Math Power 10 Practise Masters PDF

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MATHPOWER 10 O NTA R IO ED IT IO N Practice Masters

Shirley Barrett Richmond Hill, Ontario

Contributing Writer Janice Nixon Toronto, Ontario

Toronto Montréal Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. Louis Bangkok Beijing Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan New Delhi Santiago Seoul Singapore Sydney Taipei

McGraw-Hill Ryerson Limited MATHPOWER™ 10, Ontario Edition Practice Masters Copyright © 2001, McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. This publication may be reproduced for classroom purposes without the prior written permission of McGraw-Hill Ryerson Limited. McGraw-Hill Ryerson Limited shall not be held responsible for content if any revisions, additions, or deletions are made to any material provided in editable format on the enclosed CD-ROM. This package contains the MATHPOWER™ 10, Ontario Edition, Practice Masters and one CD-ROM. ISBN 0-07-560802-2 http://www.mcgrawhill.ca 1 2 3 4 5 6 7 8 9 0 CP 0 9 8 7 6 5 4 3 2 1 0 Printed and bound in Canada Care has been taken to trace ownership of copyright material contained in this text. The publishers will gladly take any information that will enable them to rectify any reference or credit in subsequent printings. The Geometer’s Sketchpad® is a registered trademark of Key Curriculum Press. CBL™ and CBR™ are trademarks of Texas Instruments Incorporated. Adobe, Acrobat, and the Acrobat logo are registered trademarks of Adobe Systems Incorporated. This product is not endorsed or sponsored by Adobe Systems Incorporated, publisher of Adobe® Acrobat® Reader 4.0 or Adobe® Acrobat® 4.0. Canadian Cataloguing in Publication Data Barrett, Shirley, dateMathpower 10, Ontario ed. Practice Masters ISBN 0-07-560802-2 Mathematics – Study and teaching (Secondary). 2. Mathematics – Problems, exercises, etc. I. Title. II. Title. Mathpower ten, Ontario edition. QA107.M37648 2000 Suppl. 2

510

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CONTENTS To the Teacher

v

Tips for Learning Math Getting Started Know Your Textbook and How to Use It Classroom Learning Homework Seeking Help Preparing for Tests and Exams Writing Tests and Exams Problem Solving Skills Solving Word Problems Goals

1 2 3 4 5 6 7 8 9 10

CHAPTER 3 Polynomials Practice 3.1 Polynomials 3.2 Multiplying Binomials 3.3 Special Products 3.4 Common Factors 3.5 Factoring x2 + bx + c 3.6 Factoring ax2 + bx + c, a ≠ 1 3.7 Factoring Special Quadratics Answers CHAPTER 3 Polynomials

29 30 31 32 33 34 35 37

CHAPTER 4 Quadratic Functions CHAPTER 1 Linear Systems Practice 1.1 Investigation: Ordered Pairs and Solutions 1.2 Solving Linear Systems Graphically 1.3 Solving Linear Systems by Substitution 1.4 Investigation: Equivalent Equations 1.5 Solving Linear Systems by Elimination 1.6 Investigation: Translating Words Into Equations 1.7 Solving Problems Using Linear Systems Answers CHAPTER 1 Linear Systems

11 12 13 14 15 16 17 19

Practice 4.1 Functions 39 4.2 Graphing y = x2 + k, y = ax2, and y = ax2 + k 40 2 4.3 Graphing y = a(x – h) + k 41 4.4 Graphing y = ax2 + bx + c by Completing the Square 42 4.5 Investigation: Sketching Parabolas in the Form y = ax(x – s) + t 43 4.6 Investigation: Finite Differences 44 4.7 Technology: Equations of Parabolas of Best Fit 45 4.8 Technology: Collecting Distance and Time Data Using CBRTM or CBLTM 46 Answers CHAPTER 4 Quadratic Functions 47

CHAPTER 2 Analytic Geometry Practice 2.1 Length of a Line Segment 2.2 Investigation: Midpoints of Horizontal and Vertical Line Segments 2.3 Midpoint of a Line Segment 2.4 Verifying Properties of Geometric Figures 2.5 Distance From a Point to a Line Answers CHAPTER 2 Analytic Geometry

