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Herausgeber: John Wiley & Sons
Kategorie: Wissenschaft und neue Technologien
Sprache: Englisch
Veröffentlichungsjahr: 2021

Beschreibung

Solve for 'X' with this practical and easy guide to everything algebra A solid understanding of algebra is the key to unlocking other areas of math and science that rely on the concepts and skills that happen in a foundational Algebra class. Algebra I All-In-One For Dummies is the key! With it, you'll get everything you need to solve the mystery of Algebra I. This book proves that algebra is for everyone with straightforward, unit-based instruction, hundreds of examples and practice problems, and two quizzes for every chapter - one in the book and another (totally different!) online. From graph and word problems to the FOIL method and common algebra terminology, Algebra I All-In-One For Dummies walks you step-by-step through ALL the concepts you need to know to slay your Algebra I class. In this handy guide, you'll also: * Receive instruction and tips on how to handle basic and intermediate algebraic tasks such as factoring and equation simplification * Banish math anxiety forever by developing an intuitive understanding of how algebra works * Get a handle on graphing problems and functions, as well as inequalities and word problems Algebra I All-In-One For Dummies is a must-read for Algebra students looking for an everything-in-one-book supplement to their coursework, as well as anyone hoping to brush up on their math before tackling a related subject, such as physics, chemistry, or a more advanced math topic.

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Algebra I All-in-One For Dummies®

Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com

Published simultaneously in Canada

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Library of Congress Control Number: 2021947882

ISBN 978-1-119-84304-7 (pbk); ISBN 978-1-119-84305-4 (ebk); ISBN 978-1-119-84306-1 (ebk)

Algebra I All-In-One For Dummies®

To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Algebra I All-In-One For Dummies Cheat Sheet” in the Search box.

Cover

Title Page

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Book 1: Starting Out with Numbers and Properties

