Pre-calculus Workbook for Dummies

339 Pages·2009·17.28 MB·English

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P r e - Ca l c u l u s
Wo r k b o o k
FOR
DUMmIES‰
by Michelle Rose Gilman,
Christopher Burger,
Karina Neal
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Pre-Calculus Workbook For Dummies®
Published by
Wiley Publishing, Inc.
111 River St.
Hoboken, NJ 07030-5774
www.wiley.com
Copyright © 2009 by Wiley Publishing, Inc., Indianapolis, Indiana
Published by Wiley Publishing, Inc., Indianapolis, Indiana
Published simultaneously in Canada
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About the Authors
Michelle Rose Gilmanis proud to be known as Noah’s mom (Hi, Noah!). A
graduate of the University of South Florida, Michelle found her niche early —
at 19 she was already working with emotionally disturbed and learning-
disabled students in hospital settings. At 21, she made the trek to California.
There she discovered her passion for helping teenage students become more
successful in school and life. What started as a small tutoring business in the
garage of her California home quickly expanded and grew to the point where
traffic control was necessary on her residential street.
Today, Michelle is the founder and CEO of the Fusion Learning Center/Fusion
Academy, a private school and tutoring/test-prep facility in Solana Beach,
California, serving more than 2,000 students per year. She has taught tens of
thousands of students since 1988. In her spare time, Michelle created the
Mentoring Approach to Learning and authored The ACT For Dummies,
Pre-Calculus For Dummies, AP Biology For Dummies, AP Chemistry For Dummies,
Chemistry Workbook For Dummies,and The GRE For Dummies.She currently
specializes in motivating the unmotivated adolescent, comforting shell-
shocked parents, and assisting her staff of 27 teachers.
Michelle lives by the following motto:
“There are people content with longing; I am not one of them.”
Christopher Burger graduated with a Bachelor of Arts degree in mathematics
from Coker College in Hartsville, South Carolina, with minors in art and the-
ater. He has taught math for more than 10 years and has tutored subjects rang-
ing from basic math to calculus for 20 years. He is currently the Director of
Independent Studies for Fusion Learning Center and Fusion Academy in
Solana Beach, California, where he not only teaches students one-on-one but
also writes curriculum, oversees a staff of 27 teachers, and maintains a high
level of academic rigor within the school. When not at school, Christopher
canbe found in local theaters directing, acting, stage managing, or doing
pretty much any job that they’ll let him do. Chris is also one of the authors
ofPre-Calculus For Dummies.
Karina Nealgraduated with a Bachelor of Science degree in combined sci-
ences with an emphasis in psychology from Santa Clara University.
Additionally, she received her certificates in educational therapy and in col-
lege counseling from the University of California, San Diego. From an early age,
teaching and tutoring have been her passions — from starting her own tutor-
ing business in high school to helping found the Fusion Learning Center and
Fusion Academy in Solana Beach, California. As that institution’s Director of
Tutoring and Mentoring, Karina teaches all levels of mathematics and science,
provides special education and college counseling consultation, and oversees
a staff of 27 tutors and teachers. Karina has over 18 years of experience in the
education field and continues to tutor and teach students in a wide range of
subjects, from remedial writing to calculus. Besides being a closet math and
science geek, Karina is dedicated to the success of her students and believes
that all students can learn.
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Dedication
We would like to dedicate this book to every student we’ve ever taught —
each one of you taught us something in return. Also, to our families and
friends who supported us during the writing.
Authors’ Acknowledgments
We would like to acknowledge Bill Gladstone, our wonderful agent from
Waterside, for the opportunity to write this book; Nicholas Angelo for being
the scanning king; Natalie Harris, project editor extraordinaire; copy editor
Todd Lothery; technical editor David Herzog; acquisitions editors Tracy
Boggier and Erin Mooney, who, for unknown reasons, continue to want to
work with us; and to everyone who has lent a helping hand or eye or brain,
wecouldn’t do it without you: TL, VS, BN, NG, and Clyde.
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Publisher’s Acknowledgments
We’re proud of this book; please send us your comments through our Dummies online registration form located
at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department
within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].
Some of the people who helped bring this book to market include the following:
Acquisitions, Editorial, and Media Development Composition Services
Project Editor: Natalie Faye Harris Project Coordinator: Patrick Redmond
Acquisitions Editor: Tracy Boggier Layout and Graphics: Carl Byers, Carrie A. Cesavice,
Reuben W. Davis, Nikki Gately
Copy Editor: Todd Lothery
Proofreaders: John Greenough, Leeann Harney
Assistant Editor:Erin Calligan Mooney
Indexer: Broccoli Information Mgt.
