Chapter 4 Resource Masters - KTL MATH CLASSES
Chapter 4Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.Study Guide and Intervention WorkbookSkills Practice WorkbookPractice WERS FOR WORKBOOKS The answers for Chapter 4 of these workbookscan be found in the back of this Chapter Resource Masters booklet.Glencoe/M cGraw-HillCopyright 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 onlyfor classroom use; be provided to students, teacher, and families without charge;and be used solely in conjunction with Glencoe’s Algebra 2. Any other reproduction,for use or sale, is prohibited without prior written permission of the publisher.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027ISBN: 0-07-828007-91 2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03 02Algebra 2Chapter 4 Resource Masters
ContentsVocabulary Builder . . . . . . . . . . . . . . . . viiLesson 4-7Study Guide and Intervention . . . . . . . . 205–206Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 207Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 208Reading to Learn Mathematics . . . . . . . . . . 209Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 210Lesson 4-1Study Guide and Intervention . . . . . . . . 169–170Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 171Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Reading to Learn Mathematics . . . . . . . . . . 173Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 174Lesson 4-8Study Guide and Intervention . . . . . . . . 211–212Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 213Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 214Reading to Learn Mathematics . . . . . . . . . . 215Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 216Lesson 4-2Study Guide and Intervention . . . . . . . . 175–176Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 177Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Reading to Learn Mathematics . . . . . . . . . . 179Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 180Chapter 4 AssessmentChapter 4 Test, Form 1 . . . . . . . . . . . . 217–218Chapter 4 Test, Form 2A . . . . . . . . . . . 219–220Chapter 4 Test, Form 2B . . . . . . . . . . . 221–222Chapter 4 Test, Form 2C . . . . . . . . . . . 223–224Chapter 4 Test, Form 2D . . . . . . . . . . . 225–226Chapter 4 Test, Form 3 . . . . . . . . . . . . 227–228Chapter 4 Open-Ended Assessment . . . . . . 229Chapter 4 Vocabulary Test/Review . . . . . . . 230Chapter 4 Quizzes 1 & 2 . . . . . . . . . . . . . . . 231Chapter 4 Quizzes 3 & 4 . . . . . . . . . . . . . . . 232Chapter 4 Mid-Chapter Test . . . . . . . . . . . . 233Chapter 4 Cumulative Review . . . . . . . . . . . 234Chapter 4 Standardized Test Practice . . 235–236Unit 1 Test/Review (Ch. 1–4) . . . . . . . . 237–238Lesson 4-3Study Guide and Intervention . . . . . . . . 181–182Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 183Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Reading to Learn Mathematics . . . . . . . . . . 185Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 186Lesson 4-4Study Guide and Intervention . . . . . . . . 187–188Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 189Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 190Reading to Learn Mathematics . . . . . . . . . . 191Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 192Lesson 4-5Standardized Test PracticeStudent Recording Sheet . . . . . . . . . . . . . . A1Study Guide and Intervention . . . . . . . . 193–194Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 195Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 196Reading to Learn Mathematics . . . . . . . . . . 197Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 198ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A36Lesson 4-6Study Guide and Intervention . . . . . . . . 199–200Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 201Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 202Reading to Learn Mathematics . . . . . . . . . . 203Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 204 Glencoe/McGraw-HilliiiGlencoe Algebra 2
