chapter 3 resource masters - wikispaces3.pdf · chapter 3 test, form 2d.....171–172 chapter 3...

Course 1

Chapter XResource Masters

Course 3

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 3. 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 3ISBN: 0-07-860146-0 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 0-07-860162-2

Study Guide and Intervention Workbook (Spanish) 0-07-860168-1

Practice: Skills Workbook 0-07-860163-0

Practice: Skills Workbook (Spanish) 0-07-860169-X

Practice: Word Problems Workbook 0-07-860164-9

Practice: Word Problems Workbook (Spanish) 0-07-860170-3

Reading to Learn Mathematics Workbook 0-07-861062-1

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 3 (0-07-860172-X).

iii

Vocabulary Builder .............................vii

Family Letter............................................ix

Family Activity ........................................x

Lesson 3-1Study Guide and Intervention ........................133Practice: Skills ................................................134Practice: Word Problems................................135Reading to Learn Mathematics......................136Enrichment .....................................................137






Chapter 3 AssessmentChapter 3 Test, Form 1 ..........................163–164Chapter 3 Test, Form 2A........................165–166Chapter 3 Test, Form 2B........................167–168Chapter 3 Test, Form 2C........................169–170Chapter 3 Test, Form 2D........................171–172Chapter 3 Test, Form 3 ..........................173–174Chapter 3 Extended Response Assessment .175Chapter 3 Vocabulary Test/Review.................176Chapter 3 Quizzes 1 & 2................................177Chapter 3 Quizzes 3 & 4................................178Chapter 3 Mid-Chapter Test ...........................179Chapter 3 Cumulative Review........................180Chapter 3 Standardized Test Practice....181–182Unit 1 Test/Review..................................183–184

Standardized Test Practice Student Recording Sheet ..............................A1

Standardized Test Practice Rubric...................A2ANSWERS .............................................A3–A28

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 3, 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 3. 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 150–151. This improves students’familiarity with the answer formats theymay encounter in test taking.

• Detailed rubrics for assessing theextended response questions on page 151are 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.

Vo

cab

ula

ry B

uild

erThis 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.

© Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 3

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsVocabulary Builder

Vocabulary TermFound

Definition/Description/Exampleon Page

abscissa [ab-SIH-suh]

converse

coordinate plane

hypotenuse

irrational number

legs

ordered pair

ordinate [OR-din-it]

origin

perfect square

© Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 3

Vocabulary TermFound

Definition/Description/Exampleon Page

principal square root

Pythagorean Theorem

Pythagorean triple

quadrants

radical sign

real number

right triangle

square root

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 3

Dear Parent or Guardian:

It is very important that we learn about all real numbers. Not

all of the numbers we encounter in life are integers, decimals,

or fractions. Even in construction, sports, and art, numbers are

not always “nice and neat.” Knowing how to find square roots,

how to apply the Pythagorean Theorem are skills that we can

use to help us deal with all real numbers.

In Chapter 3, Algebra: Real Numbers and the Pythagorean

Theorem, your child will learn how to find and estimate square

roots, to identify and classify real numbers, and to use the

Pythagorean Theorem. Your child will also learn how to draw

Venn diagrams to help solve problems and how to find the

distance between two points on a coordinate plane. In this

chapter, your child will complete a variety of daily classroom

assignments and activities and possibly 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.msmath3.net. If you have any

questions 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 3

Cross-ExamineWork with a family member to answer the following questions. If theproblem refers to an object that you do not have, feel free tosubstitute another object that can be represented by a right triangleor a rectangle. The Pythagorean Theorem states that for a righttriangle, a2 � b2 � c2, where a and b are the lengths of the legs of thetriangle and c is the length of the hypotenuse.

1. Measure the height and width of a computer screen at home or at school.Use the Pythagorean Theorem to calculate the length of the diagonal ofyour screen. For example, if the height of the screen is 8 inches and thewidth is 11 inches, then:

c2 � 82 � 112

c2 � 185c � �185�c � 13.6

The length of the diagonal is 13.6 inches.

Measure the length of the diagonal. How does the measured lengthcompare with the length you calculated above?

2. Measure the height and width of a television screen. Use thePythagorean Theorem to calculate the length of the diagonal of yourscreen.


3. Measure the height and width of your favorite framed picture. Use thePythagorean Theorem to calculate the length of the diagonal of thepicture frame.


1.See students’ work.2.See students’ work.3.See students’ work.

Less

on

3–1

© Glencoe/McGraw-Hill 133 Mathematics: Applications and Concepts, Course 3

Find each square root.

�1� Since 1 � 1 � 1, �1� � 1.

��16� Since 4 � 4 � 16, ��16� � �4.

�0.25� Since 0.5 � 0.5 � 0.25, �0.25� � 0.5.

��2356�� Since �

56� � �

56� � �

2356�

, ��2356��

56�.

Solve a2 � �49�.

a2 � �49� Write the equation.

�a2� � ��49�� Take the square root of each side.

a � �23� or ��

23� Notice that �

23

� · �23

� � �49

� and ��23

��23

�� 49

�.

The equation has two solutions, �23� and ��

23�.


1. �4� 2. �9�

3. ��49� 4. ��25�

5. �0.01� 6. ��0.64�

7. ��196�� 8. ��2

15��

ALGEBRA Solve each equation.

9. x2 � 121 10. a2 � 3,600

11. p2 � �18010�

12. t2 � �112916�

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionSquare Roots

The square root of a number is one of two equal factors of a number. The radical sign �� is used toindicate the positive square root.



1. �16� 2. ��9�

3. �36� 4. �196�

5. �121� 6. ��81�

7. ��0.04� 8. �289�

9. �0.81� 10. ��400�

11. ��1469�� 12. ��1

4090��

ALGEBRA Solve each equation.

13. s2 � 81 14. t2 � 36

15. x2 � 49 16. 256 � z2

17. 900 � y2 18. 1,024 � h2

19. c2 � �4694�

20. a2 � �12251�

21. �1100�

� d2 22. �114649�

� r2

23. b2 � �4941�

24. x2 � �142010�

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsSquare Roots

Less

on

3–1


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsSquare Roots

1. PLANNING Rosy wants a large picturewindow put in the living room of hernew house. The window is to be squarewith an area of 49 square feet. Howlong should each side of the window be?

2. GEOMETRY If the area of a square is1 square meter, how many centimeterslong is each side?

3. ART A miniature portrait of GeorgeWashington is square and has an areaof 169 square centimeters. How long iseach side of the portrait?

4. BAKING Len is baking a square cake forhis friend’s wedding. When served tothe guests, the cake will be cut intosquare pieces 1 inch on a side. The cakeshould be large enough so that each ofthe 121 guests gets one piece. Howlong should each side of the cake be?

5. ART Cara has 196 marbles that she isusing to make a square formation. Howmany marbles should be in each row?

6. GARDENING Tate is planning to put asquare garden with an area of 289 square feet in his back yard. Whatwill be the length of each side of thegarden?

7. HOME IMPROVEMENT Al has 324 squarepaving stones that he plans to use toconstruct a square patio. How manypaving stones wide will the patio be?

8. GEOMETRY If the area of a square is529 square inches, what is the length ofa side of the square?


NAME ________________________________________ DATE ______________ PERIOD _____

Pre-Activity Complete the Mini Lab at the top of page 116 in your textbook.Write your answers below.

1. Copy and complete the following table.

2. Suppose a square arrangement has 36 tiles. How many tiles are on aside?

3. What is the relationship between the number of tiles on a side and thenumber of tiles in the arrangement?

Reading the Lesson4. The opposite of _____________________________ is finding one of two equal

factors of a number.

5. Explain how you know whether a square root is the principal square rootor not.

6. To solve an equation in which one side of the equation is a squared term,what can you do to each side of the equation?

Helping You Remember7. Given enough time and enough tiles, how might you go about

determining whether a whole number is a perfect square?

Reading to Learn MathematicsSquare Roots

1

41

2Tiles on a Side

Total Number of Tiles in the Square Arrangement

3 4 5


Properties of the Geometric MeanThe square root of the product of two numbers is called their geometric mean.

Numbers Geometric Meana and c b � �ac�

12 and 48 �12 � 4�8� � �576� � 24

The geometric mean has many interesting properties. For example, twonumbers and their geometric mean satisfy their proportion below.

�ab� � �

bc�

Find the geometric mean, b, for each pair of numbers.

1. a � 2 and c � 8 2. a � 4 and c � 9 3. a � 9 and c � 16b � b � b �



Solve.

10. For each triple of numbers in Exercises 1–9, draw a triangle like the one shown at the right. What property is shown?

11. Now make this drawing for each triple of numbers.The semicircle has a diameter equal to the sum of aand c. What property do you find?

b

a c

b

a c

EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–1


Estimate �204� to the nearest whole number.

• The first perfect square less than 204 is 14.

• The first perfect square greater than 204 is 15.

196 � 204 � 225 Write an inequality.

142 � 204 � 152 196 � 142 and 225 � 152

14 � �204� � 15 Take the square root of each number.

So, �204� is between 14 and 15. Since 204 is closer to 196 than 225, the best whole

number estimate for �204� is 14.

Estimate �79.3� to nearest whole number.

• The first perfect square less than 79.3 is 64.

• The first perfect square greater than 79.3 is 81.

64 � 79.3 � 81 Write an inequality.

82 � 79.3 � 92 64 � 82 and 81 � 92

8 � �79.3� � 9 Take the square root of each number.

So, �79.3� is between 8 and 9. Since 79.3 is closer to 81 than 64, the best whole

number estimate for �79.3� is 9.

Estimate to the nearest whole number.

1. �8� 2. �37� 3. �14�

4. �26� 5. �62� 6. �48�

7. �103� 8. �141� 9. �14.3�

10. �51.2� 11. �82.7� 12. �175.2�

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionEstimating Square Roots

Most numbers are not perfect squares. You can estimate square roots for these numbers.



1. �5� 2. �18� 3. �10�

4. �34� 5. �53� 6. �80�

7. �69� 8. �99� 9. �120�

10. �77� 11. �171� 12. �230�

13. �147� 14. �194� 15. �290�

16. �440� 17. �578� 18. �730�

19. �1,010� 20. �1,230� 21. �8.42�

22. �17.8� 23. �11.5� 24. �37.7�

25. �23.8� 26. �59.4� 27. �97.3�

28. �118.4� 29. �84.35� 30. �45.92�

Practice: SkillsEstimating Square Roots

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–2


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsEstimating Square Roots

1. GEOMETRY If the area of a square is29 square inches, estimate the length ofeach side of the square to the nearestwhole number.

2. DECORATING Miki has an square rug in her living room that has an area of19 square yards. Estimate the length of a side of the rug to the nearest whole number.

3. GARDENING Ruby is planning to put asquare garden with an area of200 square feet in her back yard.Estimate the length of each side of thegarden to the nearest whole number.

4. ALGEBRA Estimate the solution ofc2 � 40 to the nearest integer.

5. ALGEBRA Estimate the solution ofx2 � 138.2 to the nearest integer.

6. ARITHMETIC The geometric mean oftwo numbers a and b can be found byevaluating �a � b�. Estimate thegeometric mean of 5 and 10 to thenearest whole number.

7. GEOMETRY The radius r of a certaincircle is given by r � �71�. Estimate theradius of the circle to the nearest foot.

8. GEOMETRY In a triangle whose baseand height are equal, the base b isgiven by the formula b � �2A�, where Ais the area of the triangle. Estimate tothe nearest whole number the base ofthis triangle if the area is 17 squaremeters.



1. How many squares are on each side of the largest possible square usingno more than 40 small squares?

2. How many squares are on each side of the smallest possible square usingat least 40 small squares?

3. The value of �40� is between two consecutive whole numbers. What arethe numbers?

Use grid paper to determine between which two consecutive wholenumbers each value is located.

4. �23� 5. �52�

6. �27� 7. �18�

Reading the Lesson8. Explain how you can estimate the square root of a number if you know

perfect squares greater than and less than the number.

For Exercises 9–12, estimate to the nearest whole number.

9. �33� 10. �71�

11. �114� 12. �211�

13. Read Example 2 on page 121 of your textbook. What is a “goldenrectangle”?

Helping You Remember14. Draw a triangle and label its sides. (Make sure your triangle is a real

triangle. For example, sides of lengths 2, 2 and 8 do not make a triangle.)Trade triangles with a partner and estimate the area of your trianglesusing Heron’s Formula.

Reading to Learn MathematicsEstimating Square Roots

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–2


Heron's FormulaA formula named after Heron of Alexandria can be used to find the area of atriangle if you know the lengths of the sides.

Step 1 Step 2Find s, the semi-perimeter. For a triangle with Substitute s, a, b, and c intosides a, b, and c, the semi-perimeter is: Heron’s Formula to find the area, A.

s � �a �

2b � c�. A � �s(s ��a)(s �� b)(s �� c)�

Estimate the area of each triangle by counting squares. Then useHeron’s Formula to compute a more exact area. Give each answer tothe nearest tenth of a unit.

1. 2. 3.

Estimated area: Estimated area: Estimated area:Computed area: Computed area: Computed area:

4. 5. 6.

Estimated area: Estimated area: Estimated area:Computed area: Computed area: Computed area:

7. Why would it be foolish to use Heron’s Formula to find the area of a righttriangle?

5

9

7

8

8

37

7

7

10

8

69

10

9

6

6

6

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

Less

on

3–3


Name all sets of numbers to which each real number belongs.

5 whole number, integer, rational number

0.666… Decimals that terminate or repeat are rational numbers, since they can be expressed as fractions. 0.666… � �

23�

��25� Since ��25� � �5, it is an integer and a rational number.

��11� �11� � 3.31662479… Since the decimal does not terminate or repeat, it is an irrational number.

Replace � with �, �, or � to make 2�14� � �5� a true sentence.

Write each number as a decimal.

2�14� � 2.25

�5� � 2.236067…

Since 2.25 is greater than 2.236067…, 2�14� � �5� .


1. 30 2. �11

3. 5�47� 4. �21�

5. 0 6. ��9�

7. �63� 8. ��101�

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

9. 2.7 � �7� 10. �11� � 3�12� 11. 4�

16� � �17� 12. 3.8� � �15�

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionThe Real Number System

Numbers may be classified by identifying to which of the following sets they belong.

Whole Numbers 0, 1, 2, 3, 4, …

Integers …, �2, �1, 0, 1, 2, …

Rational Numbers numbers that can be expressed in the form �ab

�, where a and b are integers and b 0

Irrational Numbers numbers that cannot be expressed in the form �ab

�, where a and b are integers and b 0

To compare real numbers, write each number as a decimal and then compare the decimal values.



1. 12 2. �15

3. 1�12� 4. 3.18

5. �84� 6. 9.3�

7. �2�79� 8. �25�

9. �3� 10. ��64�

11. ��12� 12. �13�

Estimate each square root to the nearest tenth. Then graph thesquare root on a number line.

13. �5� 14. �14�

15. ��6� 16. ��13�

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

17. 1.7 � �3� 18. �6� � 2�12�

19. 4�25� � �19� 20. 4.8� � �24�

21. 6�16� � �38� 22. �55� � 7.42�

23. 2.1 � �4.41� 24. 2.7� � �7.7�

�4 �2 �1�3�4 �2 �1�3

1 3 421 3 42

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsThe Real Number System


Practice: Word ProblemsThe Real Number System

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–3

1. GEOMETRY If the area of a square is33 square inches, estimate the length ofa side of the square to the nearesttenth of an inch.