Editorial Program Coordinator:Joe Niesen
Special Help
Technical Editor: David Herzog
Peter Mikulecky
Editorial Manager: Christine Meloy Beck
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Cartoons: Rich Tennant (www.the5thwave.com)
Publishing and Editorial for Consumer Dummies
Diane Graves Steele, Vice President and Publisher, Consumer Dummies
Kristin Ferguson-Wagstaffe, Product Development Director, Consumer Dummies
Ensley Eikenburg,Associate Publisher, Travel
Kelly Regan,Editorial Director, Travel
Publishing for Technology Dummies
Andy Cummings,Vice President and Publisher, Dummies Technology/General User
Composition Services
Gerry Fahey,Vice President of Production Services
Debbie Stailey,Director of Composition Services
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Contents at a Glance
Introduction.................................................................................1
Part I: Foundation (And We Don’t Mean Makeup!) ........................5
Chapter 1: Beginning at the Very Beginning: Pre-Pre-Calculus................................................................7
Chapter 2: Get Real!: Wrestling with Real Numbers................................................................................25
Chapter 3: Understanding the Function of Functions............................................................................41
Chapter 4: Go Back to Your Roots to Get Your Degree...........................................................................73
Chapter 5: Exponential and Logarithmic Functions...............................................................................91
Part II: Trig Is the Key: Basic Review,
the Unit Circle, and Graphs.......................................................105
Chapter 6: Basic Trigonometry and the Unit Circle.............................................................................107
Chapter 7: Graphing and Transforming Trig Functions.......................................................................127
Part III: Advanced Trig: Identities, Theorems, and Applications.....143
Chapter 8: Basic Trig Identities...............................................................................................................145
Chapter 9: Advanced Identities...............................................................................................................161
Chapter 10: Solving Oblique Triangles...................................................................................................177
Part IV: And the Rest . . ...........................................................193
Chapter 11: Complex Numbers and Polar Coordinates.......................................................................195
Chapter 12: Conquering Conic Sections.................................................................................................211
Chapter 13: Finding Solutions for Systems of Equations.....................................................................243
Chapter 14: Sequences, Series, and Binomials — Oh My!....................................................................275
Chapter 15:The Next Step Is Calculus...................................................................................................287
Part V: The Part of Tens ............................................................299
Chapter 16: Ten Uses for Parent Graphs................................................................................................301
Chapter 17: Ten Pitfalls to Pass Up in Pre-Calc.....................................................................................309
Index.......................................................................................313
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Table of Contents
Introduction..................................................................................1
About This Book.........................................................................................................................1
Conventions Used in This Book...............................................................................................2
Foolish Assumptions.................................................................................................................2
How This Book Is Organized.....................................................................................................2
Part I: Foundation (And We Don’t Mean Makeup!).......................................................2
Part II: Trig Is the Key: Basic Review, the Unit Circle, and Graphs............................2
Part III: Advanced Trig: Identities, Theorems, and Applications...............................3
Part IV: And the Rest . . ...................................................................................................3
Part V: The Part of Tens...................................................................................................3
Icons Used in This Book............................................................................................................3
Where to Go from Here..............................................................................................................4
Part I: Foundation (And We Don’t Mean Makeup!).........................5
Chapter 1: Beginning at the Very Beginning: Pre-Pre-Calculus....................................7
Reviewing Order of Operations: The Fun in Fundamentals..................................................7
Keeping Your Balance While Solving Equalities...................................................................10
A Picture Is Worth a Thousand Words: Graphing Equalities and Inequalities.................12
Graphing using the plug and chug method.................................................................13
Graphing using the slope-intercept form....................................................................13
Using Graphs to Find Information (Distance, Midpoint, Slope).........................................15
Finding the distance.......................................................................................................15
Calculating the midpoint...............................................................................................16
Discovering the slope....................................................................................................16
Answers to Problems on Fundamentals................................................................................20
Chapter 2: Get Real!: Wrestling with Real Numbers.....................................................25
Solving Inequalities..................................................................................................................25
Expressing Inequality Solutions in Interval Notations........................................................28
Don’t Get Drastic with Radicals and Exponents — Just Simplify Them!..........................30
Getting Out of a Sticky Situation or Rationalizing................................................................33
Answers to Problems on Real Numbers................................................................................36
Chapter 3: Understanding the Function of Functions.....................................................41
Battling Out Even versus Odd................................................................................................41
Leaving the Nest: Transforming Parent Graphs...................................................................43
Quadratic functions.......................................................................................................43
Square root functions....................................................................................................44
Absolute value functions...............................................................................................44
Cubic functions...............................................................................................................44
Cube root functions.......................................................................................................45