Course 1
Chapter XResource Masters
Course 2
Chapter 3Resource Masters
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced only forclassroom use; be provided to students, teacher, and families without charge; andbe used solely in conjunction with Glencoe Mathematics: Applications andConcepts, Course 2. Any other reproduction, for use or sale, is prohibited withoutprior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240
Mathematics: Applications and Concepts, Course 2ISBN: 0-07-860110-X Chapter 3 Resource Masters
1 2 3 4 5 6 7 8 9 10 024 12 11 10 09 08 07 06 05 04 03
Consumable Workbooks
Many of the worksheets contained in the Chapter Resource Mastersbooklets are available as consumable workbooks in both English andSpanish.
Study Guide and Intervention Workbook 0-07-860128-2
Study Guide and Intervention Workbook (Spanish) 0-07-860134-7
Practice: Skills Workbook 0-07-860129-0
Practice: Skills Workbook (Spanish) 0-07-860135-5
Practice: Word Problems Workbook 0-07-860130-4
Practice: Word Problems Workbook (Spanish) 0-07-860136-3
Reading to Learn Mathematics Workbook 0-07-861058-3
Answers for Workbooks The answers for Chapter 3 of theseworkbooks can be found in the back of this Chapter Resource Mastersbooklet.
Spanish Assessment Masters Spanish versions of forms 2A and 2C ofthe Chapter 3 Test are available in the Glencoe Mathematics: Applicationsand Concepts Spanish Assessment Masters, Course 2 (0-07-860138-X).
iii
Vocabulary Builder .............................vii
Family Letter............................................ix
Family Activity ........................................x
Lesson 3-1Study Guide and Intervention ........................129Practice: Skills ................................................130Practice: Word Problems................................131Reading to Learn Mathematics......................132Enrichment .....................................................133
Lesson 3-2Study Guide and Intervention ........................134Practice: Skills ................................................135Practice: Word Problems................................136Reading to Learn Mathematics......................137Enrichment .....................................................138
Lesson 3-3Study Guide and Intervention ........................139Practice: Skills ................................................140Practice: Word Problems................................141Reading to Learn Mathematics......................142Enrichment .....................................................143
Lesson 3-4Study Guide and Intervention ........................144Practice: Skills ................................................145Practice: Word Problems................................146Reading to Learn Mathematics......................147Enrichment .....................................................148
Lesson 3-5Study Guide and Intervention ........................149Practice: Skills ................................................150Practice: Word Problems................................151Reading to Learn Mathematics......................152Enrichment .....................................................153
Lesson 3-6Study Guide and Intervention ........................154Practice: Skills ................................................155Practice: Word Problems................................156Reading to Learn Mathematics......................157Enrichment .....................................................158
Lesson 3-7Study Guide and Intervention ........................159Practice: Skills ................................................160Practice: Word Problems................................161Reading to Learn Mathematics......................162Enrichment .....................................................163
Chapter 3 AssessmentChapter 3 Test, Form 1 ...........................165-166Chapter 3 Test, Form 2A.........................167-168Chapter 3 Test, Form 2B.........................169-170Chapter 3 Test, Form 2C ........................171-172Chapter 3 Test, Form 2D ........................173-174Chapter 3 Test, Form 3 ...........................175-176Chapter 3 Extended Response Assessment .177Chapter 3 Vocabulary Test/Review.................178Chapter 3 Quizzes 1 & 2................................179Chapter 3 Quizzes 3 & 4................................180Chapter 3 Mid-Chapter Test ...........................181Chapter 3 Cumulative Review........................182Chapter 3 Standardized Test Practice ....183-184
Standardized Test Practice Student Recording Sheet ..............................A1
Standardized Test Practice Rubric...................A2ANSWERS ..............................................A3-A30
CONTENTS
iv
Teacher’s Guide to Using the Chapter 3 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resources youuse most often. The Chapter 3 Resource Masters includes the core materials needed forChapter 3. These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theGlencoe Mathematics: Applications and Concepts, Course 2, TeacherWorks CD-ROM.
Vocabulary Builder Pages vii-viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
When to Use Give these pages to studentsbefore beginning Lesson 3-1. Encouragethem to add these pages to theirmathematics study notebook. Remind themto add definitions and examples as theycomplete each lesson.
Family Letter and Family ActivityPage ix is a letter to inform your students’families of the requirements of the chapter.The family activity on page x helps themunderstand how the mathematics studentsare learning is applicable to real life.
When to Use Give these pages to studentsto take home before beginning the chapter.
Study Guide and InterventionThere is one Study Guide and Interventionmaster for each lesson in Chapter 3.
When to Use Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Practice: Skills There is one master foreach lesson. These provide practice thatmore closely follows the structure of thePractice and Applications section of theStudent Edition exercises.
When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Practice: Word Problems There is onemaster for each lesson. These providepractice in solving word problems that applythe concepts of the lesson.
When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn Mathematics Onemaster is included for each lesson. The firstsection of each master asks questions aboutthe opening paragraph of the lesson in theStudent Edition. Additional questions askstudents to interpret the context of andrelationships among terms in the lesson.Finally, students are asked to summarizewhat they have learned using variousrepresentation techniques.
When to Use This master can be used as astudy tool when presenting the lesson or asan informal reading assessment afterpresenting the lesson. It is also a helpful toolfor ELL (English Language Learner)students.
v
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
When to Use These may be used as extracredit, short-term projects, or as activitiesfor days when class periods are shortened.
Assessment OptionsThe assessment masters in the Chapter 3Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter AssessmentChapter Tests
• Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-responseBonus question.
• The Extended-Response Assessmentincludes performance assessment tasksthat are suitable for all students. Ascoring rubric is included for evaluationguidelines. Sample answers are providedfor assessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used inconjunction with one of the chapter testsor as a review worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice and free-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed through theirstudy of Glencoe Mathematics:Applications and Concepts, Course 2. Itcan also be used as a test. This masterincludes free-response questions.
• The Standardized Test Practice offerscontinuing review of pre-algebra conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, short response, grid-in, andextended response questions. Bubble-inand grid-in answer sections are providedon the master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questions thatappear in the Student Edition on pages 146–147. This improves students’familiarity with the answer formats theymay encounter in test taking.
• Detailed rubrics for assessing theextended response questions on page 147are provided on page A2.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided for theassessment masters in this booklet.
This is an alphabetical list of new vocabulary terms you will learn inChapter 3. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.
Vo
cab
ula
ry B
uild
er
© Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Vocabulary TermFound
Definition/Description/Exampleon Page
absolute value
additive inverse
coordinate grid
coordinate plane
graph
integer [IHN-tih-juhr]
negative integer
opposite
Reading to Learn MathematicsVocabulary Builder
Vo
cab
ula
ry B
uild
er
© Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 2
Vocabulary TermFound
Definition/Description/Exampleon Page
ordered pair
origin
positive integer
quadrant
x-axis
x-coordinate
y-axis
y-coordinate
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsVocabulary Builder (continued)
Family LetterNAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill ix Mathematics: Applications and Concepts, Course 2
Dear Parent or Guardian:
“When am I ever going to use this stuff?” Students in math
classes often ask this question. Integers are everywhere. We use
them for golf scores. We use them when finding elevation, bal-
ancing a checkbook, or talking about temperature. There are
many practical uses of integers.
In Chapter 3, Algebra: Integers, your child will learn how to
order, add, subtract, multiply, divide, and find the absolute value
of integers. Your child will also learn about the coordinate sys-
tem and how to graph points. In the study of this chapter,
your child will complete a variety of daily classroom assign-
ments and activities and possibly produce a chapter project.
By signing this letter and returning it with your child, you
agree to encourage your child by getting involved. Enclosed is
an activity you can do with your child that also relates the
math we will be learning in Chapter 3 to the real world. You
may also wish to log on to the Online Study Tools for self-
check quizzes, Parent and Student Study Guide pages, and
other study help at www.msmath2.net. If you have any ques-
tions or comments, feel free to contact me at school.
Sincerely,
Fam
ily L
ette
r
Signature of Parent or Guardian ______________________________________ Date ________
Family ActivityNAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill x Mathematics: Applications and Concepts, Course 2
Ordering IntegersConsult a newspaper, watch the news, surf the Internet, or watch theweather channel with a family member. Find the high and lowtemperatures on the same day for eight cities: Buenos Aires, Moscow,Zurich, Tokyo, New York, Denver, Los Angeles, and your community.Record the date and the temperatures in the table.
High and Low Temperatures on _____________
1. Which city has the highest high temperature?
2. Which city has the lowest low temperature?
3. List the cities in order from lowest high temperature to highest hightemperature.
4. List the cities in order from lowest low temperature to highest lowtemperature.
5. Were the cities in the same order in the answers for Questions 3 and 4?Why or why not?
City
Buenos Aires
Low Temperature (�F)
Moscow
High Temperature (�F)
Zurich
Tokyo
New York
Denver
Los Angeles
Less
on
3–1
© Glencoe/McGraw-Hill 129 Mathematics: Applications and Concepts, Course 2
Write an integer that represents 160 feet below sea level.
Because it represents below sea level, the integer is �160.
Evaluate |�2|.
On the number line, the graph of �2 is
2 units away from 0. So, �2 � 2.
Write an integer for each situation.
1. 12°C above 0 2. a loss of $24
3. a gain of 20 pounds 4. falling 6 feet
Evaluate each expression.
5. 12 6. �150
7. �8 8. 75
9. �19 10. 84
�2 �1 0 2 3�3�4 1 4
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionIntegers and Absolute Value
Integers less than zero are negative integers. Integers greater than zero are positive integers.
The absolute value of an integer is the distance the number is from zero on a number line. Twovertical bars are used to represent absolute value. The symbol for absolute value of 3 is 3.
8�7�6�5�4 6 754321�3�2�1 0
negative integers positive integers
zero is neitherpositive nor negative
© Glencoe/McGraw-Hill 130 Mathematics: Applications and Concepts, Course 2
Write an integer for each situation.
1. 15�C below 0 2. a profit of $27
3. 2010 A.D. 4. average attendance is down 38 people
5. 376 feet above sea level 6. a withdrawal of $200
7. 3 points lost 8. a bonus of $150
9. a deposit of $41 10. 240 B.C.
11. a wage increase of $120 12. 60 feet below sea level
Evaluate each expression.
13. |�1| 14. |9|
15. |23| 16. |�107|
17. |�45| 18. |19|
19. |0| 20. |6|�|�2|
21. �8�4 22. |�12|�|12|
Graph each set of integers on a number line.
23. {0, 2, �3} 24. {�4, �1, 3}
�2 �1 0 2 3�3�4 1 4�2 �1 0 2 3�3�4 1 4
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsIntegers and Absolute Value
© Glencoe/McGraw-Hill 131 Mathematics: Applications and Concepts, Course 2
Practice: Word ProblemsIntegers and Absolute Value
NAME ________________________________________ DATE ______________ PERIOD _____
1. DEATH VALLEY The lowest point in theUnited States is Death Valley inCalifornia. Its altitude is 282 feet belowsea level. Write an integer to representthe altitude of Death Valley.
2. RAIN A meteorologist reported that inthe month of April there were 3 inchesmore rainfall than normal. Write aninteger to represent the amount ofrainfall above normal in April.
3. ARCHIMEDES A famous mathematicianand physicist named Archimedes wasborn in 287 B.C. Write an integer toexpress the year of his birth.
4. TEMPERATURE In our world’s tropicalrain forests, the average temperature ofevery month is 64 degrees above zeroor higher. Write an integer to expressthis temperature.
5. STOCK MARKET A certain stock gained5 points in one day and lost 4 pointsthe next day. Write integers torepresent the stock’s gains and lossesfor the two days.
6. ALTITUDE An airplane pilot changed hisaltitude by 100 meters. Describe whatthis could mean.
Less
on
3–1
© Glencoe/McGraw-Hill 132 Mathematics: Applications and Concepts, Course 2
Pre-Activity Read the introduction at the top of page 106 in your textbook.Write your answers below.
1. What does a value of �2 represent?
2. On which down did they lose the most yards?
3. How can you represent a gain of 9 yards?
Reading the Lesson4. Express each of the following in words.
5. On the following number line, draw a circle around the negative integersand label them negative. Draw a rectangle around the positive integersand label them positive.
Helping You Remember6. Show a classmate how a number line can be used to show negative and
positive integers. Explain the difference between some integers and theabsolute values of those integers. Draw a number line to show what youmean.
�2 �1 0 2 3 4�3�4 1
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsIntegers and Absolute Value
Symbols
�7
�7
|7|
Words
© Glencoe/McGraw-Hill 133 Mathematics: Applications and Concepts, Course 2
Jaime EscalanteJaime Escalante (1930– ) was born in La Paz, Bolivia,and came to the United States in 1963. For ten years,he worked at odd jobs to support himself and his family while pursuing his dream—becoming certified to teach high school mathematics in California. As a mathematicsteacher, he has become well known for his ability to inspire students to succeed in mathematics at levels they never thought possible. In 1988, the story ofMr. Escalante and a group of his students was the subject of the popular motion picture Stand and Deliver.
Mr. Escalante teaches concepts students must master if they are to succeed in high school and college mathematics.One of these is the concept of absolute value. For instance,a student should be able to solve an equation like y � 6quickly using mental math. Here’s how.
You know that 6 � 6 and �6 � 6.
So, the equation y � 6 has two solutions: 6 and �6.
Solve each equation. (Hint: One equation has no solution.)
1. a � 8 2. r � 0 3. j � �3
4. t � 1 � 15 5. 10 � m� 3 6. c � 4 � 16
7. 5z � 60 8. 12 � g � 4 9. 48 � 8x
10. 2d � 3 � 5 11. 4p � 9 � 59 12. 7z � 12 � 12
13. Suppose that the value of x can be selected from the set {�2, �1, 0, 1, 2}.Find all of the solutions of the equation x � x.
14. One of these statements is false. Which one is it? Explain.
a. The absolute value of every integer is positive.
b. There is at least one integer whose absolute value is zero.
c. The absolute value of an integer is never negative.
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
Less
on
3–1
© Glencoe/McGraw-Hill 134 Mathematics: Applications and Concepts, Course 2
Replace the � with � or � to make �1 � �6 a true sentence.
Graph each integer on a number line.
Since �1 is to the right of �6, �1 � �6.
Order the integers 2, �3, 0, �5 from least to greatest.
To order the integers, graph them on a number line.
Order the integers by reading from left to right: �5, �3, 0, 2.
1. Replace the � with < or > to make �5 � �10 a true sentence.
2. Order �1, 5, �3, and 2 from least to greatest.
3. Order 0, �4, �2, and 7 from greatest to least.
4. Order �3, �2, 4, 0, and �5 from greatest to least.
�2 �1 0 2 3�3 1 4 5�5 �4�6
�2 �1 0 2 3�3�7 1 4�5 �4�6
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionComparing and Ordering Integers
When two numbers are graphed on a number line, the number to the left is always less than (<) thenumber to the right. The number to the right is always greater than (>) the number to the left.
�2 �1 0 2 3�3�4 1 4Model
WordsSymbols
�3 is less than �1. �1 is greater than �1.
The symbol points to the lesser number.
�3 � �1 �1 � �3
Less
on
3–2
Practice: SkillsComparing and Ordering Integers
© Glencoe/McGraw-Hill 135 Mathematics: Applications and Concepts, Course 2
Replace each � with < or > to make a true sentence.
1. �15 � �16 2. �8 � �7
3. 0 � �2 4. �2 � �5
5. �25 � 3 6. �14 � �20
7. �4 � 3 8. �6 � �7
9. �7 � 2 10. �8 � �9
Determine whether each sentence is true or false. If false, change onenumber to make the sentence true.
11. �7 � 3
12. 2 � 0
13. �20 � �22
14. 12 � 15
15. 3 ��5
16. �2� �3
17. 8��10
18. �11� 11
19. �4 � 4
20. �9 � �10
Order the integers from least to greatest.
21. 12, �6, 20, �47, �11 22. 9, �6, 0, �4, 17, �11
Order the integers from greatest to least.
23. �40, 65, �7, 24, �6, 15 24. �13, 0, 7, �8, �5, 2
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsComparing and Ordering Integers
© Glencoe/McGraw-Hill 136 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
HISTORY OF WRITING For Exercises 1 and 2,use the table below. It shows importantevents in the history of writing.
EXTREME TEMPERATURES For Exercises 3–5,use the table below. It shows the extremetemperatures for four states. Temperaturesare in degrees Fahrenheit.
Extreme Temperatures (�F)Event
The Iliad and the Odyssey arecomposed by Homer. 700 BC
Aprox.Year
T’sai Lun invents paper. 105 AD
Date of oldest existing papyrus 2200 BC
Ovid wrote Metamorphosis. 5 AD
Torah is compiled. 450 BC
Metal type developed in Korea 1241 AD
State
Nebraska
Alabama
�47
Maine
3
�30
Lowest
Florida �2
Highest
118
104
101
109
1. Write each year as an integer. 2. Order the integers from Exercise 1from least to greatest. Write a sentencedescribing the earliest and most recentevents in the table.
3. Arrange the highest temperatures from greatest to least.
4. What is the median low temperaturefor these four states?
5. Nebraska’s lowest temperature was�47�F, and Maine’s lowest temperaturewas �30�F. Write a true statementusing the two temperatures with thesymbol � or �.
6. MONEY Mr. Firewalks pays closeattention to how much money is in hischecking account. One week hedeposited $230, spent $15 on a lunch,and loaned $25 to a friend. Write eachtransaction as an integer, and list themfrom least to greatest.
Pre-Activity Read the introduction at the top of page 109 in your textbook.Write your answers below.
1. What is the wind chill if there is a wind at 20 miles per hour and thetemperature is 5�?
2. Which is colder, a temperature of 15� with a 20 mile-per-hour wind or a temperature of 10� with a 10 mile-per-hour wind?
3. Graph both wind chills found in Exercise 2 on a number line.
Reading the LessonFor Exercises 4 and 5, express each of the following in words. Thengraph the numbers on a number line.
4. �1 � 0
5. 3 � �2
6. When two numbers are graphed on a number line, what can you tellabout the number to the left? the number to the right?
Helping You Remember7. Write a set of six numbers, some positive and some negative. Explain how
you can use a number line to order the numbers from least to greatest.