Chapter 1: Assembling Your Tools: Number Systems

Identifying Numbers by Name

Placing Numbers on the Number Line

Speaking in Algebra

Taking Aim at Algebra-Speak

Practice Questions Answers and Explanations

Whaddya Know? Chapter 1 Quiz

Answers to Chapter 1 Quiz

Chapter 2: Deciphering Signs in Expressions

Assigning Numbers Their Place

Going in for Operations

Tackling the Basic Binary Operations

Working with Nothing: Zero and Signed Numbers

Practice Questions Answers and Explanations

Whaddya Know? Chapter 2 Quiz

Answers to Chapter 2 Quiz

Chapter 3: Incorporating Algebraic Properties

Getting a Grip on Grouping Symbols

Spreading, Grouping, and Changing the Order

Relating Inverses and Identities

Working with Factorial

Applying the Greatest Integer Function

Practice Question Answers and Explanations

Whaddya Know? Chapter 3 Quiz

Answers to Chapter 3 Quiz

Chapter 4: Coordinating Fractions and Decimals

Converting Improper Fractions and Mixed Numbers

Finding Fraction Equivalences

Making Proportional Statements

Finding Common Denominators

Applying Fractional Operations

Simplifying Complex Fractions

Performing Operations with Decimals

Changing Fractions to Decimals and Vice Versa

Practice Question Answers and Explanations

Whaddya Know? Chapter 4 Quiz

Answers to Chapter 4 Quiz

Book 2: Operating on Operations

Chapter 5: Taming Rampaging Radicals

Simplifying Radical Terms

Working through Radical Expressions

Rationalizing Fractions

Managing Radicals as Exponential Terms

Estimating Answers

Practice Questions Answers and Explanations

Whaddya Know? Chapter 5 Quiz

Answers to Chapter 5 Quiz

Chapter 6: Exploring Exponents

Powering up with Exponential Notation

Using Negative Exponents

Multiplying and Dividing Exponentials

Raising Powers to Powers

Testing the Power of Zero

Writing Numbers with Scientific Notation

Practice Questions Answers and Explanations

Whaddya Know? Chapter 6 Quiz

Answers to Chapter 6 Quiz

Book 3: Making Things Simple by Simplifying

Chapter 7: Simplifying Algebraic Expressions

Addressing the Order of Operations

Adding and Subtracting Like Terms

Multiplying and Dividing Algebraically

Gathering Terms with Grouping Symbols

Evaluating Expressions

Checking Your Answers

Practice Questions Answers and Explanations

Whaddya Know? Chapter 7 Quiz

Answers to Chapter 7 Quiz

Chapter 8: Working with Numbers in Their Prime

Beginning with the Basics

Composing Composite Numbers

Writing Prime Factorizations

Making Use of a Prime Factor

Practice Questions Answers and Explanations

Whaddya Know? Chapter 8 Quiz

Answers to Chapter 8 Quiz

Chapter 9: Specializing in Multiplication Matters

Distributing One Factor Over Many

Distributing Signs

Mixing It up with Numbers and Variables

Distributing More Than One Term

Curses, Foiled Again — Or Not

Squaring Binomials

Multiplying the Sum and Difference of the Same Two Terms

Powering Up Binomials

Creating the Sum and Difference of Cubes

Multiplying Conjugates

Practice Questions Answers and Explanations

Whaddya Know? Chapter 9 Quiz

Answers to Chapter 9 Quiz

Chapter 10: Dividing the Long Way to Simplify Algebraic Expressions

Dividing by a Monomial

Dividing by a Binomial

Dividing by Polynomials with More Terms

Simplifying Division Synthetically

Practice Questions Answers and Explanations

Whaddya Know? Chapter 10 Quiz

Answers to Chapter 10 Quiz

Book 4: Factoring

Chapter 11: Figuring on Factoring

Factoring out the Greatest Common Factor

Using the Box Method

Changing Factoring into a Division Problem

Reducing Algebraic Fractions

Practice Questions Answers and Explanations

Whaddya Know? Chapter 11 Quiz

Answers to Chapter 11 Quiz

Chapter 12: Taking the Bite out of Binomial Factoring

Reining in Big and Tiny Numbers

Factoring the Difference of Squares

Factoring Differences and Sums of Cubes

Making Factoring a Multiple Mission

Practice Questions Answers and Explanations

Whaddya Know? Chapter 12 Quiz

Answers to Chapter 12 Quiz

Chapter 13: Factoring Trinomials and Special Polynomials

Recognizing the Standard Quadratic Expression

Focusing First on the Greatest Common Factor

Factoring Quadratic-Like Trinomials

Factoring Trinomials Using More Than One Method

Factoring by Grouping

Putting All the Factoring Together and Making Factoring Choices

Incorporating the Remainder Theorem

Practice Questions Answers and Explanations

Whaddya Know? Chapter 13 Quiz

Answers to Chapter 13 Quiz

Book 5: Solving Linear and Polynomial Equations

Chapter 14: Establishing Ground Rules for Solving Equations

Creating the Correct Setup for Solving Equations

Keeping Equations Balanced

Solving with Reciprocals

Making a List and Checking It Twice

Practice Problems Answers and Explanations

Whaddya Know? Chapter 14 Quiz