CHAPTER 5 Quadratic Equations 21 22 23 24 25 27

Practice 5.1 Solving Quadratic Equations by Graphing 5.2 Solving Quadratic Equations by Factoring 5.3 Investigation: Graphing Quadratic Functions by Factoring 5.4 The Quadratic Formula Answers CHAPTER 5 Quadratic Equations

51 52 53 54 55

(Powers With Integral Bases)

CHAPTER 6 Trigonometry Practice 6.1 Technology: Investigating Similar Triangles Using The Geometer’s Sketchpad® 6.2 Similar Triangles 6.3 The Tangent Ratio 6.4 The Sine Ratio 6.5 The Cosine Ratio 6.6 Solving Right Triangles 6.7 Problems Involving Two Right Triangles 6.8 Technology: Relationships Between Angles and Sides in Acute Triangles 6.9 The Sine Law 6.10 The Cosine Law Answers CHAPTER 6 Trigonometry

57 58 59 60 61 62 63 64 65 66 67

APPENDIX A: Review of Prerequisite Skills Practice Adding Polynomials

71

84

Exponent Rules III (Multiplying Monomials by Monomials)

85

Exponent Rules IV (Powers of Monomials)

86

Exponent Rules V (Dividing Monomials by Monomials)

87

Graphing Equations I (Graphing Linear Equations)

88

Graphing Equations II (Methods for Graphing Linear Equations)

89

Graphing Equations III (Intersecting Lines)

90

Greatest Common Factors

91

Like Terms

92

Polynomials

93

Slope I (Using Points)

94

Slope II (Linear Equations: Slope and y-Intercept Form)

95

Slope III (Parallel and Perpendicular Lines)

96

Angle Properties I (Interior and Exterior Angles of Triangles and Quadrilaterals)

72

Angle Properties II (Angles and Parallel Lines)

Solving Equations I (Using Addition and Subtraction)

97

73

Common Factoring

74

Solving Equations II (Using Division and Multiplication)

98

Congruent Triangles

75

Evaluating Expressions I (Variables in Expressions)

Solving Equations III (Multi-Step Equations)

99

76

Evaluating Expressions II (Expressions With Integers)

Solving Equations IV (With the Variable on Both Sides)

100

77

Evaluating Expressions III (Applying Formulas)

Solving Equations V (With Brackets)

101

78

Evaluating Expressions IV (Non-Linear Relations)

Solving Equations VI (With Fractions and Decimals)

102

79

Solving Proportions

103

Evaluating Radicals (The Pythagorean Theorem)

Subtracting Polynomials

104

80

Expanding and Simplifying Expressions I (The Distributive Property)

Transformations I (Translations)

105

81

Expanding and Simplifying Expressions II (Multiplying a Polynomial by a Monomial)

Transformations II (Reflections)

106

82

Exponent Rules I (Powers With Whole Number Bases)

Transformations III (Dilatations)

107

83

Answers APPENDIX A Review of Prerequisite Skills

109

Exponent Rules II

To the Teacher Tips for Learning Math These first ten masters were designed to help students start the term with some insights into how to succeed at Math. Emphasis is on • examining attitudes toward Math • identifying and using available resources • being prepared for class • using class time wisely • making time for and establishing a place to do homework • doing homework daily • staying on top of new learning • seeking help • studying productively • applying problem solving skills • setting a goal for Math You may wish to assign these masters to • all students at the beginning of the term, to be completed the first week and showing a completed Goals master • students who display a need for some assistance in any of the areas covered While the masters are intended to be completed by individual students, you may wish to suggest that students work as partners to discuss the ideas on the masters. Encourage students to keep the Tips for Learning Math masters to help them reach the goals they set.

Practice In each chapter, there is a one-page Practice master for each numbered section. Each master • provides additional practice with the skills and concepts new to the section • can be assigned as needed • includes a variety of practice in four categories: knowledge/understanding, problem solving, communication, and application

Review of Prerequisite Skills In Appendix A, after the Practice masters for Chapters 1 to 6, there are 37 masters for Review of Prerequisite Skills. These masters • provide additional practice with the prerequisite skills identified in the student text at the beginning of each chapter, and in Appendix A at the back of the text • can be assigned as needed

Copyright © 2001 McGraw-Hill Ryerson Limited

To the Teacher

v

Answers Answers are provided for all the masters •at the end of each chapter for the Practice masters •at the end of Appendix A for the Review of Prerequisite Skills masters The answers include — • numerical solutions • word solutions • diagram solutions • graphical solutions Permission to reproduce these pages is provided as you may wish to post answers for students to check their work.