�2 �1 0 2 3 4�3�4 1
�2 �1 0 2 3 4�3�4 1
�2 �1 0 2 3�3�4�5 1
Less
on
3–2
Reading to Learn MathematicsComparing and Ordering Integers
© Glencoe/McGraw-Hill 137 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 138 Mathematics: Applications and Concepts, Course 2
Quantitative ComparisonsAn unusual type of problem is found on some standardized multiple-choicetests. This problem type is called the quantitative comparison.
In each quantitative comparison question, you are given two quantities, one inColumn A and one in Column B. You are to compare the two quantities andshade one of four circles on an answer sheet.
Shade circle A if the quantity in Column A is greater;
Shade circle B if the quantity in Column B is greater;
Shade circle C if the two quantities are equal;
Shade circle D if the relationship cannot be determined from theinformation given.
Shade the correct oval to the left of each problem number.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.DCBA
DCBA
DCBA
DCBA
DCBA
DCBA
DCBA
DCBA
DCBA
DCBA
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Column A
ten billion dollars
0.006 � 2
1,000 million dollars
20 inches
0.002 � 6
the perimeter of a squarewith an area of 25 squareinches
Column B
half of one third one fifth
the greatest possibleproduct of two oddpositive numbers lessthan 20
the greatest possibleproduct of two evenpositive numbers lessthan 20
0.000000001 �x is x if greater than 0
|x| |x � 1|
|y| |�y|
2|x| if x 0 |x| if x 0
�x if x is less than 0 |x| if x is less than 0
Less
on
3–3
© Glencoe/McGraw-Hill 139 Mathematics: Applications and Concepts, Course 2
Name the ordered pair for point P. Then identify the quadrant inwhich P lies.
• Start at the origin.• Move 4 units left along the x-axis.• Move 3 units up on the y-axis.
The ordered pair for point P is (�4, 3).P is in the upper left quadrant or quadrant II.
Graph and label the point M(0, �4).
• Start at the origin.• Move 0 units along the x-axis.• Move 4 units down on the y-axis.• Draw a dot and label it M(0, �4).
Name the ordered pair for each point graphed at the right. Then identify the quadrant in which each point lies.
1. P 2. Q
3. R 4. S
Graph and label each point on the coordinate plane.
5. A(�1, 1) 6. B(0, �3)
7. C(3, 2) 8. D(�3, �1)
9. E(1, �2) 10. F(1, 3)
y
xO
�2�3�4
�2�3�4 21 43
1234
y
xO
�2�3�4
�2�3�4 21 43
1234
SR
Q P
y
xO
�2�3�4
�2�3�4 21 43
1234
(0, �4)M
P
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionThe Coordinate Plane
The coordinate plane is used to locate points. The horizontal number line is the x-axis. The verticalnumber line is the y-axis. Their intersection is the origin.
Points are located using ordered pairs. The first number in an ordered pair is the x-coordinate; thesecond number is the y-coordinate.
The coordinate plane is separated into four sections called quadrants.
© Glencoe/McGraw-Hill 140 Mathematics: Applications and Concepts, Course 2
Name the ordered pair for each point graphed at the right.Then identify the quadrant in which each point lies.
1. A 2. B
3. C 4. D
5. E 6. F
7. G 8. H
9. I 10. J
Graph and label each point on the coordinate plane.
11. N(�1, 3) 12. V(2, �4)
13. C(4, 0) 14. P(�6, 2)
15. M(�5, 0) 16. K(�1, 5)
17. I(�3, �3) 18. A(5, �3)
19. D(0, �5)
Name the ordered pair for each point on the city map at the right.
20. City Hall
21. Theater
22. Gas Station
23. Grocery
y
xO
�2�3�4�5
21 4 5 6 73
12345
�2�3�4�5�6�7
Grocery
Theater
City Hall
Gas Station
�2�3�4�5�6
y
xO�2�3�4�5�6 21 4 5 63
123456
y
xO
�2�3�4�5
�2�3�4�5 21 4 53
12345
F
I
A
B
E
DH
C GJ
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsThe Coordinate Plane
© Glencoe/McGraw-Hill 141 Mathematics: Applications and Concepts, Course 2
SCHOOL For Exercises 1–4, use the coordinate plane at the right. It shows a map of the rooms in a junior high school.
�2�3�4�5
�2�3�4�5 21 4 53
Art Entrance
Library
Science
y
xO
12345
Computer Lab
Special Services
English
HistoryCounselor
Athletic Dept.
Music
Exit
Math
Nurse
Practice: Word ProblemsThe Coordinate Plane
NAME ________________________________________ DATE ______________ PERIOD _____
1. Thalia is in the room located at (�2, 1).What room is she in? Describe in wordshow to get from the origin to this point.
2. Thalia’s next class is 8 units to theright and 5 units down on the mapfrom where she is now. In what room isThalia’s next class? Find the orderedpair that represents the location of thatroom.
3. Tyrone is in the Art room, but his nextclass is in the History room. GiveTyrone directions on how to get to theHistory room.
4. On the map, which classrooms arelocated in the third quadrant? Describethe coordinates of all points in the thirdquadrant.
5. NEIGHBORHOOD Delsin made a map ofhis neighborhood in such a way thateach intersection is a point on acoordinate plane. Right now, Delsinstands at point (�4, �3). Give theordered pair of where he will be ifmoves 5 units to the right and 7 unitsup on the map.
6. NEIGHBORHOOD Refer to Exercise 5. Inwhich quadrant is Delsin when he isdone walking? Describe this quadrant.
Less
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3–3
© Glencoe/McGraw-Hill 142 Mathematics: Applications and Concepts, Course 2
Pre-Activity Read the introduction at the top of page 112 in your textbook.Write your answers below.
1. Suppose Terrell starts at the corner of Russel and Main and walks 1 block north and 2 blocks east. Name the intersection of his location.
2. Using the words north, south, west, and east, write directions to go from the corner of School and Highland to the corner of Main and Oak.
Reading the Lesson3. The word coordinate comes from two Latin words that mean “to arrange
together.” How are coordinates used together to locate a point in acoordinate plane?
4. Look at the coordinate plane at the right. Name the ordered pair for each point graphed.
5. In the coordinate plane in Exercise 4, tell whichquadrant each of the points is in.
Helping You Remember6. Write a way to remember the names of the four quadrants of the
coordinate plane.
y
xO
�2�3�4
�2�3�4 21 43
1234A
B
C
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsThe Coordinate Plane
© Glencoe/McGraw-Hill 143 Mathematics: Applications and Concepts, Course 2
Latitude and LongitudeThis world map shows some of the latitude and longitude lines. Latitude ismeasured in degrees north and south of the equator. Longitude is measured indegrees east and west of the prime meridian, a line passing throughGreenwich, England. (Greenwich is a suburb of London.)
The latitude is usually given first. For example, the location of 30�S, 60�W islower South America.
Name a place near each location. Use an atlas or other referencesource to check your answers.
1. 30�N, 30�W 2. 30�S, 30�E 3. 60�N, 120�W
4. 15�N, 150�W 5. 30�S, 140�E 6. 25�N, 100�W
7. 40�N, 120�W 8. 45�N, 90�W 9. 40�N, 5�W
10. 60�N, 45�W 11. 35�N, 140�E 12. 0�, 60�E
EquatorP
rime
Mer
idia
n
60˚N
30˚N
30˚S, 60˚W
30˚N
0˚
0˚
0˚
30˚S 30˚S
60˚S 60˚S
60˚N
30˚E
30˚ W
60˚E
90˚E
120̊
E
150̊
E
180̊
E
60˚ W
90˚ W
120˚ W
150W̊
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
Less
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3–3
© Glencoe/McGraw-Hill 144 Mathematics: Applications and Concepts, Course 2
Find 4 � (�6).
Method 1 Use counters. Method 2 Use a number line.Combine a set of 4 positive counters • Start at 0.and a set of 6 negative counters on a mat. • Move 4 units right.
• Then move 6 units left.
Add.
1. �5 � (�2) 2. 8 � 1 3. �7 � 10
4. 16 � (�11) 5. �22 � (�7) 6. �50 � 50
7. �10 � (�10) 8. 100 � (�25) 9. �35 � �20
Evaluate each expression if a � 8, b � �8, and c � 4.
10. a � 15 11. b � (�9) 12. a � b
13. b � c 14. �10 � c 15. 12 � b
�1 0 1 3 4�2�3
�6�4
2 54 � (�6) ��2
4 � (�6) 4 � (�6) ��2
�1
� �
��
�
�
�
� �
� �
�
�
�
�
� �
�
�
�
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionAdding Integers
For integers with the same sign:• the sum of two positive integers is positive.• the sum of two negative integers is negative.
For integers with different signs, subtract their absolute values. The sum is:• positive if the positive integer has the greater absolute value.• negative if the negative integer has the greater absolute value.
To add integers, it is helpful to use counters or a number line.
Less
on
3–4
© Glencoe/McGraw-Hill 145 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Tell whether each sum is positive, negative, or zero without adding.
Add.
1. 5 � (�8) 2. �3 � 3
3. �3 � (�8) 4. �7 � (�7)
5. �8 � 10 6. �7 � 13
7. 15 � (�10) 8. �11 � (�12)
9. 25 � (�12) 10. �14 � (�13)
11. 14 � (�27) 12. �28 � 16
Evaluate each expression if a � �8, b � 12, and c � �4.
13. 5 � a 14. b � (�9)
15. c � (�5) 16. a � b
17. a � 0 18. b � c
19. �12 � b 20. a � (�7)
21. 21 � c 22. a � c
Practice: SkillsAdding Integers
© Glencoe/McGraw-Hill 146 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Write an addition expression to describe each situation. Then find each sum.
Practice: Word ProblemsAdding Integers
1. FOOTBALL A team gains 20 yards. Thenthey lose 7 yards.
2. MONEY Roger owes his mom $5. Heborrows another $6 from her.
3. GOLF Juanita’s score was 5 over par onthe first 9 holes. Her score was 4 underpar on the second 9 holes.
4. HOT AIR BALLOON A balloon rises340 feet into the air. Then it descends130 feet.
5. CYCLING A cyclist travels downhill for125 feet. Then she travels up a hill50 feet.
6. AIRPLANE A plane descends 1,200 feet.Then it descends another 500 feet.
© Glencoe/McGraw-Hill 147 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Pre-Activity Read the introduction at the top of page 120 in your textbook.Write your answers below.
1. What is the charge at the top of a cloud where there are more protonsthan electrons?
2. What is the charge at the bottom of a cloud where there are moreelectrons than protons?
Reading the LessonFor Exercises 3 and 4, tell how you would solve each of the followingon a number line. Then solve.
3. �7 � (�9)
4. �7 � 9
5. When you use counters to add integers, what property are you applyingwhen you remove zero pairs?
6. How many units away from 0 is the number 17? How many units awayfrom 0 is the number �17? What are 17 and �17 called?
Helping You Remember7. Work with a partner. Tell your partner how to use absolute values to add
integers with different signs when the positive integer has the greaterabsolute value. Then have your partner explain to you how to useabsolute values to add integers with different signs when the negativeinteger has the greater absolute value.
Reading to Learn MathematicsAdding Integers
Less
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© Glencoe/McGraw-Hill 148 Mathematics: Applications and Concepts, Course 2
Dartboard Puzzles
Three darts are thrown. Each dart must land on a different space inorder to count. Find the highest and the lowest possible scores.
1. 2. 3.
highest score: highest score: highest score:lowest score: lowest score: lowest score:
In these problems, five darts are thrown. Each dart must land on adifferent space in order to count. Solve each puzzle.
4. Find three ways to make the score �5. 5. Find three ways to make the score 0.
�5
�5
�5
�5
�5
�5
�5
�50
�5
�10
�10
�10�10
�15
�15
�10
�20
�20
�20
�25
0
0
10
10
10
10
105
55
55
5
5
50
35
25
25
20
20 2015
1515
15
15
15
20
50
�10
�10
�1
�3
�3
�3
�2
�2
�8
�7
�7
�9�8
�9
�5
�5
�6
�6
�4
�4
�1
�1
0
0
0
0
5
5
8
8
2
22
9
10
10
3
3
3
7
7
6
6
4
4
1
1
1
9
100
�75�50
�50
25
25
�150
�150
75
75
�10
�10�75
10
10
200
200
0
�1
�4�1
�4
�3
�3
�8
�8
�7
�7�2
�2
�6�6�5
�5
�8
�1 �4
�6�7
�2
26
3
5
4
3
170
�6
�5
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Less
on
3–5
© Glencoe/McGraw-Hill 149 Mathematics: Applications and Concepts, Course 2
Find 6 � 9.
6 � 9 � 6 � (�9) To subtract 9, add �9.� �3 Simplify.
Find �10 � (�12).
�10 � (�12) � �10 � 12 To subtract �12, add 12.� 2 Simplify.
Evaluate a � b if a � �3 and b � 7.
a � b � �3 � 7 Replace a with �3 and b with 7.� �3 � (�7) To subtract 7, add �7.� �10 Simplify.
Subtract.
1. 7 � 9 2. 20 � (�6)
3. �10 � 4 4. 0 � 12
5. �7 � 8 6. 13 � 18
7. �20 � (�5) 8. �8 � (�6)
9. 25 � (�14) 10. �75 � 50
11. 15 � 65 12. 19 � (�10)
Evaluate each expression if m � �2, n � 10, and p � 5.
13. m � 6 14. 9 � n
15. p � (�8) 16. p � m
17. m � n 18. �25 � p
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionSubtracting Integers
To subtract an integer, add its opposite.
© Glencoe/McGraw-Hill 150 Mathematics: Applications and Concepts, Course 2
Subtract.
1. 5 � 2 2. 6 � (�7)
3. �3 � 2 4. 8 � 13
5. �7 � (�7) 6. 6 � 12
7. 15 � (�7) 8. �15 � 6
9. �3 � 8 10. �10 � 12
11. 13 � (�12) 12. 14 � (�22)
13. 10 � (�20) 14. �16 � 14
15. �25 � 25 16. 6 � (�31)
17. �18 � (�40) 18. 15 � (�61)
Evaluate each expression if r � �4, s � 10, and t � �7.
19. r � 7 20. t � s
21. s � (�8) 22. t � r
23. s � t 24. r � s
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsSubtracting Integers
© Glencoe/McGraw-Hill 151 Mathematics: Applications and Concepts, Course 2
Subtract.
Practice: Word ProblemsSubtracting Integers
NAME ________________________________________ DATE ______________ PERIOD _____
1. FOOTBALL A team gained 5 yards ontheir first play of the game. Then theylost 6 yards. Find the total change inyardage.
2. CHECKING Your checking account isoverdrawn by $50. You write a checkfor $20. What is the balance in youraccount?
3. TEMPERATURE The average temperaturein Calgary, Canada, is 22�C in July and�11�C in January. Find the range ofthe highest and lowest temperatures inCalgary.
4. ROLLER COASTER A roller coaster beginsat 90 feet above ground level. Then itdescends 105 feet. Find the height ofthe coaster after the first descent.
5. SAVINGS Sonia has $235 in her savingsaccount. She withdraws $45. What isleft in her savings account?
6. BEACH Wai and Kuri were digging inthe sand at the beach. Wai dug a holethat was 15 inches below the surface,and Kuri dug a hole that was 9 inchesbelow the surface. Find the differencein the depths of their holes.
Less
on
3–5
© Glencoe/McGraw-Hill 152 Mathematics: Applications and Concepts, Course 2
Pre-Activity Complete the Mini Lab at the top of page 128 in your textbook.Write your answers below.
1. Write a related addition sentence for each subtraction sentence.
Use a number line to find each difference. Write an equivalentaddition sentence for each.
2. 1 � 5
3. �2 � 1
4. �3 � 4
5. 0 � 5
6. Compare and contrast subtraction sentences with their relatedaddition sentences.
Reading the LessonTell how you would solve each of the following on a number line.Then solve.
7. �8 � (�6)
8. 6 � 8
Helping You Remember9. Write the rule that tells how to subtract integers. Then give an example.
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsSubtracting Integers
© Glencoe/McGraw-Hill 153 Mathematics: Applications and Concepts, Course 2
Distance on the Number LineTo find the distance between two points on a number line, subtract theircoordinates. Then, take the absolute value of the difference.
�4 � 3 � �7
�7 � 7
You can also find the distance by finding the absolute value of the differenceof the coordinates.
�4 � 3 � 7
Graph each pair of points. Then write an expression using absolutevalue to find the distance between the points.
1. A at �5 and B at 2
2. C at �7 and D at �1
3. E at �5 and F at 5
4. W at 0 and X at 6
5. Y at �4 and Z at 0
�8 �7 �6 �5 �4 �3 �2 �1 876543210
�8 �7 �6 �5 �4 �3 �2 �1 876543210
�8 �7 �6 �5 �4 �3 �2 �1 876543210
�8 �7 �6 �5 �4 �3 �2 �1 876543210
�8 �7 �6 �5 �4 �3 �2 �1 876543210
�8 �7 �6 �5 �4 �3 �2 �1 876543210
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
Less
on
3–5
© Glencoe/McGraw-Hill 154 Mathematics: Applications and Concepts, Course 2
Multiply 5(�2).
5(�2) � �10 The integers have different signs. The product is negative.
Multiply �3(7).
�3(7) � �21 The integers have different signs. The product is negative.
Multiply �6(�9).
�6(�9) � 54 The integers have the same sign. The product is positive.
Multiply (�7)2.
(�7)2 � (�7)(�7) There are 2 factors of �7.� 49 The product is positive.
Simplify �2(6c).
�2(6c) � (�2 · 6)c Associative Property of Multiplication.� �12c Simplify.
Simplify 2(5x).
2(5x) � (2 · 5)x Associative Propery of Multiplication.� 10x Simplify.
Multiply.
1. �5(8) 2. �3(�7) 3. 10(�8)
4. �8(3) 5. �12(�12) 6. (�8)2
ALGEBRA Simplify each expression.
7. �5(7a) 8. 3(�2x) 9. 4(6f)
10. 7(6b) 11. �6(�3y) 12. 7(�8g)
ALGEBRA Evaluate each expression if a � �3, b � �4, and c � 5.
13. �2a 14. 9b 15. ab
16. �3ac 17. �2c2 18. abc
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionMultiplying Integers
The product of two integers with different signs is negative.
The product of two integers with the same sign is positive.
6
Less
on
3–6
Practice: SkillsMultiplying Integers
© Glencoe/McGraw-Hill 155 Mathematics: Applications and Concepts, Course 2
Multiply.