Answers to Chapter 14 Quiz

Chapter 15: Lining Up Linear Equations

Playing by the Rules

Using the Addition/Subtraction Property

Using the Multiplication/Division Property

Putting Several Operations Together

Solving Linear Equations with Grouping Symbols

Working with Proportions

Solving for Variables in Formulas

Practice Questions Answers and Explanations

Whaddya Know? Chapter 15 Quiz

Answers to Chapter 15 Quiz

Chapter 16: Muscling Up to Quadratic Equations

Using the Square-Root Rule

Factoring for a Solution

Solving Quadratics with Three Terms

Using the Quadratic Formula

Completing the Square

Imagining the Worst with Imaginary Numbers

Practice Problems Answers and Explanations

Whaddya Know? Chapter 16 Quiz

Answers to Chapter 16 Quiz

Book 6: Dealing with Non-Polynomial Equations and Inequalities

Chapter 17: Yielding to Higher Powers

Queuing Up to Cubic Equations

Determining How Many Possible Roots

Applying the Rational Root Theorem

Using the Factor/Root Theorem

Solving by Factoring

Solving Powers That Are Quadratic-Like

Solving Synthetically

Practice Questions Answers and Explanations

Whaddya Know? Chapter 17 Quiz

Answers to Chapter 17 Quiz

Chapter 18: Reeling in Radical and Absolute Value Equations

Raising Both Sides to Solve Radical Equations

Doubling the Fun with Radical Equations

Solving Absolute Value Equations

Checking for Absolute Value Extraneous Roots

Practice Questions Answers and Explanations

Whaddya Know? Chapter 18 Quiz

Answers to Chapter 18 Quiz

Chapter 19: Getting Even with Inequalities

Defining the Inequality Notation

Using the Rules to Work on Inequality Statements

Rewriting Inequalities Using Interval Notation

Solving Linear Inequalities

Solving Quadratic Inequalities

Dealing with Polynomial and Rational Inequalities

Solving Absolute-Value Inequalities

Solving Complex Inequalities

Practice Questions Answers and Explanations

Whaddya Know? Chapter 19 Quiz

Answers to Chapter 19 Quiz

Book 7: Evaluating Formulas and Story Problems

Chapter 20: Facing Up to Formulas

Working with Formulas

Measuring Up

Deciphering Perimeter, Area, and Volume

Getting Interested in Using Percent

Working out the Combinations and Permutations

Practice Questions Answers and Explanations

Whaddya Know? Chapter 20 Quiz

Answers to Chapter 20 Quiz

Chapter 21: Making Formulas Work in Basic Story Problems

Setting Up to Solve Story Problems

Applying the Pythagorean Theorem

Using Geometry to Solve Story Problems

Working around Perimeter, Area, and Volume

Going ’Round in Circles

Putting Distance, Rate, and Time in a Formula

Counting on Interest and Percent

Practice Questions Answers and Explanations

Whaddya Know? Chapter 21 Quiz

Answers to Chapter 21 Quiz

Chapter 22: Relating Values in Story Problems

Tackling Age Problems

Tackling Consecutive Integer Problems

Working Together on Work Problems

Throwing an Object into the Air

Practice Questions Answers and Explanations

Whaddya Know? Chapter 22 Quiz

Answers to Chapter 22 Quiz

Chapter 23: Measuring Up with Quality and Quantity Story Problems

Achieving the Right Blend with Mixture Problems

Concocting the Correct Solution 100% of the Time

Dealing with Money Problems

Practice Questions Answers and Explanations

Whaddya Know? Chapter 23 Quiz

Answers to Chapter 23 Quiz

Book 8: Getting a Grip on Graphing

Chapter 24: Getting a Handle on Graphing

Thickening the Plot with Points

Graphing Lines

Computing Slopes of Lines

Writing Equations of Lines

Picking on Parallel and Perpendicular Lines

Finding Distances between Points

Finding Midpoints of Segments

Practice Questions Answers and Explanations

Whaddya Know? Chapter 24 Quiz

Answers to Chapter 24 Quiz

Chapter 25: Extending the Graphing Horizon

Finding the Intersections of Lines

Graphing Parabolas and Circles

Curling Up with Parabolas

Plotting and Plugging in Polynomial Graphs

Investigating Graphs of Inequality Functions

Taking on Absolute-Value Function Graphs

Graphing with Transformations

Practice Questions Answers and Explanations

Whaddya Know? Chapter 25 Quiz

Answers to Chapter 25 Quiz

Chapter 26: Coordinating Systems of Equations and Graphing

Defining Solutions of Systems of Equations

Solving Systems of Linear Equations

Solving Systems Involving Non-Linear Equations

Taking on Systems of Three Linear Equations

Practice Problems Answers and Explanations

Whaddya Know? Chapter 26 Quiz

Answers to Chapter 26 Quiz

Index

About the Author

Connect with Dummies

End User License Agreement

List of Tables

Chapter 2

TABLE 2-1 Comparing Positive and Negative Numbers

Chapter 8

TABLE 8-1 Rules of Divisibility

Chapter 24

TABLE 24-1 Quadrants

TABLE 24-2 Axes

List of Illustrations

Chapter 1

FIGURE 1-1: A number line from 0 to 5 with half-unit increments.