2. GARDENING Hal has a square garden inhis back yard with an area of 210 square feet. Estimate the length ofa side of the garden to the nearesttenth of a foot.

3. ALGEBRA Estimate the solution ofa2 � 21 to the nearest tenth.

4. ALGEBRA Estimate the solution ofb2 � 67.5 to the nearest tenth.

5. ARITHMETIC The geometric mean oftwo numbers a and b can be found byevaluating �a � b�. Estimate thegeometric mean of 4 and 11 to thenearest tenth.

6. ELECTRICITY In a certain electricalcircuit, the voltage V across a 20 ohmresistor is given by the formulaV � �20P�, where P is the powerdissipated in the resistor, in watts.Estimate to the nearest tenth thevoltage across the resistor if the powerP is 4 watts.

7. GEOMETRY The length s of a side of acube is related to the surface area A of

the cube by the formula s � ��A6��. If the

surface area is 27 square inches, whatis the length of a side of the cube to thenearest tenth of an inch?

8. PETS Alicia and Ella are comparing theweights of their pet dogs. Alicia’s

reports that her dog weighs 11�15�

pounds, while Ella says that her dogweighs �125� pounds. Whose dogweighs more?


Pre-Activity Read the introduction at the top of page 125 in your textbook.Write your answers below.

1. The length of the court is 60 feet. Is this number a whole number? Is it a rational number? Explain.

2. The distance from the net to the rear spikers line is 7�12� feet. Is this

number a whole number? Is it a rational number? Explain.

3. The diagonal across the court is �4,500� feet. Can this square root bewritten as a whole number? a rational number?

Reading the Lesson4. What do rational and irrational numbers have in common? What is the

difference between rational numbers and irrational numbers? Give an example of each.

5. Match the property of real numbers with the algebraic example.

Commutative a. (x � y) � z � x � (y � z)

Associative b. pq � qp

Distributive c. h � 0 � h

Identity d. c � (�c) � 0

Inverse e. x(y � z) � xy � xz

Helping You Remember6. Think of a way to remember the relationships between the sets of

numbers in the real number system. For example, think of a rhyme thattells the order of the sets of numbers from smallest to largest.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsThe Real Number System


What Did They Invent?Each problem gives the name of an inventor. To find the invention,graph each set of points on the number line.

1. Whitcomb Judson P at �3�, R at �, Z at 0.75, I at �32�,

P at �6�, E at 2�78�

2. Johannes Kepler S at �5�, P at �12�, E at 3.75, L at �1163�

,

C at �52�, T at �

38�, O at �, E at 1.6, and E at 0.767�

3. Alessandro Volta Y at �60�, T at �30�, A at 4.3, E at 6.2, T at �496�,

R at �45�, and B at �17��

4. William Röntgen A at �32�, Y at 6�56�, X at �

134�, S at �55�, R at 5.3

5. Karl von Linde R at �140�, G at 9.6, E at 8.5, I at �90�, R at �221�,

R at �70�, F at 8�78�, E at �100�, A at 10.7,

R at 9�111�

, T at �120�, and O at 11.4

8 9 10 11 12

4 5 6 7 8

4 5 6 7 8

0 1 2 3 4

0 1 2 3 4


Less

on

3–3


Find the missing measure for each right triangle. Round to thenearest tenth.

c2 � a2 � b2 c2 � a2 � b2

c2 � 242 � 322 202 � 152 � b2

c2 � 576 � 1,024 400 � 225 � b2

c2 � 1,600 400 � 225 � 225 � b2 � 225c � �1,600� 175 � b2

c � 40 �175� � �b2�13.2 � b

The length of the hypotenuse The length of the other legis 40 feet. is about 13.2 centimeters.

Write an equation you could use to find the length of the missing sideof each right triangle. Then find the missing length. Round to thenearest tenth if necessary.

1. 2. 3.

4. a � 7 km, b � 12 km 5. a � 10 yd, c � 25 yd 6. b � 14 ft, c � 20 ft

a

15 in.

25 in.

c

9 m

5 mc

5 ft

4 ft

b

20 cm 15 cmc

32 ft

24 ft

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionThe Pythagorean Theorem

The Pythagorean Theorem describes the relationship among the lengths of the sides of any right triangle. In a right triangle, the square of the length of the hypotenuse is equal to the sum of thesquares of the lengths of the legs. You can use the Pythagorean Theorem to find the length of a side of a right triangle if the lengths of the other two sides are known.


Write an equation you could use to find the length of the missing sideof each right triangle. Then find the missing length. Round to thenearest tenth if necessary.

1. 2. 3.

4. 5. 6.

7. a � 1 m, b � 3 m 8. a � 2 in., c � 5 in.

9. b � 4 ft, c � 7 ft 10. a � 4 km, b � 9 km

11. a � 10 yd, c � 18 yd 12. b � 18 ft, c � 20 ft

13. a � 5 yd, b � 11 yd 14. a � 12 cm, c � 16 cm

15. b � 22 m, c � 25 m 16. a � 21 ft, b � 72 ft

17. a � 36 yd, c � 60 yd 18. b � 25 mm, c � 65 mm

Determine whether each triangle with sides of given lengths is aright triangle.

19. 10 yd, 15 yd, 20 yd 20. 21 ft, 28 ft, 35 ft

21. 7 cm, 14 cm, 16 cm 22. 40 m, 42 m, 58 m

23. 24 in., 32 in., 38 in. 24. 15 mm, 18 mm, 24 mm

b20 ft

13 fta

24 yd 30 ydc

18 ft

15 ft

b

11 cm3 cm

a

10 m5 m

c

7 in.

8 in.

NAME ________________________________________ DATE ______________ PERIOD _____

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on

X–4

Practice: SkillsThe Pythagorean Theorem

Less

on

3–4


NAME ________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsThe Pythagorean Theorem

1. ART What is the length of a diagonal ofa rectangular picture whose sides are12 inches by 17 inches? Round to thenearest tenth of an inch.

2. GARDENING Ross has a rectangulargarden in his back yard. He measuresone side of the garden as 22 feet andthe diagonal as 33 feet. What is thelength of the other side of his garden?Round to the nearest tenth of a foot.

3. TRAVEL Troy drove 8 miles due eastand then 5 miles due north. How far isTroy from his starting point? Roundthe answer to the nearest tenth of amile.

4. GEOMETRY What is the perimeter of aright triangle if the hypotenuse is15 centimeters and one of the legs is9 centimeters?

5. ART Anna is building a rectangularpicture frame. If the sides of the frameare 20 inches by 30 inches, what shouldthe diagonal measure? Round to thenearest tenth of an inch.

6. CONSTRUCTION A 20-foot ladder leaningagainst a wall is used to reach awindow that is 17 feet above theground. How far from the wall is thebottom of the ladder? Round to thenearest tenth of a foot.

7. CONSTRUCTION A door frame is 80 inches tall and 36 inches wide. Whatis the length of a diagonal of the doorframe? Round to the nearest tenth ofan inch.

8. TRAVEL Tina measures the distancesbetween three cities on a map. Thedistances between the three cities are45 miles, 56 miles, and 72 miles. Do thepositions of the three cities form a righttriangle?


NAME ________________________________________ DATE ______________ PERIOD _____

Less

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X–4

Less

on

3–4

Reading to Learn MathematicsThe Pythagorean Theorem


1. Find the area of each square.

2. How are the squares of the sides related to the areas of the squares?

3. Find the sum of the areas of the two smaller squares. How does the sumcompare to the area of the larger square?

4. Use grid paper to cut out three squares with sides 5, 12, and 13 units.Form a triangle with these squares. Compare the sum of the areas of thetwo smaller squares with the area of the larger square.

Reading the Lesson5. Is it possible to have a right triangle for which the Pythagorean Theorem

is not true?

6. If you know the lengths of two of the sides of a right triangle, how canyou find the length of the third side?

Use the Pythagorean Theorem to determine whether each of thefollowing measures of the sides of a triangle are the sides of a righttriangle.

7. 4, 5, 6 8. 9, 12, 15

9. 10, 24, 26 10. 5, 7, 9

Helping You Remember11. In everyday language, a leg is a limb used to support the body. How does

this meaning relate to the legs of a right triangle?


Geometric RelationshipsThe Pythagorean Theorem can be used to express relationships between parts of geometric figures. d2 � s2 � s2

The example shows how to write a formula for d2 � 2s2

the length of the diagonal of a square in terms of the d � �2�slength of the side.

Develop a formula for each problem. The dashed lines have been included to help you.

1. An equilateral triangle has three 2. A regular hexagon has six sides of thesides of the same length. Express the same length. Express the height h in altitude h in terms of the side s. terms of the length of the side s.

3. A circle is circumscribed about a 4. A circle is inscribed in a square. Express square. Express the radius r of the the radius r of the inscribed circle in circumscribed circle in terms of the terms of the side s of the square.side s of the square.

5. Use the isosceles triangle to the 6. Use the isosceles right triangle to the.right. Express the altitude h in right. Express x in terms of s.terms of the quantity a.

h

8a

5a s

x

r

s

rs

s

h

sh

s

s

d

NAME ________________________________ DATE ______________ PERIOD _____

Enrichment

Less

on

X–4


A professional ice hockey rink is 200 feet long and 85 feet wide. What is the length of the diagonal of the rink?

c2 � a2 � b2 The Pythagorean Theorem

c2 � 2002 � 852 Replace a with 200 and b with 85.

c2 � 40,000 � 7,225 Evaluate 2002 and 852.

c2 � 47,225 Simplify.

�c2� � �47,22�5� Take the square root of each side.

c � 217.3 Simplify.

The length of the diagonal of an ice hockey rink is about 217.3 feet.

Write an equation that can be used to answer the question. Thensolve. Round to the nearest tenth if necessary.

1. What is the length of the diagonal? 2. How long is the kite string?

3. How high is the ramp? 4. How tall is the tree?

h18 yd

7 yd

b15 ft

10 ft

c

25 m

30 mc6 in.

6 in.

c85 ft

200 ft

NAME ________________________________________ DATE ______________ PERIOD _____

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3–5

Study Guide and InterventionUsing The Pythagorean Theorem

You can use the Pythagorean Theorem to help you solve problems.


Write an equation that can be used to answer the question. Thensolve. Round to the nearest tenth if necessary.

1. How far apart are the spider and 2. How long is the tabletop?the fly?

3. How high will the ladder reach? 4. How high is the ramp?

5. How far apart are the two cities? 6. How far is the bear from camp?

7. How tall is the table? 8. How far is it across the pond?

d

90 m75 mh40 in.

30 in.

table

d

60 yd

camp

20 yd

Avon

Lakeview

41 mi

19 mi

c

h17 ft

15 fth

4 ft

16 ft

c

3 ft

2 ft

6 fttable

3 ft

�

NAME ________________________________ DATE ______________ PERIOD _____

Practice: SkillsUsing The Pythagorean Theorem


Practice: Word ProblemsUsing The Pythagorean Theorem

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–51. RECREATION A pool table is 8 feet long

and 4 feet wide. How far is it from onecorner pocket to the diagonally oppositecorner pocket? Round to the nearesttenth.

2. TRIATHLON The course for a localtriathlon has the shape of a righttriangle. The legs of the triangle consistof a 4-mile swim and a 10-mile run.The hypotenuse of the triangle is thebiking portion of the event. How far isthe biking part of the triathlon? Roundto the nearest tenth if necessary.

3. LADDER A ladder 17 feet long is leaningagainst a wall. The bottom of the ladderis 8 feet from the base of the wall. Howfar up the wall is the top of the ladder?Round to the nearest tenth if necessary.

4. TRAVEL Tara drives due north for22 miles then east for 11 miles. Howfar is Tara from her starting point?Round to the nearest tenth if necessary.

5. FLAGPOLE A wire 30 feet long isstretched from the top of a flagpole tothe ground at a point 15 feet from thebase of the pole. How high is theflagpole? Round to the nearest tenth ifnecessary.

6. ENTERTAINMENT Isaac’s television is25 inches wide and 18 inches high.What is the diagonal size of Isaac’stelevision? Round to the nearest tenthif necessary.


NAME ________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsUsing the Pythagorean Theorem


1. What type of triangle is formed by the sides of the mat and the diagonal?

2. Write an equation that can be used to find the length of the diagonal.

Reading the LessonDetermine whether each of the following is a Pythagorean triple.

3. 13-84-85 4. 11-60-61

5. 21-23-29 6. 12-25-37

7. The triple 8-15-17 is a Pythagorean triple. Complete the table to findmore Pythagorean triples.

8. If the sides of a square are of length s, how can you find the length of adiagonal of the square?

Helping You Remember9. Work with a partner. Write a word problem that can be solved using the

Pythagorean Theorem, including the art. Exchange problems with yourpartner and solve.

a b c Check: c2 � a2 � b2

original 8 15 17 289 � 64 � 225

2

3

5

10


A Cross-Number PuzzleUse the clues at the bottom of the page to complete the puzzle. Roundcomputational answers to the nearest whole number. You are to writeone digit in each box.

Across Down

A the square of 23.56 A the 5th to 8th digits of �

C the digits in the repeating block of �1111�

B makes Pythagorean triple with 5 and 12

D hypotenuse if legs are 16 and 30 C the largest four-digit perfect square

F perimeter of a square with area of 324 E square of hypotenuse if legs are 20 and 4

H perfect square, digits sum is 4 G perfect square that is a power of 2

J hypotenuse if legs are 40 and 50 I the square of 14

K the largest three-digit perfect square L the square root of 15,625

L twice the square root of 6,724 M other leg if hypotenuse is 53 and short

M side of a square with area of 2,100 leg is 28

N perfect square plus 1 N one angle of a right triangle

O hypotenuse if legs are 7 and 24 O makes Pythagorean triple with 20 and 21

P 10� P perimeter of a square with area of 81

Q diagonal of square with a side of 40

R the square root of 7,400

A B C

D E

F G H I

J K

L M

N O P

Q R


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NAME ________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionDistance on the Coordinate Plane

Find the distance between points (2, �3) and (5, 4).

Graph the points and connect them with a line segment.Draw a horizontal line through (2, �3) and a vertical line through (5, 4). The lines intersect at (5, �3).

Count units to find the length of each leg of the triangle. The lengths are 3 units and 7 units. Then use the Pythagorean Theorem to find the hypotenuse.

c2 � a2 � b2 The Pythagorean Theorem

c2 � 32 � 72 Replace a with 3 and b with 7.

c2 � 9 � 49 Evaluate 32 and 72.

c2 � 58 Simplify.

�c2� � �58� Take the square root of each side.

c � 7.6 Simplify.

The distance between the points is about 7.6 units.

Find the distance between each pair of points whose coordinates aregiven. Round to the nearest tenth if necessary.

1. 2. 3.

Graph each pair of ordered pairs. Then find the distance between thepoints. Round to the nearest tenth if necessary.

4. (4, 5), (0, 2) 5. (0, �4), (�3, 0) 6. (�1, 1), (�4, 4)y

xO

y

xO

y

xO

y

xO

(1, 1)

(3, �2)

y

xO

(4, 3)

(�2, 1)

y

xO

(6, 3)

(1, 1)

y

xO

(5, 4)

(5, �3)(2, �3)

7 units

3 units

You can use the Pythagorean Theorem to find the distance between two points on the coordinate plane.