1. �4(6) 2. �2(�8)
3. 12(�4) 4. �6(5)
5. �10(�9) 6. �(5)2
7. (�5)2 8. �30(5)
9. 20(�6) 10. �14(�6)
11. (�13)2 12. �7(15)
ALGEBRA Simplify each expression.
13. �3(4y) 14. 7(�3x)
15. 7(5g) 16. 7(7w)
17. 3(�3y) 18. �2(�10h)
ALGEBRA Evaluate each expression if g � �5, h � �3, and k � 4.
19. �3g 20. 5h
21. 7gk 22. �2gh
23. �10h 24. �2h2
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsMultiplying Integers
© Glencoe/McGraw-Hill 156 Mathematics: Applications and Concepts, Course 2
Multiply.
NAME ________________________________________ DATE ______________ PERIOD _____
1. TEMPERATURE Suppose the temperatureoutside is dropping 3 degrees eachhour. How much will the temperaturedrop in 8 hours?
2. DIVING A deep-sea diver descendsbelow the surface of the water at a rateof 60 feet each minute. What is thedepth of the diver after 10 minutes?
3. STOCK A computer stock lost 2 pointseach hour for 6 hours. Find the totalpoints the stock fell.
4. DROUGHT A drought can cause thelevel of the local water supply to dropby a few inches each week. Suppose thelevel of the water supply drops 2 incheseach week. How far will it havedropped in 4 weeks?
5. MONEY Mrs. Rockwell lost money onan investment at a rate of $4 per day.How much did she lose after twoweeks?
6. TENNIS BALLS Josh purchased 8 cans oftennis balls. The cans came with 3 ballsin each can. How many balls did Joshpurchase?
Reading to Learn MathematicsMultiplying Integers
© Glencoe/McGraw-Hill 157 Mathematics: Applications and Concepts, Course 2
Pre-Activity Complete the Mini Lab at the top of page 134 in your textbook.Write your answers below.
1. Write a multiplication sentence that describes the model.
Find each product using counters.
2. 3(�2) 3. 4(�3)
4. 1(�7) 5. 5(�2)
6. Write a rule for finding the sign of the product of a positive and negativeinteger.
Reading the Lesson7. Give an example that shows how multiplication is the same as repeated
addition. In your example, tell what the addend is.
8. How does the sentence 4(�2) � �2(4) illustrate the Commutative Property of Multiplication?
9. Complete each of the following sentences with the word positive ornegative.
a. The product of two integers with different signs is _______________.
b. The product of two integers with the same sign is _______________.
Helping You Remember10. You know the rule for determining the sign of the product of two integers
when the signs are alike or different. Consider the product of threeintegers. With a partner summarize the signs of the products of 3integers when three, two, one or none of the integers are positive.
NAME ________________________________________ DATE ______________ PERIOD _____
Less
on
3–6
© Glencoe/McGraw-Hill 158 Mathematics: Applications and Concepts, Course 2
Integer MazeFind your way through the maze by moving to the expression in an adjacent section withthe next highest value.
Start−50
−55
20 − 20
−32 + 28
−12 + 2
−3 + (−4)
4 + (−12)
−13 + 12−10 + 16
−35 + 5
6 − 8
5(−9)
9(−6)
−8(5)
−3(5)
−5(−6)
−1(3)
−4(2)
−3(−5)
3(−3)(−5)
−2(−5)(−1)
6(−10)9(−1)
3 + (−3)
30 − (−10)
−4(5)(−1)
3(5)(−5)
5(−4 + 9)
(−4)2
−52
−[12 − (−8)]
2[−5 • (−5)]
−2(−12 + 7)
−2(−1)
−5
0 − 6
15 − 50
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Less
on
3–7
© Glencoe/McGraw-Hill 159 Mathematics: Applications and Concepts, Course 2
Divide 30 � (�5).
30 � (�5) The integers have different signs.
30 � (�5) � �6 The quotient is negative.
Divide �100 � (�5).
�100 � (�5) The integers have the same sign.
�100 � (�5) � 20 The quotient is positive.
Divide.
1. �12 � 4 2. �14 � (�7)
3. �18
24. �6 � (�3)
5. �10 � 10 6. ��
8200
7. 350 � (�25) 8. �420 � (�3)
9. 54450
10. �
12656
ALGEBRA Evaluate each expression if d � �24, e � �4, and f � 8.
11. 12 � e 12. 40 � f
13. d � 6 14. d � e
15. f � e 16. e2 � f
17. �ed 18. ef � 2
19. f
e2
2
20. dfe
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionDividing Integers
The quotient of two integers with different signs is negative.
The quotient of two integers with the same sign is positive.
© Glencoe/McGraw-Hill 160 Mathematics: Applications and Concepts, Course 2
Divide.
1. �15 � 3 2. �24 � (�8)
3. 22 � (�2) 4. �49 � (�7)
5. �8 � (�8) 6. �36
4
7. 225 � (�15) 8. �09
9. �38 � 2 10. 644
11. �500 � (�50) 12. �189 � (�21)
ALGEBRA Evaluate each expression if m � �32, n � 2, and p � �8.
13. m � n 14. p � 4
15. p2 � m 16. m � p
17. �
np 18. p � n2
19. n
p2
2 20. 18
p� n
21. m � (np) 22. mp � n
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsDividing Integers
© Glencoe/McGraw-Hill 161 Mathematics: Applications and Concepts, Course 2
Divide.
Practice: Word ProblemsDividing Integers
NAME ________________________________________ DATE ______________ PERIOD _____
1. STOCK MARKET During a 5-dayworkweek, the stock market decreasedby 65 points. Find the average dailychange in the market for the week.
2. MOTION Mr. Diaz decreased the speedof his car by 30 miles per hour over aperiod of 10 seconds. Find the averagechange in speed each second.
3. WEATHER Over the past seven days,Mrs. Cho found that the temperatureoutside had dropped a total of35 degrees. Find the average drop intemperature each day.
4. BASKETBALL The basketball team losttheir last 6 games. They lost by a totalof 48 points. Find the average numberof points by which each game was lost.
5. POPULATION The enrollment at DavisMiddle School dropped by 60 studentsover a 5-year period. What is theaverage yearly drop in enrollment?
6. SUBMARINE A submarine descends at arate of 60 feet each minute. How longwill it take it to descend to a depth of660 feet below the surface?
Less
on
3–7
© Glencoe/McGraw-Hill 162 Mathematics: Applications and Concepts, Course 2
Pre-Activity Complete the Mini Lab at the top of page 138 in your textbook.Write your answers below.
Find each quotient using counters.
1. �6 � 2
2. �12 � 3
Reading the LessonWrite two division sentences related to each of the followingmultiplication sentences.
3. �6(�3) � 18 4. �21(�2) � 42
5. �6(3) � �18 6. 2(�21) � �42
7. Complete each of the following sentences with the word positive ornegative.
a. The quotient of two integers with different signs is _______________.
b. The quotient of two integers with the same sign is _______________.
8. In the division sentence �72 � 8 � �9, identify the dividend, the divisor,and the quotient.
Helping You Remember9. Describe how the operations of multiplication and division are opposite of
each other. Are these operations opposite in all cases? What is the oneinteger that cannot be a divisor?
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsDividing Integers
© Glencoe/McGraw-Hill 163 Mathematics: Applications and Concepts, Course 2
Division by Zero?Some interesting things happen when you try to divide by zero. For example,look at these two equations.
50 � x
00 � y
If you can write the equations above, you can also write the two equationsbelow.
0 � x � 5 0 � y � 0
However, there is no number that will make the left equation true. Thisequation has no solution. For the right equation, every number will make ittrue. The solutions for this equation are “all numbers.”
Because division by zero leads to impossible situations, it is not a “legal” stepin solving a problem. People say that division by zero is undefined, or notpossible, or simply not allowed.
Describe the solution set for each equation.
1. 4x � 0 2. x � 0 � 0
3. x � 0 � x 4. 0x � 0
5. 0x � x 6.
0x � 5
What values for x must be excluded to prevent division by 0?
7. x12 8. x �
11
9. x �1
1 10. 20x
11. 2x1� 2 12. 3x
1� 6
Explain what is wrong with this “proof.”
13. Step 1 0 � 1 � 0 and 0 � (�1) � 0
Step 2 Therefore, 00
� 1 and 00
� �1.
Step 3 Therefore, 1 � �1.
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
Less
on
3–7
Write the letter for the correct answer in the blank at the right of each question.1. Write an integer that represents 8�C below 0.
A. �8 B. 8 C. �8 D. 8 1.
2. Evaluate 3.F. 6 G. �3 H. 3 I. 0 2.
3. Evaluate �9.A. 0 B. 9 C. 18 D. �9 3.
4. Write the integers represented by S and T on the number line.F. S, 4; T, �2 G. S, �4; T, 2H. S, 2; T, �4 I. S, �2; T, 4 4.
5. Order 4, �5, 3, and 0 from least to greatest.A. 0, 3, 4, �5 B. �5, 0, 3, 4 C. 4, 3, 0, �5 D. 0, �5, 3, 4 5.
6. Simplify 4(9a).F. 13a G. 5a H. 36a I. 49a 6.
7. What value of z makes 14 � 3 � z a true sentence?A. 11 B. 17 C. �11 D. �17 7.
Replace each � to make a true sentence.
8. �4 � 0F. � G. � H. � I. � 8.
9. 3 � �6A. � B. � C. � D. � 9.
Use the graph to name the ordered pair for each point.
10. JF. (0, �2) G. (0, 2)H. (�2, 0) I. (2, 0) 10.
11. MA. (�3, 3) B. (3, 3)C. (�3, �3) D. (3, �3) 11.
12. RF. (2, 4) G. (4, 2) H. (�2, 4) I. (2, �4) 12.
13. TA. (1, �4) B. (�1, �4) C. (�1, 4) D. (�4, �1) 13.
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© Glencoe/McGraw-Hill 165 Mathematics: Applications and Concepts, Course 2
Chapter 3 Test, Form 1
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Add, subtract, multiply, or divide.
14. 8 � (�7)F. 1 G. �1 H. 15 I. �15 14.
15. �7(�6)A. �1 B. �42 C. 42 D. �13 15.
16. 18 � (�9)F. 9 G. 2 H. �9 I. �2 16.
17. 35 � 12A. �23 B. 23 C. 47 D. �47 17.
18. (�3)2
F. �9 G. �1 H. �6 I. 9 18.
19. 0 � 20A. 20 B. �20 C. 2 D. 0 19.
Evaluate each expression if a � �4, b � 6, and c � �1.
20. 10 � aF. �6 G. 6 H. 14 I. �14 20.
21. bcA. 6 B. �6 C. 5 D. �5 21.
22. �
b12
F. �18 G. �6 H. �2 I. 2 22.
23. 9 � bA. 54 B. �3 C. 3 D. 15 23.
24. b � 2F. 4 G. �4 H. 62 I. �3 24.
25. c � 5A. �4 B. 4 C. 6 D. �6 25.
Bonus Find |t � v| when t � 9 and v � 5. B:
© Glencoe/McGraw-Hill 166 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 3 Test, Form 1 (continued)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
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ent
Write the letter for the correct answer in the blank at the right of each question.
1. Write an integer that represents a 5-yard loss.A. 5 B. �5 C. �5 D. 5 1.
2. Evaluate �7.F. 7 G. � �7 H. 14 I. �7 2.
3. Evaluate 5��2.A. �7 B. �3 C. 3 D. 7 3.
4. Write the integers represented by A and B on the number line.F. A, �3; B, �5 G. A, 3; B, �5H. A, �3; B, 5 I. A, �5; B, 3 4.
5. Order 6, �2, 3, 0, and �1 from least to greatest.A. �2, �1, 0, 3, 6 B. �2, 0, �1, 3, 6C. �1, �2, 0, 3, 6 D. 0, �1, �2, 3, 6 5.
6. Simplify �8(3z).F. 24z G. �5z H. �24z I. �11z 6.
7. What value of q makes �15 � (�9) � q a true sentence?A. �24 B. �6 C. 24 D. 6 7.
Replace each � to make a true sentence.
8. �5 � 2F. � G. � H. � I. � 8.
9. �1 � �7A. � B. � C. � D. � 9.
Use the graph to name the ordered pair for each point.
10. QF. (0, 3) G. (2, �3)H. (�2, �3) I. (�2, 3) 10.
11. EA. (0, 3) B. (2, �3)C. (3, 0) D. (�3, 0) 11.
12. PF. (�2, �3) G. (�3, �2) H. (3, �2) I. (�3, 2) 12.
13. BA. (�1, �4) B. (�1, 4) C. (�4, 1) D. (1, �4) 13.
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Chapter 3 Test, Form 2A
© Glencoe/McGraw-Hill 167 Mathematics: Applications and Concepts, Course 2
Add, subtract, multiply, or divide.
14. 12 � (�5)F. 7 G. �7 H. 17 I. �17 14.
15. �8(�10)A. �80 B. 80 C. �18 D. 18 15.
16. ��
4284
F. 2 G. �2 H. �24 I. 0.5 16.
17. �37 � 8A. 45 B. �29 C. �45 D. 296 17.
18. 7(�3)
F. �213 G. 4 H. 21 I. �21 18.
19. 0 � 5A. 10 B. �5 C. 0 D. 5 19.
Evaluate each expression if x � �3, y � 8, and z � �4.
20. y � (�5)F. 3 G. �13 H. 13 I. �3 20.
21. xzA. �12 B. 12 C. �7 D. �1 21.
22. �8 � yF. 0 G. �16 H. �1 I. 1 22.
23. x � 11A. 8 B. 14 C. �8 D. �14 23.
24. z22
F. 4 G. �8 H. �4 I. 8 24.
25. x � y � zA. �1 B. 1 C. 15 D. �15 25.
Bonus Find q � r when q � �3 and r � 3. B:
© Glencoe/McGraw-Hill 168 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 3 Test, Form 2A (continued)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
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Chapter 3 Test, Form 2B
Write the letter for the correct answer in the blank at the right of each question.1. Write an integer that represents a loss of $20.
A. �20 B. �20 C. 20 D. 20 1.
2. Evaluate �4.F. �4 G. � �4 H. 4 I. 8 2.
3. Evaluate 7��3.A. 10 B. 4 C. �4 D. �10 3.
4. Write the integers represented by Q and R on the number line.F. Q, �3; R, 1 G. Q, 3; R, �1
H. Q, �1; R, 3 I. Q, 1; R, �3 4.
5. Order 3, �4, 0, 1, and �2 from least to greatest.A. �4, �2, 0, 1, 3 B. 3, 1, 0, �2, �4C. 3, 1, 0, �4, �2 D. �2, �4, 0, 1, 3
5.
6. Simplify �5(7r).F. 35r G. �35r H. 2r I. �12r 6.
7. What value of s makes �18 � (�5) � s a true sentence?A. 13 B. �23 C. 23 D. �13 7.
Replace each � to make a true sentence.
8. 10 � �10F. � G. � H. � I. � 8.
9. �3 � 5A. � B. � C. � D. � 9.
Use the graph to name the ordered pair for each point.
10. SF. (5, �5) G. (�1, 3)H. (5, 5) I. (�5, 5) 10.
11. RA. (�6, 5) B. (5, �6)C. (5, 5) D. (6, 5) 11.
12. AF. (�3, 4) G. (�3, �4) H. (3, �4) I. (�4, �3) 12.
13. MA. (3, 1) B. (�1, 3) C. (1, 3) D. (3, �1) 13.
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© Glencoe/McGraw-Hill 169 Mathematics: Applications and Concepts, Course 2
Chapter 3 Test, Form 2B (continued)
Add, subtract, multiply, or divide.
14. 11 � (�7)F. 4 G. �4 H. �18 I. 18 14.
15. �5(�11)A. 16 B. �16 C. 55 D. �55 15.
16. �15 � (�3)F. �5 G. 5 H. �18 I. 18 16.
17. �39 � 7A. �46 B. 46 C. 273 D. �32 17.
18. 8(�4)F. �2 G. 32 H. 4 I. �32 18.
19. 0 � 7A. 0 B. �7 C. �14 D. 7 19.
Evaluate each expression if a � 4, b � 7, and c � �5.
20. b � (�4)F. �3 G. �11 H. 3 I. 11 20.
21. acA. 20 B. �20 C. �1 D. 9 21.
22. �b7
F. 14 G. 0 H. 1 I. �1 22.
23. a � 13A. �17 B. 9 C. 17 D. �9 23.
24. c2 � 5F. 5 G. �5 H. 2 I. 30 24.
25. a � b � cA. 16 B. �6 C. �16 D. 6 25.
Bonus Find s � t when s � �5 and t � 5. B:
© Glencoe/McGraw-Hill 170 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Write an integer for each situation.
1. a deposit of $45 1.
2. 5�C below 0 2.
For Questions 3 and 4, evaluate each expression.
3. |�11| 3.
4. |4| � |�6| 4.
5. Graph the set of numbers {�3, 2, �5} on a number line. 5.
For Questions 6–8, replace each � with � or � to make a true sentence.
6. �16 � �22 6.
7. �5 � 1 7.
8. 12 � �1 8.
9. Order �2, 5, 0, 7, �1, and 3 from least to greatest. 9.
10. TEMPERATURE On the same day, a thermometer registered �4�F in Athens and �9�F in Seattle. Which Washington 10.city was warmer?
Name the ordered pair for each point graphed at the right. Thenidentify in which quadrant each point lies.
11. S 11.
12. T 12.
Graph and label each point.
13. Q(1, �2) 13–14.
14. W(0, 4)
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© Glencoe/McGraw-Hill 171 Mathematics: Applications and Concepts, Course 2
Chapter 3 Test, Form 2C
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Add, subtract, multiply, or divide.
15. �25 � (�12) 15.
16. 8(�11) 16.
17. 40 � (�8) 17.
18. 4 � (�2) 18.
19. (�3)2 19.
20. 6 � (�9) 20.
21. �9 � 8 21.
22. ��
63
22.
Evaluate each expression if x � �4, y � 6, and z � �3.
23. 15 � (�y) 23.
24. 20 � x 24.
25. 7 � z 25.
26. �2(3z) 26.
27. 1xy2
27.
28. x � y 28.
29. xy 29.
30. x � z 30.
For Questions 31 and 32, simplify each expression.
31. �5(3a) 31.
32. 3(�4c) 32.
33. What value of w makes �24 � (�13) � w a true sentence? 33.
Bonus Find a � b when a � �6 and b � 6. B:
© Glencoe/McGraw-Hill 172 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 3 Test, Form 2C (continued)
Write an integer for each situation.1. 300 feet above sea level 1.