Installing and Using MATHPOWER™ 10, Ontario Edition, Practice Masters CD-ROM To use the MATHPOWER™ 10, Ontario Edition, Practice Masters CD-ROM requires Adobe® Acrobat® Reader 4.0, which is included on the CD. If Acrobat Reader is not already installed on your computer, insert the MATHPOWER™ 10, Ontario Edition, Practice Masters CD in the CD-ROM drive, then follow these steps: Windows: Navigate to your CD-ROM drive using Windows Explorer or My Computer; locate “ar405eng.exe” in the “WIN” directory and double-click its icon. Macintosh: If not already visible, open the CD-ROM in a window on your desktop by doubleclicking the CD-ROM’s icon. Within that window, locate “ar405eng” in the “MAC” folder and double-click to launch. After the installer launches, follow the on-screen instructions to complete the installation. When the installation is complete, restart your computer. The program is now ready to use. If you have questions regarding the use of Acrobat Reader, click the Help button for online help. To edit the MATHPOWER™ 10, Ontario Edition, Practice Masters CD-ROM requires the full Adobe® Acrobat® Writer program. Adobe® Acrobat® Reader 4.0 System Requirements Windows I486™ or Pentium® processor-based personal computer Microsoft® Windows® 95, Windows 98, or Windows NT® 4.0 with Service Pack 3 or later 10 MB of available RAM on Windows 95 and Windows 98 (16 MB recommended) 16 MB of available RAM on Windows NT (24 MB recommended) 10 MB of available hard-disk space 50 MB of additional hard-disk space for Asian fonts (required for Acrobat Reader 4.0 CD-ROM, otherwise optional) Macintosh Apple Power Macintosh or compatible computer MAC OS software version 7.1.2 or later 4.5 MB of available RAM (6.5 MB recommended) 8 MB of available hard-disk space 50 MB of additional hard-disk space for Asian fonts (required for Acrobat Reader 4.0 CD-ROM, otherwise optional)

vi To the Teacher

Copyright © 2001 McGraw-Hill Ryerson Limited

Name

Getting Started MATHPOWER™ 10, Ontario Edition

Here you are starting into a new Math course. This page and the other Tips for Learning Math pages are just for you. You are an important resource in your success in Math. Take a look at your strengths and weaknesses when it comes to Math, and how you think and feel about Math. Complete each statement or circle the letter of the response that best suits you. 1.

When I hear the word Math, the first few things that come into my mind are

2.

What I like the least about Math is

3.

What I like the most about Math is

4.

In my last Math course, my mark was

a) better than b) worse than the marks I received in most of my other subjects. 5.

In the last few years, my Math marks have been

a)

staying about the same

6.

I plan to take Math

a)

never after this course

7.

My attitude toward Math is

about the same as

b)

getting worse

c)

getting better

b)

to the end of high school

c)

at university or college

c)

about the same as

a) more positive than b) less positive than the attitude I had when I was in grade 7. 8.

c)

Something that I would like to change about my attitude to Math is

But you are not alone. You have other resources. 9.

Circle the letter of each resource that you feel you have available, and specify when appropriate.

a) my textbook, MATHPOWER™ 10, Ontario Edition b) my Math teacher, c) my classmates, d) friends taking the same Math course, but in a different class, e) friends or family who have already taken this level of Math, f)

computer and Internet access,

Copyright © 2001 McGraw-Hill Ryerson Limited

Tips for Learning Math

1

Name

Know Your Textbook and How to Use It MATHPOWER™ 10, Ontario Edition

MATHPOWER™ 10, Ontario Edition was written for students your age, and, throughout the chapters, uses real information that will, hopefully, interest you. Find five introductions or problems with real information that interests you. 1.

