6, y � �4, and z � 10.

33. Over a five-year period, the value of a house increased from$135,000 to $150,000. What was the average change in valuefor each of these five years?

Bonus From Sunday to Monday, the minimum daily humiditydrops 3%. Over the next three days, it rises 8%, rises 16%,and then drops 21%. What is the average daily changewhen you compare the minimum humidity on Thursday to the minimum humidity on Sunday?

z � x�

y

s2 � s1�

t

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�4

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2NAME DATE PERIOD

Chapter 2 Test, Form 2B2



1. �5 ● �7

2. 3 ● |�4|

3. �|�2| ● 1

4. Evaluate |�4| � |�8|.

5. Graph the set of numbers {�2, 1, 0} on a number line.


6. In what quadrant is point B located?

7. In what quadrant is point C located?

8. What ordered pair names point A?

9. What ordered pair names point E?

10. In what quadrant is the point R(6, �2) located?

11. Evaluate �4 � b � |c| if b � 7 and c � �2.


12. 6 � (�3) � 9

13. �21 � (�15) � 31

14. �12 � 18 � (�20)

15. During one week a small town reservoir falls 3 feet, drops 2 feet, rises 3 feet, rises 1 foot, and falls 1 foot. By how manyfeet does the reservoir rise or fall overall for the week?

For Questions 16–19, find each difference.

16. 9 � (�5)

17. �15 � (�32)

18. �6 � (�5)

19. �11 � (�28) � 3

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2NAME DATE PERIOD

Chapter 2 Test, Form 2B (continued)2


20. Simplify 8b � 5b � (�3b).

21. The temperature dropped 42°F overnight from yesterday’shigh temperature of 25°F. What is the temperature thismorning?

22. Find the next term in the pattern 3, �15, 75, … .

23. Evaluate 2x � 3y when x � �5 and y � �4.

For Questions 24–26, find each product.

24. 4(6)(�2)

25. �2(3)(�1)(5)

26. 3(�3)(�2)(�1)

27. You and several friends go together to buy detergent from awarehouse store. By buying 12 economy boxes, you get a pricethat is $2 less per box than the regular price. What numberdescribes the price you pay for the total purchase compared tothe regular price?

28. Evaluate if a � 16, b � �4, and c � �8.

For Questions 29–31, find each quotient.

29. �42 � (�3)

30.

31.

32. The acceleration a of an object (in feet per second squared) is

given by a � , where t is the time in seconds, s1 is the

speed at the beginning of the time, and s2 is the speed at theend of the time. What is the acceleration of a sled testing childcar seats that goes from a speed of 88 feet per second to aspeed of 0 feet per second in 2 seconds?

33. Over the past three years, the zoo’s attendance figures havedecreased from 185,000 to 176,000. What is the averagechange in attendance for each of the last three years?

Bonus From Sunday to Monday, the maximum daily temperaturein a small pond rises 1°F. Over the next three days, it rises 4°F,falls 1°F, and then falls 8°F. What is the average daily changewhen you compare the maximum temperature on Thursday to the maximum temperature on Sunday?

s2 � s1�

t

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�150�

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2NAME DATE PERIOD

Chapter 2 Extended Response Assessment2


Instructions: Demonstrate your knowledge by giving a clear, concisesolution to each problem. Be sure to include all relevant drawingsand to justify your answers. You may show your solution in morethan one way or investigate beyond the requirements of the problem.

1. Refer to the coordinate plane at the right.

a. Write the ordered pair that names each point.

b. Multiply the x- and y-coordinates of each point by �2.

c. Graph the new points. Label the point corresponding to A as X, the point corresponding to B as Y, and the point corresponding to C as Z.

d. Describe how the new triangle is related to the originaltriangle.

2. Now we will investigate more generally what happens to pointswhen their x- and/or y-coordinates are multiplied by a negativenumber.

a. Pick a negative integer n. Fill out the table below, in which youwill choose one point (a, b) in each quadrant, and then multiplyone or both coordinates by n.

b. How does multiplying one or both coordinates of a point by anegative number change the quadrant in which a point lies?