Find the distance between each pair of points whose coordinates aregiven. Round to the nearest tenth if necessary.

1. 2. 3.

4. 5. 6.

Graph each pair of ordered pairs. Then find the distance between thepoints. Round to the nearest tenth if necessary.

7. (�3, 0), (3, �2) 8. (�4, �3), (2, 1) 9. (0, 2), (5, �2)

10. (�2, 1), (�1, 2) 11. (0, 0), (�4, �3) 12. (�3, 4), (2, �3)y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

(1, �1)

(4, �3)

y

xO

(�2, 2)(3, 3)

y

xO

(5, 6)

(2, 3)

y

xO

(�2, �1)

(0, 1)

y

xO

(�3, 2)

(2, �1)

y

xO

(�1, �2) (4, �2)

Practice: SkillsDistance on the Coordinate Plane

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–6


NAME ________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsDistance on the Coordinate Plane

1. ARCHAEOLOGY An archaeologist at adig sets up a coordinate system usingstring. Two similar artifacts arefound—one at position (1, 4) and theother at (5, 2). How far apart were thetwo artifacts? Round to the nearesttenth of a unit if necessary.

2. GARDENING Vega set up a coordinatesystem with units of feet to locate theposition of the vegetables she plantedin her garden. She has a tomato plantat (1, 3) and a pepper plant at (5, 6).How far apart are the two plants?Round to the nearest tenth if necessary.

3. CHESS April is an avid chess player.She sets up a coordinate system on herchess board so she can record theposition of the pieces during a game.In a recent game, April noted that herking was at (4, 2) at the same time thather opponent’s king was at (7, 8). Howfar apart were the two kings? Round tothe nearest tenth of a unit if necessary.

4. MAPPING Cory makes a map of hisfavorite park, using a coordinatesystem with units of yards. The old oaktree is at position (4, 8) and the graniteboulder is at position (�3, 7). How farapart are the old oak tree and thegranite boulder? Round to the nearesttenth if necessary.

5. TREASURE HUNTING Taro uses acoordinate system with units of feet tokeep track of the locations of anyobjects he finds with his metal detector.One lucky day he found a ring at (5, 7)and a old coin at (10, 19). How farapart were the ring and coin beforeTaro found them? Round to the nearesttenth if necessary.

6. GEOMETRY The coordinates of points Aand B are (�7, 5) and (4, �3),respectively. What is the distancebetween the points, rounded to thenearest tenth?

7. GEOMETRY The coordinates of pointsA, B, and C are (5, 4), (�2, 1), and(4, �4), respectively. Which point, B orC, is closer to point A?

8. THEME PARK Tom is looking at a map ofthe theme park. The map is laid out ina coordinate system. Tom is at (2, 3).The roller coaster is at (7, 8), and thewater ride is at (9, 1). Is Tom closer tothe roller coaster or the water ride?

Less

on

3–6


Reading to Learn MathematicsDistance on the Coordinate Plane

NAME ________________________________________ DATE ______________ PERIOD _____


1. What type of triangle is formed by the blue and red lines?

2. What is the length of the two red lines?

3. Write an equation you could use to determine the distance d between thelocations where the ring and necklace were found.

4. How far apart were the ring and the necklace?

Reading the Lesson5. On the coordinate plane, what are the four sections determined by the

axes called?

6. Match each term of the coordinate plane with its description.

ordinate a. point where number lines meet

y-axis b. x-coordinate

origin c. y-coordinate

abscissa d. vertical number line

x-axis e. horizontal number line

7. To find the distance between two points, draw a right triangle whosehypotenuse is the distance you want to find; find the lengths of the legs,and use ____________________________________ to solve the problem.

Helping You Remember8. Think of a way to remember the names of the four quadrants of the

coordinate plane.


A Coordinate CodeA coordinate graph can be used to make a secret code. First,choose a pair of coordinates for each letter you plan to use. Letterlabels on the points show the order of the letters in the message. Theexample at the right spells out the word HELP.

Use the chart above to decode each secret message. Some points areused more than once.

1. 2. 3.

4. 5. 6.

7. Use the chart to create a secret message of your own.

y

xO

C

G

B

FE

A

D

y

xOE

F

C

HBG

A

D

I

y

xO

EF

CH

B

GA

D

y

xO

E

F

C

HB

GA

D

I

y

xOE

G

C HBF

A

D

y

xO

EC

FA

BD

G

y

xO

BC

DA

NAME ________________________________ DATE ______________ PERIOD _____

Enrichment

(1, 1) (1, �2) (�1, 2) (�2, 2) (2, �2) (�1, �2) (�2, 0)A B C D E F G

(0, 1) (1, 0) (0, �1) (2, �1) (1, �1) (�2, 1) (�1, 0) (�2, �2) (0, 0)H I J K L M N O P

(�2, �1) (�1, 1) (2, 0) (2, 2) (0, �2) (2, 1) (1, 2) (�1, �1) (1, 2)R S T U V W X Y Z

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

For Questions 1–3, find each square root.

1. �25�A. 25 B. 5 C. 15 D. 6 1.

2. ��144�F. 144 G. 12 H. �12 I. 11 2.

3. ��196��

A. �32� B. �1

96�

C. �34� D. ��

32� 3.

4. Solve y2 � 64.F. 6.4 G. 8 H. 8 or �8 I. �8 4.

For Questions 5–7, estimate to the nearest whole number.

5. �29�A. 6 B. 5 C. 7 D. 4 5.

6. �11�F. 2 G. 4 H. 5 I. 3 6.

7. �95�A. 10 B. 9 C. 11 D. 8 7.

8. Estimate the solution of y2 � 21 to the nearest integer.F. 5 or �5 G. 4.6 or �4.6 H. 4.5 or �4.5 I. 4 or �4 8.

9. To which set(s) of numbers does �78� belong?

A. rational B. integer 9.C. irrational D. whole, integer, rational

10. Which graph shows the best estimate of �18�?F. G. 10.

H. I.

11. Which sentence is true?A. �15� � 3�

12� B. �4.3� � ��17� C. �20� � 10 D. �14.4� � 4 11.

17 19 20 2116 18

18

1 3 4 50 2

18

6 8 9 105 7

18

1 3 4 50 2

18


Chapter 3 Test, Form 1

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

12. Which set of numbers is ordered from least to greatest?

F. ��16�, ��17�, ��18�, �9 G. 2.8�2�, �8�, �11�, 3�12�

H. �5�, ��6�, 2�12�, �3 I. �10�, 4, �4�, 1.5 12.

For Questions 13–15, find the length of the missing side of each right triangle. Round to the nearest tenth if necessary.

13. a � 9 feet, b � 12 feetA. 7.9 ft B. 1.7 ftC. 4.6 ft D. 15 ft 13.

14. a � 2 centimeters, c � 5 centimetersF. 1.7 cm G. 5.4 cm H. 4.6 cm I. 2.6 cm 14.

15. a � 3 inches, b � 6 inchesA. 3 in. B. 4.2 in. C. 6.7 in. D. 5.2 in. 15.

16. REAL ESTATE José’s yard is 30 meters by 40 meters. What is the distance from one corner to the opposite corner?F. 8.4 m G. 70 m H. 50 m I. 26.5 m 16.

17. EXERCISE Sandy walked 2 miles south and then walked 4 miles east. How far was Sandy from her starting point? Round to the nearest tenth.A. 4.5 mi B. 3.5 mi C. 6.0 mi D. 3.0 mi 17.

Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary.

18. the points in the graph at the rightF. 7 units G. 7.8 unitsH. 1 unit I. 3.3 units 18.

19. (2, 5), (5, 1)A. 8.1 units B. 25 unitsC. 2.7 units D. 5 units 19.

20. (–3, 4), (–2, –1)F. 6.4 units G. 25 units H. 2.6 units I. 5.1 units 20.

Bonus SWIMMING Marina is swimming in a rectangular pool B:that is 36 feet wide and 48 feet long. How much farther will she swim if she swims diagonally across the pool than if she swims the length of the pool?

y

xO(�3, �1)

(3, 4)

c

b

a


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 1 (continued)



1. �225�A. 22.5 B. 15 C. �15 D. 14 1.

2. ��114040��

F. ��2102�

G. �35� H. ��

65� I. �

53� 2.

3. �2.56�A. 25.6 B. 1.6 C. 16 D. 0.256 3.

4. Solve v2 � 576.F. 25 G. 24 or �24 H. 23 or �23 I. �24 4.


5. �131�A. 12 B. 11 C. 10 D. 13 5.

6. �214�F. 15 G. 16 H. 13 I. 14 6.

7. �160.5�A. 13 B. 12 C. 11 D. 14 7.

8. ALGEBRA Estimate the solution of b2 � 52 to the nearest integer.F. 26 or �26 G. 26 H. 7 I. 7 or �7 8.

9. To which set(s) of numbers does 0.7� belong?A. rational B. integer, whole, rationalC. irrational D. rational, integer 9.

10. To which set(s) of numbers does ��237� belong?

F. whole G. integer, rational 10.H. irrational I. whole, integer, rational

11. Which is a true statement?

A. �12� � 3�12� B. 2�

15� � �5� C. ��1

96��

34� D. �15� � 3.9 11.


Chapter 3 Test, Form 2A

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


F. �11�, 4, 3�13�, �17� G. 6�

19�, �37�, 6�

12�, �29�

H. �5�, 2�35�, �7�, 3 I. �10, �16�, �3�

14�, �20� 12.

For Questions 13 and 14, find the length of the missing side of each triangle. Round to the nearest tenth if necessary.

13. a � 6 meters, b � 10 metersA. 4 m B. 11.7 mC. 2 m D. 8 m 13.

14. b � 15 feet, c � 20 feetF. 12 ft G. 25 ft H. 5 ft I. 13.2 ft 14.

15. Which triangle with sides of the given lengths is a right triangle?A. 6 yd, 8 yd, 10 yd B. 3 in., 4 in., 3 in. 15.C. 14 cm, 6 cm, 12 cm D. 21 ft, 13 ft, 35 ft

16. FORESTRY How far up the tree does the ladder reach?F. 4 ft G. 2 ftH. 8 ft I. 9.2 ft 16.

17. EXERCISE Chenise walked 16 feet north and then 30 feet west. How far was Chenise from her starting point?A. 32 ft B. 34 ft C. 35 ft D. 46 ft 17.


18. the points in the graph at the rightF. 8.1 units G. 1.7 unitsH. 5.7 units I. 3 units 18.

19. (–1, –2), (6, 6)A. 3.9 units B. 10.6 unitsC. 9.9 units D. 8 units 19.

20. (–3, 4), (7, –7)F. 4.6 units G. 10 units H. 14.9 units I. 11 units 20.

Bonus PACKAGING What is the length of the longest stick that B.will fit in a box that is 36 inches long, 27 inches wide,and 24 inches high?

y

xO

(�5, 1)

(2, �3)

10 ft

6 ft

c a

b


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 2A (continued)



1. �100�A. 10 B. 100 C. 1,000 D. �1,000 1.

2. ��1.69�F. �1.3 G. 1.3 H. 1.69 I. �1.69 2.

3. ��16241��

A. 0.5 B. �181� C. �1

81�

D. 0.5 3.

4. Solve d2 � 625.F. 11 G. 15 or �15 H. �25 I. 25 or �25 4.


5. �104�A. 11 B. 10 C. 12 D. 9 5.

6. �244�F. 16 G. 17 H. 15 I. 18 6.

7. �87.2�A. 8 B. 10 C. 9 D. 0.9 7.

8. ALGEBRA Estimate the solution of f 2 � 90 to the nearest integer.F. 45 G. 45 or �45 H. 9 I. 9 or �9 8.

9. To which set(s) of numbers does �5� belong?A. rational B. integer, rationalC. irrational D. whole, integer, rational 9.

10. To which set(s) of numbers does ��17� belong?

F. rational G. integer, rationalH. irrational I. whole, integer, rational 10.

11. Which is a true statement?

A. �35� � 6.4� B. �18� � 9 C. 2�34� � �6� D. �4�

14� � ��20� 11.


Chapter 3 Test, Form 2B

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


F. �8�25�, �8�

12�, ��69�, ��75� G. �24�, �27�, 5�

14�, 5�

13�

H. 2�16�, 2.1�, �3�, �5� I. �

19�, �

17�, �2�, �0.5� 12.

For Questions 13 and 14, find the length of the missing side of each triangle. Round to the nearest tenth if necessary.

13. a � 5 inches, c � 17 inchesA. 4.7 in. B. 3.5 in.C. 17.7 in. D. 16.2 in. 13.

14. a � 4 millimeters, b � 6 millimetersF. 10 mm G. 7.2 mm H. 4.5 mm I. 3.2 mm 14.

15. Which triangle with sides of the given lengths is a right triangle?A. 50 cm, 120 cm, 130 cm B. 15 in., 39 in., 35 in.C. 24 ft, 30 ft, 20 ft D. 1.3 m, 0.5 m, 1.5 m 15.

16. KITING How high above the ground is the kite? Round your answer to the nearest tenth.F. 32.6 ft G. 3.7 ftH. 24.8 ft I. 6.6 ft 16.

17. EXERCISE Darren hiked 12 miles east and then 16 miles south. How far was Darren from his starting point?A. 38 mi B. 20 mi C. 400 mi D. 21 mi 17.


18. the points in the graph at the rightF. 2.0 units G. 6.3 unitsH. 8.0 units I. 6.0 units 18.

19. (–2, –2), (–7, –5)A. 8.6 units B. 4 unitsC. 5.8 units D. 6.4 units 19.

20. (3, 1), (8, 6)F. 7.1 units G. 8.0 units H. 8.6 units I. 13.0 units 20.

Bonus Graph the points A(2, 2), B(14, 2) and C(8, 10). Connect B:the points to form a triangle and then find the perimeter.

y

xO

(�1, 3)

(5, 5)

15 ft

29 ft

b

ca


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 2B (continued)


1. �81� 1.

2. ��900� 2.

3. ��12251�� 3.

Solve each equation.

4. c2 � 1,225 4.

5. �13261�

� m2 5.


6. �66� 6.

7. �92� 7.

8. �220� 8.

ALGEBRA Estimate the solution of each equation to the nearest integer.

9. x2 � 47 9.

10. 115 � p2 10.

For Questions 11 and 12, name all sets of numbers to which each real number belongs.

11. ��400� 11.

12. �0.15 12.

13. Estimate �39� to the nearest tenth. Then 13.graph the square root on a number line.

14. Order �41�, 6�12�, 6�

78�, and �47� from least to greatest. 14.

Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary.

15. a � 10 inches; b � 24 inches 15.

16. b � 15 millimeters; c � 17 millimeters 16.

5 6 7 8


Chapter 3 Test, Form 2C

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

For Questions 17 and 18, determine whether a triangle with sides of the given lengths is a right triangle.

17. 60 feet, 80 feet, 100 feet 17.

18. 19 centimeters, 13 centimeters, 12 centimeters 18.

19. LADDER A 10-foot ladder is leaning against a house. 19.The base of the ladder is 5 feet from the side of the house.At what height does the ladder touch the house? Round to the nearest tenth if necessary.

