Table Of Content12Math 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
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Design
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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
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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
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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
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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
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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.)
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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.
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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.
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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.
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