3. In an investment club, members pool their money and theirknowledge to invest in the stocks of various companies. Membersshare any profits or losses equally.

a. One club charges each member a $250 initial investment andmonthly investments of $30. In its first year, the 15-memberclub loses $1320. In its second year, the club makes a $990profit. Write and evaluate an expression to find each member’snet gain or loss after two years.

b. Another club charges each member a $150 initial investmentand monthly investments of $20. In its first year, the 25-member club loses $1750. In its second year, the club makesa $1200 profit. Write and evaluate an expression to find eachmember’s net gain or loss after two years.

c. Compare the results of the two investment clubs.

Quadrant of (a, b) I II III IV

Coordinates of (a, b)

Coord. and quad. of (na, b)

Coord. and quad. of (a, nb)

Coord. and quad. of (na, nb)

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2NAME DATE PERIOD

Chapter 2 Mid-Chapter Test(Lessons 2–1 through 2–3)

2


For Questions 1–2, name the coordinate of each point on thenumber line at the right.

1. C

2. D

Replace each ● with � or � to make a true sentence.

3. �8 ● �2

4. |�3| ● �|�2|

5. 4 ● �5

6. �6 ● |�7|

Order each set of numbers from greatest to least.

7. �12, 10, �8, 0, 3

8. �4, 6, �5, �3, 2, 5

Graph each point on the same coordinate plane.

9. P(3, 0)

10. Q(�2, �1)

11. R(4, �3)


12. What ordered pair names point A?

13. What ordered pair names point D?

14. In what quadrant is point C located?

15. In what quadrant is point B located?


16. �9 � 18

17. 84 � (�35) � (�27)

18. �8 � 4 � (�9) � 15

19. Simplify 12x � (�9x) � 6x.

20. Evaluate �11 � y � z if y � �4 and z � 8.

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1. Graph the set of numbers {3, �2, 0} on a number line.


2. |�12| ● �10

3. �8 ● �|�7|

4. Evaluate �|�6| � |�2|.

For Questions 5–7, graph each point on the same coordinateplane.

5. A(2, �3)

6. B(3, 4)

7. C(�3, �4)

8. In what quadrant is the point T(4, �1) located?

1. Find the sum: �11 � 8 � (�7).

2. Evaluate a � b � (�12) if a � �16 and b � 28.

3. Find the difference: 120 � (�54).

4. Write and evaluate an expression to find the difference (in thenumber of floors) between the 21st story of a building and theparking level three stories below the ground floor.

5. Find the product: �2(7)(�3)(�1).

6. Evaluate (�2s)(5t) if s � �1 and t � 8.

7. What is the value of b if b � �90 � (�15)?

8. Over the past four years, the value of a car has decreased from$22,000 to $12,000. What is the average change in value foreach of the last four years?

2NAME DATE PERIOD

2


Chapter 2 Quiz A(Lessons 2–1 through 2–2)

2NAME DATE PERIOD

Chapter 2 Quiz B(Lessons 2–3 through 2–6)

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2


1. Write an equation for the sentence below. (Lesson 1–1)Six less than four times a is the same as eleven more than theproduct of b and c.

2. Find the value of 6 � 2(7 � 4) � 6. (Lesson 1–2)

3. Name the property shown by the statement below. (Lesson 1–3) 8 � 6 � (5 � 11) � 8 � (6 � 5) � 11

4. Simplify 6(2x � 3) � 4x. (Lesson 1–4)

5. Mrs. Esposito buys apples at $2 per pound and walnuts at $5 per pound. If she spends three times as much on walnuts as apples and her total bill is $20, how many pounds of applesdoes she buy? (Lesson 1–5)

6. The frequency table gives the number of goals a soccer team scored in 11 games. In how many games did the team score at least two goals? (Lesson 1–6)

7. What kind of a graph or plot is best to use to display how aquantity changes over time? (Lesson 1–7)

8. Order 11, �25, 36, �64, �2, and 3 from least to greatest.(Lesson 2–1)

For Questions 9–10, refer to the coordinate plane at the right. (Lesson 2–2)

9. Write the ordered pair that names point W.

10. Name the quadrant in which point Vis located.

11. Find the sum: �22 � (�31). (Lesson 2–3)

12. Evaluate �a � b � c if a � �12, b � 22, and c � �8. (Lesson 2–4)

13. At 20°F with a 5-mile-per-hour wind, the windchill factor is16°F. At this temperature with a 45-mile-per-hour wind, thewindchill factor drops 38°F. What is the windchill factor at20°F with a 45-mile-per-hour wind? (Lesson 2–4)

14. Find the product of �2, 3, �1, and 8. (Lesson 2–5)

15. Evaluate if x � �6 and y � 2. (Lesson 2–6)

16. Find the quotient: (�126) � (�9). (Lesson 2–6)

3xy��4

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Chapter 2 Cumulative Review

2NAME DATE PERIOD

2


Write the letter for the correct answer in the blank at the right of theproblem.

