Sách Algebra demystified - rhonda huettenmueller

ALGEBRA DEMYSTIFIED - RHONDA HUETTENMUELLER

Contents
Preface ix
CHAPTER 1 Fractions 1
CHAPTER 2Introduction to Variables 37
CHAPTER 3 Decimals 55
CHAPTER 4 Negative Numbers 65
CHAPTER 5 Exponents and Roots 79
CHAPTER 6 Factoring 113
CHAPTER 7 Linear Equations 163
CHAPTER 8 Linear Applications 197
CHAPTER 9 Linear Inequalities 285
CHAPTER 10 Quadratic Equations 319
CHAPTER 11 Quadratic Applications 353
Appendix 417
Final Review 423
Index 437
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PREFACE
This book is designed to take the mystery out of algebra. Each section contains
exactly one new idea—unlike most math books, which cover several
ideas at once. Clear, brief explanations are followed by detailed examples.
Each section ends with a few Practice problems, most similar to the examples.
Solutions to the Practice problems are also given in great detail. The goal is
to help you understand the algebra concepts while building your skills and
confidence.
Each chapter ends with a Chapter Review, a multiple-choice test designed
to measure your mastery of the material. The Chapter Review could also be
used as a pretest. If you think you understand the material in a chapter, take
the Chapter Review test. If you answer all of the questions correctly, then
you can safely skip that chapter. When taking any multiple-choice test, work
the problems before looking at the answers. Sometimes incorrect answers
look reasonable and can throw you off. Once you have finished the book,
take the Final Review, which is a multiple-choice test based on material from
each chapter.
Spend as much time in each section as you need. Try not to rush, but do
make a commitment to learning on a schedule. If you find a concept difficult,
you might need to work the problems and examples several times. Try not to
jump around from section to section as most sections extend topics from
previous sections.
Not many shortcuts are used in this book. Does that mean you shouldn’t
use them? No. What you should do is try to find the shortcuts yourself. Once
you have found a method that seems to be a shortcut, try to figure out why it
works. If you understand how a shortcut works, you are less likely to use it
incorrectly (a common problem with algebra students).
Because many find fraction arithmetic difficult, the first chapter is devoted
almost exclusively to fractions. Make sure you understand the steps in this
chapter because they are the same steps used in much of the rest of the book.
For example, the steps used to compute 7
36
þ 5
16 are exactly those used to
compute
2x
x2 þ x 2
þ 6
x þ 2
.
Copyright 2003 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
Even those who find algebra easy are stumped by word problems (also
called ‘‘applications’’). In this book, word problems are treated very carefully.
Two important skills needed to solve word problems are discussed
earlier than the word problems themselves. First, you will learn how to
find quantitative relationships in word problems and how to represent
them using variables. Second, you will learn how to represent multiple quantities
using only one variable.
Most application problems come in ‘‘families’’—distance problems, work
problems, mixture problems, coin problems, and geometry problems, to
name a few. As in the rest of the book, exactly one topic is covered in
each section. If you take one section at a time and really make sure you
understand why the steps work, you will find yourself able to solve a great
many applied problems—even those not covered in this book.
Good luck.
RHONDA HUETTENMUELLER