12Math FM_4th pass 7/25/08 8:53 AM Page i 12 PEARSON Foundations for College Mathematics Chad Coene Duncan LeBlanc Bonnie Edwards Robert Sherk Glenn Gadsby Karen Timson Catherine Heideman Frank Torti Gordon Cooke Carolyn Kieran Ed Haines Simona Matei Margaret Sinclair 12Math FM_4th pass 7/25/08 8:53 AM Page ii Publisher Mike Czukar All rights reserved.This publication is protected by copyright,and permission should be obtained Research and Communications Manager from the publisher prior to any prohibited Barbara Vogt reproduction,storage in a retrieval system,or transmission in any form or by any means, Editorial Team electronic,mechanical,photocopying,recording, Claire Burnett or likewise.For information regarding permission, Nirmala Nutakki write to the Permissions Department. Sarah Mawson Lynda Cowan The information and activities presented in this Stephanie Kleven book have been carefully edited and reviewed. Ioana Gagea However,the publisher shall not be held liable for Margaret McClintock any damages resulting,in whole or in part,from Ellen Davidson the reader’s use ofthis material. Jane Schell Karen Alley Cheri Westra Judy Wilson Editorial Contributor Bob Berglind Photo Research Carrie Gleason Design Word & Image Design Studio Inc. Composition Lapiz Digital Services,India Copyright ©2009 Pearson Education Canada, a division ofPearson Canada Inc. ISBN-13:978-0-321-49367-5 ISBN-10:0-321-49367-2 Printed and bound in Canada 4 5 – TC – 12 11 12Math FM_4th pass 7/25/08 8:53 AM Page iii Consultants and Advisers Technology Consultants Carolyn Kieran Université de Québec à Montréal Duncan LeBlanc Toronto District School Board Advisers Charlotte Cutajar Toronto District School Board Peggy Leroux Waterloo Catholic District School Board Sandra G.McCarthy Ottawa-Carleton District School Board Gizele Price Dufferin-Peel Catholic District School Board Dwight Stead Dufferin-Peel Catholic District School Board iii 12Math FM_4th pass 7/25/08 8:53 AM Page iv Reviewers Tina Bawa Judi Hanta Simona Matei London District Catholic Hamilton-Wentworth Catholic Peel District School Board School Board District School Board Linda McLaren Gerry Bossy Paul Higgins Catholic District School Board Lambton Kent District Greater Essex County District ofEastern Ontario School Board School Board Jason Murray Mandy Clark Victoria Kudrenski Halton District School Board Limestone District School Hamilton-Wentworth District Board School Board Chris Schleihauf Lambton Kent District School Gordon Doctorow Susan Lavigne Board Independent Math Formerly Thames Valley Consultant,Toronto District School Board Linda Vardy Formerly Kawartha Pine Ridge Heather L.Edwards Thuy Leu District School Board Upper Grand District Waterloo Region District School Board School Board Justin Veiga Toronto Catholic District Veronica Gervais Frieda Leung School Board Ottawa-Carleton Catholic Peel District School Board School Board Jim Vincent Susanne Ling Peel District School Board Tina Grandy York Region District School Peel District School Board Board Ann Winacott Durham District School Board Gary Greer William Lozinski Limestone District School Formerly Windsor-Essex Kevin Wong Board Catholic District School Board Halton Catholic District School Board Linda Lu Ed Haines Hamilton-Wentworth District Michael Zahra Formerly District School Board School Board Algonquin and Lakeshore ofNiagara Catholic District School Board iv 12Math FM_4th pass 7/25/08 9:26 AM Page v Table of Contents Trigonometry Two-Variable Data Activate Prior Knowledge 2 Activate Prior Knowledge 126 1.1 Trigonometric Ratios in Right Triangles 4 Transitions:Getting Extra Practice 129 1.2 Technology:Investigating the Sine, 3.1 One- and Two-Variable Data 130 Cosine,and Tangent of Obtuse Angles 13 3.2 Using Scatter Plots to Identify Relationships 138 1.3 Sine,Cosine,and Tangent of Obtuse Angles 20 3.3 Line of Best Fit 148 Game:Trigonometric Search 25 Mid-Chapter Review 158 Mid-Chapter Review 26 3.4 Technology:Analysing Data Using a 1.4 The Sine Law 27 Graphing Calculator 159 Transitions:Collecting Important Ideas 34 Game:Give It to Me Straight 165 1.5 The Cosine Law 35 3.5 Technology:Analysing Data Using a 1.6 Problem Solving with Oblique Triangles 42 Spreadsheet 166 1.7 Research: Occupations Using Trigonometry 50 3.6 Technology:Analysing Data Using Study Guide 53 Fathom 172 Chapter Review 54 3.7 Exploration: Conducting an Experiment Practice Test 57 to Collect Two-Variable Data 180 Chapter Problem:Designing a Stage 58 Study Guide 185 Chapter Review 186 Practice Test 189 Geometry Chapter Problem:Temperatures around the Globe 190 Activate Prior Knowledge 60 Statistical Literacy Transitions:Managing Your Time 66 2.1 Area Applications 67 2.2 Working with Composite Objects 76 Activate Prior Knowledge 192 Mid-Chapter Review 86 Transitions:Ethical Conduct 195 2.3 Optimizing Areas and Perimeters 87 4.1 Interpreting Statistics 196 2.4 Technology:Optimizing Area and 4.2 Research:Statistics in the Media 206 Perimeter Using a Spreadsheet 97 4.3 Surveys and Questionnaires 208 2.5 Technology:Dynamic Investigations of 4.4 Exploration: Conducting a Survey to Collect Optimal Measurements 103 Two-Variable Data 218 2.6 Optimizing Volume and Surface Area 105 Mid-Chapter Review 222 Puzzle:Cube Creations 114 4.5 The Use and Misuse of Statistics 223 2.7 Technology:Optimizing Surface Area Using a 4.6 Understanding Indices 233 Spreadsheet 115 4.7 Research: Indices and E-STAT 241 Study Guide 119 4.8 Research: Statistical Literacy and Occupations 246 Chapter Review 120 Game:Concept Clues 249 Practice Test 123 Study Guide 250 Chapter Problem:A Winning Design 124 Chapter Review 251 Practice Test 254 Chapter Problem:To Ban or Not to Ban? 256 Project A:For the Birds! 