1. Write an equation for the sentence below.

Three less than the quotient of b and 5 equals 4 more than twice b.

A. � 3 � 6b B. � 4 � 2b

C. � 3 � 2b � 4 D. 3 � � 4 � 2b

2. Annie buys a pair of pants for $25 and several T-shirts for $8 each. Writean expression for her total cost if she buys n T-shirts.

A. n(8 � 25) B. 25 � 8n C. 25 � D. 25n � 8

3. Find the value of 14 � 2 � 5 � 2 � 3.A. 1 B. 2 C. 14 D. 21

4. Name the property of equality shown by the statement below.

If 2b � 10 � 5x and 5x � 15, then 2b � 10 � 15. A. Reflexive Property of EqualityB. Transitive Property of EqualityC. Symmetric Property of EqualityD. Multiplication Property of Equality

5. Name the property shown by the statement below.

6 � (5 � 3) � 6 � (3 � 5)A. Commutative Property of AdditionB. Commutative Property of MultiplicationC. Associative Property of AdditionD. Associative Property of Multiplication

6. Simplify 3(4 � 2a) � 8(a � 6).A. 20 � 14a B. 2a � 60 C. 60 � 2a D. 50 � 14a

7. How many ways are there to make $1.20 using quarters and/or dimes?A. 2 B. 3 C. 4 D. 5

8. Use the frequency table to determine how many out of 20 students wear shoes larger than size 7.A. 7 B. 12C. 15 D. 16

9. The stem-and-leaf plot shows the number of times students ran the length of a football field in 15 minutes. How many students ran this length fewerthan 25 times?A. 4 B. 5 C. 7 D. 8

Stem Leaf1 6 92 0 3 5 63 1 2 2 4 8

3 |1 � 31

Shoe Size Frequency6 47 18 79 5

10 3

8�n

b�5

b�5

b � 3�

5b�5

Chapter 2 Standardized Test Practice(Chapters 1–2)

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2NAME DATE PERIOD

2


10. You want to show how the number of computers per 100 students haschanged in your state over the past 20 years. The most appropriate wayto display your data would be aA. histogram.B. stem-and-leaf plot.C. cumulative frequency table.D. line graph.

11. Which of the following statements is true?A. |�5| � |�3| B. �|�5| � �|3|C. �3 � �5 D. |�5| � 3

12. Evaluate |�8| � |9|.A. �17 B. �1 C. 1 D. 17

For Questions 13–14, refer to the coordinate planeat the right.

13. What ordered pair names point D?A. (�3, 0) B. (0, 3)C. (3, 0) D. (0, �3)

14. In which quadrant is point E located?A. I B. IIC. III D. IV

15. Find the sum: �15 � (�11) � 20.A. 16 B. 6 C. �6 D. �16

16. Simplify �8b � (�3b) � (�5b) � 4b.A. 2b B. �2b C. �10b D. �20b

17. Evaluate �12 � x � y when x � �6 and y � �4.A. �22 B. �10 C. �2 D. 2

18. Find the value of p if �2(3)(�1)(�5) � p.A. �30 B. �11 C. 30 D. 60

19. What is the value of k if �216 � 9 � k?A. �24 B. �22 C. 22 D. 24

20. Over seven years, the number of books in a school library increased from1160 to 2000. What was the average change in the number of books in thelibrary for each of the seven years?A. 115 B. 120 C. 134 D. 840

O x

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EA

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Chapter 2 Standardized Test Practice(Chapters 1–2) (continued)

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© Glencoe/McGraw-Hill A1 Algebra: Concepts and Applications

Preparing for Standardized TestsAnswer Sheet

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•

123456789

/•

0123456789

/•

0123456789

•

0123456789

B

B

B

B

B

B

B

B

C

C

C

C

C

C

C

C

D

D

D

D

D

D

D

D

E

E

E

E

E

E

E

E

Answers (Lesson 2-1)


© G

lenc

oe/M

cGra

w-H

ill52

Alg

ebra

: Con

cep

ts a

nd A

pp

licat

ions

Gra

ph

ing

Inte

ger

s on

a N

um

ber

Lin

eN

ame

the

coor

din

ate

of e

ach

poi

nt.

