com Table of Contents Title Page Dedication Copyright Page Introduction Part 1 - A Final Farewell to Numbers Chapter 1 - Getting Cozy with Numbers Chapter 2 - Making Friends with Fractions Chapter 3 - Encountering Expressions Part 2 - Equations and Inequalities Chapter 4 - Solving Basic Equations Chapter 5 - Graphing Linear Equations Chapter 6 - Cooking Up Linear Equations Chapter 7 - Linear Inequalities Part 3 - Systems of Equations and Matrix Algebra Chapter 8 - Systems of Linear Equations and Inequalities Chapter 9 - The Basics of the Matrix Part 4 - Now You’re Playing with (Exponential) Power! Chapter 10 - Introducing Polynomials Chapter 11 - Factoring Polynomials Chapter 12 - Wrestling with Radicals www.com Chapter 13 - Quadratic Equations and Inequalities Chapter 14 - Solving High-Powered Equations Part 5 - The Function Junction Chapter 15 - Introducing the Function Chapter 16 - Graphing Functions Part 6 - Please, Be Rational! Chapter 17 - Rational Expressions Chapter 18 - Rational Equations and Inequalities Part 7 - Wrapping Things Up Chapter 19 - Whipping Word Problems Chapter 20 - Final Exam Appendix A - Solutions to “You’ve Got Problems” Appendix B Index www.com For my wife, Lisa, who makes my life worth living, and my son, Nicholas, who taught me that waking up in the morning with the people you love is just the best thing in the world.com ALPHA BOOKS Published by the Penguin Group Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, USA Penguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario M4P 2Y3, Canada (a division of Pearson Penguin Canada Inc.) Penguin Books Ltd, 80 Strand, London WC2R 0RL, England Penguin Ireland, 25 St Stephen’s Green, Dublin 2, Ireland (a division of Penguin Books Ltd.) Penguin Group (Australia), 250 Camberwell Road, Camberwell, Victoria 3124, Australia (a division of Pearson Australia Group Pty.) Penguin Books India Pvt., 11 Community Centre, Panchsheel Park, New Delhi—110 017, India Penguin Group (NZ), 67 Apollo Drive, Rosedale, North Shore, Auckland 1311, New Zealand (a division of Pearson New Zealand Ltd.) Penguin Books (South Africa) (Pty.) Ltd, 24 Sturdee Avenue, Rosebank, Johannesburg 2196, South Africa Penguin Books Ltd., Registered Offices: 80 Strand, London WC2R 0RL, England Copyright © 2007 by W. Michael Kelley All rights reserved. No part of this book shall be reproduced, stored in a retrieval system, or transmitted by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission from the publisher. No patent liability is assumed with respect to the use of the information contained herein.
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Special books, or book excerpts, can also be created to fit specific needs. For details, write: Special Markets, Alpha Books, 375 Hudson Street, New York, NY 10014.com Introduction Picture this scene in your mind. I am a high school student, chock-full of hormones and sugary snack cakes, thanks to puberty and the fact that I just spent the $3 my mom gave me for a healthy lunch on Twinkies and doughnuts in the cafeteria. I am young enough that I still like school, but old enough to understand that I’m not supposed to act like it, and my mind is active, alert, and tuned in.
There are only two more classes to go and my day is over, and with that in mind, I head for algebra class. In retrospect, I think the teacher must have had some sort of diabolical fun-sucking and joy-destroying laser ray gun hidden in the drop-down ceiling of that classroom, because just walking into algebra class put me in a bad mood. It’s as hot as a varsity football player’s armpit in that windowless, dank dungeon, and strangely enough, it always smells like a roomful of people just finished jogging in place. Vague yet acrid sweat and body odor attack my senses, and I slink down into my chair.
“I have to stay awake today,” I tell myself. “I am on the brink of getting hopelessly lost, so if I drift off again, I won’t understand anything, and we have a big test in a few days.” However, no matter how I chide and cajole myself into paying attention, it is utterly impossible. The teacher walks in and turns on a small oscillating fan in a vain effort to move the stinky air around and revive her class. Immediately she begins, in a soft, soothing voice, and the world in my peripheral vision begins to blur.
Uh oh, soft monotonous vocal delivery, the droning white noise of a fan, the compelling malodorous warmth that only occupies rooms built out of brightly painted cinderblock … all elements that have thwarted my efforts to stay awake in class before. I look around the room, and within 10 minutes most of the students are asleep. The few that are still conscious are writing notes to boyfriends or girlfriends. The school’s star soccer player sits next to me, eyes wide and staring at his Trapper Keeper notebook, having regressed into a vegetative state as soon as class began.