2. a loss of $13 2.
For Questions 3 and 4, evaluate each expression.
3. |�13| 3.
4. |3|�|�5| 4.
5. Graph the set of numbers on a number line: {�6, 2, �3}. 5.
For Questions 6–8, replace each � with � or � to make a true sentence.
6. �7 � �5 6.
7. 0 � �35 7.
8. �1 � 1 8.
9. Order 3, �8, 4, 2, �5, and �1 from least to greatest. 9.
10. TEMPERATURE On the same day, a thermometer registered 10.�10�F in Duluth and �7�F in St. Paul. Which Minnesota city was warmer?
Name the ordered pair for each point graphed at the right. Thenidentify in which quadrant each point lies.
11. R 11.
12. Q 12.
Graph and label each point.
13. A(�3, �2) 13–14.
14. S(0, 2)
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© Glencoe/McGraw-Hill 173 Mathematics: Applications and Concepts, Course 2
Chapter 3 Test, Form 2C
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 3 Test, Form 2D
Add, subtract, multiply, or divide.
15. �2 � 4 15.
16. 7(�10) 16.
17. �60
317.
18. 6 � (�3) 18.
19. (�5)2 19.
20. �1 � (�11) 20.
21. �10 � 7 21.
22. �8 � (�4) 22.
Evaluate each expression if a � �8, b � 5, and c � �2.
23. 8 � (�b) 23.
24. 16 � c 24.
25. 9 � c 25.
26. �5(3c) 26.
27. ab � 10 27.
28. a � b 28.
29. ab 29.
30. a � c 30.
For Questions 31 and 32, simplify each expression.
31. �6(5z) 31.
32. �4(�2y) 32.
33. What value of d makes �25 � (�16) � d a true sentence? 33.
Bonus Find |x�y| when x � �7 and y � 7. B:
© Glencoe/McGraw-Hill 174 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 3 Test, Form 2D (continued)
Chapter 3 Test, Form 3
Write an integer for each situation.
1. 380 meters above sea level 1.
2. a loss of 11 yards 2.
For Questions 3 and 4, evaluate each expression.
3. |�16| 3.
4. |�3|�|1| 4.
5. Graph the set of numbers {5, �3, 2, �4} on a number line. 5.
For Questions 6–8, replace each � with � or � to make a true sentence.
6. �28 � �30 6.
7. �8 � 5 7.
8. 11 � �10 8.
9. Order �5, �7, 4, 0, �3, and 10 from least to greatest. 9.
10. TEMPERATURE On the same day, a thermometer registered 10.�8�C in Chicago, Illinois and �5�C in Detroit, Michigan.Which city was colder?
Name the ordered pair for each point graphed at the right. Thenidentify in which quadrant each point lies.
11. A 11.
12. B 12.
Graph and label each point.
13. L(�2, �4) 13–14.
14. M(0, �3)
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© Glencoe/McGraw-Hill 175 Mathematics: Applications and Concepts, Course 2
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 3 Test, Form 3 (continued)
Add, subtract, multiply, or divide.
15. �40 � 12 15.
16. 6(�4) 16.
17. �03
17.
18. �5 � 3 � 2 18.
19. �(112) 19.
20. �13 � 18 � (�2) 20.
21. �18 � (�21) 21.
22. �56 � (�7) 22.
Evaluate each expression if q � �8, r � 5, and s � �3.
23. q � r 23.
24. �2qr 24.
25. �9 � s 25.
26. qs � 8 26.
27. �rs2 27.
28. �10
s2
� q 28.
29. �s � 2 29.
30. q � r � s 30.
For Questions 31 and 32, simplify each expression.
31. �5(7e) 31.
32. (�2b)(3c) 32.
33. What value of a makes �18 � (�3) � a a true statement? 33.
Bonus PATTERNS Find the next two numbers in the following B:pattern: 96, �48, 24, �12, …Then describe the pattern.
© Glencoe/McGraw-Hill 176 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Ass
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Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one way orinvestigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.
1. Horatio, Glen, Carlos, and Meredith played in the company golftournament. Their scores after the first round are listed below.
Horatio: two over par (�2)Glen: three under par (�3)Carlos: four over par (�4)Meredith: one under par (�1)
a. Explain how to compare integers.
b. Order the golf scores from least to greatest.
c. Explain what is meant by the absolute value of a number.
d. Find the absolute value of Glen’s score.
e. Glen’s second round score is �2. Use counters to find Glen’s total scoreafter two rounds.
f. Meredith’s second round score is �3. Find her total score after tworounds.
g. Horatio’s second round score is �3. Use counters to find the differencebetween Horatio’s first and second round scores.
2. On graph paper, draw a coordinate plane.
a. Graph and label the point A(4, 6). Describe how you locate this point.Identify the quadrant in which the point lies.
b. Multiply the x-coordinate of point A by �2 and multiply the y-coordinate of point A by �1. Name the new point B and give itscoordinates. Graph point B and identify the quadrant in which it lies.
c. Divide the x-coordinate of point B by 4 and divide the y-coordinate ofpoint B by �3. Name the new point C and give its coordinates. Graphpoint C and identify the quadrant in which it lies.
© Glencoe/McGraw-Hill 177 Mathematics: Applications and Concepts, Course 2
Chapter 3 Extended Response Assessment
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
© Glencoe/McGraw-Hill 178 Mathematics: Applications and Concepts, Course 2
Chapter 3 Vocabulary Test/Review
Choose from the terms above to complete each sentence.
1. Vertical bars before and after a number indicate 1._______________, the distance a number is from zero on a number line.
2. A(n) _______________ is a number that can be graphed on 2.a number line.
3. When you _______________ a point, you locate its position 3.on a coordinate plane by drawing a dot at the location of its ordered pair.
4. The _______________ is the opposite of any number. When 4.added to the number, the sum equals 0.
5. The _______________ is the first number of an ordered pair. 5.It corresponds to a number on the x-axis.
6. The _______________ is the vertical number line of a 6.coordinate plane.
7. A(n) _______________ is an integer less than zero. 7.
8. The point at which the number lines of a coordinate plane 8.intersect is called the _______________.
9. Two integers that are the same distance from 0 on a 9.number line, but on opposite sides of 0, are called _______________ .
10. A(n) _______________ is one of four sections of a coordinate 10.plane.
In your own words, define each term.
11. coordinate plane
12. ordered pair
absolute value (p. 107)additive inverse (p. 121)coordinate grid (p. 112)coordinate plane (p. 112)graph (p. 106)integer (p. 106)
negative integer (p. 106)opposite (p. 121)ordered pair (p. 112)origin (p. 112)positive integer (p. 106)quadrant (p. 113)
x-axis (p. 112)x-coordinate (p. 112)y-axis (p. 112)y-coordinate (p. 112)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
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© Glencoe/McGraw-Hill 179 Mathematics: Applications and Concepts, Course 2
1. MULTIPLE-CHOICE TEST ITEM Order the integers �2, 4, 7, �5, 1.and 1 from least to greatest A. �2, �5, 1, 4, 7 B. 1, �2, 4, �5, 7C. �5, �2, 1, 4, 7 D. 7, 4, 1, �2, �5
Write an integer for each situation. 2.
2. 15�F below 0 3. a deposit of $24 3.
Evaluate each expression.
4. |�3| 4.
5. |9| 5.
6. |13|�|�2| 6.
Replace each � with � or � to make a true sentence.
7. �34 � �134 7.
8. �27 � �8 8.
9. 12 � �12 9.
10. �111 � �888 10.
On the coordinate plane, graph and label each point.
1. S(1, 0) 1–3.
2. R(�3, �1)
3. T(3, �2)
4. Find 12 � (�7). 4.
5. Evaluate x � y if x � �8 and y � 4. 5.
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Chapter 3 Quiz(Lessons 3-3 and 3-4)
Chapter 3 Quiz(Lessons 3-1 and 3-2)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
© Glencoe/McGraw-Hill 180 Mathematics: Applications and Concepts, Course 2
1. Find the quotient of �56 and 14. 1.
Divide.
2. �63 � (�9) 2.
3. �21 � 7 3.
Evaluate each expression if r � 18, s � �4, and t � �3.
4. r � t 4.
5. st � 6 5.
Subtract or multiply.
1. �8 � 5 1.
2. �10(�3) 2.
3. �(92) 3.
4. 15 � (�20) 4.
Evaluate each expression if f � �4, g � 2, and h � 7.
5. �9g 5.
6. �h � 3 6.
7. h � f 7.
8. fgh 8.
Simplify each expression.
9. �2(9e) 9.
10. 5(�4s) 10.
Chapter 3 Quiz(Lessons 3-5 and 3-6)
Chapter 3 Quiz(Lesson 3-7)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Write the letter for the correct answer in the blank at the right of each question.
1. Evaluate |�5|.A. �4 B. 5 C. �|5| D. �5 1.
2. Evaluate |�6|�|2|.F. 4 G. �8 H. 8 I. �4 2.
3. Order the integers 6, 4, 18, �4, 3, and �7 from least to greatest.A. 3, 4, 6, 18, �4, �7 B. 18, 6, 4, 3, �4, �7C. �4, �7, 3, 4, 6, 18 D. �7, �4, 3, 4, 6, 18 3.
4. Find �8 � 12.F. �20 G. �4 H. 20 I. 4 4.
5. Evaluate a � b if a � �3 and b � �14.A. �17 B. �11 C. 17 D. 11 5.
6. Identify the quadrant in which (�1, 4) lies.F. I G. II H. III I. IV 6.
Write an integer for each situation. 7.
7. a deposit of $50 8. 3 inches below normal 8.
Replace each � with � or � to make a true sentence. 9.
9. 14 � �2 10. �111 � �11 10.
Name the ordered pair for each letter and identify its quadrant.
11. Q 11.
12. U 12.
13. X 13.
14. Z 14.
15. Find (�12) � 8 � (�7). 15.
© Glencoe/McGraw-Hill 181 Mathematics: Applications and Concepts, Course 2
Chapter 3 Mid-Chapter Test(Lessons 3-1 through 3-4)
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
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1. Evaluate the expression 2d � 5f if d � 4 and f � 2. 1.(Lesson 1-4)
TENNIS For Questions 2–4, use the stem-and-leaf plot below. It shows the number of matches won by each member of the East High School Tennis Team.
2. How many members are on 2.the tennis team? (Lesson 2-5)
3. Find the mean, median, mode, 3.and range for these data.(Lessons 2-3, 2-4)
3|1 � 31
4. Write a sentence or two to describe the distribution of the 4.number of matches won. (Lesson 2-5)
5. Evaluate |3| � |�2|. (Lesson 3-1) 5.
6. Order 61, �72, 50, �31, �12, and 12 from least to greatest. 6.(Lesson 3-2)
7. Which is greater, �9 or 8? (Lesson 3-2) 7.
Graph and label each point. (Lesson 3-3)
8. A(2, �2) 9. M(�3, �1) 8–9.
Add, subtract, multiply, or divide.
10. 4 � (�4) (Lesson 3-4) 10.
11. �18 � 12 (Lesson 3-5) 11.
12. �5(�6) (Lesson 3-6) 12.
13. 12 � (�3) (Lesson 3-7) 13.
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© Glencoe/McGraw-Hill 182 Mathematics: Applications and Concepts, Course 2
Chapter 3 Cumulative Review(Chapters 1–3)
Stem Leaf0 3 41 5 7 82 0 2 2 4 73 1 3 5 54 05 4
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
essm
ent
1. Evaluate 7b � a if a � 5 and b � 2. (Lesson 1-4)
A. 9 B. 33 C. 12 D. 21 1.
2. If there are 28 basketball games during a season, how many gamesended in a winning score of 70–79points? (Lesson 2-1)
F. 28 G. 8H. 3 I. 5 2.
3. Find the median of the following data. 5, 9, 13, 4, 7, 5, 10 (Lesson 2-4)
A. 5 B. 7 C. 8 D. 9 3.
4. ENVIRONMENT The bar graph represents the content (inpercents) of U.S. landfills.Which is not a true statement? (Lesson 2-7)
F. The mode is paper.G. Metal makes up 8% of
landfills.H. Plastic and paper make up
most of landfills.I. The median is 24%. 4.
5. What is the range of data in the followingbox-and-whisker plot?(Lessons 2-3, 2-6)
A. 5 B. 16 C. 7 D. 15 5.
6. Evaluate |9| � |�4|. (Lesson 3-1)
F. 13 G. �13 H. �5 I. 5 6.
7. In which quadrant is the point (�5, 7) located? (Lesson 3-2)
A. I B. II C. III D. IV 7.
8. Evaluate �x � 11 if x � �10. (Lesson 3-5)
F. �21 G. 21 H. �1 I. 1 8.
9. Evaluate ac � b if a � �8, b � �6, and c � 3. (Lessons 3-6, 3-7)
A. �144 B. 4 C. 16 D. �4 9. DCBA
IHGF
DCBA
IHGF
DCBA
2 4 6 8 10 12 14 16 18 2220
IHGF
Other
Food
& Ya
rd W
aste
Rubb
er &
Leath
er
Metal
15
20
10
0
5
25
30
35
Perc
ent
Plasti
cPa
per
U.S. Landfill Content
8%
24%
6%
11%
30%
21%
DCBA
IHGF
DCBA
© Glencoe/McGraw-Hill 183 Mathematics: Applications and Concepts, Course 2
Standardized Test Practice (Chapters 1–4)
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
Score Frequency
50–59 2
60–69 5
70–79 ?
80–89 12
90–99 6
10. Solve 20 � n4 (Lesson 1-5) 10. 11.
11. Evaluate �ba if a � 16 and b � �2. (Lesson 3-7)
12. The frequency table 12.summarizes the number of DVDs owned by students in a classroom.Describe the interval and scale. (Lesson 2-1)
13. Find 6 � (�12). (Lesson 3-4) 13.
14. GEOMETRY Consider the points A(�2, 4), B(3, 4), C(3, 0), and D(�2, 0). (Lesson 3-3)
a. Graph the points in the same coordinate plane. Describe howyou locate point A.
b. Multiply the x-coordinate of point B by �1 and multiply the
y-coordinate of point B by 12. Name the new point B and give its
coordinates. Graph point B and identify the quadrant in which it lies.
y
xO
�2�3�4
�2�3�4 21 43
1234
Part 3: Extended Response
Instructions: Write your answers below or to the right of the questions.
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
Part 2: Short Response\Grid In
Instructions: Enter your grid in answers by writing each digit of the answer in acolumn box and then shading in the appropriate circle that corresponds to that entry.Write answers to short answer questions in the space provided.
© Glencoe/McGraw-Hill 184 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice (continued)
(Chapters 1–4)
Numberof DVDs Tally
0–4 5
5–9 52
10–14 55
15–19 3
20–24 2 2
3
10
7
5
Frequency
© Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 2
Standardized Test PracticeStudent Recording Sheet (Use with pages 146–147 of the Student Edition.)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Part 1:
Solve the problem and write your answer in the blank.
For grid in questions, also enter your answer by writing each number or symbolin a box. Then fill in the corresponding circle for that number or symbol.
11. 12. 14. 19.
12. (grid in)
13.
14. (grid in)
15.
16.
17.
18.
19. (grid in)
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
Select the best answer from the choices given and fill in the corresponding oval.
Multiple Choice
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
Part 2: Short Response/Grid in
Record your answer for Question 20 on the back of this paper.
Part 3: Extended Response
An
swer
s
General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.
Exercise 20 Rubric
Standardized Test PracticeRubric (Use to score the Extended Response question on page 147 of the Student Edition.)
Score Specific Criteria4 The 3 points are correctly graphed on a coordinate plane with all labels in place. The
quadrant where no point on the graph is represented is recognized as quadrant IV.The figure formed by connecting the points is recognized as a triangle. Anunderstanding that the way to double the size of the triangle is to multiply eachordered pair by 2 is demonstrated. The table in expanded and all values arecorrectly computed.
3 All of the parts of the question are correctly answered, but the graph is not correctlylabeled. OROne of the points is not correctly graphed, but all other parts of the question arecorrect. ORThe quadrant where no point on the graph is represented is not recognized asquadrant IV, but all other parts of the question are correct. ORThe figure formed by connecting the points is not recognized as a triangle, but allother parts of the question are correct. ORThere is no understanding that the way to double the size of the triangle is tomultiply the ordered pair by 2, but all other parts of the question are correct. ORThere are computational errors in the expanded table, but all other parts of thequestion are correct.
2 Two parts of the question (the graph, the recognition of the quadrant, therecognition of the triangle, the understanding of how to double the size of the figure,or the completion of the table) are incorrect.
1 Only one or two parts of the question (the graph, the recognition of the quadrant,the recognition of the triangle, the understanding of how to double the size of thefigure, or the completion of the table) are correct.
0 Response is completely incorrect.
© Glencoe/McGraw-Hill A2 Mathematics: Applications and Concepts, Course 2
© Glencoe/McGraw-Hill A3 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
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0M
athe
mat
ics:
App
licat
ions
and
Con
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s, C
ours
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Wri
te a
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each
sit
uat
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.
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elow
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152.
a pr
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10 A
.D.
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38 p
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6 fe
et a
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a w
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f $2
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ost
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of $
150
150
9.a
depo
sit
of $
4141
10.
240
B.C
.�
240
11.
a w
age
incr
ease
of
$120
120
12.
60 f
eet
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24.
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NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsIn
teg
ers
and
Ab
solu
te V
alu
e
Lesson 3–1
©G
lenc
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ill12
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Wri
te a
n i
nte
ger
that
rep
rese
nts
160
fee
t b
elow
sea
lev
el.
Bec
ause
it
repr
esen
ts b
elow
sea
leve
l,th
e in
tege
r is
�16
0.
Eva
luat
e |�
2|.
On
th
e n
um
ber
lin
e,th
e gr
aph
of
�2
is
2 u
nit
s aw
ay f
rom
0.S
o,�
2 �
2.
Wri
te a
n i
nte
ger
for
each
sit
uat
ion
.
1.12
°C a
bove
012
2.a
loss
of
$24
�24
3.a
gain
of
20 p
oun
ds20
4.fa
llin
g 6
feet
�6
Eva
luat
e ea
ch e
xpre
ssio
n.
5.1
212
6.�
150
150
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88
8.7
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NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Inte
ger
s an
d A
bso
lute
Val
ue
Inte
gers
less
tha
n ze
ro a
re n
egat
ive
inte
ger
s.In
tege
rs g
reat
er t
han
zero
are
po
siti
ve in
teg
ers.