20. ROSES The Garden Club has a garden in the shape of a 20.right triangle. If one leg is 16 feet long and the hypotenuse is 20 feet long, how long is the remaining leg, along which the roses are planted? Round to the nearest tenth if necessary.

21. WALKING To get to Green Thumb Floral Shop from her 21.house, Jody must walk 7 blocks east and then 4 blocks south. What is the actual distance between Jody’s house and the floral shop? Use a diagram and round to the nearest tenth if necessary.


22. 22.

23. (2, �4), (�3, 5) 23.

24. (1, �3), (�5, �1) 24.

25. (3, 5), (1, �2) 25.

Bonus TATAMIS The traditional floor covering for houses in B:Japan are tatamis. A tatami is a rectangular-shaped mat that measures 6 feet by 3 feet. If a room requires 16 tatamis (4 tatamis by 4 tatamis) to completely cover the floor, what is the distance in feet from one corner of the room to the opposite corner? Use a diagram and round to the nearest tenth.

y

xO

(�5, 1)

(3, �2)


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 2C (continued)


1. �64� 1.

2. ��811�� 2.

3. ��100� 3.

Solve each equation.

4. y2 � 441 4.

5. �499�

� n2 5.


6. �22� 6.

7. �79� 7.

8. �199� 8.


9. d2 � 85 9.

10. 132 � z2 10.

For Questions 11 and 12, name all sets of numbers to which each real number belongs, to the nearest integer.

11. �7� 11.

12. �38� 12.

13. Estimate �96� to the nearest tenth. Then graph the square 13.root on a number line.

14. Order �15�, �19�, 3�34�, and 3.3� from least to

greatest.14.


15. a � 8 inches; b � 6 inches 15.

16. a � 4 meters; c � 6 meters 16.

8 9 10 11


Chapter 3 Test, Form 2D

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Chapter 3 Test, Form 2D (continued)

For Questions 17 and 18, determine whether a trianglewith sides of the given lengths is a right triangle.

17. 7 centimeters, 24 centimeters, 25 centimeters 17.

18. 8 millimeters, 9 millimeters, 15 millimeters 18.

19. CAMPING How high is the tent at its 19.highest point? Round to the nearest tenth if necessary.

20. LADDER A ladder is leaning against a house. The top of 20.the ladder is 12 feet from the ground, and the base of the ladder is 9 feet from the side of the house. How long is the ladder? Use a diagram and round to the nearest tenth if necessary.

21. WALKING From her house, JoAnn must walk 18 blocks west 21.and then 12 blocks north to get to her favorite health food store. What is the actual distance between JoAnn’s house and the health food store? Round to the nearest tenth if necessary.


22. 22.

23. (�5, 4), (2, �4) 23.

24. (�6, –2), (�1, 3) 24.

25. (5, �1), (�4, 5) 25.

Bonus TATAMIS The traditional floor covering for houses in B:Japan are tatamis. A tatami is a rectangular-shaped mat that measures 6 feet by 3 feet. A room requires 4 tatamis (2 tatamis by 2 tatamis) to completely cover the floor. What is the distance in feet from one corner of the room to the opposite corner? Use a diagram and round to the nearest tenth.

y

xO

(�5, �2)

(�2, 4)

4 ft

9 ft


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 3


1. ��2,500� 1.

2. ��114649�� 2.

3. �4.41� 3.

4. Solve the equation r2 � 4.84. 4.

5. Find a number that when squared equals 5.5696. 5.


6. �154.5� 6.

7. �59� 7.

8. �270.2� 8.


9. e2 � 66.5 9.

10. t2 � 105 10.


11. �37� 11.

12. 652 12.

13. Estimate ��209� to the nearest tenth. Then 13.graph the square root on a number line.

14. Order �53�, 7�18�, 7.6�, and �50� from least to greatest. 14.

Write an equation you could use to find the missing side of each right triangle. Then find the missing length.Round to the nearest tenth if necessary.

15. a � 1.7 centimeters; c � 2.2 centimeters 15.

16. b � 36 millimeters; c � 39 millimeters 16.

�15 �14 �13 �12


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Chapter 3 Test, Form 3 (continued)

For Questions 17 and 18, determine whether a trianglewith sides of the given lengths is a right triangle.

17. 24 meters, 45 meters, 51 meters 17.

18. 48 feet, 69 feet, 92 feet 18.

19. LADDER A 16-foot ladder is leaning against a house, 19.touching the house at a height of 12 feet. How far away from the house is the base of the ladder? Round to the nearest tenth.

20. TULIPS Samuel has a garden that is shaped like a right 20.triangle. One leg is 15 feet long, and the hypotenuse is 19 feet long. He has a limited number of tulip bulbs that he wants to plant. How many more feet will he have to cover if he plants them along the two legs rather than along the hypotenuse? Use a diagram and round to the nearest tenth.

21. TATAMIS The floors of houses in Japan are traditionally 21.covered by tatamis. Tatamis are rectangular-shaped straw mats that measure 6 feet by 3 feet. If a room is 8 tatamis by 8 tatamis, what is the distance in feet from one corner to the opposite corner? Use a diagram and round to the nearest tenth.


22. 22.

23. (5, 0), (2, 4) 23.

24. (–2, 2), (1, 3) 24.

25. (–3, 2), (4, –2) 25.

Bonus GEOMETRY The formula for the area of a triangle is B:

�12�bh. Find the area of a right triangle with a hypotenuse

length of 13 inches and one leg length of 5 inches.

y

xO

(5, �2)

(�5, 2)


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Extended Response Assessment

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. a. Explain what is meant by the square root of a number.

b. How many square roots does 36 have?

c. Draw a model to use in estimating �150�. Explain your reasoning.

2. a. Explain how the diagram below demonstrates the PythagoreanTheorem for a right triangle with legs of length 2.

b. Write a word problem that can be solved by using the PythagoreanTheorem.

c. Solve the problem in part b. Explain each step.

3. a. Explain what is meant by the real number system.

b. What is the difference between rational and irrational numbers?Give an example of each.

A

CB


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Chapter 3 Vocabulary Test/Review

Choose from the terms above to complete each sentence.

1. The _______________ is the vertical number line in the 1.coordinate plane.

2. A real number that cannot be expressed as a decimal that 2.terminates or repeats is called a(n) _______________.

3. The sides of a right triangle that form a 90� angle are 3.called _______________.

4. The first number in an ordered pair is the x-coordinate or 4._______________.

5. The _______________ is the horizontal number line in the 5.coordinate plane.

6. The _______________ of the Pythagorean Theorem states 6.that if the sides of a triangle have lengths a, b, and c units such that c2 � a2 � b2, then the triangle is a right triangle.

7. The set of _______________ contains the set of rational 7.numbers.

8. The _______________ of a right triangle is always the 8.longest side of the triangle.

9. The second number in an ordered pair is the y-coordinate 9.or _______________.

10. The point where the zero points of the two number lines 10.meet at right angles in the coordinate plane is called the _______________.

In your own words, define each term.

11. Pythagorean Theorem

12. Pythagorean triple

abscissa (p. 142)

converse (p. 134)

coordinate plane (p. 142)

hypotenuse (p. 132)

irrational number (p. 125)

legs (p. 132)

ordered pair (p. 142)

ordinate (p. 142)

origin (p. 142)

perfect square (p. 116)

principal square root (p. 117)

Pythagorean Theorem (p. 132)

Pythagorean triple (p. 138)

quadrants (p. 142)

radical sign (p. 116)

real number (p. 125)

right triangle (p. 132)

square root (p. 116)

x-axis (p. 142)

x-coordinate (p. 142)

y-axis (p. 142)

y-coordinate (p. 142)


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


1. 1.9 1.

2. ��36� 2.

3. �45� 3.

4. �22� 4.

5. 8.4� 5.

Estimate each square root to the nearest tenth. Then 6.graph the square root on a number line.

6. �10�

7. ��80� 7.

For Questions 8 and 9, replace each � with �, �, or � to make a true sentence.

8. �15� � 4.0 8.

9. �9�34� � ��99� 9.

10. Order �7�, 2.5, 2.9�, and �10� from least to greatest. 10.

�9 �8 �7 �6

1 3 42

Chapter 3 Quiz(Lessons 3-1 and 3-2)


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


1. �225� 1.

2. ��6841�� 2.

For Questions 3 and 4, estimate to the nearest whole number.

3. �19� 3.

4. �40.4� 4.

5. Solve a2 � 400. 5.

Chapter 3 Quiz(Lesson 3-3)

For Questions 1–3, write an equation you could use to find the length of the missing side of each right triangle.Then find the missing length. Round to the nearest tenth if necessary.

1. 2. 1.

2.

3. a � 15 centimeters, b � 19 centimeters 3.

4. Determine whether a triangle with sides of 3 miles, 6 miles, 4.and 8 miles is a right triangle.

5. MULTIPLE-CHOICE TEST ITEM A television screen is 7 inches wide, and its diagonal measures 9.5 inches. Find the height of the screen. Round to the nearest tenth if necessary.A. about 6.4 in. B. about 11.8 in.C. about 16.5 in. D. about 4.06 in. 5.

a cm

9 cm4 cmc in.

10 in.

7 in.

Chapter 3 Quiz(Lesson 3-6)

Chapter 3 Quiz(Lessons 3-4 and 3-5)


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


1. 2. 1.

2.

3–4.

For Questions 3 and 4, graph each pair of ordered pairs.Then find the distance between the points. Round to the nearest tenth if necessary.

3. (1, 4) and (6, 1) 4. (–3, –2) and (4, –3) 3.

4.5. The coordinates of points A and B are (1, –2) and (–1, 3).

What is the distance between the points to the nearest tenth? 5.

y

xO

y

xO

(�4, 2)(3, 3)

y

xO

(�2, �1)

(1, 4)



1. �19�A. 4 B. 5 C. 10 D. 9 1.

2. �171�F. 14 G. 12 H. 13 I. 86 2.

3. Solve f 2 � 169.A. 13 B. 13 or �13 C. �13 D. 84.5 3.


4. �36�F. rational G. integer, rationalH. irrational I. whole, integer, rational 4.

5. ��11556

�

A. rational B. integer, rationalC. irrational D. whole, integer, rational 5.

6. Estimate the solution of b2 � 525 to the nearest integer.F. 21 or �21 G. 22 or �22 H. 23 or �23 I. 26 or �26 6.

7. Solve �449�

� x2. 7.

Estimate each square root to the nearest tenth. Then graph the square root on a number line.

8. �17� 8.

9. ��102� 9.

10. Order �32�, 5�12�, 5.9, �25� from least to greatest. 10.

�12 �11 �10 �9

3 4 5 6


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

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

1. Evaluate (16 – 5) 4 – 6 2. (Lesson 1-2) 1.

2. Evaluate |m � n| if m � �6 and n � �9. (Lesson 1-4) 2.

3. Find 5(�2)(3). (Lesson 1-6) 3.

Multiply or divide. Write in simplest form. 4.

4. 3�15� 3�

34� (Lesson 2-3) 5. �

1352�

�68� (Lesson 2-4) 5.

Add or subtract. Write in simplest form. 6.

6. �5�49� � ��2�

29�� (Lesson 2-5) 7. �

1115�

� �25� (Lesson 2-6) 7.

8. Solve �14�x � 1.7. (Lesson 2-7) 8.

9. Write 6.54 � 10�4 in standard notation. (Lesson 2-9) 9.

10. Find �324�. (Lesson 3-1) 10.

11. Solve d2 � �2851�

. (Lesson 3-1) 11.

12. Estimate the solution of r2 � 105 to the nearest integer. 12.(Lesson 3-2)

13. Name all sets of numbers to which 0.2�3� belongs. 13.(Lesson 3-3)

14. Order �90�, �95�, 9�12� and 9.7 from least to greatest. 14.

(Lesson 3-3)

15. The legs of a right triangle are 4.2 inches and 2.1 inches. 15.Find the length of the hypotenuse. Round to the nearest tenth. (Lesson 3-4)

16. How far is the submarine from the 16.boat? Round to the nearest tenth.(Lesson 3-5)

Find the distance between each pair of points. Round to the nearest tenth if necessary. (Lesson 3-6)

17. (10, 4), (1, 2) 17.

18. (�3, �6), (5, �4) 18.

d

47 yd

105 yd


Chapter 3 Cumulative ReviewNAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

1. Evaluate |m| � |n| if m � �5 and n � 6. (Lesson 1-3)

A. �11 B. �1 C. 1 D. 11 1.

2. Solve �9y � 72. (Lesson 1-9)

F. �648 G. �8 H. 63 I. 81 2.

3. Write 0.3�8� as a fraction in simplest form. (Lesson 2-1)

A. �13080�

B. �1590�

C. �3989�

D. 2�1129�

3.

4. Find 2�34� 1 �

13�. Write in simplest form. (Lesson 2-3)

F. 2�116�

G. 2�14� H. 3�1

12�

I. 3�23� 4.

5. Find �58� � �1

30�

. Write in simplest form. (Lesson 2-6)

A. �3470�

B. �49� C. �1

36�

D. �3870�

5.

6. GEOMETRY If the area of a square is 289 square feet, what is the length of the sides? (Lesson 3-1)

F. 14 ft G. 35 ft H. 17 ft I. 5 ft 6.

7. Which is the best estimate of the value of ��86�? (Lesson 3-2)

A. �43 B. �9 C. �8 D. �10 7.

8. To which set does �15 not belong? (Lesson 3-3)

F. whole G. rational H. integers I. real 8.

9. Which lengths will form the sides of a right triangle?(Lesson 3-4)

A. 24 feet, 32 feet, 40 feet B. 7 feet, 8 feet, 9 feetC. 4 feet, 5 feet, 6 feet D. 18 feet, 27 feet, 36 feet 9.

10. Which point is not 5 units away from the point (0, 3)?(Lesson 3-6)

F. (4, 6) G. (4, 0) H. (0, 8) I. (�4, 5) 10. IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA


Standardized Test Practice (Chapter 3)

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

11. Find 27 � (�85). (Lesson 1-5) 11. 12.

12. Solve d � 1.25 � 6.17. (Lesson 2-7)

13. Find ��2851��. (Lesson 3-1) 13.

14. Estimate the solution of t2 � 98 to the 14.nearest whole number. (Lesson 3-2)

15. Use the triangle at the right to find the missing length. (Lesson 3-4)

a. Write an equation you could use to find the length of the missing side.

b. Find the length of the missing side. Round to the nearest tenth ifnecessary.

b cm

9 cm

11 cm

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

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.


NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

1. VIDEOS Marcos is going to buy cabinets for his 160 videos. 1.If the cabinet that he has picked out holds 55 videos, how many cabinets does he need to buy?

2. Name the property shown by the statement 2.(6 � x) � 0 � 6 � x.

3. Graph the set of integers {�4, 0, �1, 5} on a number line. 3.

4. Evaluate |f| � g if f � �4 and g � 10. 4.

5. Find �21 � (�9). 5.

Multiply or divide.

6. �4(�4)(�2) 6.

7. �64 (�4) 7.

8. ENROLLMENT There are 116 fewer students at Eastside 8.Middle School than at Jordan Middle School. Define a variable and write an expression for the number of students at Eastside Middle School.

9. If you decrease a number by 12, the result is �19. Write 9.and solve an equation to find the number.

Solve each equation. Check your solution.

10. 48 � y � �6 10.

