CliffsNotes
Algebra II
Quick Review
2nd Edition
By Edward Kohn, MS, and David A. Herzog
Houghton Mifflin Harcourt
Boston New York
About the Authors
Ed Kohn is an outstanding educator and author, with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at the Sherman Oaks Center for Enriched Studies. Formerly an instructor at Fairleigh Dickinson University, David Alan Herzog is the author of over 100 audio visual titles and computer programs and has written and edited several books in mathematics and science.
Publishers Acknowledgments
Editorial
Acquisitions Editor: Greg Tubach
Project Editor: Suzanne Snyder
Copy Editor: Kelly Henthorne
Technical Editors: Mary Jane Sterling and Tom Page
Composition
Indexer: Potomac Indexing, LLC
Proofreader: Henry Lazarek
Wiley Publishing, Inc. Composition Services
Copyright 2013 by Houghton Mifflin Harcourt Publishing Company
All rights reserved
www.hmhbooks.com
No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system without the prior written permission of Houghton Mifflin Harcourt Publishing Company unless such copying is expressly permitted by federal copyright law. Address inquiries to Permissions, Houghton Mifflin Harcourt Publishing Company, 215 Park Avenue South, New York, New York 10003.
The publisher and the author make no representations 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 fitness for a particular purpose. No warranty may be created or extended by sales or promotional 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 rendering legal, accounting, or other professional services. If professional assistance is required, the services of a competent professional person should be sought. Neither the publisher nor the author shall be liable for damages arising herefrom. The fact that an organization 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 information the organization or website may provide or recommendations it may make. Further, readers 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.
Trademarks: CliffsNotes, the CliffsNotes logo, Cliffs, CliffsAP, CliffsComplete, CliffsQuickReview, CliffsStudySolver, CliffsTestPrep, CliffsNote-a-Day, cliffsnotes.com, and all related trademarks, logos, and trade dress are trademarks or registered trademarks of Houghton Mifflin Harcourt Publishing Company. All other trademarks are the property of their respective owners. Houghton is not associated with any product or vendor mentioned in this book.
ISBN 978-0-470-87634-3 (pbk)
eISBN 978-0-544-17942-4
Library of Congress Control Number: 2011922780
INTRODUCTION
CliffsNotes Algebra II Quick Review, 2nd Edition is a comprehensive study guide to the many topics of a second course in algebra, including information on subjects ranging from linear equations in one, two, and three variables, through inequalities, complex numbers, conic sections, quadratic equations, and logarithms. Whether you are looking for an in-depth treatment of the entire subject matter of the course or occasional reinforcement of one or more aspects of algebra, this is the place to find it.
For the purpose of this review, your knowledge of the following fundamental ideas is assumed:
- Natural numbers
- Whole numbers
- Integers
- Rational numbers
- Irrational numbers
- Real numbers
- Rules for positive and negative numbers
- Exponents
- Grouping symbols
- Order of operations
- Scientific notation
- Absolute value
If you feel that you are weak in any of these topics, refer to CliffsNotes Algebra I Quick Review, 2nd Edition.
Why You Need This Book
Can you answer yes to any of these questions?
- Do you need to review the fundamentals of Algebra II fast?
- Do you need a course supplement to Algebra II?
- Do you need to prepare for your Algebra II test?
- Do you need a concise, comprehensive reference for Algebra II?
- Do you need a no-nonsense approach to Algebra II that gets you the results you need?
If so, then CliffsNotes Algebra II Quick Review, 2nd Edition is for you!
How to Use This Book
Youre in charge here. You get to decide how to use this book. You can read it straight through (not usually a good idea with a math book) or just look for the information that you want and then put the book back on the shelf for later use. Here are a few of the recommended ways to search for information about a particular topic:
- Look for areas of interest in the books Table of Contents or use the index to find specific topics.
- Flip through the book, looking for subject areas at the top of each page.
- Get a glimpse of what youll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter.
- Use the Chapter Check-Out at the end of each chapter to gauge your grasp of the important information you need to know.
- Test your knowledge more completely in the Review Questions and look for additional sources of information in the Resource Center.
- Look in the Glossary for important terms and definitions. If a word is boldfaced in the text, you can find a more complete definition in the books glossary.
Hundreds of Practice Questions Online!
Go to www.cliffsnotes.com/math/algebra-ii-quizzes for hundreds of additional Algebra II practice questions to help prepare you for your next quiz or test. The questions are organized by this books chapter sections, so its easy to use the book and then quiz yourself online to make sure you know the subject. Go to CliffsNotes.com to test yourself anytime and find other free homework help.
CHAPTER 1
LINEAR SENTENCES IN ONE VARIABLE
Chapter Check-In
- Solving linear equations
- Solving problems by using formulas
- Understanding linear inequalities
- Dealing with compound inequalities
- Solving absolute value inequalities
Linear sentences in one variable may be equations or inequalities. What they have in common is that the variable has an exponent of 1, which is understood and so never written (except for teaching purposes). They also can be represented on a graph in the form of a straight line (covered in ). This chapter examines many ways of writing and solving linear sentences.
Linear Equations
An equation