Algebra I Essentials For Dummies E-Book

Mary Jane Sterling

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2010

Seitenzahl: 217

Beschreibung

With its use of multiple variables, functions, and formulas algebracan be confusing and overwhelming to learn and easy to forget.Perfect for students who need to review or reference criticalconcepts, Algebra I Essentials For Dummies provides contentfocused on key topics only, with discrete explanations of criticalconcepts taught in a typical Algebra I course, from functions andFOILs to quadratic and linear equations. This guide is also aperfect reference for parents who need to review critical algebraconcepts as they help students with homework assignments, as wellas for adult learners headed back into the classroom who just needa refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials ForDummies. Now students who are prepping for exams, preparing tostudy new material, or who just need a refresher can have aconcise, easy-to-understand review guide that covers an entirecourse by concentrating solely on the most important concepts. Fromalgebra and chemistry to grammar and Spanish, our expert authorsfocus on the skills students most need to succeed in asubject.

Leseprobe

Algebra I Essentials For Dummies®

Table of Contents

Introduction

About This Book

Conventions Used in This Book

Foolish Assumptions

Icons Used in This Book

Where to Go from Here

Chapter 1: Setting the Scene for Actions in Algebra

Making Numbers Count

Facing reality with reals

Going green with naturals

Wholesome whole numbers

Integrating integers

Behaving with rationals

Reacting to irrationals

Picking out primes and composites

Giving Meaning to Words and Symbols

Valuing vocabulary

Signing up for symbols

Going for grouping

Operating with Signed Numbers

Adding signed numbers

Subtracting signed numbers

Multiplying and dividing signed numbers

Dealing with Decimals and Fractions

Changing fractions to decimals

Changing decimals to fractions

Chapter 2: Examining Powers and Roots

Expanding and Contracting with Exponents

Exhibiting Exponent Products

Taking Division to Exponents

Taking on the Power of Zero

Taking on the Negativity of Exponents

Putting Powers to Work

Circling around Square Roots

Chapter 3: Ordering and Distributing: The Business of Algebra

Taking Orders for Operations

Dealing with Distributing

Making Numbers and Variables Cooperate

Relating negative exponents to fractions

Creating powers with fractions

Making Distributions Over More Than One Term

Chapter 4: Factoring in the First and Second Degrees

Making Factoring Work

Facing the factoring method

Factoring out numbers and variables

Getting at the Basic Quadratic Expression

Following Up on FOIL and unFOIL

Making UnFOIL and the GCF Work Together

Getting the Best of Binomials

Facing up to the difference of two perfect squares

Creating factors for the difference of perfect cubes

Finishing with the sum of perfect cubes

Chapter 5: Broadening the Factoring Horizon

Grabbing Onto Grouping

Getting the groups together

Grouping and unFOILing in the same package

Tackling Multiple Factoring Methods

Beginning with binomials

Finishing with binomials

Recognizing when you have a quadratic-like expression

Knowing When Enough Is Enough

Recruiting the Remainder Theorem

Getting real with synthetic division

Making good choices for synthetic division

Factoring Rational Expressions

Chapter 6: Solving Linear Equations

Playing by the Rules

Solving Equations with Two Terms

Depending on division

Making use of multiplication

Reciprocating the invitation

Taking on Three Terms

Eliminating a constant term

Vanquishing the extra variable term

Breaking Up the Groups

Nesting isn’t for the birds

Distributing first

Multiplying before distributing

Focusing on Fractions

Promoting proportions

Taking advantage of proportions

Changing Formulas by Solving for Variables

Chapter 7: Tackling Second-Degree Quadratic Equations

Recognizing Quadratic Equations

Finding Solutions for Quadratic Equations

Applying Factorizations

Zeroing in on the multiplication property of zero

Solving quadratics by factoring and applying the multiplication property of zero

Solving Three-Term Quadratics

Applying Quadratic Solutions

Calling On the Quadratic Formula

Ignoring Reality with Imaginary Numbers

Chapter 8: Expanding the Equation Horizon

Queuing Up to Cubic Equations

Solving perfectly cubed equations

Going for the greatest common factor