11. �56 � �7a 11.

12. Write 11�49� as a decimal. 12.

13. Write 0.58 as a fraction in simplest form. 13.

14. ALGEBRA Evaluate pq if p � 1�140�

and q � �17�. 14.

15. Find 5�14� ��7�

12��. Write in simplest form. 15.

�2 0 2�4 4


Unit 1 Test (Chapters 1–3)

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Add or subtract. Write in simplest form.

16. �6�78� � ��1�

38�� 16.

17. 6�34� � 3�

12� 17.

Solve each equation. Check your solution.

18. a – 6�13� � 6�

13� 18.

19. �1d.7�

� �9.3 19.

20. Evaluate 25 42. 20.

21. Write 0.00169 using scientific notation. 21.


22. ��121� 22.

23. ��2851�� 23.

24. Estimate �126� to the nearest whole number. 24.

25. Name all sets of numbers to which 5.86 belongs. 25.


26. a � 9 inches; b � 12 inches 26.

27. b � 14 centimeters; c � 28 centimeters 27.

28. How long is the ladder? Round to the nearest 28.tenth.

Find the distance between the points whose coordinates are given. Round to the nearest tenth if necessary.

29. (�6, 2), (1, 4) 29.

30. (�2, �3), (�4, 6) 30.

15 ft

3 ft


NAME ________________________________________ DATE ______________ PERIOD _____

Unit 1 Test (continued)

© Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 3

An

swer

s

Standardized Test PracticeStudent Recording Sheet (Use with pages 150–151 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 of symbol.

9. 12.

10.

11.

12. (grid in)

13.

14.

15.

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. IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Part 2: Short Response/Grid in

Record your answers for Questions 16 and 17 on the back of this paper.

Part 3: Extended Response

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 16 Rubric

Standardized Test PracticeRubrics (Use to score the Extended Response questions on page 151 of the Student Edition.)

Score Specific Criteria4 The equation 142 � x2 � 122 is given. The equation is correctly solved showing each

step with appropriate explanation. The length is shown to be about 7.2 m.

3 The correct equation is given, but one computational error is made in the solution.ORThe correct equation is given, but one step or correct explanation is missing from thesolution.

2 The correct equation is given, but two computational errors are made in thesolution. ORThe correct equation is given, but the explanations for the steps are incorrect or notgiven.

1 The equation is not correct, but the incorrect equation is solved correctly. ORThe correct equation is given, but there is no solution.

0 Response is completely incorrect.

Score Specific Criteria4 The two points are correctly graphed on a coordinate plane. A complete explanation

of how to find the distance between the points is given. The distance is found to beabout 5.8 units.

3 The two points are correctly graphed and the distance is correctly determined, butthe explanation is not complete. ORThe two points are correctly graphed and a complete explanation is given, but acomputational error is made.

2 The two points are not correctly graphed, but the correct distance between thegraphed points is given with the correct explanation. ORThe two points are correctly graphed and the distance is correctly determined, butthe explanation is not given.

1 The two points are correctly graphed, but the distance is not found and noexplanation is given. ORThe two points are not correctly graphed, but a partial explanation of how the findthe distance is given.

0 Response is completely incorrect.

Exercise 17 Rubric



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qu

are

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Lesson 3–1

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ince

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a2�

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rite

the

equa

tion.

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the

squ

are

root

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each

sid

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a�

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ice

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d ��

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d e

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y Gu

ide

and

Inte

rven

tion

Sq

uar

e R

oo

ts

The

squ

are

root

of

a nu

mbe

r is

one

of

two

equa

l fac

tors

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a nu

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r.T

he r

adic

al s

ign

�2�

is u

sed

toin

dica

te t

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ositi

ve s

quar

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ot.

Answers (Lesson 3-1)

An

swer

s


©G

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and

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s, C

ours

e 3

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ME

____

____

____

____

____

____

____

____

____

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E _

____

____

____

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ER

IOD

__

___

Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 11

6 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.C

opy

and

com

plet

e th

e fo

llow

ing

tabl

e.

2.S

upp

ose

a sq

uar

e ar

ran

gem

ent

has

36

tile

s.H

ow m

any

tile

s ar

e on

asi

de?

6

3.W

hat

is

the

rela

tion

ship

bet

wee

n t

he

nu

mbe

r of

til

es o

n a

sid

e an

d th

en

um

ber

of t

iles

in

th

e ar

ran

gem

ent?

Th

e sq

uar

e o

f th

e n

um

ber

of

tile

s o

n a

sid

e is

th

e n

um

ber

of

tile

s in

th

e ar

ray.

Rea

din

g t

he

Less

on

4.T

he

oppo

site

of

____

____

____

____

____

____

____

_ is

fin

din

g on

e of

tw

o eq

ual

fact

ors

of a

nu

mbe

r.sq

uar

ing

a n

um

ber

5.E

xpla

in h

ow y

ou k

now

wh

eth

er a

squ

are

root

is

the

prin

cipa

l sq

uar

e ro

otor

not

.T

he

pri

nci

pal

sq

uar

e ro

ot

is t

he

po

siti

ve s

qu

are

roo

to

f a

nu

mb

er.

6.T

o so

lve

an e

quat

ion

in

wh

ich

on

e si

de o

f th

e eq

uat

ion

is

a sq

uar

ed t

erm

,w

hat

can

you

do

to e

ach

sid

e of

th

e eq

uat

ion

?Ta

ke t

he

squ

are

roo

t.

Hel

pin

g Y

ou

Rem

emb

er7.

Giv

en e

nou

gh t

ime

and

enou

gh t

iles

,how

mig

ht

you

go

abou

tde

term

inin

g w

het

her

a w

hol

e n

um

ber

is a

per

fect

squ

are?

Sam

ple

answ

er:W

ith

as

man

y ti

les

as t

he

giv

en n

um

ber

,try

to

arra

ng

e th

em in

a s

qu

are

pat

tern

.If

a sq

uar

e ca

n b

e fo

rmed

,th

en t

he

nu

mb

er is

a p

erfe

ct s

qu

are.

Read

ing

to L

earn

Mat

hem

atic

sS

qu

are

Ro

ots

1

41

2T

iles

on

a S

ide

Tot

al N

um

ber

of

Til

es i

n

the

Sq

uar

e A

rran

gem

ent

93

164

255

Lesson 3–1

©G

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5M

athe

mat

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App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Sq

uar

e R

oo

ts

1.PL

AN

NIN

GR

osy

wan

ts a

lar

ge p

ictu

rew

indo

w p

ut

in t

he

livi

ng

room

of

her

new

hou

se.T

he

win

dow

is

to b

e sq

uar

ew

ith

an

are

a of

49

squ

are

feet

.How

lon

g sh

ould

eac

h s

ide

of t

he

win

dow

be?

7 ft

2.G

EOM

ETRY

If t

he

area

of

a sq

uar

e is

1 sq

uar

e m

eter

,how

man

y ce

nti

met

ers

lon

g is

eac

h s

ide?

100

cm

3.A

RT

A m

inia

ture

por

trai

t of

Geo

rge

Was

hin

gton

is

squ

are

and

has

an

are

aof

169

squ

are

cen

tim

eter

s.H

ow l

ong

isea

ch s

ide

of t

he

port

rait

?13

cm

4.B

AK

ING

Len

is

baki

ng

a sq

uar

e ca

ke f

orh

is f

rien

d’s

wed

din

g.W

hen

ser

ved

toth

e gu

ests

,th

e ca

ke w

ill

be c

ut

into

squ

are

piec

es 1

in

ch o

n a

sid

e.T

he

cake

shou

ld b

e la

rge

enou

gh s

o th

at e

ach

of

the

121

gues

ts g

ets

one

piec

e.H

owlo

ng

shou

ld e

ach

sid

e of

th

e ca

ke b

e?11

in.

5.A

RT

Car

a h

as 1

96 m

arbl

es t

hat

sh

e is

usi

ng

to m

ake

a sq

uar

e fo

rmat

ion

.How

man

y m

arbl

es s

hou

ld b

e in

eac

h r

ow?

14 m

arb

les

6.G

AR

DEN

ING

Tat

e is

pla

nn

ing

to p

ut

asq

uar

e ga

rden

wit

h a

n a

rea

of

289

squ

are

feet

in

his

bac

k ya

rd.W

hat

wil

l be

th

e le

ngt

h o

f ea

ch s

ide

of t

he

gard

en?

17 f

t

7.H

OM

E IM

PRO

VEM

ENT

Al

has

324

squ

are

pavi

ng

ston

es t

hat

he

plan

s to

use

to

con

stru

ct a

squ

are

pati

o.H

ow m

any

pavi

ng

ston

es w

ide

wil

l th

e pa

tio

be?

18 s

ton

es

8.G

EOM

ETRY

If t

he

area

of

a sq

uar

e is

529

squ

are

inch

es,w

hat

is

the

len

gth

of

a si

de o

f th

e sq

uar

e?23

in.



©G

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athe

mat

ics:

App

licat

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Con

cept

s, C

ours

e 3

Est

imat

e �

204

�to

th

e n

eare

st w

hol

e n

um

ber

.

•T

he

firs

t pe

rfec

t sq

uar

e le

ss t

han

204

is

14.

•T

he

firs

t pe

rfec

t sq

uar

e gr

eate

r th

an 2

04 i

s 15

.

196

�20

4 �

225

Writ

e an

ineq

ualit

y.

142

�20

4 �

152

196

�14

2an

d 22

5 �

152

14 �

�20

4�

�15

Take

the

squ

are

root

of

each

num

ber.

So,

�20

4�

is b

etw

een

14

and

15.S

ince

204

is

clos

er t

o 19

6 th

an 2

25,t

he

best

wh

ole

nu

mbe

r es

tim

ate

for

�20

4�

is 1

4.

Est

imat

e �

79.3

�to

nea

rest

wh

ole

nu

mb

er.

•T

he

firs

t pe

rfec

t sq

uar

e le

ss t

han

79.

3 is

64.

•T

he

firs

t pe

rfec

t sq

uar

e gr

eate

r th

an 7

9.3

is 8

1.

64�

79.3

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Writ

e an

ineq

ualit

y.

82�

79.3

�92

64 �

82an

d 81

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8 �

�79

.3�

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the

squ

are

root

of

each

num

ber.

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�79

.3�

is b

etw

een

8 a

nd

9.S

ince

79.

3 is

clo

ser

to 8

1 th

an 6

4,th

e be

st w

hol

e

nu

mbe

r es

tim

ate

for

�79

.3�

is 9

.

Est

imat

e to

th

e n

eare

st w

hol

e n

um

ber

.

1.�

8�3

2.�

37�6

3.�

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4.�

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5.�

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711

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82.7

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12.

�17

5.2

�13

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Est

imat

ing

Sq

uar

e R

oo

ts

Mos

t nu

mbe

rs a

re n

ot p

erfe

ct s

quar

es.

You

can

estim

ate

squa

re r

oots

for

thes

e nu

mbe

rs.

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Pro

per

ties

of

the

Geo

met

ric

Mea

nT

he

squ

are

root

of

the

prod

uct

of

two

nu

mbe

rs i

s ca

lled

th

eir

geom

etri

c m

ean

.

Nu

mb

ers

Geo

met

ric

Mea

na

and

cb

��

ac �

12 a

nd

48�

12�

4�

8��

�57

6�

�24

Th

e ge

omet

ric

mea

n h

as m

any

inte

rest

ing

prop

erti

es.F

or e

xam

ple,

two

nu

mbe

rs a

nd

thei

r ge

omet

ric

mea

n s

atis

fy t

hei

r pr

opor

tion

bel

ow.

�a b��

�b c�

Fin

d t

he

geom

etri

c m

ean

,b,f

or e

ach

pai

r of

nu

mb

ers.

1.a

�2

and

c�

82.

a�

4 an

d c

�9

3.a

�9

and

c�

16b

�4

b�

6b

�12

4.a

�16

an

d c

�4

5.a

�16

an

d c

�36

6.a

�12

an

d c

�3

b�

8b

�24

b�

6

7.a

�18

an

d c

�8

8.a

�2

and

c�

189.

a�

27 a

nd

c�

12b

�12

b�

6b

�18

Sol

ve.

10.

For

eac

h t

ripl

e of

nu

mbe

rs i

n E

xerc

ises

1–9

,dra

w

a tr

ian

gle

like

th

e on

e sh

own

at

the

righ

t.W

hat

pr

oper

ty i

s sh

own

?A

ll o

f th

e tr

ian

gle

s ar

e ri

gh

t.

11.

Now

mak

e th

is d

raw

ing

for

each

tri

ple

of n

um

bers

.T

he

sem

icir

cle

has

a d

iam

eter

equ

al t

o th

e su

m o

f a

and

c.W

hat

pro

pert

y do

you

fin

d?T

he

seg

men

tw

ith

len

gth

b e

xact

ly m

eets

th

e se

mic

ircl

e.b

ac

b

ac

Enric

hmen

tN

AM

E__

____

____

____

____

____

____

____

____

____

__D

ATE

___

____

____

___

PE

RIO

D

____

_

Lesson 3–1

Answers (Lessons 3-1 and 3-2)

An

swer

s


©G

lenc

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cGra

w-H

ill14

0M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Est

imat

ing

Sq

uar

e R

oo

ts

1.G

EOM

ETRY

If t

he

area

of

a sq

uar

e is

29 s

quar

e in

ches

,est

imat

e th

e le

ngt

h o

fea

ch s

ide

of t

he

squ

are

to t

he

nea

rest

wh

ole

nu

mbe

r.5

in.

2.D

ECO

RA

TIN

GM

iki

has

an

squ

are

rug

in h

er l

ivin

g ro

om t

hat

has

an

are

a of

19 s

quar

e ya

rds.

Est

imat

e th

e le

ngt

h

of a

sid

e of

th

e ru

g to

th

e n

eare

st

wh

ole

nu

mbe

r.4

yd

3.G

AR

DEN

ING

Ru

by i

s pl

ann

ing

to p

ut

asq

uar

e ga

rden

wit

h a

n a

rea

of20

0 sq

uar

e fe

et i

n h

er b

ack

yard

.E

stim

ate

the

len

gth

of

each

sid

e of

th

ega

rden

to

the

nea

rest

wh

ole

nu

mbe

r.14

ft

4.A

LGEB

RA

Est

imat

e th

e so

luti

on o

fc2

�40

to

the

nea

rest

in

tege

r.6

or

–6

5.A

LGEB

RA

Est

imat

e th

e so

luti

on o

fx2

�13

8.2

to t

he

nea

rest

in

tege

r.12

or

–12

6.A

RIT

HM

ETIC

Th

e ge

omet

ric

mea

nof

two

nu

mbe

rs a

and

bca

n b

e fo

un

d by

eval

uat

ing

�a

�b

�.E

stim

ate

the

geom

etri

c m

ean

of

5 an

d 10

to

the

nea

rest

wh

ole

nu

mbe

r.7

7.G

EOM

ETRY

Th

e ra

diu

s r

of a

cer

tain

circ

le i

s gi

ven

by

r�

�71 �

.Est

imat

e th

era

diu

s of

th

e ci

rcle

to

the

nea

rest

foo

t.8

ft

8.G

EOM

ETRY

In a

tri

angl

e w

hos

e ba

sean

d h

eigh

t ar

e eq

ual

,th

e ba

se b

is

give

n b

y th

e fo

rmu

la b

��

2A �,w

her

e A

is t

he

area

of

the

tria

ngl

e.E

stim

ate

toth

e n

eare

st w

hol

e n

um

ber

the

base

of

this

tri

angl

e if

th

e ar

ea i

s 17

squ

are

met

ers.