1.S

�3

2.U

03.

T�

2

4.R

�5

5.W

46.

V1

Gra

ph

eac

h s

et o

f n

um

ber

s on

a n

um

ber

lin

e.

7.{�

2, 0

, 3}

8.{�

5, �

3, �

1}

9.{2

, 4, �

4}10

.{�

1, 3

, 5}

11.{

�4,

�2,

2}

12.

{�3,

�1,

1, 3

}

Wri

te �

or �

in e

ach

bla

nk

to m

ake

a tr

ue

sen

ten

ce.

13.2

7

14.

4 �

215

.�

3 0

16.�

5 �

217

.�

1 2

18.

�5

�8

19.�

4 3

20.

0 �

921

.�

6 �

3

Eva

luat

e ea

ch e

xpre

ssio

n.

22.|

4|4

23.

|�

5|5

24.|

�8|

8

25.

|10

|10

26.|

3| �

|�

2|5

27.

|�

7| �

|�

12|

19��

�

�

��

��

�

�5

�4

�3

�2

�1

01

23

45

�5

�4

�3

�2

�1

01

23

45

�5

�4

�3

�2

�1

01

23

45

�5

�4

�3

�2

�1

01

23

45

�5

�4

�3

�2

�1

01

23

45

�5

�4

�3

�2

�1

01

23

45

�5

�4

�3

�2

�1

01

23

45

RS

TU

VW

NA

ME

DAT

EP

ER

IOD

Skil

ls P

ract

ice

2–1

2–1

© G

lenc

oe/M

cGra

w-H

ill51

Alg

ebra

: Con

cep

ts a

nd A

pp

licat

ions

NA

ME

DAT

EP

ER

IOD

Stud

y G

uide

2–1

2–1

Gra

ph

ing

Inte

ger

s on

a N

um

ber

Lin

e

Th

e n

um

bers

dis

play

ed o

n t

he

nu

mbe

r li

ne

belo

w b

elon

g to

th

e se

tof

in

tege

rs. T

he

arro

ws

at b

oth

en

ds o

f th

e n

um

ber

lin

e in

dica

teth

at t

he

nu

mbe

rs c

onti

nu

e in

defi

nit

ely

in b

oth

dir

ecti

ons.

Not

ice

that

th

e in

tege

rs a

re e

qual

ly s

pace

d.

Use

dot

s to

gra

ph n

um

bers

on

a n

um

ber

lin

e. Y

ou c

an l

abel

th

e do

tsw

ith

cap

ital

let

ters

.

Th

e co

ordi

nat

e of

Bis

�3

and

the

coor

din

ate

of D

is 0

.

Bec

ause

3 i

s to

th

e ri

ght

of �

3 on

th

e n

um

ber

lin

e, 3

��

3. A

nd

beca

use

�5

is t

o th

e le

ft o

f 1,

�5

�1.

Bec

ause

3 a

nd

�3

are

the

sam

e di

stan

ce f

rom

0, t

hey

hav

e th

e sa

me

abso

lute

val

ue,

3. U

setw

o ve

rtic

al l

ines

to

repr

esen

t ab

solu

te v

alu

e.

|3|

�3

Th

e ab

solu

te v

alu

e of

3 i

s 3.

|�

3| �

3T

he

abso

lute

val

ue

of �

3 is

3.

Exa

mp

le:

Eva

luat

e |

�12

| �

|10

|.

|�

12|

�|

10|

�12

�10

|�

12|

�12

an

d |

10|

�10

�22

Nam

e th

e co

ord

inat

e of

eac

h p

oin

t.

1.B

�4

2.D

�3

3.G

5

Gra

ph

eac

h s

et o

f n

um

ber

s on

a n

um

ber

lin

e.

4.{�

3, 2

, 4}

5.{�

1, 0

, 3}

Wri

te �

or �

in e

ach

bla

nk

to m

ake

a tr

ue

sen

ten

ce.

6.�

7

57.

�3

�

88.

|�

1|

0

Eva

luat

e ea

ch e

xpre

ssio

n.