Th
e ab
solu
te v
alu
eof
an
inte
ger
is t
he d
ista
nce
the
num
ber
is f
rom
zer
o on
a n
umbe
r lin
e.Tw
ove
rtic
al b
ars
are
used
to
repr
esen
t ab
solu
te v
alue
.The
sym
bol f
or a
bsol
ute
valu
e of
3 is
3
.
8�
7�6�
5�4
67
54
32
1�
3�2�
10
nega
tive
inte
gers
posi
tive
inte
gers
zero
is n
eith
erpo
sitiv
e no
r neg
ativ
e
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A4 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill13
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
106
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.W
hat
doe
s a
valu
e of
�2
repr
esen
t?a
2-ya
rd lo
ss
2.O
n w
hic
h d
own
did
th
ey l
ose
the
mos
t ya
rds?
3rd
do
wn
3.H
ow c
an y
ou r
epre
sen
t a
gain
of
9 ya
rds?
�9
or
9
Rea
din
g t
he
Less
on
4.E
xpre
ss e
ach
of
the
foll
owin
g in
wor
ds.
5.O
n t
he
foll
owin
g n
um
ber
lin
e,dr
aw a
cir
cle
arou
nd
the
neg
ativ
e in
tege
rsan
d la
bel
them
neg
ativ
e.D
raw
a r
ecta
ngl
e ar
oun
d th
e po
siti
ve i
nte
gers
and
labe
l th
em p
osit
ive.
Hel
pin
g Y
ou
Rem
emb
er6.
Sh
ow a
cla
ssm
ate
how
a n
um
ber
lin
e ca
n b
e u
sed
to s
how
neg
ativ
e an
dpo
siti
ve i
nte
gers
.Exp
lain
th
e di
ffer
ence
bet
wee
n s
ome
inte
gers
an
d th
eab
solu
te v
alu
es o
f th
ose
inte
gers
.Dra
w a
nu
mbe
r li
ne
to s
how
wh
at y
oum
ean
.S
ee s
tud
ents
’wo
rk.
�2
�1
02
34
�3
�4
1
nega
tive
posi
tive
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Read
ing
to L
earn
Mat
hem
atic
sIn
teg
ers
and
Ab
solu
te V
alu
e
Sym
bol
s
�7
�7
neg
ativ
e se
ven
|7|
po
siti
ve s
even
abso
lute
val
ue
of
seve
n
Wor
ds
©G
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cGra
w-H
ill13
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Prac
tice:
Wor
d Pr
oble
ms
Inte
ger
s an
d A
bso
lute
Val
ue
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.D
EATH
VA
LLEY
Th
e lo
wes
t po
int
in t
he
Un
ited
Sta
tes
is D
eath
Val
ley
inC
alif
orn
ia.I
ts a
ltit
ude
is
282
feet
bel
owse
a le
vel.
Wri
te a
n i
nte
ger
to r
epre
sen
tth
e al
titu
de o
f D
eath
Val
ley.
�28
2
2.R
AIN
A m
eteo
rolo
gist
rep
orte
d th
at i
nth
e m
onth
of A
pril
th
ere
wer
e 3
inch
esm
ore
rain
fall
th
an n
orm
al.W
rite
an
inte
ger
to r
epre
sen
t th
e am
oun
t of
rain
fall
abo
ve n
orm
al i
n A
pril
.3
3.A
RC
HIM
EDES
A f
amou
s m
ath
emat
icia
nan
d ph
ysic
ist
nam
ed A
rch
imed
es w
asbo
rn i
n 2
87 B
.C.W
rite
an
in
tege
r to
expr
ess
the
year
of
his
bir
th.
�28
7
4.TE
MPE
RA
TUR
EIn
ou
r w
orld
’s t
ropi
cal
rain
for
ests
,th
e av
erag
e te
mpe
ratu
re o
fev
ery
mon
th i
s 64
deg
rees
abo
ve z
ero
or h
igh
er.W
rite
an
in
tege
r to
exp
ress
this
tem
pera
ture
.64
5.ST
OC
K M
AR
KET
A c
erta
in s
tock
gai
ned
5 po
ints
in
on
e da
y an
d lo
st 4
poi
nts
the
nex
t da
y.W
rite
in
tege
rs t
ore
pres
ent
the
stoc
k’s
gain
s an
d lo
sses
for
the
two
days
.5;
�4
6.A
LTIT
UD
EA
n a
irpl
ane
pilo
t ch
ange
d h
isal
titu
de b
y 10
0 m
eter
s.D
escr
ibe
wh
atth
is c
ould
mea
n.
Sam
ple
an
swer
:T
he
airp
lan
e co
uld
be
flyi
ng
100
met
ers
hig
her
or
100
met
ers
low
er,1
00 o
r �
100.
Lesson 3–1
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A5 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill13
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Rep
lace
th
e �
wit
h �
or �
to m
ake
�1
��
6 a
tru
e se
nte
nce
.
Gra
ph e
ach
in
tege
r on
a n
um
ber
lin
e.
Sin
ce �
1 is
to
the
righ
t of
�6,
�1
��
6.
Ord
er t
he
inte
gers
2,�
3,0,
�5
from
lea
st t
o gr
eate
st.
To
orde
r th
e in
tege
rs,g
raph
th
em o
n a
nu
mbe
r li
ne.
Ord
er t
he
inte
gers
by
read
ing
from
lef
t to
rig
ht:
�5,
�3,
0,2.
1.R
epla
ce t
he
�w
ith
< o
r >
to m
ake
�5
��
10 a
tru
e se
nte
nce
.�
2.O
rder
�1,
5,�
3,an
d 2
from
lea
st t
o gr
eate
st.
�3,
�1,
2,5
3.O
rder
0,�
4,�
2,an
d 7
from
gre
ates
t to
lea
st.
7,0,
�2,
�4
4.O
rder
�3,
�2
,4,0
,an
d �
5 fr
om g
reat
est
to l
east
.4,
|�2|
,0,�
3,�
5
�2
�1
02
3�
31
45
�5
�4
�6
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�1
02
3�
3�
71
4�
5�
4�
6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Co
mp
arin
g a
nd
Ord
erin
g In
teg
ers
Whe
n tw
o nu
mbe
rs a
re g
raph
ed o
n a
num
ber
line,
the
num
ber
to t
he le
ft is
alw
ays
less
tha
n (<
) th
enu
mbe
r to
the
rig
ht.T
he n
umbe
r to
the
rig
ht is
alw
ays
grea
ter
than
(>
) th
e nu
mbe
r to
the
left.
�2
�1
02
3�
3�
41
4M
od
el
Wo
rds
Sym
bo
ls�
3 is
less
than
�1.
�1
is g
reat
er th
an �
1.
The
sym
bol p
oint
s to
th
e le
sser
num
ber.
�3
� �
1�
1 �
�3
©G
lenc
oe/M
cGra
w-H
ill13
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Jaim
e Es
cala
nte
Jaim
e E
scal
ante
(19
30–
)
was
bor
n i
n L
a P
az,B
oliv
ia,
and
cam
e to
th
e U
nit
ed S
tate
s in
196
3.F
or t
en y
ears
,h
e w
orke
d at
odd
jobs
to
supp
ort
him
self
an
d h
is f
amil
y w
hil
e pu
rsu
ing
his
dre
am—
beco
min
g ce
rtif
ied
to t
each
h
igh
sch
ool
mat
hem
atic
s in
Cal
ifor
nia
.As
a m
ath
emat
ics
teac
her
,he
has
bec
ome
wel
l kn
own
for
his
abi
lity
to
insp
ire
stu
den
ts t
o su
ccee
d in
mat
hem
atic
s at
lev
els
they
nev
er t
hou
ght
poss
ible
.In
198
8,th
e st
ory
ofM
r.E
scal
ante
an
d a
grou
p of
his
stu
den
ts w
as t
he
subj
ect
of t
he
popu
lar
mot
ion
pic
ture
Sta
nd
an
d D
eliv
er.
Mr.
Esc
alan
te t
each
es c
once
pts
stu
den
ts m
ust
mas
ter
if
they
are
to
succ
eed
in h
igh
sch
ool
and
coll
ege
mat
hem
atic
s.O
ne
of t
hes
e is
th
e co
nce
pt o
f ab
solu
te v
alu
e.F
or i
nst
ance
,a
stu
den
t sh
ould
be
able
to
solv
e an
equ
atio
n l
ike
y
�6
quic
kly
usi
ng
men
tal
mat
h.H
ere’
s h
ow.
You
kn
ow t
hat
6
�6
and
�6
� 6
.
So,
the
equ
atio
n
y�
6 h
as t
wo
solu
tion
s:6
and
�6.
Sol
ve e
ach
eq
uat
ion
.(H
int:
On
e eq
uat
ion
has
no
solu
tion
.)
1.a
�
8 2.
r
�0
3.j
�
�3
8,�
80
no
so
luti
on
4.t
�
1�
155.
10 �
m
� 3
6.c
�
4�
1614
,�14
7,�
720
,�20
7.5
z�
608.
12�
g
� 4
9.48
�8
x12
,�12
3,�
36,
�6
10.
2d
�
3 �
511
.4
p�
9 �
59
12.
7z
� 1
2 �
12
1,�
117
,�17
0
13.
Su
ppos
e th
at t
he
valu
e of
xca
n b
e se
lect
ed f
rom
th
e se
t {�
2,�
1,0,
1,2}
.F
ind
all
of t
he
solu
tion
s of
th
e eq
uat
ion
x
�x.
0,1,
2
14.
On
e of
th
ese
stat
emen
ts i
s fa
lse.
Wh
ich
on
e is
it?
Exp
lain
.
a.T
he
abso
lute
val
ue
of e
very
in
tege
r is
pos
itiv
e.
b.
Th
ere
is a
t le
ast
one
inte
ger
wh
ose
abso
lute
val
ue
is z
ero.
c.T
he
abso
lute
val
ue
of a
n i
nte
ger
is n
ever
neg
ativ
e.S
tate
men
t a
isfa
lse;
the
abso
lute
val
ue
of
0 is
0,w
hic
h is
no
t p
osi
tive
.
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
Lesson 3–1
Answers (Lessons 3-1 and 3-2)
© Glencoe/McGraw-Hill A6 Mathematics: Applications and Concepts, Course 2
Prac
tice:
Wor
d Pr
oble
ms
Co
mp
arin
g a
nd
Ord
erin
g In
teg
ers
©G
lenc
oe/M
cGra
w-H
ill13
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
HIS
TORY
OF
WR
ITIN
GF
or E
xerc
ises
1 a
nd
2,u
se t
he
tabl
e be
low
.It
show
s im
port
ant
even
ts i
n t
he
his
tory
of
wri
tin
g.
EXTR
EME
TEM
PER
ATU
RES
For
Exe
rcis
es 3
–5,
use
th
e ta
ble
belo
w.I
t sh
ows
the
extr
eme
tem
pera
ture
s fo
r fo
ur
stat
es.T
empe
ratu
res
are
in d
egre
es F
ahre
nh
eit.
Ext
rem
e T
emp
erat
ure
s (�
F)
Eve
nt
Th
e Il
iad
and
the
Od
ysse
yar
eco
mpo
sed
by H
omer
.70
0 B
C
Ap
rox.
Yea
r
T’s
ai L
un
in
ven
ts p
aper
.10
5 A
D
Dat
e of
old
est
exis
tin
g pa
pyru
s22
00 B
C
Ovi
d w
rote
Met
amor
phos
is.
5 A
D
Tor
ah i
s co
mpi
led.
450
BC
Met
al t
ype
deve
lope
d in
Kor
ea12
41 A
D
Sta
te
Neb
rask
a
Ala
bam
a
�47
Mai
ne
3
�30
Low
est
Flo
rida
�2
Hig
hes
t
118
104
101
109
1.W
rite
eac
h y
ear
as a
n i
nte
ger.
�70
0,10
5,�
2200
,5,�
450,
1241
2.O
rder
th
e in
tege
rs f
rom
Exe
rcis
e 1
from
lea
st t
o gr
eate
st.W
rite
a s
ente
nce
desc
ribi
ng
the
earl
iest
an
d m
ost
rece
nt
even
ts i
n t
he
tabl
e.�
2200
,�70
0,�
450,
5,10
5,12
41;
See
stu
den
ts’
wo
rk.
3.A
rran
ge t
he
hig
hes
t te
mpe
ratu
res
from
gre
ates
t to
lea
st.
118,
109,
104,
101
4.W
hat
is
the
med
ian
low
tem
pera
ture
for
thes
e fo
ur
stat
es?
�16
5.N
ebra
ska’
s lo
wes
t te
mpe
ratu
re w
as�
47�F
,an
d M
ain
e’s
low
est
tem
pera
ture
was
�30
�F.W
rite
a t
rue
stat
emen
tu
sin
g th
e tw
o te
mpe
ratu
res
wit
h t
he
sym
bol
�or
�.
Sam
ple
an
swer
:�
47 �
�30
6.M
ON
EYM
r.F
irew
alks
pay
s cl
ose
atte
nti
on t
o h
ow m
uch
mon
ey i
s in
his
chec
kin
g ac
cou
nt.
On
e w
eek
he
depo
site
d $2
30,s
pen
t $1
5 on
a l
un
ch,
and
loan
ed $
25 t
o a
frie
nd.
Wri
te e
ach
tran
sact
ion
as
an i
nte
ger,
and
list
th
emfr
om l
east
to
grea
test
.�
25,�
15,
230
Lesson 3–2
Prac
tice:
Ski
llsC
om
par
ing
an
d O
rder
ing
Inte
ger
s
©G
lenc
oe/M
cGra
w-H
ill13
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Rep
lace
eac
h �
wit
h <
or
> to
mak
e a
tru
e se
nte
nce
.
1.�
15 �
�16
�2.
�8
��
7�
3.0
��
2�
4.�
2 �
�5
�
5.�
25 �
3�
6.�
14 �
�20
�
7.�
4�
3�
8.�
6�
�7
�
9.�
7�
2
�10
.�
8 �
�9
�
Det
erm
ine
wh
eth
er e
ach
sen
ten
ce i
s tr
ue
or f
als
e.If
fa
lse,
chan
ge o
ne
nu
mb
er t
o m
ake
the
sen
ten
ce t
rue.
11.
�7
�3
tru
e
12.
2 �
0tr
ue
13.
�20
��
22fa
lse;
Sam
ple
an
swer
:�
20�
22
14.
12 �
15tr
ue
15.
3 �
�5
fals
e;S
amp
le a
nsw
er:
3 �
�1
16.
�2
��
3fa
lse;
Sam
ple
an
swer
:�
2�
3
17.
8�
�10
tr
ue
18.
�11
�11
tru
e
19.
�4
�4
tru
e
20.
�9
��
10
tru
e
Ord
er t
he
inte
gers
fro
m l
east
to
grea
test
.
21.
12,�
6,20
,�47
,�11
22.
9,�
6,0,
�4,
17,�
11�
47,�
11,�
6,12
,20
�11
,�6,
�4,
0,9,
17
Ord
er t
he
inte
gers
fro
m g
reat
est
to l
east
.
23.
�40
,65,
�7,
24,�
6,15
24.
�13
,0,
7,�
8,�
5,2
65
,24,
15,�
6,�
7,�
40�
13,
7,2
,0,
�5,
�8
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A7 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill13
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Qu
anti
tati
ve C
om
par
iso
ns
An
un
usu
al t
ype
of p
robl
em i
s fo
un
d on
som
e st
anda
rdiz
ed m
ult
iple
-ch
oice
test
s.T
his
pro
blem
typ
e is
cal
led
the
quan
tita
tive
com
pari
son
.
In e
ach
qu
anti
tati
ve c
ompa
riso
n q
ues
tion
,you
are
giv
en t
wo
quan
titi
es,o
ne
inC
olu
mn
A a
nd
one
in C
olu
mn
B.Y
ou a
re t
o co
mpa
re t
he
two
quan
titi
es a
nd
shad
e on
e of
fou
r ci
rcle
s on
an
an
swer
sh
eet.
Sh
ade
circ
le A
if t
he
quan
tity
in
Col
um
n A
is
grea
ter;
Sh
ade
circ
le B
if t
he
quan
tity
in
Col
um
n B
is
grea
ter;
Sh
ade
circ
le C
if t
he
two
quan
titi
es a
re e
qual
;
Sh
ade
circ
le D
if t
he
rela
tion
ship
can
not
be
dete
rmin
ed f
rom
th
ein
form
atio
n g
iven
.
Sh
ade
the
corr
ect
oval
to
the
left
of
each
pro
ble
m n
um
ber
.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
DC
BA
DC
BA
DC
BA
DC
BA
DC
BA
DC
BA
DC
BA
DC
BA
DC
BA
DC
BA
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
B A C B A A D C A C
Col
um
n A
ten
bil
lion
dol
lars
0.00
6�
2
1,00
0 m
illi
on d
olla
rs
20 i
nch
es
0.00
2�
6
the
peri
met
er o
f a
squ
are
wit
h a
n a
rea
of 2
5 sq
uar
ein
ches
Col
um
n B
hal
f of
on
e th
ird
one
fift
h
the
grea
test
pos
sibl
epr
odu
ct o
f tw
o od
dpo
siti
ve n
um
bers
les
sth
an 2
0
the
grea
test
pos
sibl
epr
odu
ct o
f tw
o ev
enpo
siti
ve n
um
bers
les
sth
an 2
0
0.00
0000
001
�x
is x
if g
reat
er t
han
0
|x|
|x�
1|
|y|
|�y|
2|x|
if
x
0|x
| if
x
0
�x
if x
is l
ess
than
0|x
|if
xis
les
s th
an 0
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
109
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.W
hat
is
the
win
d ch
ill
if t
her
e is
a w
ind
at 2
0 m
iles
per
hou
r an
d th
ete
mpe
ratu
re i
s 5�
?�
15
2.W
hic
h i
s co
lder
,a t
empe
ratu
re o
f 15
�w
ith
a 2
0 m
ile-
per-
hou
r w
ind
or a
te
mpe
ratu
re o
f 10
�w
ith
a 1
0 m
ile-
per-
hou
r w
ind?
10�
wit
h 1
0 m
ph
win
d
3.G
raph
bot
h w
ind
chil
ls f
oun
d in
Exe
rcis
e 2
on a
nu
mbe
r li
ne.
