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Pre-calculus Workbook for Dummies PDF

339 Pages·2009·17.28 MB·English
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0011__443300662200--ffffiirrss..iinndddd iivv 44//11//0099 1100::0088::2299 PPMM 01_421314-ffirs.qxp 4/3/09 8:53 PM Page i 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 01_421314-ffirs.qxp 4/3/09 8:53 PM Page ii 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 No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley &Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries, and may not be used without written permission.All other trademarks are the property of their respective owners. Wiley Publishing, Inc., is not associated with any product or vendor mentioned in this book. LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND THE AUTHOR MAKE NO REPRESENTA- TIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDING WITHOUT LIMITATION WARRANTIES OF FIT- NESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES OR PROMO- TIONAL MATERIALS. THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY SITUATION. THIS WORK IS SOLD WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN REN- DERING LEGAL, ACCOUNTING, OR OTHER PROFESSIONAL SERVICES. IF PROFESSIONAL ASSISTANCE IS REQUIRED, THE SERVICES OF A COMPETENT PROFESSIONAL PERSON SHOULD BE SOUGHT. NEITHER THE PUB- LISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM. THE FACT THAT AN ORGAN- IZATION OR WEBSITE IS REFERRED TO IN THIS WORK AS A CITATION AND/OR A POTENTIAL SOURCE OF FURTHER INFORMATION DOES NOT MEAN THAT THE AUTHOR OR THE PUBLISHER ENDORSES THE INFORMA- TION THE ORGANIZATION OR WEBSITE MAY PROVIDE OR RECOMMENDATIONS IT MAY MAKE. FURTHER, READ- ERS SHOULD BE AWARE THAT INTERNET WEBSITES LISTED IN THIS WORK MAY HAVE CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRITTEN AND WHEN IT IS READ. For general information on our other products and services, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002. For technical support, please visit www.wiley.com/techsupport. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be avail- able in electronic books. Library of Congress Control Number: 2009923971 ISBN: 978-0-470-42131-4 Manufactured in the United States of America 10 9 8 7 6 5 4 3 2 1 01_421314-ffirs.qxp 4/3/09 8:53 PM Page iii 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. 01_421314-ffirs.qxp 4/3/09 8:53 PM Page iv 01_421314-ffirs.qxp 4/3/09 8:53 PM Page v 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. 01_421314-ffirs.qxp 4/3/09 8:53 PM Page vi 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 317-572-4002. 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 Editorial Assistants:Jennette ElNaggar, David Lutton 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 02_421314-ftoc.qxp 4/3/09 8:54 PM Page vii 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 02_421314-ftoc.qxp 4/3/09 8:54 PM Page viii 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

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