9.|

9|9

10.

|�

15|

1511

.|

�20

| �

|10

|10

��

�

4–2

–10

12

34

–3–2

–10

12

3–4

4–3

–2–1

01

23

56

–5–4B

DF

EG

4–3

–2–1

0

3 un

its3

units

12

3–4

4–3

–2–1

01

23

5–5

–4

AB

CD

EF

4–3

–2–1

0

inte

gers

nega

tive

inte

gers

pos

itive

inte

gers

12

35

–5–4



© G

lenc

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cGra

w-H

ill54

Alg

ebra

: Con

cep

ts a

nd A

pp

licat

ions

NA

ME

DAT

EP

ER

IOD

Rea

ding

to

Lear

n M

athe

mat

ics

Gra

phi

ng In

tege

rs o

n a

Num

ber

Lin

e2

–12

–1

Key

Ter

ms

abso

lute

val

ue

the

dis

tanc

e a

num

ber

is fr

om 0

on

a nu

mb

er li

neco

ord

inat

e (c

o O

Rd

i net

)th

e nu

mb

er t

hat

corr

esp

ond

s to

a

poi

nt o

n a

num

ber

line

gra

ph

to p

lot

poi

nts

nam

ed b

y nu

mb

ers

on a

num

ber

line

nu

mb

er li

ne

a lin

e w

ith e

qua

l dis

tanc

es m

arke

d o

ff to

re

pre

sent

num

ber

s

Rea

din

g t

he

Les

son

1.R

efer

to

the

nu

mbe

r li

ne.

a.W

hat

do

the

arro

wh

eads

on

eac

h e

nd

of t

he

nu

mbe

r li

ne

mea

n?

The

line

and

the

set

of

num

ber

s co

ntin

uein

finit

ely

in e

ach

dir

ecti

on.

b.

Wh

at i

s th

e ab

solu

te v

alu

e of

�3?

Wh

at

is t

he

abso

lute

val

ue

of 3

? E

xpla

in.

3, 3

; �3

and

3 a

re b

oth

3 u

nits

aw

ay f

rom

zer

o o

n th

e nu

mb

erlin

e.

2.R

efer

to

the

Ven

n d

iagr

am s

how

n a

t th

e ri

ght.

Wri

te

tru

eor

fal

sefo

r ea

ch o

f th

e fo

llow

ing

stat

emen

ts.

a.A

ll w

hol

e n

um

bers

are

in

tege

rs.

true

b.

All

nat

ura

l n

um

bers

are

in

tege

rs.

true

c.A

ll w

hol

e n

um

bers

are

nat

ura

l n

um

bers

.fa

lse

d.

All

nat

ura

l n

um

bers

are

wh

ole

nu

mbe

rs.

true

e.A

ll w

hol

e n

um

bers

are

pos

itiv

e n

um

bers

.fa

lse

f.A

ll i

nte

gers

are

nat

ura

l n

um

bers

.fa

lse

g.W

hol

e n

um

bers

are

a s

ubs

et o

f n

atu

ral

nu

mbe

rs.

fals

e

h.N

atu

ral

nu

mbe

rs a

re a

su

bset

of

inte

gers

.tr

ue

Nat

ural

Num

bers

Who

leN

umbe

rsIn

tege

rs

�5

54

32

10

�4

�1

�2

�3

Hel

pin

g Y

ou

Rem

emb

er3.

On

e w

ay t

o re

mem

ber

a m

ath

emat

ical

con

cept

is

to c

onn

ect

it t

o so

met

hin

g yo

u h

ave

seen

or

hea

rd i

n e

very

day

life

. Des

crib

e a

situ

atio

n t

hat

ill

ust

rate

s th

e co

nce

pt o

fab

solu

te v

alu

e.

Sam

ple

ans

wer

: On

a fo

otb

all f

ield

, the

dis

tanc

e fr

om

eac

h g

oal

line

to t

he 5

0-ya

rd li

ne is

50

yard

s.

© G

lenc

oe/M

cGra

w-H

ill53

Alg

ebra

: Con

cep

ts a

nd A

pp

licat

ions

NA

ME

DAT

EP

ER

IOD

Pra

ctic

e2

–12

–1

Gra

ph

ing

Inte

ger

s on

a N

um

ber

Lin

eN

ame

the

coor

din

ate

of e

ach

poi

nt.

1.A

�4

2.B

33.

C�

1

4.D

55.