Grouping cubes

Solving cubics with integers

Using Synthetic Division

Working Quadratic-Like Equations

Rooting Out Radicals

Chapter 9: Reconciling Inequalities

Introducing Interval Notation

Comparing inequality and interval notation

Graphing inequalities

Performing Operations on Inequalities

Adding and subtracting numbers to inequalities

Multiplying and dividing inequalities

Finding Solutions for Linear Inequalities

Expanding to More Than Two Expressions

Taking on Quadratic and Rational Inequalities

Using a similar process with more than two factors

Identifying the factors in fractional inequalities

Chapter 10: Absolute-Value Equations and Inequalities

Acting on Absolute-Value Equations

Working Absolute-Value Inequalities

Chapter 11: Making Algebra Tell a Story

Making Plans to Solve Story Problems

Finding Money and Interest Interesting

Investigating investments and interest

Greening up with money

Formulating Distance Problems

Making the distance formula work for you

Figuring distance plus distance

Figuring distance and fuel

Stirring Things Up with Mixtures

Chapter 12: Putting Geometry into Story Problems

Triangulating a Problem with the Pythagorean Theorem

Being Particular about Perimeter

Triangulating triangles

Squaring up to squares and rectangles

Recycling circles

Making Room for Area Problems

Ruminating about rectangles and squares

Taking on triangles

Rounding up circles

Validating with Volume

Prodding prisms and boxing boxes

Cycling cylinders

Pointing to pyramids and cones

Chapter 13: Grappling with Graphing

Preparing to Graph a Line

Incorporating Intercepts

Sliding the Slippery Slope

Computing slope

Combining slope and intercept

Creating the slope-intercept form

Graphing with slope-intercept

Making Parallel and Perpendicular Lines Toe the Line

Criss-Crossing Lines

Turning the Curve with Curves

Going around in circles with a circular graph

Putting up with parabolas

Chapter 14: Ten Warning Signs of Algebraic Pitfalls

Including the Middle Term

Keeping Distributions Fair

Creating Two Fractions from One

Restructuring Radicals

Including the Negative (Or Not)

Making Exponents Fractional

Keeping Bases the Same

Powering Up a Power

Making Reasonable Reductions

Catching All the Negative Exponents

Algebra I Essentials For Dummies®

Mary Jane Sterling

Algebra I Essentials For Dummies®

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Copyright © 2010 by Wiley Publishing, Inc., Indianapolis, Indiana

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Library of Congress Control Number: 2010922563

ISBN: 978-0-470-61834-9

Manufactured in the United States of America

10 9 8 7 6 5 4 3 2 1

About the Author

Mary Jane Sterling has been an educator since graduating from college. Teaching at the junior high, high school, and college levels, she has had the full span of experiences and opportunities to determine how best to explain how mathematics works. She has been teaching at Bradley University in Peoria, Illinois, for the past 30 years. She is also the author of Algebra I For Dummies, 2nd Edition; Algebra II For Dummies; Trigonometry For Dummies; Math Word Problems For Dummies; Business Math For Dummies; and Linear Algebra For Dummies.

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Introduction

One of the most commonly asked questions in a mathematics classroom is, “What will I ever use this for?” Some teachers can give a good, convincing answer. Others hem and haw and stare at the floor. My favorite answer is, “Algebra gives you power.” Algebra gives you the power to move on to bigger and better things in mathematics. Algebra gives you the power of knowing that you know something that your neighbor doesn’t know. Algebra gives you the power to be able to help someone else with an algebra task or to explain to your child these logical mathematical processes.

Algebra is a system of symbols and rules that is universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end. What power!

About This Book

What could be more essential than Algebra I Essentials For Dummies? In this book, you find the main points, the nitty-gritty (made spiffy-jiffy), and a format that lets you find what you need about an algebraic topic as you need it. I keep the same type of organization that you find in Algebra I For Dummies, 2nd Edition, but I keep the details neat, sweet, and don’t repeat. The fundamentals are here for your quick reference or, if you prefer, a more thorough perusal. The choice is yours.