Rea
din
g t
he
Less
on
For
Exe
rcis
es 4
an
d 5
,exp
ress
eac
h o
f th
e fo
llow
ing
in w
ord
s.T
hen
grap
h t
he
nu
mb
ers
on a
nu
mb
er l
ine.
4.�
1 �
0n
egat
ive
1 is
less
th
an 0
5.3
��
23
is g
reat
er t
han
neg
ativ
e 2
6.W
hen
tw
o n
um
bers
are
gra
phed
on
a n
um
ber
lin
e,w
hat
can
you
tel
lab
out
the
nu
mbe
r to
th
e le
ft?
the
nu
mbe
r to
th
e ri
ght?
Sam
ple
an
swer
:Th
e n
um
ber
to
th
e le
ft is
alw
ays
less
th
anth
e n
um
ber
to
th
e ri
gh
t.T
he
nu
mb
er t
o t
he
rig
ht
is a
lway
sg
reat
er t
han
th
e n
um
ber
to
th
e le
ft.
Hel
pin
g Y
ou
Rem
emb
er7.
Wri
te a
set
of
six
nu
mbe
rs,s
ome
posi
tive
an
d so
me
neg
ativ
e.E
xpla
in h
owyo
u c
an u
se a
nu
mbe
r li
ne
to o
rder
th
e n
um
bers
fro
m l
east
to
grea
test
.S
ee s
tud
ents
’wo
rk.
�2
�1
02
34
�3
�4
1
�2
�1
02
34
�3
�4
1
�2
�1
02
3�
3�
4�
51
Lesson 3–2
Read
ing
to L
earn
Mat
hem
atic
sC
om
par
ing
an
d O
rder
ing
Inte
ger
s
©G
lenc
oe/M
cGra
w-H
ill13
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A8 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill14
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Nam
e th
e or
der
ed p
air
for
each
poi
nt
grap
hed
at
the
righ
t.T
hen
id
enti
fy t
he
qu
adra
nt
in w
hic
h e
ach
poi
nt
lies
.
1.A
(�1,
1),I
I2.
B(5
,5),
I
3.C
(�5,
�5)
,III
4.D
(4,�
3),I
V
5.E
(3,0
),x-
axis
6.F
(�5,
4),I
I
7.G
(0,�
5),y
-axi
s8.
H(�
2,�
2),I
II
9.I
(�3,
6),I
I10
.J
(3,�
5),I
V
Gra
ph
an
d l
abel
eac
h p
oin
t on
th
e co
ord
inat
e p
lan
e.
11.
N(�
1,3)
12.
V(2
,�4)
13.
C(4
,0)
14.
P(�
6,2)
15.
M(�
5,0)
16.
K(�
1,5)
17.
I(�
3,�
3)18
.A
(5,�
3)
19.
D(0
,�5)
Nam
e th
e or
der
ed p
air
for
each
poi
nt
on t
he
city
map
at
the
righ
t.
20.
Cit
y H
all
(0,0
)
21.
Th
eate
r(�
7,�
5)
22.
Gas
Sta
tion
(7,2
)
23.
Gro
cery
(�5,
5)
y
xO �2
�3
�4
�5
21
45
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3
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ery
Thea
ter
City
Hal
l
Gas
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ion�
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6
y
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F
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NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsT
he
Co
ord
inat
e P
lan
e
Lesson 3–3
©G
lenc
oe/M
cGra
w-H
ill13
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Nam
e th
e or
der
ed p
air
for
poi
nt
P.T
hen
id
enti
fy t
he
qu
adra
nt
inw
hic
h P
lie
s.
•S
tart
at
the
orig
in.
•M
ove
4 u
nit
s le
ft a
lon
g th
e x-
axis
.•
Mov
e 3
un
its
up
on t
he
y-ax
is.
Th
e or
dere
d pa
ir f
or p
oin
t P
is (
�4,
3).
Pis
in
th
e u
pper
lef
t qu
adra
nt
or q
uad
ran
t II
.
Gra
ph
an
d l
abel
th
e p
oin
t M
(0,�
4).
•S
tart
at
the
orig
in.
•M
ove
0 u
nit
s al
ong
the
x-ax
is.
•M
ove
4 u
nit
s do
wn
on
th
e y-
axis
.•
Dra
w a
dot
an
d la
bel
it M
(0,�
4).
Nam
e th
e or
der
ed p
air
for
each
poi
nt
grap
hed
at
the
righ
t.T
hen
id
enti
fy t
he
qu
adra
nt
in w
hic
h
each
poi
nt
lies
.
1.P
(2,�
3),I
V2.
Q(�
3,�
2),I
II
3.R
(1,3
),I
4.S
(�2,
2),I
I
Gra
ph
an
d l
abel
eac
h p
oin
t on
th
e co
ord
inat
e p
lan
e.
5.A
(�1,
1)6.
B(0
,�3)
7.C
(3,2
)8.
D(�
3,�
1)
9.E
(1,�
2)10
.F
(1,3
)
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( 0, �
4)M
P
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Th
e C
oo
rdin
ate
Pla
ne
The
co
ord
inat
e p
lan
eis
use
d to
loca
te p
oint
s.T
he h
oriz
onta
l num
ber
line
is t
he x
-axi
s.T
he v
ertic
alnu
mbe
r lin
e is
the
y-a
xis.
The
ir in
ters
ectio
n is
the
ori
gin
.
Poi
nts
are
loca
ted
usin
g o
rder
ed p
airs
.The
firs
t nu
mbe
r in
an
orde
red
pair
is t
he x
-co
ord
inat
e;th
ese
cond
num
ber
is t
he y
-co
ord
inat
e.
The
coo
rdin
ate
plan
e is
sep
arat
ed in
to fo
ur s
ectio
ns c
alle
d q
uad
ran
ts.
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A9 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill14
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
112
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.S
upp
ose
Ter
rell
sta
rts
at t
he
corn
er o
f R
uss
el a
nd
Mai
n a
nd
wal
ks
1 bl
ock
nor
th a
nd
2 bl
ocks
eas
t.N
ame
the
inte
rsec
tion
of
his
loc
atio
n.
Hig
hla
nd
an
d M
ob
ile
2.U
sin
g th
e w
ords
nor
th,s
outh
,wes
t,an
d ea
st,w
rite
dir
ecti
ons
to g
o fr
om
the
corn
er o
f S
choo
l an
d H
igh
lan
d to
th
e co
rner
of
Mai
n a
nd
Oak
.S
amp
le a
nsw
er:W
alk
6 b
lock
s w
est,
1 b
lock
so
uth
,an
d 1
blo
ck w
est.
Rea
din
g t
he
Less
on
3.T
he
wor
d co
ord
inat
eco
mes
fro
m t
wo
Lat
in w
ords
th
at m
ean
“to
arr
ange
toge
ther
.”H
ow a
re c
oord
inat
es u
sed
toge
ther
to
loca
te a
poi
nt
in a
coor
din
ate
plan
e?S
amp
le a
nsw
er:T
he
loca
tio
n o
f a
po
int
in a
co
ord
inat
e p
lan
e d
epen
ds
on
po
siti
on
alo
ng
an
x-a
xis
and
po
siti
on
alo
ng
a y
-axi
s.B
oth
po
siti
on
s,ca
lled
th
e x-
coo
rdin
ate
and
th
e y-
coo
rdin
ate,
are
nee
ded
in o
rder
to
loca
te a
po
int
in a
co
ord
inat
e p
lan
e.T
he
pai
r o
f co
ord
inat
es is
cal
led
an
ord
ered
pai
r.T
he
pai
r o
f co
ord
inat
esis
ord
ered
su
ch t
hat
th
e x-
coo
rdin
ate
is a
lway
s th
e fi
rst
nu
mb
er o
f th
ep
air
and
th
e y-
coo
rdin
ate
is a
lway
s th
e se
con
d n
um
ber
of
the
pai
r.
4.L
ook
at t
he
coor
din
ate
plan
e at
th
e ri
ght.
Nam
e th
e or
dere
d pa
ir f
or e
ach
poi
nt
grap
hed
.A
(�3,
3);
B(3
,2);
C(3
,�2)
5.In
th
e co
ordi
nat
e pl
ane
in E
xerc
ise
4,te
ll w
hic
hqu
adra
nt
each
of
the
poin
ts i
s in
.P
oin
t A
is in
qu
adra
nt
II,p
oin
t B
is in
qu
adra
nt
I,an
dp
oin
t C
is in
qu
adra
nt
IV.
Hel
pin
g Y
ou
Rem
emb
er6.
Wri
te a
way
to
rem
embe
r th
e n
ames
of
the
fou
r qu
adra
nts
of
the
coor
din
ate
plan
e.S
amp
le a
nsw
er:
Beg
in in
th
e q
uad
ran
t w
her
e b
oth
co
ord
inat
es a
re p
osi
tive
(th
e u
pp
er-r
igh
t q
uad
ran
t).T
his
isq
uad
ran
t I.
Nam
e th
e re
st o
f th
e q
uad
ran
ts b
y g
oin
g c
ou
nte
rclo
ckw
ise
aro
un
d t
he
qu
adra
nts
:II
(up
per
-lef
t q
uad
ran
t),I
II (l
ow
er-l
eft
qu
adra
nt)
,IV
(lo
wer
-rig
ht
qu
adra
nt)
.
y
xO �2
�3
�4
�2
�3
�4
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43
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B C
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Read
ing
to L
earn
Mat
hem
atic
sT
he
Co
ord
inat
e P
lan
e
©G
lenc
oe/M
cGra
w-H
ill14
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
SCH
OO
LF
or E
xerc
ises
1–4
,use
th
e co
ord
inat
e p
lan
e at
th
e ri
ght.
It
show
s a
map
of
the
room
s in
a
jun
ior
hig
h s
choo
l.
�2
�3
�4
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�2
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45
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Art
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nce
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ary
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nce
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xO12345
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pute
r Lab
Spec
ial S
ervi
ces
Engl
ish
Hist
ory
Coun
selo
r
Athl
etic
Dep
t.
Mus
ic
Exit
Mat
h
Nurs
e
Prac
tice:
Wor
d Pr
oble
ms
Th
e C
oo
rdin
ate
Pla
ne
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.T
hal
ia i
s in
th
e ro
om l
ocat
ed a
t (�
2,1)
.W
hat
roo
m i
s sh
e in
? D
escr
ibe
in w
ords
how
to
get
from
th
e or
igin
to
this
poi
nt.
Co
mp
ute
r L
ab;
mov
e 2
un
its
toth
e le
ft a
nd
on
e u
nit
up
.
2.T
hal
ia’s
nex
t cl
ass
is 8
un
its
to t
he
righ
t an
d 5
un
its
dow
n o
n t
he
map
from
wh
ere
she
is n
ow.I
n w
hat
roo
m i
sT
hal
ia’s
nex
t cl
ass?
Fin
d th
e or
dere
dpa
ir t
hat
rep
rese
nts
th
e lo
cati
on o
f th
atro
om.
Mu
sic
roo
m;
(6,�
4)
3.T
yron
e is
in
th
e A
rt r
oom
,bu
t h
is n
ext
clas
s is
in
th
e H
isto
ry r
oom
.Giv
eT
yron
e di
rect
ion
s on
how
to
get
to t
he
His
tory
roo
m.
Sam
ple
an
swer
:W
alk
9 u
nit
s to
th
e ri
gh
t,an
dth
en 5
un
its
do
wn
.
4.O
n t
he
map
,wh
ich
cla
ssro
oms
are
loca
ted
in t
he
thir
d qu
adra
nt?
Des
crib
eth
e co
ordi
nat
es o
f al
l po
ints
in
th
e th
ird
quad
ran
t.S
cien
ce a
nd
Mat
hro
om
s;th
e x-
an
d y
-co
ord
inat
esar
e al
l neg
ativ
e.
5.N
EIG
HB
OR
HO
OD
Del
sin
mad
e a
map
of
his
nei
ghbo
rhoo
d in
su
ch a
way
th
atea
ch i
nte
rsec
tion
is
a po
int
on a
coor
din
ate
plan
e.R
igh
t n
ow,D
elsi
nst
ands
at
poin
t (�
4,�
3).G
ive
the
orde
red
pair
of
wh
ere
he
wil
l be
if
mov
es 5
un
its
to t
he
righ
t an
d 7
un
its
up
on t
he
map
.(1
,4)
6.N
EIG
HB
OR
HO
OD
Ref
er t
o E
xerc
ise
5.In
wh
ich
qu
adra
nt
is D
elsi
n w
hen
he
isdo
ne
wal
kin
g? D
escr
ibe
this
qu
adra
nt.
Qu
adra
nt
I;S
amp
le a
nsw
er:
Qu
adra
nt
I is
the
up
per
-rig
ht
qu
adra
nt.
Lesson 3–3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A10 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill14
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d 4
�(�
6).
Met
hod
1U
se c
oun
ters
.M
eth
od 2
Use
a n
um
ber
lin
e.C
ombi
ne
a se
t of
4 p
osit
ive
cou
nte
rs•
Sta
rt a
t 0.
and
a se
t of
6 n
egat
ive
cou
nte
rs o
n a
mat
.•
Mov
e 4
un
its
righ
t.•
Th
en m
ove
6 u
nit
s le
ft.
Ad
d.
1.�
5 �
(�2)
�7
2.8
�1
93.
�7
�10
3
4.16
�(�
11)
55.
�22
�(�
7)�
296.
�50
�50
0
7.�
10 �
(�10
)�
208.
100
�(�
25)
759.
�35
��
20�
15
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
�8,
b �
�8,
and
c �
4.
10.
a �
1523
11.
b �
(�9)
�17
12.
a �
b0
13.
b �
c�
414
.�
10 �
c�
615
.12
�b
4
�1
01
34
�2
�3
�6 �
4 25
4 �
( �6)
��
2
4 �
( �6)
4 �
( �6)
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2
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�
��
��
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NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Ad
din
g In
teg
ers
For
inte
gers
with
the
sam
e si
gn:
• th
e su
m o
f tw
o po
sitiv
e in
tege
rs is
pos
itive
.•
the
sum
of
two
nega
tive
inte
gers
is n
egat
ive.
For
inte
gers
with
diff
eren
t si
gns,
sub
trac
t th
eir
abso
lute
val
ues.
The
sum
is:
• po
sitiv
e if
the
posi
tive
inte
ger
has
the
grea
ter
abso
lute
val
ue.
• ne
gativ
e if
the
nega
tive
inte
ger
has
the
grea
ter
abso
lute
val
ue.
To a
dd in
tege
rs,
it is
hel
pful
to
use
coun
ters
or
a nu
mbe
r lin
e.
©G
lenc
oe/M
cGra
w-H
ill14
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Lati
tud
e an
d L
on
git
ud
eT
his
wor
ld m
ap s
how
s so
me
of t
he
lati
tude
an
d lo
ngi
tude
lin
es.L
atit
ude
is
mea
sure
d in
deg
rees
nor
th a
nd
sou
th o
f th
e eq
uat
or.L
ongi
tude
is
mea
sure
d in
degr
ees
east
an
d w
est
of t
he
prim
e m
erid
ian
,a l
ine
pass
ing
thro
ugh
Gre
enw
ich
,En
glan
d.(G
reen
wic
h i
s a
subu
rb o
f L
ondo
n.)
Th
e la
titu
de i
s u
sual
ly g
iven
fir
st.F
or e
xam
ple,
the
loca
tion
of
30�S
,60�
W i
slo
wer
Sou
th A
mer
ica.
(Sam
ple
an
swer
s ar
e g
iven
.Stu
den
ts m
ay p
rovi
de
mo
re s
pec
ific
pla
ces.
)
Nam
e a
pla
ce n
ear
each
loc
atio
n.U
se a
n a
tlas
or
oth
er r
efer
ence
sou
rce
to c
hec
k y
our
answ
ers.
1.30
�N,3
0�W
2.30
�S,3
0�E
3.60
�N,1
20�W
Atl
anti
c O
cean
So
uth
Afr
ica
Can
ada
4.15
�N,1
50�W
5.30
�S,1
40�E
6.25
�N,1
00�W
Haw
aii
Au
stra
liaM
exic
o
7.40
�N,1
20�W
8.45
�N,9
0�W
9.40
�N,5
�WC
alifo
rnia
Wis
con
sin
Sp
ain
10.
60�N
,45�
W11
.35
�N,1
40�E
12.
0�,6
0�E
Gre
enla
nd
Jap
anIn
dia
n O
cean
Equ
ator
Prime Meridian60
˚N
30˚N
30˚S
, 60 ˚
W
30˚N
0 ˚
0 ˚
0 ˚
30˚S
30˚S
60˚S
60˚S
60˚N
30˚E
30˚W
60˚E
90˚E
120̊E
150̊E
180̊
E
60˚W
90˚W
120˚W
150W̊En
richm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 3–3
Answers (Lessons 3-3 and 3-4)
© Glencoe/McGraw-Hill A11 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill14
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wri
te a
n a
dd
itio
n e
xpre
ssio
n t
o d
escr
ibe
each
sit
uat
ion
.Th
en f
ind
eac
h s
um
.
Prac
tice:
Wor
d Pr
oble
ms
Ad
din
g In
teg
ers
1.FO
OTB
ALL
A t
eam
gai
ns
20 y
ards
.Th
enth
ey l
ose
7 ya
rds.
20�
(�7)
;13
2.M
ON
EYR
oger
ow
es h
is m
om $
5.H
ebo
rrow
s an
oth
er $
6 fr
om h
er.
(�5)
�(�
6);
�11
3.G
OLF
Juan
ita’
s sc
ore
was
5 o
ver
par
onth
e fi
rst
9 h
oles
.Her
sco
rew
as 4
un
der
par
on t
he
seco
nd
9 h
oles
.5
�(�
4);
1
4.H
OT
AIR
BA
LLO
ON
A b
allo
on r
ises
340
feet
in
to t
he
air.
Th
en i
t de
scen
ds13
0fe
et.
340
�(�
130)
;21
0
5.C
YC
LIN
GA
cyc
list
tra
vels
dow
nh
ill
for
125
feet
.Th
en s
he
trav
els
up
a h
ill
50fe
et.
�12
5�
50;
�75
6.A
IRPL
AN
EA
pla
ne
desc
ends
1,2
00 f
eet.
Th
en i
t de
scen
ds a
not
her
500
fee
t.�
1,20
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lenc
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cGra
w-H
ill14
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Tel
l w
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um
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Prac
tice:
Ski
llsA
dd
ing
Inte
ger
s
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A12 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill14
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Dar
tbo
ard
Pu
zzle
s
Th
ree
dar
ts a
re t
hro
wn
.Eac
h d
art
mu
st l
and
on
a d
iffe
ren
t sp
ace
inor
der
to
cou
nt.