FIGURE 1-2: A number line from –10 to 10 with one-unit increments.

Chapter 2

FIGURE 2-1: A number line.

FIGURE 2-2: Another number line.

FIGURE 2-3: Positive and negative numbers on a number line.

Chapter 8

FIGURE 8-1: Finding the prime factors using a tree.

Chapter 9

FIGURE 9-1: Pascal’s Triangle can help you find powers of binomials.

Chapter 19

FIGURE 19-1: The graphs of greater-than and less-than-or-equal-to.

FIGURE 19-2: A graph of the inequality.

FIGURE 19-3: A graph of the interval.

FIGURE 19-4: A graph of the inequality.

FIGURE 19-5: A graph of the interval.

FIGURE 19-6: A graph of an inequality.

FIGURE 19-7: A graph of an inequality.

FIGURE 19-8: A number line helps you find the signs of the factors and their pr...

FIGURE 19-9: Filling in the signs between the critical numbers.

FIGURE 19-10: The sign changes at each critical number in this problem.

FIGURE 19-11: The sign of the quotient is shown.

FIGURE 19-12: The 1 and –1 are included in the solution.

Chapter 20

FIGURE 20-1: Triangulating the “right” way.

Chapter 21

FIGURE 21-1: Fencing three sides of the field.

FIGURE 21-2: Volume is determined by multiplying length, width, and height.

FIGURE 21-3: Some people believe pyramids have preservation powers.

FIGURE 21-4: Basketballs, globes, planets, and sometimes oranges are spheres.

FIGURE 21-5: The diameter is the longest distance across a circle.

FIGURE 21-6: The corral along a river.

FIGURE 21-7: ABC is similar to DEF.

FIGURE 21-8: Trapezoidal room.

Chapter 23

FIGURE 23-1: Visualizing containers can help with mixture problems.

FIGURE 23-2: Assigning prices and pounds.

Chapter 24

FIGURE 24-1: Identifying quadrants.

FIGURE 24-2: Graphing

FIGURE 24-3: Horizontal lines are parallel to the x-axis.

FIGURE 24-4: When all the x-coordinates are the same, you get a vertical line.

FIGURE 24-5: Pick a line — see its slope.

FIGURE 24-6: Horizontal lines have a 0 slope. Vertical lines have an undefined ...

FIGURE 24-7: Parallel lines are like railroad tracks; perpendicular lines meet ...

Chapter 25

FIGURE 25-1: The intersection of two lines at a point (1,–2).

FIGURE 25-2: The simplest parabola.

FIGURE 25-3: A steeper parabola and a flatter parabola.

FIGURE 25-4: Parabolas spooning.

FIGURE 25-5: Pretty parabolas all in a row.

FIGURE 25-6: The circle has a radius of 5.

FIGURE 25-7: The x-intercepts and the graph of the polynomial.

FIGURE 25-8: The intercepts help with the graph of the polynomial.

FIGURE 25-9: Use a dashed line when the line is not included.

FIGURE 25-10: The origin is included in the solution.

FIGURE 25-11: The negative values are flipped over the x-axis.

FIGURE 25-12: The 2 multiplier steepens the graph.

FIGURE 25-13: Parabolas galore.

Guide

Cover

Title Page

Table of Contents

Begin Reading

Index

About the Author

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Introduction

“ What is algebra?” “Is it really that important in the study of other math courses?” “Where did it come from?” And my favorite question from students: “What do I need this for?”

Algebra is really the basis of most courses that you take in high school and college. You can’t do anything in calculus without a good algebra background. And there’s lots of algebra in geometry. You even need algebra in computer science! Algebra was created, modified, and continues to be tweaked so that ideas and procedures can be shared by everyone. With all people speaking the same “language,” there are fewer misinterpretations.

Algebra, or al-jabr in Arabic, means “a reunion of broken pieces.” How appropriate!

About This Book

This book covers just about everything you’d ever want to know about basic algebra. And it provides opportunities for further discoveries. You’ll find explanations, examples, practice opportunities, and problems to test your comprehension. This book starts with basic operations and terminology, gives you information on simplifying and organizing expressions, runs through equation-solving, introduces applications, and goes visual with the graphing. When finished, you should:

Be familiar with notation and terminology.