6 m

©G

lenc

oe/M

cGra

w-H

ill13

9M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Est

imat

e to

th

e n

eare

st w

hol

e n

um

ber

.

1.�

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2.�

18�4

3.�

10�3

4.�

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171

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12.

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16.

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578

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18.

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22.

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6

25.

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28.

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8.4

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30.

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.92

�7

Prac

tice:

Ski

llsE

stim

atin

g S

qu

are

Ro

ots

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 3–2



©G

lenc

oe/M

cGra

w-H

ill14

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Her

on

's F

orm

ula

A f

orm

ula

nam

ed a

fter

Her

on o

f Ale

xan

dria

can

be

use

d to

fin

d th

e ar

ea o

f a

tria

ngl

e if

you

kn

ow t

he

len

gth

s of

th

e si

des.

Ste

p 1

Ste

p 2

Fin

d s,

the

sem

i-per

imet

er.F

or a

tria

ngle

with

S

ubst

itute

s,

a, b

, an

d c

into

side

s a,

b,

and

c, t

he s

emi-p

erim

eter

is:

Her

on’s

For

mul

a to

fin

d th

e ar

ea,

A.

s�

�a�

2b�

c�

.A

��

s(s

��

a)(s

��

b)(s

��

c)�

Est

imat

e th

e ar

ea o

f ea

ch t

rian

gle

by

cou

nti

ng

squ

ares

.Th

en u

seH

eron

’s F

orm

ula

to

com

pu

te a

mor

e ex

act

area

.Giv

e ea

ch a

nsw

er t

oth

e n

eare

st t

enth

of

a u

nit

.E

stim

ates

will

var

y.S

amp

le e

stim

ates

giv

en.

1.2.

3.

Est

imat

ed a

rea:

16E

stim

ated

are

a:36

Est

imat

ed a

rea:

28C

ompu

ted

area

:15

.6C

ompu

ted

area

:37

.4C

ompu

ted

area

:24

.0

4.5.

6.

Est

imat

ed a

rea:

22E

stim

ated

are

a:13

Est

imat

ed a

rea:

19C

ompu

ted

area

:21

.2C

ompu

ted

area

:11

.8C

ompu

ted

area

:17

.4

7.W

hy

wou

ld i

t be

foo

lish

to

use

Her

on’s

For

mu

la t

o fi

nd

the

area

of

a ri

ght

tria

ngl

e?T

he

area

of

a ri

gh

t tr

ian

gle

eq

ual

s o

ne-

hal

f th

ep

rod

uct

of

the

leg

s.

5

9

7

8

8

377

7

10

8

69

10

9

6

6

6

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

©G

lenc

oe/M

cGra

w-H

ill14

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 12

0 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.H

ow m

any

squ

ares

are

on

eac

h s

ide

of t

he

larg

est

poss

ible

squ

are

usi

ng

no

mor

e th

an 4

0 sm

all

squ

ares

?6

squ

ares

2.H

ow m

any

squ

ares

are

on

eac

h s

ide

of t

he

smal

lest

pos

sibl

e sq

uar

e u

sin

gat

lea

st 4

0 sm

all

squ

ares

?7

squ

ares

3.T

he

valu

e of

�40�

is b

etw

een

tw

o co

nse

cuti

ve w

hol

e n

um

bers

.Wh

at a

reth

e n

um

bers

?6

and

7

Use

gri

d p

aper

to

det

erm

ine

bet

wee

n w

hic

h t

wo

con

secu

tive

wh

ole

nu

mb

ers

each

val

ue

is l

ocat

ed.

4.�

23�4

and

55.

�52�

7 an

d 8

6.�

27�5

and

67.

�18�

4 an

d 5

Rea

din

g t

he

Less

on

8.E

xpla

in h

ow y

ou c

an e

stim

ate

the

squ

are

root

of

a n

um

ber

if y

ou k

now

pe

rfec

t sq

uar

es g

reat

er t

han

an

d le

ss t

han

th

e n

um

ber.

Sam

ple

answ

er:W

rite

an

ineq

ual

ity

that

giv

es t

he

clo

sest

per

fect

squ

ares

less

th

an a

nd

gre

ater

th

an t

he

nu

mb

er.

Th

en t

ake

the

squ

are

roo

ts o

f th

e p

erfe

ct s

qu

ares

to

est

imat

e th

e b

est

wh

ole

nu

mb

er f

or

the

squ

are

roo

t o

f th

e g

iven

nu

mb

er.

For

Exe

rcis

es 9

–12,

esti

mat

e to

th

e n

eare

st w

hol

e n

um

ber

.

9.�

33�6

10.

�71�

8

11.

�11

4�

1112

.�

211

�15

13.

Rea

d E

xam

ple

2 on

pag

e 12

1 of

you

r te

xtbo

ok.W

hat

is

a “g

olde

nre

ctan

gle”

?a

rect

ang

le in

wh

ich

th

e le

ng

th o

f th

e lo

ng

er s

ide

div

ided

by

the

len

gth

of

the

sho

rter

sid

e is

eq

ual

to�1

�2�

5��

Hel

pin

g Y

ou

Rem

emb

er14

.D

raw

a t

rian

gle

and

labe

l it

s si

des.

(Mak

e su

re y

our

tria

ngl

e is

a r

eal

tria

ngl

e.F

or e

xam

ple,

side

s of

len

gth

s 2,

2 an

d 8

do n

ot m

ake

a tr

ian

gle.

)T

rade

tri

angl

es w

ith

a p

artn

er a

nd

esti

mat

e th

e ar

ea o

f yo

ur

tria

ngl

esu

sin

g H

eron

’s F

orm

ula

.S

ee s

tud

ents

’wo

rk.

Read

ing

to L

earn

Mat

hem

atic

sE

stim

atin

g S

qu

are

Ro

ots

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 3–2


An

swer

s


©G

lenc

oe/M

cGra

w-H

ill14

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Nam

e al

l se

ts o

f n

um

ber

s to

wh

ich

eac

h r

eal

nu

mb

er b

elon

gs.

1.12

wh

ole

,in

teg

er,r

atio

nal

2.�

15in

teg

er,r

atio

nal

3.1 �

1 2�ra

tio

nal

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18ra

tio

nal

5.�8 4�

wh

ole

,in

teg

er,r

atio

nal

6.9.

3�ra

tio

nal

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2 �7 9�

rati

on

al8.

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wh

ole

,in

teg

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atio

nal

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rati

on

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inte

ger

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11.

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on

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imat

e ea

ch s

qu

are

root

to

the

nea

rest

ten

th.T

hen

gra

ph

th

esq

uar

e ro

ot o

n a

nu

mb

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ine.

13.

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14.

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15.

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lace

eac

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.

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14

13

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5NA

ME

____

____

____

____

____

____

____

____

____

____

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E _

____

____

____

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ER

IOD

__

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Prac

tice:

Ski

llsT

he

Rea

l Nu

mb

er S

yste

m

Lesson 3–3

©G

lenc

oe/M

cGra

w-H

ill14

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Nam

e al

l se

ts o

f n

um

ber

s to

wh

ich

eac

h r

eal

nu

mb

er b

elon

gs.

5w

hol

e n

um

ber,

inte

ger,

rati

onal

nu

mbe

r

0.66

6 …D

ecim

als

that

ter

min

ate

or r

epea

t ar

e ra

tion

al n

um

bers

,sin

ce t

hey

can

be

exp

ress

ed a

s fr

acti

ons.

0.66

6…�

�2 3�

��

25�S

ince

��

25��

�5,

it i

s an

in

tege

r an

d a

rati

onal

nu

mbe

r.

��

11��

11��

3.31

6624

79…

Sin

ce t

he

deci

mal

doe

s n

ot t

erm

inat

e or

rep

eat,

it

is a

n i

rrat

ion

al n

um

ber.

Rep

lace

�w

ith

�,�

,or

�to

mak

e 2 �

1 4��

�5�

a tr

ue

sen

ten

ce.

Wri

te e

ach

nu

mbe

r as

a d

ecim

al.

2 �1 4�

�2.

25

�5�

�2.

2360

67…

Sin

ce 2

.25

is g

reat

er t

han

2.2

3606

7…,2

�1 4��

�5�

.

Nam

e al

l se

ts o

f n

um

ber

s to

wh

ich

eac

h r

eal

nu

mb

er b

elon

gs.

1.30

wh

ole

,in

teg

er,r

atio

nal

2.�

11in

teg

er,r

atio

nal

3.5 �

4 7�ra

tio

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rati

on

al

5.0

wh

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atio

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inte

ger

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ion

al

7.�6 3�

wh

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irra

tio

nal

Rep

lace

eac

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7�

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NA

ME

____

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____

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ER

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Stud

y Gu

ide

and

Inte

rven

tion

Th

e R

eal N

um

ber

Sys

tem

Num

bers

may

be

clas

sifie

d by

iden

tifyi

ng t

o w

hich

of

the

follo

win

g se

ts t

hey

belo

ng.

Wh

ole

Nu

mb

ers

0, 1

, 2,

3,

4, …

Inte

ger

s…

, �

2, �

1, 0

, 1,

2,

…

Rat

ion

al N

um

ber

snu

mbe

rs t

hat

can

be e

xpre

ssed

in t

he fo

rm �a b�,

whe

re a

and

bar

e in

tege

rs a

nd b

0

Irra

tio

nal

Nu

mb

ers

num

bers

tha

t ca

nnot

be

expr

esse

d in

the

form

�a b�, w

here

aan

d b

are

inte

gers

and

b

0

To c

ompa

re r

eal n

umbe

rs,

writ

e ea

ch n

umbe

r as

a d

ecim

al a

nd t

hen

com

pare

the

de

cim

al v

alue

s.



©G

lenc

oe/M

cGra

w-H

ill14

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

125

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.T

he

len

gth

of

the

cou

rt i

s 60

fee

t.Is

th

is n

um

ber

a w

hol

e n

um

ber?

Is

it a

ra

tion

al n

um

ber?

Exp

lain

.

yes;

yes;

60 �

�6 10 �

2.T

he

dist

ance

fro

m t

he

net

to

the

rear

spi

kers

lin

e is

7�1 2�

feet

.Is

this

nu

mbe

r a

wh

ole

nu

mbe

r? I

s it

a r

atio

nal

nu

mbe

r? E

xpla

in.

no

;ye

s;7 �

1 2��

�1 25 �

3.T

he

diag

onal

acr

oss

the

cou

rt i

s �

4,50

0�

feet

.Can

th

is s

quar

e ro

ot b

ew

ritt

en a

s a

wh

ole

nu

mbe

r? a

rat

ion

al n

um

ber?

no

;n

o

Rea

din

g t

he

Less

on

4.W

hat

do

rati

onal

an

d ir

rati

onal

nu

mbe

rs h

ave

in c

omm

on?

Wh

at i

s th

e di

ffer

ence

bet

wee

n r

atio

nal

nu

mbe

rs a

nd

irra

tion

al n

um

bers

? G

ive

an

exam

ple

of e

ach

.S

amp

le a

nsw

er:

Rat

ion

al a

nd

irra

tio

nal

nu

mb

ers

are

bo

th t

ypes

of

real

nu

mb

ers.

A r

atio

nal

nu

mb

er c

an b

eex

pre

ssed

as

a d

ecim

al t

hat

ter

min

ates

or

rep

eats

,bu

t an

irra

tio

nal

nu

mb

er c

ann

ot.

1.41

is r

atio

nal

an

d �

2 �is

irra

tio

nal

.

5.M

atch

th

e pr

oper

ty o

f re

al n

um

bers

wit

h t

he

alge

brai

c ex

ampl

e.

Com

mu

tati

vea.

(x�

y)�

z�

x�

(y�

z)

Ass

ocia

tive

b.p

q�

qp

Dis

trib

uti

vec.

h�

0�

h

Iden

tity

d.c

�(�

c)�

0

Inve

rse

e.x(

y�

z)�

xy�

xz

Hel

pin

g Y

ou

Rem

emb

er6.

Th

ink

of a

way

to

rem

embe

r th

e re

lati

onsh

ips

betw

een

th

e se

ts o

fn

um

bers

in

th

e re

al n

um

ber

syst

em.F

or e

xam

ple,

thin

k of

a r

hym

e th

atte

lls

the

orde

r of

th

e se

ts o

f n

um

bers

fro

m s

mal

lest

to

larg

est.

See

stu

den

ts’w

ork

.

dceab

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Read

ing

to L

earn

Mat

hem

atic

sT

he

Rea

l Nu

mb

er S

yste

m

©G

lenc

oe/M

cGra

w-H

ill14

5M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Prac

tice:

Wor

d Pr

oble

ms

Th

e R

eal N

um

ber

Sys

tem

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 3–3

1.G

EOM

ETRY

If t

he

area

of

a sq

uar

e is

33 s

quar

e in

ches

,est

imat

e th

e le

ngt

h o

fa

side

of

the

squ

are

to t

he

nea

rest

ten

th o

f an

in

ch.

5.7

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IOD

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roy

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ina

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ME

____

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Lesson X–4

Prac

tice:

Ski

llsT

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Lesson 3–4


An

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s


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mat

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App

licat

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Con

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met

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Th

e P

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App

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Con

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NA

ME

____

____

____

____

____

____

____

____

____

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DAT

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____

____

____

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ER

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___

Lesson X–4 Lesson 3–4

Read

ing

to L

earn

Mat

hem

atic

sT

he

Pyt

hag

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Pre-

Act

ivit

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om

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te t

he

Min

i Lab

at

the

top

of

pag

e 13

2 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

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elo

w.

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ind

the

area

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e sa

me.

3.F

ind

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sum

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ow d

oes

the

sum

com

pare

to

the

area

of

the

larg

er s

quar

e?25

un

its2

;Th

ey a

re e

qu

al.

4.U

se g

rid

pape

r to

cu

t ou

t th

ree

squ

ares

wit

h s

ides

5,1

2,an

d 13

un

its.

For

m a

tri

angl

e w

ith

th

ese

squ

ares

.Com

pare

th

e su

m o

f th

e ar

eas

of t

he

two

smal

ler

squ

ares

wit

h t

he

area

of

the

larg

er s

quar

e.T

hey

are

th

e sa

me.

Rea

din

g t

he

Less

on

5.Is

it

poss

ible

to

hav

e a

righ

t tr

ian

gle

for

wh

ich

th

e P

yth

agor

ean

Th

eore

mis

not

tru

e?n

o

6.If

you

kn

ow t

he

len

gth

s of

tw

o of

th

e si

des

of a

rig

ht

tria

ngl

e,h

ow c

anyo

u f

ind

the

len

gth

of

the

thir

d si

de?

Sam

ple

an

swer

:If

th

e tw

okn

ow

n s

ides

are

bo

th le

gs

of

the

tria

ng

le,f

ind

th

e su

m o

fth

e sq

uar

es o

f th

eir

len

gth

s an

d t

hen

fin

d t

he

squ

are

roo

t o

fth

is s

um

.If

on

e si

de

is a

leg

an

d t

he

oth

er is

th

ehy

po

ten

use

,su

btr

act

the

squ

are

of

the

len

gth

of

the

kno

wn

leg

fro

m t

he

squ

are

of

the

len

gth

of

the

hyp

ote

nu

se,a

nd

then

fin

d t

he

squ

are

roo

t o

f th

e re

sult

.