I begin to chant my daily mantra to myself, “I hate this class, I hate this class, I hate this class …” and I really mean it. As far as I am concerned, algebra is the most boring thing that was ever created, and it exists solely to destroy my happiness. Can you relate to that story? Even though the individual details may not match your experience, did you have a similar mantra? Some people have a hard time believing that a math major really hated math during his formative years. I guess the math after algebra got more interesting, or my attention span widened a little bit.
However, that’s not the normal course of events. Luckily, my extremely bad experience with math didn’t prevent me from taking more classes, and eventually my opinion changed, but most people hit the brick wall of algebra and give up on math forever in hopeless despair.com That was when I decided to go back and revisit the horribly boring and difficult mathematics classes I took, and write books that would not only explain things more clearly, but make a point of speaking in everyday language. Besides, I have always thought learning was much more fun when you could laugh along the way, but that’s not necessarily the opinion of most math people. In fact, one of the mathematicians who reviewed my book The Complete Idiot’s Guide to Calculus before it was released told me, “I don’t think your jokes are appropriate.
Math books shouldn’t contain humor, because the math inside is already fun enough.” I believe that logic is insane. In this book, I’ve tried to present algebra in an interesting and relevant way, and attempted to make you smile a few times in spite of the pain. I didn’t want to write a boring textbook, but at the same time, I didn’t want to write an algebra joke book so ridiculously crammed with corny jokes that it insults your intelligence. I also tried to include as much practice as humanly possible without making this book a million pages long.
(Such books are hard to carry and tend to cost too much; besides, you wouldn’t believe how expensive the shipping costs are if you buy them online!) Each section contains fully explained examples and practice problems to try on your own in little sidebars labeled “You’ve Got Problems.” Additionally, Chapter 20 is jam-packed with practice problems based on the examples throughout the book, to help you identify your weaknesses if you’ve taken algebra before, or to test your overall knowledge once you’ve worked your way through the book. Remember, it doesn’t hurt to go back to your algebra textbook and work out even more problems to hone your skills once you’ve exhausted the practice problems in this book, because repetition and practice transforms novices into experts. Algebra is not something that can only be understood by a few select people. You can understand it and excel in your algebra class.
Think of this book as a personal tutor, available to you 24 hours a day, 7 days a week, always ready to explain the mysteries of math to you, even when the going gets rough.com How This Book Is Organized This book is presented in seven sections: In Part 1, “A Final Farewell to Numbers,” you’ll firm up all of your basic arithmetic skills to make sure they are finely tuned and ready to face the challenges of algebra. You’ll calculate greatest common factors and least common multiples, review exponential rules, tour the major algebraic properties, and explore the correct order of operations. In Part 2, “Equations and Inequalities,” the preparation is over, and it’s time for full-blown algebra. You’ll solve equations, draw graphs, create equations of lines, and investigate inequality statements with one and two variables.
In Part 3, “Systems of Equations and Matrix Algebra,” you’ll find the shared solutions of multiple equations and learn the basics of matrix algebra, a comparatively new branch of algebra that’s really caught on since the dawn of the computer age. Things get a little more intense in Part 4, “Now You’re Playing with (Exponential) Power!” because the exponents are no longer content to stay small. You’ll learn to cope with polynomials and radicals, and how to solve equations that contain variables raised to the second, third, and fourth powers. Part 5, “The Function Junction,” introduces you to the mathematical function, which takes center stage as you advance in your mathematical career.
You’ll learn how to calculate a function’s domain and range, find its inverse, and graph it without having to resort to a monotonous and repetitive table of values. Fractions are back in the spotlight in Part 6, “Please, Be Rational!” You’ll learn how to do all the things you used to do with simple fractions (like add, subtract, multiply, and divide them) when the contents of the fractions get more complicated. Finally, in Part 7, “Wrapping Things Up,” you’ll face algebra’s playground bully, the word problem. However, once you learn a few approaches for attacking word problems head on, you won’t fear them anymore.
You’ll also get a chance to practice all of your skills in the “Final Exam”; don’t worry, it won’t be graded.com Things to Help You Out Along the Way As a teacher, I constantly found myself going off on tangents—everything I mentioned reminded me of something else. These peripheral snippets are captured in this book as well. Here’s a guide to the different sidebars you’ll see peppering the pages that follow. You’ve Got Problems Math is not a spectator sport! Once I introduce a topic, I’ll explain how to work out a certain type of problem, and then you have to try it on your own.