Teacher’s Guide to Using theChapter 4 Resource MastersThe Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 4 Resource Masters includes the core materials neededfor Chapter 4. These materials include worksheets, extensions, and assessment options.The answers 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 theAlgebra 2 TeacherWorks CD-ROM.Vocabulary BuilderPracticePages 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.There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.WHEN TO USE Give these pages tostudents before beginning Lesson 4-1.Encourage them to add these pages to theirAlgebra 2 Study Notebook. Remind themto add definitions and examples as theycomplete each lesson.Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.Study Guide and InterventionEach lesson in Algebra 2 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.WHEN TO USE Use these masters asWHEN TO USE This master can be usedreteaching 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.as a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.Skills PracticeThere is one master foreach lesson. These provide computationalpractice at a basic level.EnrichmentThere 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 masters can beused with students who have weakermathematics backgrounds or needadditional reinforcement.WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened. Glencoe/McGraw-HillivGlencoe Algebra 2
Assessment OptionsIntermediate AssessmentThe assessment masters in the Chapter 4Resource Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use. Four free-response quizzes are includedto 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 andfree-response questions.Chapter AssessmentCHAPTER TESTSContinuing Assessment Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents. The Cumulative Review providesstudents an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 2. It can also beused as a test. This master includesfree-response questions. Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations. The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiplechoice, grid-in, and quantitativecomparison questions. Bubble-in andgrid-in answer sections are provided onthe master. Forms 2C and 2D are composed of freeresponse 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.AnswersAll of the above tests include a freeresponse Bonus question. Page A1 is an answer sheet for theStandardized Test Practice questionsthat appear in the Student Edition onpages 216–217. This improves students’familiarity with the answer formats theymay encounter in test taking. The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment. The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red. 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 in conjunction with one of the chapter tests or as areview worksheet. Glencoe/McGraw-Hill Full-size answer keys are provided forthe assessment masters in this booklet.vGlencoe Algebra 2
NAME DATE4PERIODReading to Learn MathematicsThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 4.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.Vocabulary TermFoundon PageDefinition/Description/Example Cramer’s RuleKRAY·muhrsdeterminant dilationdy·LAY·shuhnelementexpansion by minorsidentity matriximageinverse isometryeye·SAH·muh·tree matrixMAY·trihks(continued on the next page) Glencoe/McGraw-HillviiGlencoe Algebra 2Vocabulary BuilderVocabulary Builder
NAME DATE4PERIODReading to Learn MathematicsVocabulary BuilderVocabulary Term(continued)Foundon PageDefinition/Description/Examplematrix equationpreimagereflectionrotation scalar multiplicationSKAY·luhrsquare matrixtransformationtranslationvertex matrixzero matrix Glencoe/McGraw-HillviiiGlencoe Algebra 2
NAME DATE4-1PERIODStudy Guide and InterventionIntroduction to MatricesOrganize DataMatrixa rectangular array of variables or constants in horizontal rows and vertical columns,usually enclosed in brackets.Example 1Owls’ eggs incubate for 30 days and their fledgling period is also30 days. Swifts’ eggs incubate for 20 days and their fledgling period is 44 days.Pigeon eggs incubate for 15 days, and their fledgling period is 17 days. Eggs of theking penguin incubate for 53 days, and the fledgling time for a king penguin is360 days. Write a 2 4 matrix to organize this information. Source: The Cambridge FactfinderOwlIncubationFledgling 30 30SwiftPigeonKing Penguin2044151753360 10 3 45 What are the dimensions of matrix A if A 132 8 15 80 ?Since matrix A has 2 rows and 4 columns, the dimensions of A are 2 4.Example 2ExercisesState the dimensions of each matrix. 15 5 27 4 6 05 1. 2314 70 24 3 4 4 63 3 42 90 2. [16 12 0] 1 3 71 393. 45 92 7844 27 16 5 253 65 4. A travel agent provides for potential travelers the normal high temperatures for themonths of January, April, July, and October for various cities. In Boston these figures are36 , 56 , 82 , and 63 . In Dallas they are 54 , 76 , 97 , and 79 . In Los Angeles they are68 , 72 , 84 , and 79 . In Seattle they are 46 , 58 , 74 , and 60 , and in St. Louis they are38 , 67 , 89 , and 69 . Organize this information in a 4 5 matrix. Source: The New York Times AlmanacJanuaryAprilJulyOctober Boston Dallas Los Angeles Seattle St. Louis 3654684638 5676725867 8297847489 6379796069 Glencoe/McGraw-Hill169Glencoe Algebra 2Lesson 4-1A matrix can be described by its dimensions. A matrix with m rows and n columns is anm n matrix.