Use

th

e P

yth

agor

ean

Th

eore

m t

o d

eter

min

e w

het

her

eac

h o

f th

efo

llow

ing

mea

sure

s of

th

e si

des

of

a tr

ian

gle

are

the

sid

es o

f a

righ

ttr

ian

gle.

7.4,

5,6

no

8.9,

12,1

5ye

s

9.10

,24,

26ye

s10

.5,

7,9

no

Hel

pin

g Y

ou

Rem

emb

er11

.In

eve

ryda

y la

ngu

age,

a le

gis

a l

imb

use

d to

su

ppor

t th

e bo

dy.H

ow d

oes

this

mea

nin

g re

late

to

the

legs

of

a ri

ght

tria

ngl

e?S

amp

le a

nsw

er:

Th

e le

gs

of

a ri

gh

t tr

ian

gle

su

pp

ort

th

e hy

po

ten

use

.



©G

lenc

oe/M

cGra

w-H

ill15

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Wri

te a

n e

qu

atio

n t

hat

can

be

use

d t

o an

swer

th

e q

ues

tion

.T

hen

solv

e.R

oun

d t

o th

e n

eare

st t

enth

if

nec

essa

ry.

1.H

ow f

ar a

part

are

th

e sp

ider

an

d2.

How

lon

g is

th

e ta

blet

op?

the

fly?

62�

22�

�2 ;5.

2 ft

c2�

22�

32;

3.6

ft

3.H

ow h

igh

wil

l th

e la

dder

rea

ch?

4.H

ow h

igh

is

the

ram

p?

172

�h

2�

152 ;

8 ft

162

�42

�h

2 ;15

.5 f

t

5.H

ow f

ar a

part

are

th

e tw

o ci

ties

?6.

How

far

is

the

bear

fro

m c

amp?

c2�

192

�41

2 ;45

.2 m

i60

2�

d2

�20

2 ;56

.6 y

d

7.H

ow t

all

is t

he

tabl

e?8.

How

far

is

it a

cros

s th

e po

nd?

d2

�75

2�

902 ;

117.

2 m

402

�30

2�

h2 ;

26.5

in.

d

90 m

75 m

h40

in.

30 in

.

tabl

e

d60 y

d

cam

p

20 y

d

Avon

Lake

view 41

mi

19 m

i

c

h17

ft

15 ft

h

4 ft

16 ft

c

3 ft

2 ft

6 ft

tabl

e3

ft

�

NA

ME

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Ski

llsU

sin

g T

he

Pyt

hag

ore

an T

heo

rem

©G

lenc

oe/M

cGra

w-H

ill15

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

A p

rofe

ssio

nal

ice

hoc

key

rin

k i

s 20

0 fe

et

lon

g an

d 8

5 fe

et w

ide.

Wh

at i

s th

e le

ngt

h

of t

he

dia

gon

al o

f th

e ri

nk

?

c2�

a2

�b2

The

Pyt

hago

rean

The

orem

c2�

200

2�

852

Rep

lace

aw

ith 2

00 a

nd b

with

85.

c2�

40,

000

�7,

225

Eva

luat

e 20

02an

d 85

2 .

c2�

47,

225

Sim

plify

.

�c2 �

� �

47,2

2�

5�Ta

ke t

he s

quar

e ro

ot o

f ea

ch s

ide.

c�

217.

3S

impl

ify.

Th

e le

ngt

h o

f th

e di

agon

al o

f an

ice

hoc

key

rin

k is

abo

ut

217.

3 fe

et.

Wri

te a

n e

qu

atio

n t

hat

can

be

use

d t

o an

swer

th

e q

ues

tion

.Th

enso

lve.

Rou

nd

to

the

nea

rest

ten

th i

f n

eces

sary

.

1.W

hat

is

the

len

gth

of

the

diag

onal

?2.

How

lon

g is

th

e ki

te s

trin

g?

c2�

62�

62;

c�

8.5

in.

c2�

252

�30

2 ;c

�39

.1 m

3.H

ow h

igh

is

the

ram

p?4.

How

tal

l is

th

e tr

ee?

152

�10

2�

b2 ;

b�

11.2

ft

182

�h

2�

72;

h�

16.6

yd

h18

yd 7

yd

b15

ft 10 ft

c 25 m

30 m

c6

in.

6 in

.

c85

ft

200

ft

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 3–5

Stud

y Gu

ide

and

Inte

rven

tion

Usi

ng

Th

e P

yth

ago

rean

Th

eore

m

You

can

use

the

Pyt

hago

rean

The

orem

to

help

you

sol

ve p

robl

ems.


An

swer

s


©G

lenc

oe/M

cGra

w-H

ill15

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Read

ing

to L

earn

Mat

hem

atic

sU

sin

g t

he

Pyt

hag

ore

an T

heo

rem

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

137

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.W

hat

typ

e of

tri

angl

e is

for

med

by

the

side

s of

th

e m

at a

nd

the

diag

onal

?ri

gh

t

2.W

rite

an

equ

atio

n t

hat

can

be

use

d to

fin

d th

e le

ngt

h o

f th

e di

agon

al.

d2

�40

2�

402

Rea

din

g t

he

Less

on

Det

erm

ine

wh

eth

er e

ach

of

the

foll

owin

g is

a P

yth

agor

ean

tri

ple

.

3.13

-84-

85ye

s4.

11-6

0-61

yes

5.21

-23-

29n

o6.

12-2

5-37

no

7.T

he

trip

le 8

-15-

17 i

s a

Pyt

hag

orea

n t

ripl

e.C

ompl

ete

the

tabl

e to

fin

dm

ore

Pyt

hag

orea

n t

ripl

es.

8.If

th

e si

des

of a

squ

are

are

of l

engt

h s

,how

can

you

fin

d th

e le

ngt

h o

f a

diag

onal

of

the

squ

are?

Sam

ple

an

swer

:U

sin

g t

wo

ad

jace

nt

sid

es o

f th

e sq

uar

e,th

e d

iag

on

al f

orm

s th

e hy

po

ten

use

of

ari

gh

t tr

ian

gle

,so

use

th

e P

yth

ago

rean

Th

eore

m.T

he

len

gth

of

the

dia

go

nal

is t

he

squ

are

roo

t o

f 2s

2 .

Hel

pin

g Y

ou

Rem

emb

er9.

Wor

k w

ith

a p

artn

er.W

rite

a w

ord

prob

lem

th

at c

an b

e so

lved

usi

ng

the

Pyt

hag

orea

n T

heo

rem

,in

clu

din

g th

e ar

t.E

xch

ange

pro

blem

s w

ith

you

rpa

rtn

er a

nd

solv

e.S

ee s

tud

ents

’wo

rk.

ab

cC

hec

k:c

2�

a2

�b2

orig

inal

811

531

728

9�

64�

225

2

1613

013

41,

156

�25

6�

900

3

2414

515

12,

601

�57

6�

2,02

5

5

4017

518

57,

225

�1,

600

�5,

625

1

080

150

170

28,9

00 �

6,40

0�

22,5

00

©G

lenc

oe/M

cGra

w-H

ill15

5M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Prac

tice:

Wor

d Pr

oble

ms

Usi

ng

Th

e P

yth

ago

rean

Th

eore

m

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 3–5

1.R

ECR

EATI

ON

A p

ool

tabl

e is

8 f

eet

lon

gan

d 4

feet

wid

e.H

ow f

ar i

s it

fro

m o

ne

corn

er p

ocke

t to

th

e di

agon

ally

opp

osit

eco

rner

poc

ket?

R

oun

d to

th

e n

eare

stte

nth

.8.

9 ft

2.TR

IATH

LON

Th

e co

urs

e fo

r a

loca

ltr

iath

lon

has

th

e sh

ape

of a

rig

ht

tria

ngl

e.T

he

legs

of

the

tria

ngl

e co

nsi

stof

a 4

-mil

e sw

im a

nd

a 10

-mil

e ru

n.

Th

e h

ypot

enu

se o

f th

e tr

ian

gle

is t

he

biki

ng

port

ion

of

the

even

t.H

ow f

ar i

sth

e bi

kin

g pa

rt o

f th

e tr

iath

lon

? R

oun

dto

th

e n

eare

st t

enth

if

nec

essa

ry.

10.8

mi

3.LA

DD

ERA

lad

der

17 f

eet

lon

g is

lea

nin

gag

ain

st a

wal

l.T

he

bott

om o

f th

e la

dder

is 8

fee

t fr

om t

he

base

of

the

wal

l.H

owfa

r u

p th

e w

all

is t

he

top

of t

he

ladd

er?

Rou

nd

to t

he

nea

rest

ten

th i

f n

eces

sary

.15

ft

4.TR

AV

ELT

ara

driv

es d

ue

nor

th f

or22

mil

es t

hen

eas

t fo

r 11

mil

es.H

owfa

r is

Tar

a fr

om h

er s

tart

ing

poin

t?R

oun

d to

th

e n

eare

st t

enth

if

nec

essa

ry.

24.6

mi

5.FL

AG

POLE

A w

ire

30 f

eet

lon

g is

stre

tch

ed f

rom

th

e to

p of

a f

lagp

ole

toth

e gr

oun

d at

a p

oin

t 15

fee

t fr

om t

he

base

of

the

pole

.How

hig

h i

s th

efl

agpo

le?

Rou

nd

to t

he

nea

rest

ten

th i

fn

eces

sary

.26

.0 f

t

6.EN

TER

TAIN

MEN

TIs

aac’

s te

levi

sion

is

25 i

nch

es w

ide

and

18 i

nch

es h

igh

.W

hat

is

the

diag

onal

siz

e of

Isa

ac’s

tele

visi

on?

Rou

nd

to t

he

nea

rest

ten

thif

nec

essa

ry.

30.8

in.



©G

lenc

oe/M

cGra

w-H

ill15

8M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Dis

tan

ce o

n t

he

Co

ord

inat

e P

lan

e

Fin

d t

he

dis

tan

ce b

etw

een

poi

nts

(2,

�3)

an

d (

5,4)

.

Gra

ph t

he

poin

ts a

nd

con

nec

t th

em w

ith

a l

ine

segm

ent.

Dra

w a

hor

izon

tal

lin

e th

rou

gh (

2,�

3) a

nd

a ve

rtic

al l

ine

thro

ugh

(5,

4).T

he

lin

es i

nte

rsec

t at

(5,

�3)

.

Cou

nt

un

its

to f

ind

the

len

gth

of

each

leg

of

the

tria

ngl

e.T

he

len

gth

s ar

e 3

un

its

and

7 u

nit

s.T

hen

u

se t

he

Pyt

hag

orea

n T

heo

rem

to

fin

d th

e h

ypot

enu

se.

c2�

a2�

b2T

he P

ytha

gore

an T

heor

em

c2�

32�

72R

epla

ce a

with

3 a

nd b

with

7.

c2�

9 �

49E

valu

ate

32an

d 72

.

c2�

58S

impl

ify.

�c2 �

��

58�Ta

ke t

he s

quar

e ro

ot o

f ea

ch s

ide.

c�

7.6

Sim

plify

.

Th

e di

stan

ce b

etw

een

th

e po

ints

is

abou

t 7.

6 u

nit

s.

Fin

d t

he

dis

tan

ce b

etw

een

eac

h p

air

of p

oin

ts w

hos

e co

ord

inat

es a

regi

ven

.Rou

nd

to

the

nea

rest

ten

th i

f n

eces

sary

.

1.2.

3.

5.4

un

its

6.3

un

its

3.6

un

its

Gra

ph

eac

h p

air

of o

rder

ed p

airs

.Th

en f

ind

th

e d

ista

nce

bet

wee

n t

he

poi

nts

.Rou

nd

to

the

nea

rest

ten

th i

f n

eces

sary

.

4.(4

,5),

(0,2

)5

un

its

5.(0

,�4)

,(�

3,0)

5 u

nit

s6.

(�1,

1),(

�4,

4)4.

2 u

nit

sy

xO

( �4,

4)

( �1,

1)

y

xO

( �3,

0)

( 0, �

4)

y

xO

( 0, 2

)( 4, 5

)

y

xO

( 1, 1

) ( 3, �

2)

y

xO

( 4, 3

)

( �2,

1)

y

xO

( 6, 3

)

( 1, 1

)

y

xO

( 5, 4

)

( 5, �

3)( 2

, �3)

7 un

its

3 un

its

You

can

use

the

Pyt

hago

rean

The

orem

to

find

the

dist

ance

bet

wee

n tw

o po

ints

on

the

coor

dina

te p

lane

.

©G

lenc

oe/M

cGra

w-H

ill15

7M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

A C

ross

-Nu

mb

er P

uzz

leU

se t

he

clu

es a

t th

e b

otto

m o

f th

e p

age

to c

omp

lete

th

e p

uzz

le.R

oun

dco

mp

uta

tion

al a

nsw

ers

to t

he

nea

rest

wh

ole

nu

mb

er.Y

ou a

re t

o w

rite

one

dig

it i

n e

ach

box

.

Acr

oss

Dow

n

Ath

e sq

uar

e of

23.

56A

the

5th

to

8th

dig

its

of �

Cth

e di

gits

in

th

e re

peat

ing

bloc

k of

� 11 11�B

mak

es P

yth

agor

ean

tri

ple

wit

h 5

an

d 12

Dh

ypot

enu

se i

f le

gs a

re 1

6 an

d 30

Cth

e la

rges

t fo

ur-

digi

t pe

rfec

t sq

uar

e

Fpe

rim

eter

of

a sq

uar

e w

ith

are

a of

324

Esq

uar

e of

hyp

oten

use

if

legs

are

20

and

4

Hpe

rfec

t sq

uar

e,di

gits

su

m i

s 4

Gpe

rfec

t sq

uar

e th

at i

s a

pow

er o

f 2

Jh

ypot

enu

se i

f le

gs a

re 4

0 an

d 50

Ith

e sq

uar

e of

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rges

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t pe

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t sq

uar

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25

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,100

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8

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Om

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and

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Lesson 3–5


An

swer

s


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ics:

App

licat

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ours

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NA

ME

____

____

____

____

____

____

____

____

DAT

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____

____

____

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Prac

tice:

Wor

d Pr

oble

ms

Dis

tan

ce o

n t

he

Co

ord

inat

e P

lan

e

1.A

RC

HA

EOLO

GY

An

arc

hae

olog

ist

at a

dig

sets

up

a co

ordi

nat

e sy

stem

usi

ng

stri

ng.

Tw

o si

mil

ar a

rtif

acts

are

fou

nd—

one

at p

osit

ion

(1,

4) a

nd

the

oth

er a

t (5

,2).

How

far

apa

rt w

ere

the

two

arti

fact

s?

Rou

nd

to t

he

nea

rest

ten

th o

f a

un

it i

f n

eces

sary

.4.