Fin
d t
he
hig
hes
t an
d t
he
low
est
pos
sib
le s
core
s.
1.2.
3.
hig
hes
t sc
ore:
18h
igh
est
scor
e:�
2h
igh
est
scor
e:50
0lo
wes
t sc
ore:
�21
low
est
scor
e:�
23lo
wes
t sc
ore:
�37
5
In t
hes
e p
rob
lem
s,fi
ve d
arts
are
th
row
n.E
ach
dar
t m
ust
lan
d o
n a
dif
fere
nt
spac
e in
ord
er t
o co
un
t.S
olve
eac
h p
uzz
le.
4.F
ind
thre
e w
ays
to m
ake
the
scor
e �
5.5.
Fin
d th
ree
way
s to
mak
e th
e sc
ore
0.
An
swer
s w
ill v
ary.
�5
�5
�5
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25
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26
3
5
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3
17
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NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
©G
lenc
oe/M
cGra
w-H
ill14
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
120
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.W
hat
is
the
char
ge a
t th
e to
p of
a c
lou
d w
her
e th
ere
are
mor
e pr
oton
sth
an e
lect
ron
s?p
osi
tive
2.W
hat
is
the
char
ge a
t th
e bo
ttom
of
a cl
oud
wh
ere
ther
e ar
e m
ore
elec
tron
s th
an p
roto
ns?
neg
ativ
e
Rea
din
g t
he
Less
on
For
Exe
rcis
es 3
an
d 4
,tel
l h
ow y
ou w
ould
sol
ve e
ach
of
the
foll
owin
gon
a n
um
ber
lin
e.T
hen
sol
ve.
3.�
7 �
(�9)
Sta
rtin
g a
t 0,
mov
e le
ft 7
un
its,
then
mov
e le
ftan
oth
er 9
un
its;
�16
.
4.�
7 �
9S
tart
ing
at
0,m
ove
left
7 u
nit
s,th
en m
ove
rig
ht
9 u
nit
s;2.
5.W
hen
you
use
cou
nte
rs t
o ad
d in
tege
rs,w
hat
pro
pert
y ar
e yo
u a
pply
ing
wh
en y
ou r
emov
e ze
ro p
airs
?A
dd
itiv
e In
vers
e P
rop
erty
6.H
ow m
any
un
its
away
fro
m 0
is
the
nu
mbe
r 17
? H
ow m
any
un
its
away
from
0 i
s th
e n
um
ber
�17
? W
hat
are
17
and
�17
cal
led?
17;
17;
op
po
site
s o
r ad
dit
ive
inve
rses
Hel
pin
g Y
ou
Rem
emb
er7.
Wor
k w
ith
a p
artn
er.T
ell
you
r pa
rtn
er h
ow t
o u
se a
bsol
ute
val
ues
to
add
inte
gers
wit
h d
iffe
ren
t si
gns
wh
en t
he
posi
tive
in
tege
r h
as t
he
grea
ter
abso
lute
val
ue.
Th
en h
ave
you
r pa
rtn
er e
xpla
in t
o yo
u h
ow t
o u
seab
solu
te v
alu
es t
o ad
d in
tege
rs w
ith
dif
fere
nt
sign
s w
hen
th
e n
egat
ive
inte
ger
has
th
e gr
eate
r ab
solu
te v
alu
e.S
ee s
tud
ents
’wo
rk.
Read
ing
to L
earn
Mat
hem
atic
sA
dd
ing
Inte
ger
s
Lesson 3–4
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A13 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill15
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Su
btr
act.
1.5
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32.
6 �
(�7)
13
3.�
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7.15
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13 �
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14 �
(�22
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10 �
(�20
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14.
�16
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15.
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16.
6 �
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17.
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76
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luat
e ea
ch e
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ssio
n i
f r
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4,s
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d t
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r �
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s �
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s �
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14
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsS
ub
trac
tin
g In
teg
ers
Lesson 3–5
©G
lenc
oe/M
cGra
w-H
ill14
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d 6
�9.
6 �
9 �
6 �
(�9)
To s
ubtr
act
9, a
dd �
9.�
�3
Sim
plify
.
Fin
d �
10 �
(�12
).
�10
�(�
12)
��
10 �
12To
sub
trac
t �
12,
add
12.
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Sim
plify
.
Eva
luat
e a
�b
if a
��
3 an
d b
�7.
a �
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Rep
lace
aw
ith �
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d b
with
7.
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(�7)
To s
ubtr
act
7, a
dd �
7.�
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S
impl
ify.
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btr
act.
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�9
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2.20
�(�
6)26
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10 �
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144.
0 �
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5.�
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5
7.�
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(�5)
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3910
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75 �
50�
125
11.
15 �
65�
5012
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29
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f m
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17.
m �
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25 �
p�
30
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Su
btr
acti
ng
Inte
ger
sTo
sub
trac
t an
inte
ger,
add
its o
ppos
ite.
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A14 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill15
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 12
8 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.W
rite
a r
elat
ed a
ddit
ion
sen
ten
ce f
or e
ach
su
btra
ctio
n s
ente
nce
.S
amp
le a
nsw
ers:
3 �
(�5)
��
2;�
1 �
(�4)
��
5
Use
a n
um
ber
lin
e to
fin
d e
ach
dif
fere
nce
.Wri
te a
n e
qu
ival
ent
add
itio
n s
ente
nce
for
eac
h.
2.1
�5
1 �
5 �
�4;
1 �
(�5)
��
4
3.�
2 �
1�
2 �
1 �
�3;
�2
�(�
1) �
�3
4.�
3 �
4�
3 �
4 �
�7;
�3
�(�
4) �
�7
5.0
�5
0�
5 �
�5;
0 �
(�5)
��
5
6.C
omp
are
and
con
tras
tsu
btra
ctio
n s
ente
nce
s w
ith
th
eir
rela
ted
addi
tion
sen
ten
ces.
Sam
ple
an
swer
:Th
e su
btr
acti
on
pro
ble
ms
giv
e th
e sa
me
answ
er a
s th
eir
rela
ted
ad
dit
ion
pro
ble
ms.
Su
btr
acti
ng
a p
osi
tive
inte
ger
is t
he
sam
e as
ad
din
g a
neg
ativ
e in
teg
er.
Rea
din
g t
he
Less
on
Tel
l h
ow y
ou w
ould
sol
ve e
ach
of
the
foll
owin
g on
a n
um
ber
lin
e.T
hen
sol
ve.
7.�
8 �
(�6)
Sam
ple
an
swer
:C
han
ge
the
sub
trac
tio
n s
ente
nce
to
an
ad
dit
ion
sen
ten
ce.T
o s
ub
trac
t n
egat
ive
6,ad
d p
osi
tive
6.T
hen
,on
a n
um
ber
lin
e st
art
at 0
,mov
e le
ft 8
un
its,
then
mov
e ri
gh
t 6
un
its;
�2.
8.6
�8
Sam
ple
an
swer
:C
han
ge
the
sub
trac
tio
n s
ente
nce
to
an
ad
dit
ion
sen
ten
ce.T
o s
ub
trac
t 8,
add
neg
ativ
e 8.
Th
en,o
n a
nu
mb
erlin
e st
art
at 0
,mov
e ri
gh
t 6
un
its,
then
mov
e le
ft 8
un
its;
�2.
Hel
pin
g Y
ou
Rem
emb
er9.
Wri
te t
he
rule
th
at t
ells
how
to
subt
ract
in
tege
rs.T
hen
giv
e an
exa
mpl
e.To
su
btr
act
an in
teg
er,a
dd
its
op
po
site
.Sam
ple
an
swer
:12
�(�
3) �
12 �
3 �
15
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Read
ing
to L
earn
Mat
hem
atic
sS
ub
trac
tin
g In
teg
ers
©G
lenc
oe/M
cGra
w-H
ill15
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Su
btr
act.
Prac
tice:
Wor
d Pr
oble
ms
Su
btr
acti
ng
Inte
ger
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.FO
OTB
ALL
A t
eam
gai
ned
5 y
ards
on
thei
r fi
rst
play
of
the
gam
e.T
hen
th
eylo
st 6
yar
ds.F
ind
the
tota
l ch
ange
in
yard
age.
�1
yd
2.C
HEC
KIN
GYo
ur
chec
kin
g ac
cou
nt
isov
erdr
awn
by
$50.
You
wri
te a
ch
eck
for
$20.
Wh
at i
s th
e ba
lan
ce i
n y
our
acco
un
t?�
$70
3.TE
MPE
RA
TUR
ET
he
aver
age
tem
pera
ture
in C
alga
ry,C
anad
a,is
22�
C i
n J
uly
an
d�
11�C
in
Jan
uar
y.F
ind
the
ran
ge o
fth
e h
igh
est
and
low
est
tem
pera
ture
s in
Cal
gary
.33
°C
4.R
OLL
ER C
OA
STER
A r
olle
r co
aste
r be
gin
sat
90
feet
abo
ve g
rou
nd
leve
l.T
hen
it
desc
ends
105
fee
t.F
ind
the
hei
ght
ofth
e co
aste
r af
ter
the
firs
t de
scen
t.�
15 f
t
5.SA
VIN
GS
Son
ia h
as $
235
in h
er s
avin
gsac
cou
nt.
Sh
e w
ith
draw
s $4
5.W
hat
is
left
in
her
sav
ings
acc
oun
t?$1
90
6.B
EAC
HW
ai a
nd
Ku
ri w
ere
digg
ing
inth
e sa
nd
at t
he
beac
h.W
ai d
ug
a h
ole
that
was
15
inch
es b
elow
th
e su
rfac
e,an
d K
uri
du
g a
hol
e th
at w
as 9
in
ches
belo
w t
he
surf
ace.
Fin
d th
e di
ffer
ence
in t
he
dept
hs
of t
hei
r h
oles
.6
in.
Lesson 3–5
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A15 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill15
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Mu
ltip
ly 5
(�2)
.
5(�
2) �
�10
The
inte
gers
hav
e di
ffere
nt s
igns
.The
pro
duct
is n
egat
ive.
Mu
ltip
ly �
3(7)
.
�3(
7) �
�21
The
inte
gers
hav
e di
ffere
nt s
igns
.The
pro
duct
is n
egat
ive.
Mu
ltip
ly �
6(�
9).
�6(
�9)
�54
The
inte
gers
hav
e th
e sa
me
sign
.The
pro
duct
is p
ositi
ve.
Mu
ltip
ly (
�7)
2 .
(�7)
2�
(�7)
(�7)
The
re a
re 2
fact
ors
of �
7.�
49T
he p
rodu
ct is
pos
itive
.
Sim
pli
fy �
2(6c
).
�2(
6c)
�(�
2 · 6
)cA
ssoc
iativ
e P
rope
rty
of M
ultip
licat
ion.
��
12c
Sim
plify
.
Sim
pli
fy 2
(5x)
.
2(5x
) �
(2 ·
5)x
Ass
ocia
tive
Pro
pery
of
Mul
tiplic
atio
n.�
10x
Sim
plify
.
Mu
ltip
ly.
1.�
5(8)
�40
2.�
3(�
7)21
3.10
(�8)
�80
4.�
8(3)
�24
5.�
12(�
12)
144
6.(�
8)2
64
ALG
EBR
AS
imp
lify
eac
h e
xpre
ssio
n.
7.�
5(7a
)�
35a
8.3(
�2x
)�
6x9.
4(6f
)24
f10
.7(
6b)
42b
11.
�6(
�3y
)18
y12
.7(
�8g
)�
56g
ALG
EBR
AE
valu
ate
each
exp
ress
ion
if
a�
�3,
b�
�4,
and
c�
5.
13.
�2a
614
.9b
�36
15.
ab12
16.
�3a
c45
17.
�2c
2�
5018
.ab
c60
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Mu
ltip
lyin
g In
teg
ers
The
pro
duct
of
two
inte
gers
with
dif
fere
nt
sign
s is
neg
ativ
e.
The
pro
duct
of
two
inte
gers
with
the
sam
esi
gn is
po
siti
ve.
6
©G
lenc
oe/M
cGra
w-H
ill15
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Dis
tan
ce o
n t
he
Nu
mb
er L
ine
To
fin
d th
e di
stan
ce b
etw
een
tw
o po
ints
on
a n
um
ber
lin
e,su
btra
ct t
hei
rco
ordi
nat
es.T
hen
,tak
e th
e ab
solu
te v
alu
e of
th
e di
ffer
ence
.
�4
� 3
��
7
�7
�7
You
can
als
o fi
nd
the
dist
ance
by
fin
din
g th
e ab
solu
te v
alu
e of
th
e di
ffer
ence
of t
he
coor
din
ates
.
�4
� 3
�
7
Gra
ph
eac
h p
air
of p
oin
ts.T
hen
wri
te a
n e
xpre
ssio
n u
sin
g ab
solu
teva
lue
to f
ind
th
e d
ista
nce
bet
wee
n t
he
poi
nts
.
1.A
at �
5 an
d B
at 2
�5
� 2
�
7
2.C
at�
7 an
d D
at �
1�
7 �
(�
1)
�6
3.E
at �
5 an
d F
at 5
�5
� 5
�
10
4.W
at 0
an
d X
at 6
0 �
6
�6
5.Y
at �
4 an
d Z
at 0
�4
� 0
�
4Y
Z
�8
�7
�6
�5
�4
�3
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�1
87
65
43
21
0WX
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�7
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87
65
43
21
0
EF
�8
�7
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87
65
43
21
0
CD
�8
�7
�6
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87
65
43
21
0
AB
�8
�7
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87
65
43
21
0
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�3
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87
65
43
21
0
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
Lesson 3–5
Answers (Lessons 3-5 and 3-6)
© Glencoe/McGraw-Hill A16 Mathematics: Applications and Concepts, Course 2
Prac
tice:
Wor
d Pr
oble
ms
Mu
ltip
lyin
g In
teg
ers
©G
lenc
oe/M
cGra
w-H
ill15
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Mu
ltip
ly.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.TE
MPE
RA
TUR
ES
upp
ose
the
tem
pera
ture
outs
ide
is d
ropp
ing
3 de
gree
s ea
chh
our.
How
mu
ch w
ill
the
tem
pera
ture
drop
in
8 h
ours
?�
24�
2.D
IVIN
GA
dee
p-se
a di
ver
desc
ends
belo
w t
he
surf
ace
of t
he
wat
er a
t a
rate
of 6
0 fe
et e
ach
min
ute
.Wh
at i
s th
ede
pth
of
the
dive
r af
ter
10 m
inu
tes?
�60
0 ft
3.ST
OC
KA
com
pute
r st
ock
lost
2 p
oin
tsea
ch h
our
for
6 h
ours
.Fin
d th
e to
tal
poin
ts t
he
stoc
k fe
ll.
�12
po
ints
4.D
RO
UG
HT
A d
rou
ght
can
cau
se t
he
leve
l of
th
e lo
cal
wat
er s
upp
ly t
o dr
opby
a f
ew i
nch
es e
ach
wee
k.S
upp
ose
the
leve
l of
th
e w
ater
su
pply
dro
ps 2
in
ches
each
wee
k.H
ow f
ar w
ill
it h
ave
drop
ped
in 4
wee
ks?
�8
in.
5.M
ON
EYM
rs.R
ockw
ell
lost
mon
ey o
nan
in
vest
men
t at
a r
ate
of $
4 pe
r da
y.H
ow m
uch
did
sh
e lo
se a
fter
tw
ow
eeks
?�
$56
6.TE
NN
IS B
ALL
SJo
sh p
urc
has
ed 8
can
s of
ten
nis
bal
ls.T
he
can
s ca
me
wit
h 3
bal
lsin
eac
h c
an.H
ow m
any
ball
s di
d Jo
shpu
rch
ase?
24 t
enn
is b
alls
Lesson 3–6
Prac
tice:
Ski
llsM
ult
iply
ing
Inte
ger
s
©G
lenc
oe/M
cGra
w-H
ill15
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Mu
ltip
ly.
1.�
4(6)
�24
2.�
2(�
8)16
3.12
(�4)
�48
4.�
6(5)
�30
5.�
10(�
9)90
6.�
(5)2
�25
7.(�
5)2
258.
�30
(5)
�15
0
9.20
(�6)
�12
010
.�
14(�
6)84
11.
(�13
)216
912
.�
7(15
)�
105
ALG
EBR
AS
imp
lify
eac
h e
xpre
ssio
n.
13.
�3(
4y)
�12
y14
.7(
�3x
)�
21x
15.
7(5g
)35
g16
.7(
7w)
49w
17.
3(�
3y)
�9y
18.
�2(
�10
h)
20h
ALG
EBR
AE
valu
ate
each
exp
ress
ion
if
g �
�5,
h �
�3,
and
k �
4.
19.
�3g
1520
.5h
�15
21.
7gk
�14
022
.�
2gh
�30
23.
�10
h30
24.
�2h
2�
18
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A17 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill15
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Inte
ger
Maz
eF
ind
you
r w
ay t
hro
ugh
th
e m
aze
by m
ovin
g to
th
e ex
pres
sion
in
an
adj
acen
t se
ctio
n w
ith
the
nex
t h
igh
est
valu
e.
Sta
rt−5
0
−55
20 −
20
−32
+ 28
−12
+ 2
−3 +
(−4)
4 +
(−12
)
−13
+ 12
−10
+ 16
−35
+ 5 6 −
8
5(−9
)
9(−6
)−8(5
)
−3(5
)
−5(−
6)
−1(3
)
−4(2
)
−3(−
5)
3(−3
)(−5
)
−2(−
5)(−
1)
6(−1
0)9(
−1)
3 +
(−3)
30 −
(−1
0)
−4(5
)(−1
)
3(5)
(−5)
5(−4
+ 9
)
(−4)
2
−52
−[12
− (
−8)]
2[−5
• (
−5)]
−2(−
12 +
7)
−2(−
1)
−5
0 −
6
15 −
50
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
tRe
adin
g to
Lea
rn M
athe
mat
ics
Mu
ltip
lyin
g In
teg
ers
©G
lenc
oe/M
cGra
w-H
ill15
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 13
4 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.W
rite
a m
ult
ipli
cati
on s
ente
nce
th
at d
escr
ibes
th
e m
odel
.4(
�2)
��
8
Fin
d e
ach
pro
du
ct u
sin
g co
un
ters
.
