[Dummies 01] • Algebra I Workbook For Dummies · 2nd Edtion by Sterling, Mary Jane -- Read -- Imperial Library of Trantor

Index

Introduction

About This Book Conventions Used in This Book Foolish Assumptions How This Book Is Organized

Part I: Getting Down to the Nitty-Gritty on Basic Operations Part II: Changing the Format of Expressions Part III: Seek and Ye Shall Find. . .Solutions Part IV: Solving Story Problems and Sketching Graphs Part V: The Part of Tens

Icons Used in This Book Where to Go from Here

Part I: Getting Down to the Nitty-Gritty on Basic Operations

Chapter 1: Deciphering Signs in Numbers

Assigning Numbers Their Place Reading and Writing Absolute Value Adding Signed Numbers Making a Difference with Signed Numbers Multiplying Signed Numbers Dividing Signed Numbers Answers to Problems on Signed Numbers

Chapter 2: Incorporating Algebraic Properties

Getting a Grip on Grouping Symbols Distributing the Wealth Making Associations Work Computing by Commuting Answers to Problems on Algebraic Properties

Chapter 3: Making Fractions and Decimals Behave

Converting Improper and Mixed Fractions Finding Fraction Equivalences Making Proportional Statements Finding Common Denominators Adding and Subtracting Fractions Multiplying and Dividing Fractions Simplifying Complex Fractions Changing Fractions to Decimals and Vice Versa Performing Operations with Decimals Answers to Problems on Fractions

Chapter 4: Exploring Exponents

Multiplying and Dividing Exponentials Raising Powers to Powers Using Negative Exponents Writing Numbers with Scientific Notation Answers to Problems on Discovering Exponents

Chapter 5: Taming Rampaging Radicals

Simplifying Radical Expressions Rationalizing Fractions Arranging Radicals as Exponential Terms Using Fractional Exponents Simplifying Expressions with Exponents Estimating Answers Answers to Problems on Radicals

Chapter 6: Simplifying Algebraic Expressions

Adding and Subtracting Like Terms Multiplying and Dividing Algebraically Incorporating Order of Operations Evaluating Expressions Answers to Problems on Algebraic Expressions

Part II: Changing the Format of Expressions

Chapter 7: Specializing in Multiplication Matters

Distributing One Factor over Many Curses, FOILed Again — Or Not Squaring Binomials Multiplying the Sum and Difference of the Same Two Terms Cubing Binomials Creating the Sum and Difference of Cubes Raising Binomials to Higher Powers Answers to Problems on Multiplying Expressions

Chapter 8: 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 Answers to Problems on Division

Chapter 9: Figuring on Factoring

Pouring Over Prime Factorizations Factoring Out the Greatest Common Factor Reducing Algebraic Fractions Answers to Problems on Factoring Expressions

Chapter 10: Taking the Bite Out of Binomial Factoring

Factoring the Difference of Squares Factoring Differences and Sums of Cubes Making Factoring a Multiple Mission Answers to Problems on Factoring

Chapter 11: Factoring Trinomials and Special Polynomials

Focusing First on the Greatest Common Factor (GCF) “Un”wrapping the FOIL Factoring Quadratic-Like Trinomials Factoring Trinomials Using More Than One Method Factoring by Grouping Putting All the Factoring Together Answers to Problems on Factoring Trinomials and Other Expressions

Part III: Seek and Ye Shall Find. . .Solutions

Chapter 12: Lining Up Linear Equations

Using the Addition/Subtraction Property Using the Multiplication/Division Property Putting Several Operations Together Solving Linear Equations with Grouping Symbols Working It Out with Fractions Solving Proportions Answers to Problems on Solving Linear Equations

Chapter 13: Muscling Up to Quadratic Equations

Using the Square Root Rule Solving by Factoring Using the Quadratic Formula Completing the Square Dealing with Impossible Answers Answers to Problems on Solving Quadratic Equations

Chapter 14: Yielding to Higher Powers

Determining How Many Possible Roots Applying the Rational Root Theorem Using the Factor/Root Theorem Solving By Factoring Solving Powers That Are Quadratic-Like Answers to Problems on Solving Higher Power Equations

Chapter 15: Reeling in Radical and Absolute Value Equations

Squaring Both Sides to Solve Radical Equations Doubling the Fun with Radical Equations Solving Absolute Value Equations Answers to Problems on Radical and Absolute Value Equations

Chapter 16: Getting Even with Inequalities

Using the Rules to Work on Inequality Statements Rewriting Inequalities by Using Interval Notation Solving Linear Inequalities Solving Quadratic Inequalities Dealing with Polynomial and Rational Inequalities Solving Absolute Value Inequalities Solving Complex Inequalities Answers to Problems on Working with Inequalities

Part IV: Solving Story Problems and Sketching Graphs

Chapter 17: Facing Up to Formulas

Working with Formulas Deciphering Perimeter, Area, and Volume

Using perimeter formulas to get around Squaring off with area formulas Working with volume formulas

Getting Interested in Using Percent Answers to Problems on Using Formulas

Chapter 18: Making Formulas Work in Basic Story Problems

Applying the Pythagorean Theorem Using Geometry to Solve Story Problems Putting Distance, Rate, and Time in a Formula

Examining the distance-rate-time formula Going the distance with story problems

Answers to Making Formulas Work in Basic Story Problems

Chapter 19: Relating Values in Story Problems

Tackling Age Problems Tackling Consecutive Integer Problems Working Together on Work Problems Answers to Relating Values in Story Problems

Chapter 20: Measuring Up with Quality and Quantity Story Problems

Achieving the Right Blend with Mixtures Problems Concocting the Correct Solution One Hundred Percent of the Time Dealing with Money Problems Answers to Problems on Measuring Up with Quality and Quantity

Chapter 21: Getting a Handle on Graphing

Thickening the Plot with Points Sectioning Off by Quadrants Using Points to Lay Out Lines Graphing Lines with Intercepts Computing Slopes of Lines Graphing with the Slope-Intercept Form Changing to the Slope-Intercept Form Writing Equations of Lines Picking on Parallel and Perpendicular Lines Finding Distances between Points Finding the Intersections of Lines Graphing Parabolas and Circles Graphing with Transformations Answers to Problems on Graphing

Part V: The Part of Tens

Chapter 22: Ten Common Errors That Get Noticed

Squaring a Negative or Negative of a Square Squaring a Binomial Operating on Radicals Distributing a Negative Throughout Fracturing Fractions Raising a Power to a Power Making Negative Exponents Flip Making Sense of Reversing the Sense Using the Slope Formula Correctly Writing Several Fractions as One

Chapter 23: Ten Quick Tips to Make Algebra a Breeze

Flipping Proportions Multiplying Through to Get Rid of Fractions Zeroing In on Fractions Finding a Common Denominator Dividing by 3 or 9 Dividing by 2, 4, or 8 Commuting Back and Forth Factoring Quadratics Making Radicals Less Rad, Baby Applying Acronyms

Cheat Sheet

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