NAME DATE4-1PERIODStudy Guide and Intervention(continued)Introduction to MatricesEquations Involving MatricesEqual MatricesTwo matrices are equal if they have the same dimensions and each element of one matrix isequal to the corresponding element of the other matrix.You can use the definition of equal matrices to solve matrix equations. 2y 2 Solve 4xy x 8 for x and y.Since the matrices are equal, the corresponding elements are equal. When you write thesentences to show the equality, two linear equations are formed.4x 2y 2y x 8This system can be solved using substitution.4x 2y 2First equation4x 2(x 8) 2Substitute x 8 for y.4x 2x 16 2Distributive Property6x 18Add 2x to each side.x 3Divide each side by 6.To find the value of y, substitute 3 for x in either equation.y x 8Second equationy 3 8Substitute 3 for x.y 5Subtract.The solution is (3, 5).ExampleExercisesSolve each equation.1. [5x 4y] [20 20](4, 5) x 2y 1 4. 3x 4y 22 (4, 2.5)16x 18 8x y20 7. 12 y 4x 12 13 45 , 8 3x 1.5 7.510. 2y 2.4 8.0 (2, 5.2) Glencoe/McGraw-Hill 28 4y 3x2. y 3x 2 43 , 6 2x 3y 35. x 2y 12 (6, 3) 8x 6y 3 8. 12x 4y 11 34 , 12 2x 3y 1711. 4x 0.5y 8 (2.5, 4)170 2y 4 5x x y 5 3. ( 2, 7) 5x 3y 1 6. 2x y 18 ( 5, 8) x y 37 2 2y 519 9. x (18, 21) x y 012. x y 25 ( 12.5, 12.5)Glencoe Algebra 2
NAME DATE4-1PERIODSkills PracticeIntroduction to Matrices 3 2 4 1. 1 4 0 2 32. [0 15] 1 2 3 2 3. 1 8 2 2 6 1 2 4. 3 4 5 3 3 2 7 9 9 3 3 6 5. 3 4 45 2 4 1 6. 1 1 4 1 3 Lesson 4-1State the dimensions of each matrix.Solve each equation.7. [5x 3y] [15 12] (3, 4) 7x 14 9. 14 2y ( 2, 7)8. [3x 2] [7] 310. [2x 8y z] [10 16 1] (5, 2, 1) 8 x 4 11. 2y 8 2 (4, 5)20 10x 12. 56 6y 32 (2, 4) 5x 20 13. 24 8y ( 4, 3) 3x 2 5x 2 14. 7y 2 3y 10 (0, 2) 4x 1 3x 15. 9y 5 y 3 (1, 1)16. x 9 17. 16 4y (9, 4, 3) 3z 9 5x 4x 1 13 (1, 4, 0)18. 4y 3 8z 4z 2x 6y 19. y 2 x (3, 1) x 4y 20. 3y x 3 (12, 3) Glencoe/McGraw-Hill 3x 1 18 7 2y 4 12 4z 1228 (2, 11, 7)171Glencoe Algebra 2
NAME DATE4-1PracticePERIOD(Average)Introduction to MatricesState the dimensions of each matrix.1. [ 3 3 7] 1 3 2 2 2 3 0 0 3 43. 5 16 4 7 1 4 5 8 1 2. 2 18 2 3Solve each equation.4. [4x 42] [24 6y] (6, 7)5. [ 2x 22 3z] [6x 2y 45] (0, 11, 15)6x 36 6. 2y 3 17 ( 6, 7)20 7x 8 7. 8y 3 2y 3 (4, 1) 3x 4x 3 6y 2y 16 ( 3, 2) 6x 12 3x 21 9. 3y 6 8y 5 ( 1, 1)8. 5 3x 1 5 10. 2y 1 3z 2 3yx 1 3x y 8 5z 4 ( 1, 1, 1) 11. y 4 17 (7, 13) 5x 8y 1 12. 3x 11 y (3, 2) 2x y 0 13. 3x 2y 2 (2, 4)14. TICKET PRICES The table at the right givesticket prices for a concert. Write a 2 3 matrixthat represents the cost of a ticket. 6 12 18 8 15 22 ChildStudentAdultCost Purchasedin Advance 6 12 18Cost Purchasedat the Door 8 15 22CONSTRUCTION For Exercises 15 and 16, use the following information.During each of the last three weeks, aroad-building crew has used three truck-loadsof gravel. The table at the right shows theamount of gravel in each load.Week 1Week 2Week 3Load 1 40 tons Load 1 40 tons Load 1 32 tonsLoad 2 32 tons Load 2 40 tons Load 2 24 tonsLoad 3 24 tons Load 3 32 tons Load 3 24 tons15. Write a matrix for the amount of gravelin each load. 40 32 24 40 40 32 40 40 32 or 32 40 24 32 24 24 24 32 24 16. What are the dimensions of the matrix? 3 3 Glencoe/McGraw-Hill172Glencoe Algebra 2