2.3(
�2)
�6
3.4(
�3)
�12
4.1(
�7)
�7
5.5(
�2)
�10
6.W
rite
a r
ule
for
fin
din
g th
e si
gn o
f th
e pr
odu
ct o
f a
posi
tive
an
d n
egat
ive
inte
ger.
A p
osi
tive
inte
ger
tim
es a
neg
ativ
e in
teg
er e
qu
als
an
egat
ive
inte
ger
.
Rea
din
g t
he
Less
on
7.G
ive
an e
xam
ple
that
sh
ows
how
mu
ltip
lica
tion
is
the
sam
e as
rep
eate
dad
diti
on.I
n y
our
exam
ple,
tell
wh
at t
he
adde
nd
is.
Sam
ple
an
swer
:3(
�9)
�(�
9) �
(�9)
�(�
9) �
�27
Th
e ad
den
d is
�9.
8.H
ow d
oes
the
sen
ten
ce 4
(�2)
��
2(4)
ill
ust
rate
th
e C
omm
uta
tive
P
rope
rty
of M
ult
ipli
cati
on?
Sam
ple
an
swer
:Th
e se
nte
nce
sh
ow
s th
at if
yo
uch
ang
e th
e o
rder
of
the
nu
mb
ers,
the
resu
lt is
sti
ll th
e sa
me.
Fro
m t
he
exam
ple
in t
he
Min
i Lab
,we
kno
w t
hat
4(�
2) �
�8.
Th
eref
ore
,by
the
Co
mm
uta
tive
Pro
per
ty o
f M
ult
iplic
atio
n,�
2(4)
��
8.9.
Com
plet
e ea
ch o
f th
e fo
llow
ing
sen
ten
ces
wit
h t
he
wor
d po
siti
veor
neg
ativ
e.
a.T
he
prod
uct
of
two
inte
gers
wit
h d
iffe
ren
t si
gns
is _
____
____
____
__.
neg
ativ
e
b.
Th
e pr
odu
ct o
f tw
o in
tege
rs w
ith
th
e sa
me
sign
is
____
____
____
___.
po
siti
ve
Hel
pin
g Y
ou
Rem
emb
er10
.Yo
u k
now
th
e ru
le f
or d
eter
min
ing
the
sign
of
the
prod
uct
of
two
inte
gers
wh
en t
he
sign
s ar
e al
ike
or d
iffe
ren
t.C
onsi
der
the
prod
uct
of
thre
ein
tege
rs.W
ith
a p
artn
er s
um
mar
ize
the
sign
s of
th
e pr
odu
cts
of 3
inte
gers
wh
en t
hre
e,tw
o,on
e or
non
e of
th
e in
tege
rs a
re p
osit
ive.
Th
ep
rod
uct
of
3 in
teg
ers
is p
osi
tive
wh
en a
ll 3
inte
ger
s ar
ep
osi
tive
or
wh
en o
nly
on
e in
teg
er is
po
siti
ve a
nd
th
e p
rod
uct
is n
egat
ive
in o
ther
cas
es.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 3–6
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A18 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill16
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Div
ide.
1.�
15 �
3�
52.
�24
�(�
8)3
3.22
�(�
2)�
114.
�49
�(�
7)7
5.�
8 �
(�8)
16.
�364
�9
7.22
5 �
(�15
)�
158.
�0 90
9.�
38 �
2�
1910
.6 44
16
11.
�50
0 �
(�50
)10
12.
�18
9 �
(�21
)9
ALG
EBR
AE
valu
ate
each
exp
ress
ion
if
m�
�32
,n�
2,an
d p
��
8.
13.
m �
n�
1614
.p
�4
�2
15.
p2�
m�
216
.m
�p
4
17.
� np 4
18.
p �
n2
�2
19.
np2 216
20.18
p�n
�
2
21.
m �
(np)
222
.m p
�n
6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsD
ivid
ing
Inte
ger
s
Lesson 3–7
©G
lenc
oe/M
cGra
w-H
ill15
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Div
ide
30 �
(�5)
.
30 �
(�5)
The
inte
gers
hav
e di
ffere
nt s
igns
.
30 �
(�5)
��
6T
he q
uotie
nt is
neg
ativ
e.
Div
ide
�10
0 �
(�5)
.
�10
0 �
(�5)
The
inte
gers
hav
e th
e sa
me
sign
.
�10
0 �
(�5)
�20
The
quo
tient
is p
ositi
ve.
Div
ide.
1.�
12 �
4�
32.
�14
�(�
7)2
3. �18
2�
94.
�6
�(�
3)2
5.�
10 �
10�
16.
� �8 20 0
4
7.35
0 �
(�25
)�
148.
�42
0 �
(�3)
140
9.5 44 50
1210
.�
12 656 �
16
ALG
EBR
AE
valu
ate
each
exp
ress
ion
if
d �
�24
,e�
�4,
and
f�
8.
11.
12 �
e�
312
.40
�f
5
13.
d�
6�
414
.d
�e
6
15.
f�
e�
216
.e2
�f
2
17.
�ed
�6
18.
ef�
2�
16
19.
f e22 4
20.
d fe 12
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Div
idin
g In
teg
ers
The
quo
tient
of
two
inte
gers
with
diff
eren
t si
gns
is n
egat
ive.
The
quo
tient
of
two
inte
gers
with
the
sam
e si
gn is
pos
itive
.
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A19 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill16
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 13
8 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
Fin
d e
ach
qu
otie
nt
usi
ng
cou
nte
rs.
1.�
6�
2�
3
2.�
12 �
3�
4
Rea
din
g t
he
Less
on
Wri
te t
wo
div
isio
n s
ente
nce
s re
late
d t
o ea
ch o
f th
e fo
llow
ing
mu
ltip
lica
tion
sen
ten
ces.
3.�
6(�
3) �
184.
�21
(�2)
�42
18 �
(�3)
��
6;42
�(�
21)
��
2;18
�(�
6) �
�3
42 �
(�2)
��
21
5.�
6(3)
��
186.
2(�
21)
��
42�
18 �
3 �
�6;
�42
�(�
21)
�2;
�18
�(�
6) �
3�
42 �
2 �
�21
7.C
ompl
ete
each
of
the
foll
owin
g se
nte
nce
s w
ith
th
e w
ord
posi
tive
orn
egat
ive.
a.T
he
quot
ien
t of
tw
o in
tege
rs w
ith
dif
fere
nt
sign
s is
___
____
____
____
.n
egat
ive
b.
Th
e qu
otie
nt
of t
wo
inte
gers
wit
h t
he
sam
e si
gn i
s __
____
____
____
_.p
osi
tive
8.In
th
e di
visi
on s
ente
nce
�72
�8
��
9,id
enti
fy t
he
divi
den
d,th
e di
viso
r,an
d th
e qu
otie
nt.
div
iden
d:
�72
;d
ivis
or:
8;q
uo
tien
t:�
9
Hel
pin
g Y
ou
Rem
emb
er9.
Des
crib
e h
ow t
he
oper
atio
ns
of m
ult
ipli
cati
on a
nd
divi
sion
are
opp
osit
e of
each
oth
er.A
re t
hes
e op
erat
ion
s op
posi
te i
n a
ll c
ases
? W
hat
is
the
one
inte
ger
that
can
not
be
a di
viso
r?M
ult
iplic
atio
n is
th
e o
pp
osi
te o
fd
ivis
ion
in t
hat
th
e p
rod
uct
of
a q
uo
tien
t an
d d
ivis
or
giv
esth
e d
ivid
end
.Eve
n t
ho
ug
h y
ou
can
tak
e th
e p
rod
uct
of
zero
and
a n
um
ber
,zer
o c
ann
ot
be
a d
ivis
or.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
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ER
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Read
ing
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ivid
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s
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athe
mat
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App
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Con
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ours
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Div
ide.
Prac
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Wor
d Pr
oble
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Div
idin
g In
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NA
ME
____
____
____
____
____
____
____
____
____
____
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E _
____
____
____
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ER
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__
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1.ST
OC
K M
AR
KET
Du
rin
g a
5-da
yw
orkw
eek,
the
stoc
k m
arke
t de
crea
sed
by 6
5 po
ints
.Fin
d th
e av
erag
e da
ily
chan
ge i
n t
he
mar
ket
for
the
wee
k.�
13 p
oin
ts
2.M
OTI
ON
Mr.
Dia
z de
crea
sed
the
spee
dof
his
car
by
30 m
iles
per
hou
r ov
er a
peri
od o
f 10
sec
onds
.Fin
d th
e av
erag
ech
ange
in
spe
ed e
ach
sec
ond.
�3
mp
h p
er s
3.W
EATH
ERO
ver
the
past
sev
en d
ays,
Mrs
.Ch
o fo
un
d th
at t
he
tem
pera
ture
outs
ide
had
dro
pped
a t
otal
of
35de
gree
s.F
ind
the
aver
age
drop
in
tem
pera
ture
eac
h d
ay.
�5
deg
rees
per
day
4.B
ASK
ETB
ALL
Th
e ba
sket
ball
tea
m l
ost
thei
r la
st 6
gam
es.T
hey
los
t by
a t
otal
of 4
8 po
ints
.Fin
d th
e av
erag
e n
um
ber
of p
oin
ts b
y w
hic
h e
ach
gam
e w
as l
ost.
�8
po
ints
per
gam
e
5.PO
PULA
TIO
NT
he
enro
llm
ent
at D
avis
Mid
dle
Sch
ool
drop
ped
by 6
0 st
ude
nts
over
a 5
-yea
r pe
riod
.Wh
at i
s th
eav
erag
e ye
arly
dro
p in
en
roll
men
t?�
12 s
tud
ents
an
nu
ally
6.SU
BM
AR
INE
A s
ubm
arin
e de
scen
ds a
t a
rate
of
60 f
eet
each
min
ute
.How
lon
gw
ill
it t
ake
it t
o de
scen
d to
a d
epth
of
660
feet
bel
ow t
he
surf
ace?
11 m
in
Lesson 3–7
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A20 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill16
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Div
isio
n b
y Ze
ro?
Som
e in
tere
stin
g th
ings
hap
pen
wh
en y
ou t
ry t
o di
vide
by
zero
.For
exa
mpl
e,lo
ok a
t th
ese
two
equ
atio
ns.
5 0�
x
0 0�
y
If y
ou c
an w
rite
th
e eq
uat
ion
s ab
ove,
you
can
als
o w
rite
th
e tw
o eq
uat
ion
sbe
low
.
0�
x�
5 0
�y
�0
How
ever
,th
ere
is n
o n
um
ber
that
wil
l m
ake
the
left
equ
atio
n t
rue.
Th
iseq
uat
ion
has
no
solu
tion
.For
th
e ri
ght
equ
atio
n,e
very
nu
mbe
r w
ill
mak
e it
tru
e.T
he
solu
tion
s fo
r th
is e
quat
ion
are
“al
l n
um
bers
.”
Bec
ause
div
isio
n b
y ze
ro l
eads
to
impo
ssib
le s
itu
atio
ns,
it i
s n
ot a
“le
gal”
step
in s
olvi
ng
a pr
oble
m.P
eopl
e sa
y th
at d
ivis
ion
by
zero
is
un
defi
ned
,or
not
poss
ible
,or
sim
ply
not
all
owed
.
Des
crib
e th
e so
luti
on s
et f
or e
ach
eq
uat
ion
.
1.4x
�0
2.x
�0
�0
0al
l nu
mb
ers
3.x
�0
�x
4.0 x
�0
0al
l nu
mb
ers
but
0
5.0 x
� x
6.0 x
� 5
no
so
luti
on
no
so
luti
on
Wh
at v
alu
es f
or x
mu
st b
e ex
clu
ded
to
pre
ven
t d
ivis
ion
by
0?
7. x1 2
08.
x�1
1
1
9. x
�11
�
110
. 20 x
0
11. 2x
1 �2
1
12. 3x
1 �6
�
2
Exp
lain
wh
at i
s w
ron
g w
ith
th
is “
pro
of.”
13.
Ste
p 1
0�
1�
0 an
d 0
�(�
1)�
0
Ste
p 2
The
refo
re,
0 0�
1 an
d 0 0
��
1.S
tep
2 in
volv
es d
ivis
ion
by
zero
.
Ste
p 3
The
refo
re,
1�
�1.
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
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ATE
___
____
____
___
PE
RIO
D
____
_
Lesson 3–7
Answers (Lesson 3-7)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. D
G
C
I
A
G
B
H
A
G
D
F
C
4
B
F
D
H
B
H
A
I
B
I
C
F
B
F
D
H
A
G
A
H
B
I
B
H
A
Chapter 3 Assessment Answer KeyForm 1 Form 2APage 165 Page 166 Page 167
(continued onthe next page)
© Glencoe/McGraw-Hill A21 Mathematics: Applications and Concepts, Course 2
An
swer
s
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: 10
D
F
C
I
B
I
B
I
A
G
C
F
D
G
A
H
B
F
D
G
A
I
A
H
B
6
B
I
A
H
B
H
B
I
C
F
B
F
Chapter 3 Assessment Answer KeyForm 2A (continued) Form 2BPage 168 Page 169 Page 170
© Glencoe/McGraw-Hill A22 Mathematics: Applications and Concepts, Course 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13–14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
B: 12
�11
�12c
�15a
�1
�24
2
�2
18
4
�5
21
2
�17
�3
9
6
�5
�88
�37
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Q
(�1, �3); III
(�3, 2); II
Athens
�2, �1, 0, 3, 5, 7�
�
�
0 3�3�6
10
11
�5
45
Chapter 3 Assessment Answer KeyForm 2CPage 171 Page 172
(continued on the next page)
© Glencoe/McGraw-Hill A23 Mathematics: Applications and Concepts, Course 2
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13–14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
B: 14
�9
8y
�30z
�6
�40
�3
�4
30
7
�8
13
2
�17
�12
25
9
�20
�70
2
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S
A
(1,�2); IV
(3, 1); I
St. Paul
�8, �5, �1, 2, 3, 4
�
�
�
0 3�3�6
8
13
�13
300
Chapter 3 Assessment Answer KeyForm 2DPage 173 Page 174
© Glencoe/McGraw-Hill A24 Mathematics: Applications and Concepts, Course 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13–14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
B:6, �3; Divide the
previous term by �2.
6
�6bc
�35e
�6
1
�2
�45
3
�12
80
�13
8
3
3
�121
�6
0
�24
�28
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1234
LM
(2, 0); x-axis
(�3, 3); II
Chicago
�7, �5, �3, 0, 4, 10
�
�
�
�2 0 2�4 4
2
16
�11
380
Chapter 3 Assessment Answer KeyForm 3Page 175 Page 176
© Glencoe/McGraw-Hill A25 Mathematics: Applications and Concepts, Course 2
An
swer
s
© Glencoe/McGraw-Hill A26 Mathematics: Applications and Concepts, Course 2
Chapter 3 Assessment Answer Key Page 177, Extended Response Assessment
Scoring Rubric
Level Specific Criteria
4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.
3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.
2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.
1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.
0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.
© Glencoe/McGraw-Hill A27 Mathematics: Applications and Concepts, Course 2
Chapter 3 Assessment Answer Key Page 177, Extended Response Assessment
Scoring Rubric
1. a. You can use a number line tocompare integers. The valuesincrease as you go right and decreaseas you go left.
b. �3, �1, �2, �4
c. The absolute value of a number isthe number of units its graph is fromthe graph of 0 on the number line.
d. |�3|�3
e. �3 � (�2)
Glen’s score after two rounds is �1.
f. �1 � (�3) � �4
g. �2 � (�3)
The difference between Horatio’s firstand second round scores is 5.
2.
a. Graph A(4, 6) by starting at theorigin, moving 4 units to the rightand 6 units up.Point A lies in quadrant I.
b. 4 · (�2) � �8 and 6 · (�1) � �6, sopoint B has coordinates (�8, �6).Point B lies in quadrant III.
c. �8 � 4 � �2 and �6 � (�3) � 2, sopoint C has coordinates (�2, 2).Point C lies in quadrant II.
y
xO
�4�6�8
�4�6�8 42 86
2468
(�2, 2)
(4, 6)
C
A
(�8, �6)B
�
�
�
�
�
�
�
�
�
�
�
�
�
�
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In addition to the scoring rubric found on page A26, the following sample answersmay be used as guidance in evaluating extended response assessment items.
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. Sample answer: aplane in which ahorizontal numberline and a verticalnumber lineintersect at theirzero points
12. Sample answer: thepair of numbers (x-coordinate,y-coordinate) usedto locate a point inthe coordinateplane
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lessons 3-3 and 3-4)
Page 179
1–3.
4.
5.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lesson 3-7)
Page 180
1.
2.
3.
4.
5. 2
�6
�3
7
�4
�20s
�18e
�56
11
�10
�18
35
�81
30
�13
�4
5
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1234
S
RT
�
�
�
�
15
9
3
24
�15
C
quadrant
opposites
origin
negative integer
y-axis
x-coordinate
additive inverse
graph
integer
absolute value
Chapter 3 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 3-1 and 3-2) Quiz (Lessons 3-5 and 3-6)
Page 178 Page 179 Page 180
© Glencoe/McGraw-Hill A28 Mathematics: Applications and Concepts, Course 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
1.
2.
3.
4.
5.
6.
7.
8–9.
10.
11.
12.
13. �4
30
�30
0
y
xO
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1234
MA
8
�72, �31, �12,12, 50, 61
1
Sample answer: Themean and median
number of wins areclose, indicating thedata are fairly well-
centered in themiddle of the range
of possible wins.About half of the
data values clusterfrom 17 to 35.
25; 23; 22 and 35; 51
16
18
�11
(�1, 4); II
(3, �2); IV
(�6, �1); III
(5, 4); I
�
�
�350
G
A
I
D
F
B
Chapter 3 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 181 Page 182
© Glencoe/McGraw-Hill A29 Mathematics: Applications and Concepts, Course 2
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. 11.
12.
13.
14. a. Graph A(�2, 4) by starting atthe origin, moving 2 units tothe left and 4 units up.
b. �1 � 3 � �3 and �12
� � 4 � 2, so point B� has coordinates (�3, 2). Point B� lies inquadrant II.
�6
interval 5; scale0 to 24
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
8
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
8 0
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
Chapter 3 Assessment Answer KeyStandardized Test PracticePage 183 Page 184
© Glencoe/McGraw-Hill A30 Mathematics: Applications and Concepts, Course 2
y
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B�
A B
D C