Page

Topic

2.

Page

Topic

3.

Page

Topic

4.

Page

Topic

5.

Page

Topic

Read pages xii to xxi in your textbook. Then, identify each statement as True or False. 6. Examples with fully worked solutions are provided. ________________ 7. Many of the Applications and Problem Solving questions are connected to other subjects and other Math topics. ________________ 8. Communicate Your Understanding means that I have an opportunity to demonstrate my understanding of a topic ________________ 9. Core sections are numbered and usually include an Investigation to actively involve me in my own learning. ________________ 10. There are Cumulative Review sections, at the end of Chapters 2, 4, and 6 that I can use when studying. ________________ 11. Detailed instructions involving Technology are provided in two appendixes at the back of the text to help me recall essential skills. ________________ 12. A Glossary is found near the end of the book to help me understand Math terms. ________________ 13. I can use the Review of Key Concepts sections and Chapter Test sections to test myself. ________________ 14. a) b) c) d) e)

Circle the letter of each thing you can learn about when using MATHPOWER™ 10, Ontario Edition. how Math is connected to other disciplines how people use Math in their careers how to use problem solving strategies to tackle problems how to use technology, such as calculators and computer spreadsheets how different topics in Math are interconnected

15. Circle the letter of each worthwhile use of the Answers that appear near the end of the book. a) verify whether my answers are right b) if an answer is not right, work backward from the given answer to understand where I made my mistake, and then correct it

2 Tips for Learning Math

Copyright © 2001 McGraw-Hill Ryerson Limited

Name

Classroom Learning MATHPOWER™ 10, Ontario Edition

Whether your Math class is 30 min or 70 min, you will gain the most from that time with your Math teacher and your classmates, if you • come to class prepared • listen actively • take clear notes • use your time productively 1. a) c) e) g) i) k)

Circle the letter of each thing that you bring to Math class. textbook, MATHPOWER™ 10, Ontario Edition b) pens and/or pencils d) ruler f) diskette h) completed and checked homework j) questions to ask about concepts that confuse me l)

notebook eraser calculator other tools _____________________ a positive attitude enthusiasm

2. Circle the letter of each way that you actively listen in Math class. Place an X beside the letter of each way you would like to try. a) anticipating what is coming next b) trying to connect new concepts with familiar concepts c) sketching diagrams to illustrate my understanding d) asking questions to clarify my understanding e) identifying when the teacher says something particularly important 3. a) b) c) d) e) f)

Circle the letter of each way your Math teacher points out important information. says it directly implies with tone of voice repeats writes it on the board highlights it on the board, in a special place or in a special way other ways ____________________________________________________________________________

4. Circle the letter of each technique that you use to make your Math notes clear. Place an X beside the letter of each technique you would like to try. a) record date b) record textbook page references c) start a new page d) write legibly e) make lists f) draw diagrams g) highlight key points h) other techniques _______________________________________________________________________ 5. a) b) c) d)

Circle the letter of each good reason for using your Math class time productively. The teacher is available to clarify and provide direction. Classmates are present to work with. Ideas are fresh. I will have less homework.

Copyright © 2001 McGraw-Hill Ryerson Limited

Tips for Learning Math

3

Name

Homework MATHPOWER™ 10, Ontario Edition

In a subject like Math, where the concepts build day after day and year after year, it is vital that you keep up daily. Always do your homework. You must do your homework daily, and to get it done you need to • make time for it • have a work space • be free of distractions to be able to concentrate 1. a) b) c) d) e) f) g) h) i) j) k) l) m)

Circle the letter of each thing that competes with Math homework for your time. other homework special assignments or projects sports practices/games music lessons/practice watching television or videos listening to the radio playing video games or playing cards visiting with friends talking on the telephone household chores part-time job shopping others _____________________________________________________________________

2. Circle the letter of each work space that you use for doing your Math homework. Place an X beside the letter of a space you would like to try. a) own room b) a shared room c) the kitchen d) the dining room e) another room at home f) the library g) another space ________________________________________________ Whenever and wherever you do your Math homework, you must have all the tools you need, and you must have minimal distractions. Complete each statement. 3.

The best time of day for me to be alert and have enough time to co...