Have confidence in finding the correct answer.

Look forward to more challenges with Algebra II and other courses.

Each new topic provides:

Example problems with answers and solutions.

Practice problems with answers and solutions.

Each chapter provides:

A test with problems representing the topics covered.

Solutions to the test problems.

Online quizzes are also available for even more practice and confidence-building.

This book also has a few conventions to keep in mind:

New terms introduced in a chapter, as well as variables, are in

italics.

Keywords in lists and numbered steps are in

boldface.

Any websites appear in

monofont

The final answers to problems appear in

bold.

Then the explanation follows.

Foolish Assumptions

You are reading this book to learn more about algebra, so I'm assuming that you have some of the other basic math skills coming in: familiarity with fractions and their operations, comfort with handling decimals and the operations involved, some experience with integers (signed whole numbers) and how they operate, and some graphing knowledge — how to place points on a graphing plane. If you don’t have as much knowledge as you’d like related to some items mentioned, you might want to refer to some resources such as Basic Math & Pre-Algebra For Dummies or Pre-Algebra Essentials For Dummies.

I am also assuming that you’re as excited about mathematics as I am. Oh, okay, you don’t have to be that excited. But you’re interested and eager and anxious to increase your mathematical abilities. That’s the main thing you need.

Icons Used in This Book

You’ll see the following five icons throughout the book:

Each example is an algebra question based on the discussion and explanation, followed by a solution. Work through these examples, and then refer to them to help you solve the practice problems that follow them as well as the quiz questions at the end of the chapter.

This icon points out important information that you need to focus on. Make sure you understand this information fully before moving on. You can skim through these icons when reading a chapter to make sure you remember the highlights.

Tips are hints that can help speed you along when answering a question. See whether you find them useful when working on practice problems.

This icon flags common mistakes that students make if they’re not careful. Take note and proceed with caution!

When you see this icon, it’s time to put on your thinking cap and work out a few practice problems on your own. The answers and detailed solutions are available so you can feel confident about your progress.

Beyond the Book

In addition to what you’re reading right now, this book comes with a Cheat Sheet that provides quick access to some formulas and rules and processes that are frequently used. To get this Cheat Sheet, simply go to www.dummies.com and type Algebra I All In One For Dummies Cheat Sheet in the Search box.

You’ll also have access to online quizzes related to each chapter. These quizzes provide a whole new set of problems for practice and confidence-building. To access the quizzes, follow these simple steps:

Go to

www.dummies.com/go/getaccess

Select your product from the drop-down list on that page.

Follow the prompts to validate your product, and then check your email for a confirmation message that includes your PIN and instructions for logging in.

If you do not receive this email within two hours, please check your spam folder before contacting us through our Technical Support website at http://support.wiley.com or by phone at 877-762-2974.

Now you’re ready to go! You can come back to the practice material as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time.

Your registration is good for one year from the day you activate your PIN.

Where to Go from Here

This book is organized so that you can safely move from whichever chapter you choose to start with and in whatever order you like. You can strengthen skills you feel less confident in or work on those that need some attention.

If you haven’t worked on any algebra recently, I’d recommend that you start out with Chapter 1 and some other chapters in the first unit. It’s important to know the vocabulary and basic notation so you understand what is being presented in later chapters.

If you’re all set with the basic operations, then a good place to go is Chapter 11, where you find out about factoring different types of expressions. Factoring makes it possible to simplify expressions and solve equations.

When you’re ready for the “What do I need this for?” question, go to Chapter 20 or Chapter 21, where you see some of the many types of applications that use algebraic expressions and solutions.

There are other resources, such as Basic Math & Pre-Algebra For Dummies and Pre-Algebra Essentials For Dummies (John Wiley & Sons, Inc.), if you think you need more background. And, of course, when you’ve finished here and are ready for the next challenge, be sure to check out Algebra II For Dummies and Pre-Calculus For Dummies. And that’s just the beginning!

Book 1