E�

26.

F1

Gra

ph

eac

h s

et o

f n

um

ber

s on

a n

um

ber

lin

e.

7.{�

5, 0

, 2}

8.{4

, �1,

�2}

9.{3

, �4,

�3}

10.

{�2,

5, 1

}

11.{

2, �

5, 0

}12

.{�

4, 3

, �2,

4}

Wri

te �

or �

in e

ach

bla

nk

to m

ake

a tr

ue

sen

ten

ce.

13.7

9

14.

0 �

115

.�

2 2

16.6

�

317

.�

4 �

518

.�

7 �

3

19.�

8 0

20.

�11

2

21.

�5

�6

Eva

luat

e ea

ch e

xpre

ssio

n.

22.|

�4|

423

.|

6|6

24.|

�3|

�|

1|4

25.

|9|

�|

�8|

1

26.|

�7|

�|

�2|

527

.|

�8|

�|

11|

19

��

�

��

�

��

�

4–3

–2–1

01

23

5–5

–44

–3–2

–10

12

35

–5–4

4–3

–2–1

01

23

5–5

–44

–3–2

–10

12

35

–5–4

4–3

–2–1

01

23

5–5

–44

–3–2

–10

12

35

–5–4

4–3

–2–1

01

23

5–5

–4AE

CF

BD

Answers (Lessons 2-1 and 2-2)


© G

lenc

oe/M

cGra

w-H

ill56

Alg

ebra

: Con

cep

ts a

nd A

pp

licat

ions

NA

ME

DAT

EP

ER

IOD

Stud

y G

uide

2–2

2–2

Th

e C

oord

inat

e P

lan

e

Th

e tw

o in

ters

ecti

ng

lin

es a

nd

the

grid

at

the

righ

t fo

rm

a co

ord

inat

e sy

stem

. Th

e h

oriz

onta

l n

um

ber

lin

e is

cal

led

the

x-ax

is,a

nd

the

vert

ical

nu

mbe

r li

ne

is c

alle

d th

e y-

axis

. T

he

x- a

nd

y-ax

es d

ivid

e th

e co

ordi

nat

e pl

ane

into

fou

rq

uad

ran

ts. P

oin

t S

in Q

uad

ran

t I

is t

he

grap

h o

f th

e or

der

ed p

air

(3, 2

). T

he

x-co

ord

inat

eof

poi

nt

Sis

3, a

nd

the

y-co

ord

inat

eof

poi

nt

Sis

2.

Th

e po

int

at w

hic

h t

he

axes

mee

t h

as c

oord

inat

es (

0, 0

) an

d is

cal

led

the

orig

in.

Exa

mp

le 1

:W

hat

is

the

orde

red

pair

for

poi

nt

J?

In

wh

at q

uad

ran

t is

poi

nt

Jlo

cate

d?Yo

u m

ove

4 u

nit

s to

th

e le

ft o

f th

e or

igin

an

d th

en 1

un

it u

p to

get

to

J. S

o th

e or

dere

d pa

ir f

or J

is (

�4,

1).

Poi

nt

Jis

lo

cate

d in

Qu

adra

nt

II.

Exa

mp

le 2

:G

raph

M(�

2, �

4) o

n t

he

coor

din

ate

plan

e.

Sta

rt a

t th

e or

igin

. Mov

e le

ft o

n t

he

x-ax

is t

o �

2 an

d th

en d

own

4 u

nit

s. D

raw

a d

ot h

ere

and

labe

l it

M.

Wri

te t

he

ord

ered

pai

r th

at n

ames

eac

h p

oin

t.

1.P

(1, 3

)2.

Q(�

4, �

3)

3.R

(0, 2

)4.

T(�

4, 0

)

Gra

ph

eac

h p

oin

t on

th

e co

ord

inat

e p

lan

e. N

ame

the

qu

adra

nt,

if a

ny,

in w

hic

h e

ach

poi

nt

is lo

cate

d.

5.A

(5, �

1)IV

6.B

(�3,

0)

none

7.C

(�3,

1)

II8.

D(0

, 1)

none

9.E

(3, 3

)I

10.