This book isn’t like a mystery novel; you don’t have to read it from beginning to end. I divide the book into some general topics — from the beginning vocabulary and processes and operations to the important tool of factoring to equations and applications. So you can dip into the book wherever you want, to find the information you need.

Conventions Used in This Book

I don’t use many conventions in this book, but you should be aware of the following:

When I introduce a new term, I put that term in italics and define it nearby (often in parentheses).

I express numbers or numerals either with the actual symbol, such as 8, or the written-out word: eight. Operations, such as + are either shown as this symbol or written as plus. The choice of expression all depends on the situation — and on making it perfectly clear for you.

Foolish Assumptions

I don’t assume that you’re as crazy about math as I am — and you may be even more excited about it than I am! I do assume, though, that you have a mission here — to brush up on your skills, improve your mind, or just have some fun. I also assume that you have some experience with algebra — full exposure for a year or so, maybe a class you took a long time ago, or even just some preliminary concepts.

You may be delving into the world of algebra again to refresh those long-ago lessons. Is your kid coming home with assignments that are beyond your memory? Are you finally going to take that calculus class that you’ve been putting off? Never fear. Help is here!

Icons Used in This Book

The little drawings in the margin of the book are there to draw your attention to specific text. Here are the icons I use in this book:

To make everything work out right, you have to follow the basic rules of algebra (or mathematics in general). You can’t change or ignore them and arrive at the right answer. Whenever I give you an algebra rule, I mark it with this icon.

An explanation of an algebraic process is fine, but an example of how the process works is even better. When you see the Example icon, you’ll find one or more problems using the topic at hand.

Paragraphs marked with the Remember icon help clarify a symbol or process. I may discuss the topic in another section of the book, or I may just remind you of a basic algebra rule that I discuss earlier.

The Tip icon isn’t life-or-death important, but it generally can help make your life easier — at least your life in algebra.

The Warning icon alerts you to something that can be particularly tricky. Errors crop up frequently when working with the processes or topics next to this icon, so I call special attention to the situation so you won’t fall into the trap.

Where to Go from Here

If you want to refresh your basic skills or boost your confidence, start with the fractions, decimals, and signed numbers in the first chapter. Other essential concepts are the exponents in Chapter 2 and order of operations in Chapter 3. If you’re ready for some factoring practice and need to pinpoint which method to use with what, go to Chapters 4 and 5. Chapters 6, 7, and 8 are for you if you’re ready to solve equations; you can find just about any type you’re ready to attack. Chapters 9 and 10 get you back into inequalities and absolute value. And Chapters 11 and 12 are where the good stuff is: applications — things you can do with all those good solutions. I finish with some graphing in Chapter 13 and then give you a list of pitfalls to avoid in Chapter 14.

Studying algebra can give you some logical exercises. As you get older, the more you exercise your brain cells, the more alert and “with it” you remain. “Use it or lose it” means a lot in terms of the brain. What a good place to use it, right here!

The best why for studying algebra is just that it’s beautiful. Yes, you read that right. Algebra is poetry, deep meaning, and artistic expression. Just look, and you’ll find it. Also, don’t forget that it gives you power.

Welcome to algebra! Enjoy the adventure!

Chapter 1

Setting the Scene for Actions in Algebra

In This Chapter

Enumerating the various number systems

Becoming acquainted with “algebra-speak”

Operating on and simplifying expressions

Converting fractions to decimals and decimals to fractions

What exactly is algebra? What is it really used for? In a nutshell, algebra is a systematic study of numbers and their relationships, using specific rules. You use variables (letters representing numbers), and formulas or equations involving those variables, to solve problems. The problems may be practical applications, or they may be puzzles for the pure pleasure of solving them!

In this chapter, I acquaint you with the various number systems. You’ve seen the numbers before, but I give you some specific names used to refer to them properly. I also tell you how I describe the different processes performed in algebra — I want to use the correct language, so I give you the vocabulary. And, finally, I get very specific about fractions and decimals and show you how to move from one type to the other with ease.