5 u

nit

s

2.G

AR

DEN

ING

Veg

a se

t u

p a

coor

din

ate

syst

em w

ith

un

its

of f

eet

to l

ocat

e th

epo

siti

on o

f th

e ve

geta

bles

sh

e pl

ante

din

her

gar

den

.Sh

e h

as a

tom

ato

plan

tat

(1,

3) a

nd

a pe

pper

pla

nt

at (

5,6)

.H

ow f

ar a

part

are

th

e tw

o pl

ants

?R

oun

d to

th

e n

eare

st t

enth

if

nec

essa

ry.

5 ft

3.C

HES

SA

pril

is

an a

vid

ches

s pl

ayer

.S

he

sets

up

a co

ordi

nat

e sy

stem

on

her

ches

s bo

ard

so s

he

can

rec

ord

the

posi

tion

of

the

piec

es d

uri

ng

a ga

me.

In a

rec

ent

gam

e,A

pril

not

ed t

hat

her

kin

g w

as a

t (4

,2)

at t

he

sam

e ti

me

that

her

opp

onen

t’s k

ing

was

at

(7,8

).H

owfa

r ap

art

wer

e th

e tw

o ki

ngs

? R

oun

d to

the

nea

rest

ten

th o

f a

un

it i

f n

eces

sary

.6.

7 u

nit

s

4.M

APP

ING

Cor

y m

akes

a m

ap o

f h

isfa

vori

te p

ark,

usi

ng

a co

ordi

nat

esy

stem

wit

h u

nit

s of

yar

ds.T

he

old

oak

tree

is

at p

osit

ion

(4,

8) a

nd

the

gran

ite

bou

lder

is

at p

osit

ion

(�

3,7)

.How

far

apar

t ar

e th

e ol

d oa

k tr

ee a

nd

the

gran

ite

bou

lder

? R

oun

d to

th

e n

eare

stte

nth

if

nec

essa

ry.

7.1

yd

5.TR

EASU

RE

HU

NTI

NG

Tar

o u

ses

aco

ordi

nat

e sy

stem

wit

h u

nit

s of

fee

t to

keep

tra

ck o

f th

e lo

cati

ons

of a

ny

obje

cts

he

fin

ds w

ith

his

met

al d

etec

tor.

On

e lu

cky

day

he

fou

nd

a ri

ng

at (

5,7)

and

a ol

d co

in a

t (1

0,19

).H

ow f

arap

art

wer

e th

e ri

ng

and

coin

bef

ore

Tar

o fo

un

d th

em?

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nd

to t

he

nea

rest

ten

th i

f n

eces

sary

.13

ft

6.G

EOM

ETRY

Th

e co

ordi

nat

es o

f po

ints

Aan

d B

are

(�7,

5) a

nd

(4,�

3),

resp

ecti

vely

.Wh

at i

s th

e di

stan

cebe

twee

n t

he

poin

ts,r

oun

ded

to t

he

nea

rest

ten

th?

13.6

un

its

7.G

EOM

ETRY

Th

e co

ordi

nat

es o

f po

ints

A,B

,an

d C

are

(5,4

),(�

2,1)

,an

d(4

,�4)

,res

pect

ivel

y.W

hic

h p

oin

t,B

orC

,is

clos

er t

o po

int

A?

B

8.TH

EME

PAR

KT

om i

s lo

okin

g at

a m

ap o

fth

e th

eme

park

.Th

e m

ap i

s la

id o

ut

ina

coor

din

ate

syst

em.T

om i

s at

(2,

3).

Th

e ro

ller

coa

ster

is

at (

7,8)

,an

d th

ew

ater

rid

e is

at

(9,1

).Is

Tom

clo

ser

toth

e ro

ller

coa

ster

or

the

wat

er r

ide?

rolle

r co

aste

r

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Con

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s, C

ours

e 3

Fin

d t

he

dis

tan

ce b

etw

een

eac

h p

air

of p

oin

ts w

hos

e co

ord

inat

es a

regi

ven

.Rou

nd

to

the

nea

rest

ten

th i

f n

eces

sary

.

1.2.

3.

5 u

nit

s5.

8 u

nit

s2.

8 u

nit

s

4.5.

6.

4.2

un

its

5.1

un

its

3.6

un

its

Gra

ph

eac

h p

air

of o

rder

ed p

airs

.Th

en f

ind

th

e d

ista

nce

bet

wee

n t

he

poi

nts

.Rou

nd

to

the

nea

rest

ten

th i

f n

eces

sary

.

7.(�

3,0)

,(3,

�2)

8.(�

4,�

3),(

2,1)

9.(0

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(5,�

2)

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un

its

7.2

un

its

6.4

un

its

10.

(�2,

1),(

�1,

2)11

.(0

,0),

(�4,

�3)

12.

(�3,

4),(

2,�

3)

1.4

un

its

5 u

nit

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6 u

nit

s

y

xO

( �3,

4)

( 2, �

3)

y

xO

( �4,

�3)

( 0, 0

)

y

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1)

( �1,

2)

y

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) ( 5, �

2)

y

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�3)

( 2, 1

)

y

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( �3,

0)

( 3, �

2)

y

xO

( 1, �

1)

( 4, �

3)

y

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( �2,

2)

( 3, 3

)

y

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( 5, 6

)

( 2, 3

)

y

xO

( �2,

�1)

( 0, 1

)

y

xO

( �3,

2)

( 2, �

1)

y

xO

( �1,

�2)

( 4, �

2)

Prac

tice:

Ski

llsD

ista

nce

on

th

e C

oo

rdin

ate

Pla

ne

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 3–6



©G

lenc

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mat

ics:

App

licat

ions

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Con

cept

s, C

ours

e 3

A C

oo

rdin

ate

Co

de

A c

oord

inat

e gr

aph

can

be

use

d to

mak

e a

secr

et c

ode.

Fir

st,

choo

se a

pai

r of

coo

rdin

ates

for

eac

h l

ette

r yo

u p

lan

to

use

.Let

ter

labe

ls o

n t

he

poin

ts s

how

th

e or

der

of t

he

lett

ers

in t

he

mes

sage

.Th

eex

ampl

e at

th

e ri

ght

spel

ls o

ut

the

wor

d H

EL

P.

Use

th

e ch

art

abov

e to

dec

ode

each

sec

ret

mes

sage

.Som

e p

oin

ts a

reu

sed

mor

e th

an o

nce

.

1.2.

3.

AT

ON

E P

MS

TAR

T N

OW

SE

ND

MO

NE

Y

4.5.

6.

NE

ED

A C

AR

BR

ING

FO

OD

VIC

TOR

Y

7.U

se t

he

char

t to

cre

ate

a se

cret

mes

sage

of

you

r ow

n.

An

swer

s w

illva

ry.

y

xO

C G

B

F EA

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y

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A

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y

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BD

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y

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(1,1

)(1

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2)(�

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AB

CD

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Lesson 3–6

©G

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mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Read

ing

to L

earn

Mat

hem

atic

sD

ista

nce

on

th

e C

oo

rdin

ate

Pla

ne

NA

ME

____

____

____

____

____

____

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Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

142

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.W

hat

typ

e of

tri

angl

e is

for

med

by

the

blu

e an

d re

d li

nes

?ri

gh

t

2.W

hat

is

the

len

gth

of

the

two

red

lin

es?

3 u

nit

s,2

un

its

3.W

rite

an

equ

atio

n y

ou c

ould

use

to

dete

rmin

e th

e di

stan

ce d

betw

een

th

elo

cati

ons

wh

ere

the

rin

g an

d n

eckl

ace

wer

e fo

un

d.d

2�

32�

22

4.H

ow f

ar a

part

wer

e th

e ri

ng

and

the

nec

klac

e?ab

ou

t 3.

6 u

nit

s

Rea

din

g t

he

Less

on

5.O

n t

he

coor

din

ate

plan

e,w

hat

are

th

e fo

ur

sect

ion

s de

term

ined

by

the

axes

cal

led?

qu

adra

nts

6.M

atch

eac

h t

erm

of

the

coor

din

ate

plan

e w

ith

its

des

crip

tion

.

ordi

nat

ea.

poin

t w

her

e n

um

ber

lin

es m

eet

y-ax

isb

.x-

coor

din

ate

orig

inc.

y-co

ordi

nat

e

absc

issa

d.

vert

ical

nu

mbe

r li

ne

x-ax

ise.

hor

izon

tal

nu

mbe

r li

ne

7.T

o fi

nd

the

dist

ance

bet

wee

n t

wo

poin

ts,d

raw

a r

igh

t tr

ian

gle

wh

ose

hyp

oten

use

is

the

dist

ance

you

wan

t to

fin

d;fi

nd

the

len

gth

s of

th

e le

gs,

and

use

___

____

____

____

____

____

____

____

____

_ to

sol

ve t

he

prob

lem

.th

e P

yth

ago

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Th

eore

m

Hel

pin

g Y

ou

Rem

emb

er8.

Th

ink

of 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

eb

oth

co

ord

inat

es a

re p

osi

tive

(th

e u

pp

er-r

igh

t q

uad

ran

t).

Th

is is

qu

adra

nt

I.N

ame

the

rest

of

the

qu

adra

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by

go

ing

cou

nte

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ise

aro

un

d t

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qu

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(up

per

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II (l

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(lo

wer

-rig

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adra

nt)

.

ebadc


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. D

G

A

I

A

F

B

G

B

H

B

12 ft

I

D

G

A

H

C

H

D

G

D

H

A

F

A

I

B

H

C

H

B

Chapter 3 Assessment Answer KeyForm 1 Form 2APage 163 Page 164 Page 165

(continued on the next page)


12.

13.

14.

15.

16.

17.

18.

19.

20.

B.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 32 units

F

C

G

B

H

A

G

D

G

D

F

C

I

C

F

B

I

C

F

A

51 in.

H

B

F

B

H

A

I

B

H

Chapter 3 Assessment Answer KeyForm 2A (continued) Form 2BPage 166 Page 167 Page 168


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.

B: 26.8 ft

7.3 units

6.3 units

10.3 units

8.5 units

8.1 blocks

12 ft

8.7 ft

no

yes

172 � a2 � 152;8 mm

c2 � 102 � 242;26 in.

�41�, 6�12

�, �47�, 6�78

�

5 6 7 8

39

6.2

rational

integer, rational

11 or �11

7 or �7

15

10

8

�161� or ��

161�

35 or �35

�151�

�30

9

Chapter 3 Assessment Answer KeyForm 2CPage 169 Page 170


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: 13.4 ft

10.8 units

7.1 units

10.6 units

6.7 units

21.6 blocks

15 ft

8.1 ft

no

yes

62 � 42 � b2;4.5 m

c2 � 82 � 62;10 in.

3.3�, 3�34

�, �15�, �19�

8 9 10 11

96

9.8

rational

irrational

11 or �11

9 or �9

14

9

5

�37

� or ��37

�

21 or �21

�10

��19

�

8

Chapter 3 Assessment Answer KeyForm 2DPage 171 Page 172


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.

B: 30 in2

8.1 units

3.2 units

5 units

10.8 units

53.7 ft

7.7 ft

10.6 ft

no

yes

392 � a2 � 362; 15 mm

2.22 � 1.72 � b2;1.4 cm

�50�, 7�18

�, �53�, 7.6�

�15 �14 �13 �12

209�

�14.5;

whole, rational,integer

irrational

10 or �10

8 or �8

16

8

12

2.36 or �2.36

2.2 or �2.2

2.1

��1123�

�50

Chapter 3 Assessment Answer KeyForm 3Page 173 Page 174


Chapter 3 Assessment Answer Key Page 175, 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.

An

swer

sA

nsw

ers

Chapter 3 Assessment Answer Key Page 175, Extended Response Assessment

Sample Answers

1. a. If x squared equals y, then thesquare root of the number y is x.

b. There are two square roots because62 � 36 and (�6)2 � 36.

c.

150 is closer to 144 (12 12) than169 (13 13 square). Thus �150� � 12.

2. a. The area of the square on leg A�C�, 4,plus the area of the square on leg B�C�, 4, equals the area of thesquare on the hypotenuse, 8.

b. Sample answer: How far is it fromthe top of a 16-foot pole to a point onthe ground 12 feet from the bottom ofthe pole?

c. Sample answer: The pole makes aright angle with the ground. Thus aright triangle ABC is formed.

By the Pythagorean Theorem,d2 � 162 � 122 � 400. Thus, d � 20.

3. a. The real number system is made upof the sets of rational numbers andirrational numbers. Together, theymake up all the points of a numberline.

b. Rational numbers are all numbers

that can be expressed in the form �ab�

where a and b are integers and b 0. Rational numbers includewhole numbers, such as 5, andintegers, such as –3. An irrationalnumber is a number that cannot be

expressed as �ab� where a and b are

integers and b 0. An example of anirrational number is �2�.

B

C A

d ft 16 ft

12 ft

122 � 144 150

�

In addition to the scoring rubric found on page A23, the following sample answers may be used as guidance in evaluating open-ended assessment items.


1. y-axis

2. irrational number

3. legs

4. abscissa

5. x-axis

6. converse

7. real numbers

8. hypotenuse

9. ordinate

10. origin

11. In a right triangle,the square of thelength of thehypotenuse is equalto the sum of thesquares of thelengths of the legs.

12. three numbers thatsatisfy thePythagoreanTheorem

1.

2.

3.

4.

5.

Quiz (Lesson 3-3)

Page 177

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

Quiz (Lesson 3-6)

Page 178

1.

2.

3–4.

3.

4.

5. about 5.4 units

7.1 units

5.8 units

y

xO

(6, 1)(1, 4)

(�3, �2)(4, �3)

7.1 units

5.8 units

A

no

c2 � 152 � 192;24.2 cm

92 � a2 � 42;8.1 cm

c2 � 72 � 102;12.2 in.

2.5, �7�, 2.9�, �10�

�

�

��9 ��8 ��7 ��6

80�

�8.9;

1 3 42

10

3.2;

rational

irrational

rational

integers, rational

rational

20 or �20

6

4

��89

�

15

Chapter 3 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 3-1 and 3-2) Quiz (Lessons 3-4 and 3-5)

Page 176 Page 177 Page 178


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18. 8.2 units

9.2 units

115.0 yd

4.7 in.

�90�, 9�12

�, 9.7,�95�

rational

10 or �10

�59

� or ��59

�

18

0.000654

6.8

�13

�

�7�23

�

�58

�

12

�30

15

41

�25�, 5�12

�, �32�, 5.9

�12 �11 �10 �9

102�

�10.1

3 4 5 6

17

4.1

�27

� or ��27

�

H

A

I

B

H

A

Chapter 3 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 179 Page 180


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. 12.

13.

14.

15. a. 92 � b2 � 112

b. 6.3

10 or �100 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

9/5

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

29.4

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

211

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Chapter 3 Assessment Answer KeyStandardized Test PracticePage 181 Page 182


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. 9.2 units

7.3 units

15.3 ft

a2 � 142 � 282;24.2 cm

92 � 122 � c2; 15 in.

real, rational

11

�59

�

�11

1.69 � 10�3

512

�15.81

12�23

�

3�14

�

�8�14

�

��170�

�15

�

�2590�

11.4�

8

�54

n � 12 � �19; �7

s � number of students at Jordan

Middle School;s � 116

16

�32

�12

14

�2 0 2�4 4

Additive Identity

3

Chapter 3 Assessment Answer KeyUnit 1 TestPage 183 Page 184


chapter 3 resource masters - wikispaces3.pdf · chapter 3 test, form 2d.....171–172 chapter 3...

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