F(�

1, �

2)III

Ox

y

BC

A

E

F

DOx

y

12

34

4 3 2 1 –1 –2 –3 –4

–1–2

–3–4

TR

P

Q

Ox

y

1Quad

rant

I

Quad

rant

IV

Quad

rant

II

Quad

rant

III

23

4

4 3 2 1 –1 –2 –3 –4

–1–2

–3–4

J

M

Ox

y

1Quad

rant

I

Quad

rant

IV

Quad

rant

II

Quad

rant

III

23

4

4 3 2 1 –1 –2 –3 –4

–1–2

–3–4

S

© G

lenc

oe/M

cGra

w-H

ill55

Alg

ebra

: Con

cep

ts a

nd A

pp

licat

ions

NA

ME

DAT

EP

ER

IOD

Enri

chm

ent

2–1

2–1

Ven

n D

iag

ram

sA

type

of

draw

ing

call

ed a

Ven

n d

iagr

amca

n b

e u

sefu

l in

exp

lain

ing

con

diti

onal

stat

emen

ts. A

Ven

n d

iagr

am u

ses

circ

les

to r

epre

sen

t se

ts o

f ob

ject

s.

Con

side

r th

e st

atem

ent

“All

rab

bits

hav

e lo

ng

ears

.” T

o m

ake

a V

enn

dia

gram

for

this

sta

tem

ent,

a la

rge

circ

le is

dra

wn

to

repr

esen

t al

l an

imal

s w

ith

lon

g ea

rs. T

hen

a sm

alle

r ci

rcle

is d

raw

n in

side

th

e fi

rst

to r

epre

sen

t al

l rab

bits

. Th

e V

enn

dia

gram

show

s th

at e

very

rab

bit

is in

clu

ded

in t

he

grou

p of

lon

g-ea

red

anim

als.

Th

e se

t of

rab

bits

is c

alle

d a

sub

set

of t

he

set

of lo

ng-

eare

d an

imal

s.

Th

e V

enn

dia

gram

can

als

o ex

plai

n h

ow t

o w

rite

th

e st

atem

ent,

“A

ll r

abbi

ts h

ave

lon

g ea

rs,”

in if

-th

en f

orm

. Eve

ry r

abbi

t is

in t

he

grou

p of

lon

g-ea

red

anim

als,

so

ifan

an

imal

is a

rab

bit,

th

en it

has

lon

g ea

rs.

For

each

sta

tem

ent,

dra

w a

Ven

n d

iag

ram

. Th

e w

rite

th

e se

nte

nce

in if

-th

en f

orm

.

1.E

very

dog

has

lon

g h

air.

2.A

ll r

atio

nal

nu

mbe

rs a

re r

eal.

If a

n an

imal

is a

do

g, t

hen

itIf

a n

umb

er is

rat

iona

l, th

enha

s lo

ng h

air.

it is

rea

l.

3.P

eopl

e w

ho

live

in I

owa

like

cor

n.

4.S

taff

mem

bers

are

all

owed

in t

he

facu

lty

lou

nge

.

If a

per

son

lives

in Io

wa,

then

the

per

son

likes

co

rn.

If a

per

son

is a

sta

ff m

emb

er,

then

the

per

son

is a

llow

ed in

the

facu

lty

loun

ge.

anim

als

with

long

ear

s

rabb

its

anim

als

with

long

hai

r

dogs

real

num

bers

ratio

nal

num

bers

peop

le w

holik

e co

rn

peop

le w

holiv

e in

Iow

a

peop

le in

the

facu

lty lo

unge

staf

fm

embe

rs



© G

lenc

oe/M

cGra

w-H

ill58

Alg

ebra

: Con

cep

ts a

nd A

pp

licat

ions

NA

ME

DAT

EP

ER

IOD

Pra

ctic

e2

–22

–2

Th

e C

oord

inat

e P

lan

eW

rite

th

e or

der

ed p

air

that

nam

es e

ach

poi

nt.

1.A

(�3,

4)

2.B

(5, 2

)

3.C

(�4,

�3)

4.D

(2, �

4)

5.E

(�1,

1)

6.F

(1, 0

)

7.G

(0, �

2)8.

H(�

2, 5

)

9.J

(�2,

�4)

10.

K(5

, �1)

Gra

ph

eac

h p

oin

t on

th

e co

ord

inat

e p

lan

e.