NAME DATE4-1PERIODReading to Learn MathematicsIntroduction to MatricesPre-ActivityHow are matrices used to make decisions?Read the introduction to Lesson 4-1 at the top of page 154 in your textbook.What is the base price of a Mid-Size SUV? 27,975Lesson 4-1Reading the Lesson1. Give the dimensions of each matrix. 3 2 5 a. 1 0 6 2 3b. [1 4 0 8 2] 1 52. Identify each matrix with as many of the following descriptions that apply: row matrix,column matrix, square matrix, zero matrix.a. [6 5 4 3] row matrix 0 b. 0 column matrix; zero matrix 0 c. [0] row matrix; column matrix; square matrix; zero matrix3. Write a system of equations that you could use to solve the following matrix equation forx, y, and z. (Do not actually solve the system.) 3x 9 x y 5 3x 9, x y 5, y z 6 y z 6 Helping You Remember4. Some students have trouble remembering which number comes first in writing thedimensions of a matrix. Think of an easy way to remember this.Sample answer: Read the matrix from top to bottom, then from left toright. Reading down gives the number of rows, which is written first inthe dimensions of the matrix. Reading across gives the number ofcolumns, which is written second. Glencoe/McGraw-Hill173Glencoe Algebra 2
NAME DATE4-1PERIODEnrichmentTessellationsA tessellation is an arangement of polygons covering a planewithout any gaps or overlapping. One example of a tessellationis a honeycomb. Three congruent regular hexagons meet ateach vertex, and there is no wasted space between cells. Thistessellation is called a regular tessellation since it is formedby congruent regular polygons.A semi-regular tessellation is a tessellation formed by two ormore regular polygons such that the number of sides of thepolygons meeting at each vertex is the same.For example, the tessellation at the left has two regulardodecagons and one equilateral triangle meeting at eachvertex. We can name this tessellation a 3-12-12 for thenumber of sides of each polygon that meet at one vertex.Name each semi-regular tessellation shown according to the numberof sides of the polygons that meet at each vertex.1.2.3-3-3-3-64-6-12An equilateral triangle, two squares, and a regular hexagon can beused to surround a point in two different orders. Continue eachpattern to see which is a semi-regular tessellation.3. 3-4-4-64. 3-4-6-4not semi-regularsemi-regularOn another sheet of paper, draw part of each design. Then determineif it is a semi-regular tessellation.5. 3-3-4-12not semi-regular Glencoe/McGraw-Hill6. 3-4-3-127. 4-8-8not semi-regular174semi-regular8. 3-3-3-4-4semi-regularGlencoe Algebra 2
NAME DATE4-2PERIODStudy Guide and InterventionOperations with MatricesAdd and Subtract MatricesAddition of MatricesSubtraction of MatricesExample 1 a b c j k l
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 4 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 4 Resource Mastersincludes the core materials needed for Chapter 4. These materials include worksheets, extensions, and assessment options.
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 9 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 9 Resource Mastersincludes the core materials needed for Chapter 9. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 5 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 5 Resource Mastersincludes the core materials needed for Chapter 5. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 6 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 6 Resource Mastersincludes the core materials needed for Chapter 6. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 1 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 1 Resource Mastersincludes the core materials needed for Chapter 1. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 7 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 7 Resource Mastersincludes the core materials needed for Chapter 7. These material
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 3 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 3 Resource Mastersincludes the core materials needed for Chapter 3. These materials include worksheets, extensions, and assessment options.
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