258 Project B:Making Headlines with Statistics 260 Cumulative Review Chapters 1–4 262 v 12Math FM_4th pass 7/25/08 9:26 AM Page vi Graphical Models Annuities and Mortgages Activate Prior Knowledge 266 Activate Prior Knowledge 406 Transitions:Teaching Yourself 268 Transitions:Evaluations 408 5.1 Trends in Graphs 269 7.1 The Amount of an Annuity 409 5.2 Rate of Change 278 7.2 The Present Value of an Annuity 419 5.3 Linear Models 288 7.3 The Regular Payment of an Annuity 426 5.4 Quadratic Models 298 7.4 Technology:Using a Spreadsheet to Mid-Chapter Review 308 Investigate Annuities 433 Game:Curves of Concentration 309 7.5 Saving for Education and Retirement 439 5.5 Exponential Models 310 Mid-Chapter Review 442 5.6 Selecting a Regression Model for Data 319 7.6 Research:What Is a Mortgage? 443 5.7 Technology:Applying Trends in Data 328 7.7 Technology:Amortizing a Mortgage 446 Study Guide 331 Game:Mortgage Tic-Tac-Toe 455 Chapter Review 332 7.8 Technology:Using Technology to Practice Test 335 Generate an Amortization Table 456 Chapter Problem:Modelling the Price of Diamonds 336 7.9 Technology:Reducing the Interest Costs of a Mortgage 461 Study Guide 467 Algebraic Models Chapter Review 468 Practice Test 471 Chapter Problem:Planning Ahead 472 Activate Prior Knowledge 338 Transitions:Learning with Others 341 6.1 Using Formulas to Solve Problems 342 Budgets 6.2 Rearranging Formulas 350 6.3 Laws of Exponents 358 6.4 Technology:Patterns in Exponents 366 Activate Prior Knowledge 474 Mid-Chapter Review 371 Transitions:Your Financial Future 476 6.5 Rational Exponents 372 8.1 Research:Choosing a Home 477 Game:Power Dominoes 379 8.2 The Costs of Owning or Renting a Home 479 6.6 Exponential Equations 380 8.3 Research:Estimating Living Costs 488 6.7 Applications of Exponential Equations 387 Mid-Chapter Review 492 6.8 Research:Occupations Using 8.4 Designing Monthly Budgets 493 Mathematical Modelling 396 8.5 Technology:Creating a Budget Using a Study Guide 399 Spreadsheet 505 Chapter Review 400 Game:Budget Shuffle Challenge 510 Practice Test 403 8.6 Research:Making Decisions about Chapter Problem:A Butterfly Conservatory 404 Buying or Renting 511 8.7 Research:Occupations Involving Finance 516 Study Guide 519 Chapter Review 520 Practice Test 523 Chapter Problem:Preparing with Financing 524 Project C:Will Women Eventually Run as Fast as Men? 526 Project D:A Home of Their Own 528 Cumulative Review Chapters 1–8 530 Glossary 535 Answers 543 Technology Index 587 Index 589 Acknowledgments 593 Course Study Guide(See inside back cover.) vi 12Math FM_4th pass 7/25/08 9:26 AM Page vii About Pearson Foundations for College Mathematics 12 Whether you are planning for an apprenticeship program,for college admissions,or for work,Foundations for College Mathematics 12 will help you achieve your goals. This book organizes the course into four major mathematical topics.By studying each topic separately,you can make the best use of your time and efforts,focus on new concepts for an extended period,and develop greater understanding,and better recall. ■ Chapter 1,Trigonometry This mathematical strand is important in such careers as carpentry,plumbing,landscape ■ Chapter 2,Geometry design,theatre design,or commercial arts. ■ Are you interested in running your own Chapter 3,Two-Variable Data business? Researching and analysing data would ■ Chapter 4,Statistical Literacy be part of preparing a sound business plan. Knowing how to model situations using ■ Chapter 5,Graphical Models graphs,tables,or formulas,is a key skill for ■ technologists,financial planners,and business Chapter 6,Algebraic Models managers. ■ Chapter 7,Annuities and Understanding the principles of investments, Mortgages loans,and budgets has applications in your personal life,and in careers in banking, ■ Chapter 8,Budgets insurance,and business. vii 12Math FM_4th pass 7/25/08 9:26 AM Page viii Your Book Highlights In addition to the Chapters,this book supports your learning with these additional tools. • A Glossary of key math terms • Answers so that you can check your work • A Technology Index to reference specific calculator or software instructions • An Index • A Course Study Guide,printed on the inside back cover,as a quick reference for key formulas,theorems,or properties. • A Student CD-ROM with software files for selected activities in this book. viii 12Math FM_4th pass 7/25/08 9:26 AM Page ix Chapter Structure Each chapter starts with a page like this ... See What You’ll Learnand Why. Check the list ofKey Words. ...followed by a review feature. Activate Prior Knowledgelets you review knowledge from previous grades,or from earlier chapters. Each chapter also has a Transitions feature, and a Game or Puzzle. Each Transitionspage highlights a key principle related to independent study,or your choice ofpathway beyond grade 12. Each Gameor Puzzleis an opportunity to reinforce the work ofthe chapter. ix