11.K

(0, �

3)12

.L

(�2,

3)

13.M

(4, 4

)14

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2–4

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u t

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Use

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sim

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pres

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each

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er a

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the

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ill b

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. If

the

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the

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Exp

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Neg

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Form 1APage 81 Page 82

Form 1BPage 83 Page 84

Chapter 2 Answer Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

A

B

C

B

D

C

A

D

C

A

D

B

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

Bonus

D

B

C

A

C

A

B

B

D

D

C

B

B

A

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

D

C

A

B

B

C

A

B

D

C

B

C

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

Bonus

C

A

C

D

B

D

A

D

D

A

A

C

B

C


Form 2APage 85 Page 86


20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

Bonus

�24k

4507 m

�18

�80

�24

�$410

�16

512

�19

8

25

�16 ft persecond squared

�4

$3000

0%

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

�

�

�

�6

(�4, 2)

(2, 4)

IV

III

II

37

�24

2

down 9

�19

31

4

3

�12

–1 0 1 2 3


Form 2BPage 87 Page 88


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

�

�

�

12

Point B lies on the x-axis. It is not located

in a quadrant.

IV

(4, 3)

(�4, �2)

IV

5

12

�5

�14

falls 2 ft

14

17

�1

14

–1 0 1–3 –2

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

Bonus

6b

�17�F

�375

2

�48

30

�18

�$24

�6

14

�6

�16

�44 ft persecond squared

�3000

�1�F


Score General Description Specific Criteria

4 SuperiorA correct solution thatis supported by well-developed, accurateexplanations

3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation

2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem

1 Nearly UnsatisfactoryA correct solution with nosupporting evidence orexplanation

0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given

Page 89, Extended Response AssessmentScoring Rubric

Chapter 2 Assessment Answer Key

• Shows thorough understanding of the concepts of points on the coordinate plane, translating between verbal sentences and equations, and solving equations.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.


• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.


• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.

• Final computation is correct.• No written explanations or work is shown to substantiate

the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.


• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.


Extended Response AssessmentSample Answers

Page 89


1. a. A(2, 1), B(3, �2), C(�3, 0)

b. (�4, �2), (�6, 4), (6, 0)

c.

d. The new triangle has the same shape, but its sides seem to be twiceas long. It also seems to be rotated halfway around the origin.

2. a. A sample table is shown below for n � �3.

b. Multiplying the x-coordinate by a negative number moves the pointhorizontally to the quadrant next to it. Multiplying the y-coordinateby a negative number moves the point vertically to the quadrantabove or below it. Multiplying both coordinates by a negativenumber moves the point to the quadrant diagonally across from it.

3. a. � �$22

b. � �$22

c. Both clubs lost the same amount per person, $22, but members ofthe first club invested $970 each, while those in the second clubinvested $630 each.

$1200 � $1750

25

$990 � $1320

15

Quadrant of (a, b) I II III IV

Coordinates of (a, b) (2, 3) (�1, 3) (–3, –3) (1, �2)

Coord. and quad. of (na, b) (�6, 3); II (3, 3); I (9, –3); IV (�3, �2); III

Coord. and quad. of (a, nb) (2, �9); IV (�1, �9); III (–3, 9); II (1, 6); I

Coord. and quad. of (na, nb) (�6, �9); III (3, �9); IV (9, 9); I (�3, 6); II

O x

y

Z

X

Y


Mid-Chapter TestPage 90

Quiz APage 91


Quiz BPage 91

1.

2.

3.

4.

5.

6.

7.

8.

�10

0

174

21 � (�3) � 24

�42

80

6

�$2500

1.

2.

3.

4.

5–7.

8.

�

�

�8

IV

O x

y

C A

B

–1 0 1 2–2 3

1.

2.

3.

4.

5.

6.

7.

8.

9–11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

�1

4

�

�

�

�

10, 3, 0, �8, �12

6, 5, 2, �3, �4, �5

(0, �4)

(�2, 3)

III

I

9

22

2

9x

�7

O x

y

Q

R

P


Cumulative Review Standardized Test PracticePage 92 Page 93 Page 94


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

4a � 6 � bc � 117

AssociativeProperty (�)

8x � 18

2 lb

6

line graph�64, �25, �2, 3,

11, 36

(�1, 4)

IV

�53

42

�22�F48

914

1�2

1.

2.

3.

4.

5.

6.

7.

8.

9.

C

B

C

B

A

B

B

C

A

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

D

C

B

D

B

C

C

B

A

A

B

Documents

Glencoe Algebra, chapter 2