The complete idiot's guide to algebra

From the author of the highly successful The Complete Idiot's Guide to Calculus comes the perfect book for high school and college students. Following a standard algebra curriculum, it will teach students the basics so that they can make sense of their textbooks and get through algebra class with flying colors. Cover Page 1 Title Page 5 Copyright Page 6 Contents at a Glance 7 Contents 9 Foreword 15 Introduction 17 Acknowledgments 20 Part One: A Final Farewell To Numbers 23 Chapter One:Getting Cozy With Numbers 25 Classifying Number Sets 26 Familiar Classifications 26 Intensely Mathematical Classifications 27 Persnickety Signs 28 Addition and Subtraction 29 Multiplication and Division 30 Opposites and Absolute Values 31 Come Together with Grouping Symbols 31 Important Assumptions 33 Associative Property 34 Commutative Property 35 Identity Properties 36 Inverse Properties 36 Chapter Two: Making Friends with Fractions 39 What Is a Fraction? 40 Ways to Write Fractions 41 Simplifying Fractions 42 Locating the Least Common Denominator 43 Operations with Fractions 46 Adding and Subtracting Fractions 46 Multiplying Fractions 47 Dividing Fractions 48 Chapter Three: Encountering Expressions 51 Introducing Variables 52 Translating Words into Math 53 Behold the Power of Exponents 54 Big Things Come in Small Packages 54 Exponential Rules 55 Living Large with Scientific Notation 57 Dastardly Distribution 58 Get Your Operations in Order 59 Evaluating Expressions 61 Part Two: Equations and Inequalities 63 Chapter Four: Solving Basic Equations 65 Maintaining a Balance 66 Adding and Subtracting 67 Multiplying and Dividing 68 Equations with Multiple Steps 69 Absolute Value Equations 73 Equations with Multiple Variables 75 Chapter Five: Graphing Linear Equations 77 Climb Aboard the Coordinate Plane 78 Sketching Line Graphs 82 Graphing with Tables 83 Graphing with Intercepts 84 It’s a Slippery Slope 86 Calculating Slope of a Line 86 Interpreting Slope Values 88 Kinky Absolute Value Graphs 89 Chapter Six: Cooking Up Linear Equations 93 Point-Slope Form 94 Slope-Intercept Form 95 Graphing with Slope-Intercept Form 96 Standard Form of a Line 98 Tricky Linear Equations 100 How to Get from Point A to Point B 101 Parallel and Perpendicular Lines 103 Chapter Seven: Linear Inequalities 105 Equations vs. Inequalities 106 Solving Basic Inequalities 107 The Inequality Mood Swing 107 Graphing Solutions 108 Compound Inequalities 111 Solving Compound Inequalities 111 Graphing Compound Inequalities 112 Inequalities with Absolute Values 113 Inequalities Involving “Less Than” 113 Inequalities Involving “Greater Than” 114 Graphing Linear Inequalities 116 Part Three: Systems of Equations and Matrix Algebra 119 Chapter Eight: Systems of Linear Equations and Inequalities 121 Solving a System by Graphing 122 The Substitution Method 124 The Elimination Method 126 Systems That Are Out of Whack 127 Systems of Inequalities 129 Chapter Nine :The Basics of the Matrix 133 What Is a Matrix? 134 Matrix Operations 134 Multiplying by a Scalar 135 Adding and Subtracting Matrices 135 Multiplying Matrices 137 When Can You Multiply Matrices? 137 Use Your Fingers to Calculate Matrix Products 138 Determining Determinants 140 2 × 2 Determinants 141 3 × 3 Determinants 142 Cracking Cramer’s Rule 143 Part Four: Now You’re Playing with (Exponential) Power! 147 Chapter Ten: Introducing Polynomials 149 Classifying Polynomials 150 Adding and Subtracting Polynomials 152 Multiplying Polynomials 153 Products of Monomials 153 Binomials, Trinomials, and Beyond 154 Dividing Polynomials 156 Long Division 156 Synthetic Division 158 Chapter Eleven: Factoring Polynomials 163 Greatest Common Factors 164 Factoring by Grouping 165 Special Factoring Patterns 166 Factoring Trinomials Using Their Coefficients 169 Factoring with the Bomb Method 171 Chapter Twelve: Wrestling with Radicals 173 Introducing the Radical Sign 174 Simplifying Radical Expressions 174 Unleashing Radical Powers 176 Radical Operations 177 Addition and Subtraction 177 Multiplication 178 Division 179 Solving Radical Equations 181 When Things Get Complex 182 There’s Something in Your i 183 Simplifying Complex Expressions 184 Chapter Thirteen: Quadratic Equations and Inequalities 187 Solving Quadratics by Factoring 188 Completing the Square 190 Solving Basic Exponential Equations 191 Bugging Out with Squares 192 The Quadratic Formula 194 All Signs Point to the Discriminant 195 Solving One-Variable Quadratic Inequalities 197 Chapter Fourteen: Solving High-Powered Equations 201 There’s No Escaping Your Roots! 202 Finding Factors 203 Baby Steps to Solving Cubic Equations 204 Calculating Rational Roots 205 What About Imaginary and Irrational Roots? 208 Part Five: The Function Junction 211 Chapter Fifteen: Introducing the Function 213 Getting to Know Your Relations 213 Operating on Functions 216 Composition of Functions 218 Inverse Functions 219 Defining Inverse Functions 220 Calculating Inverse Functions 221 Bet You Can’t Solve Just One: Piecewise-Defined Functions 222 Chapter Sixteen: Graphing Functions 225 Second Verse, Same as the First 226 Two Important Line Tests 228 The Vertical Line Test 228 The Horizontal Line Test 229 Determining Domain and Range 230 Important Function Graphs 233 Graphing Function Transformations 235 Making Functions Flip Out 235 Stretching Functions 236 Moving Functions Around 237 Multiple Transformations 238 Part Six: Please, Be Rational! 241 Chapter Seventeen: Rational Expressions 243 Simplifying Rational Expressions 244 Combining Rational Expressions 246 Multiplying and Dividing Rationally 249 Encountering Complex Fractions 251 Chapter Eighteen: Rational Equations and Inequalities 255 Solving Rational Equations 255 Proportions and Cross Multiplying 258 Investigating Variation 259 Direct Variation 260 Indirect Variation 262 Solving Rational Inequalities 264 Part Seven: Wrapping Things Up 269 Chapter Nineteen: Whipping Word Problems 271 Interest Problems 272 Simple Interest 273 Compound Interest 274 Area and Volume Problems 276 Speed and Distance Problems 278 Mixture and Combination Problems 280 Chapter Twenty: A Plethora of Practice 283 Appendixes A: Solutions to “You’ve Got Problems” 297 Appendixes B: Glossary 317 Index 325 This book will not make advanced mathematicians out of students, but it does follow a standard algebra curriculum and will help students learn the basics of algebra so that they can make sense of their textbooks and get through algebra class with flying colours