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<p><b>Introduction</b><b> 1</b></p> <p>About This Book 1</p> <p>Foolish Assumptions 2</p> <p>Icons Used in This Book 2</p> <p>Beyond the Book 3</p> <p>Where to Go from Here 3</p> <p><b>Part 1: Setting the Foundation: The Nuts And Bolts of Pre-Calculus</b><b> 5</b></p> <p><b>Chapter 1: Preparing for Pre-Calculus</b><b> 7</b></p> <p>Reviewing Order of Operations: The Fun in Fundamentals 8</p> <p>Keeping Your Balance While Solving Equalities 10</p> <p>When Your Image Really Counts: Graphing Equalities and Inequalities 12</p> <p>Graphing with two points 12</p> <p>Graphing by using the slope-intercept form 13</p> <p>Graphing inequalities 14</p> <p>Using Graphs to Find Distance, Midpoint, and Slope 15</p> <p>Finding the distance 15</p> <p>Calculating the midpoint 16</p> <p>Discovering the slope 16</p> <p>Answers to Problems on Fundamentals 19</p> <p><b>Chapter 2: Real Numbers Come Clean</b><b> 25</b></p> <p>Solving Inequalities 25</p> <p>Expressing Inequality Solutions in Interval Notation 28</p> <p>Radicals and Exponents — Just Simplify! 30</p> <p>Getting Out of a Sticky Situation, or Rationalizing 33</p> <p>Answers to Problems on Real Numbers 35</p> <p><b>Chapter 3: Controlling Functions by Knowing Their Function</b><b> 39</b></p> <p>Using Both Faces of the Coin: Even and Odd 40</p> <p>Leaving the Nest: Transforming Parent Graphs 42</p> <p>Quadratic functions 42</p> <p>Square root functions 42</p> <p>Absolute value functions 43</p> <p>Cubic functions 43</p> <p>Cube root functions 44</p> <p>Steeper or flatter 44</p> <p>Translations 46</p> <p>Reflections 46</p> <p>Combinations of transformations 46</p> <p>Graphing Rational Functions 49</p> <p>Piecing Together Piecewise Functions 52</p> <p>Combining Functions 54</p> <p>Evaluating Composition of Functions 55</p> <p>Working Together: Domain and Range 57</p> <p>Unlocking the Inverse of a Function: Turning It Inside Out 59</p> <p>Answers to Problems on Functions 61</p> <p><b>Chapter 4: Searching for Roots</b><b> 75</b></p> <p>Factoring a Factorable Quadratic 75</p> <p>Solving a Quadratic Polynomial Equation 78</p> <p>Completing the square 78</p> <p>Quadratic formula 79</p> <p>Solving High-Order Polynomials 80</p> <p>Factoring by grouping 80</p> <p>Determining positive and negative roots: Descartes’ Rule of Signs 81</p> <p>Counting on imaginary roots 81</p> <p>Getting the rational roots 81</p> <p>Finding roots through synthetic division 82</p> <p>Using Roots to Create an Equation 84</p> <p>Graphing Polynomials 85</p> <p>Answers to Problems on Roots and Degrees 89</p> <p><b>Chapter 5: Exponential and Logarithmic Functions</b><b> 95</b></p> <p>Working with Exponential Functions 95</p> <p>Eagerly Engaging Edgy Logarithmic Solutions 98</p> <p>Making Exponents and Logs Work Together 101</p> <p>Using Exponents and Logs in Practical Applications 103</p> <p>Answers to Problems on Exponential and Logarithmic Functions 106</p> <p><b>Part 2: Trig is the Key: Basic Review, The Unit Circle, and Graphs</b><b> 113</b></p> <p><b>Chapter 6: Basic Trigonometry and the Unit Circle</b><b> 115</b></p> <p>Finding the Six Trigonometric Ratios 115</p> <p>Solving Word Problems with Right Triangles 118</p> <p>Unit Circle and the Coordinate Plane: Finding Points and Angles 121</p> <p>Finding Ratios from Angles on the Unit Circle 124</p> <p>Solving Trig Equations 127</p> <p>Making and Measuring Arcs 129</p> <p>Answers to Problems on Basic Trig and the Unit Circle 131</p> <p><b>Chapter 7: Graphing and Transforming Trig Functions</b><b> 137</b></p> <p>Getting a Grip on Periodic Graphs 137</p> <p>Parent Graphs and Transformations: Sine and Cosine 138</p> <p>Tangent and Cotangent: More Family Members 141</p> <p>Generations: Secant and Cosecant 143</p> <p>Answers to Problems on Graphing and Transforming Trig Functions 147</p> <p><b>Part 3: Digging Into Advanced Trig: Identities, Theorems, and Applications</b><b> 155</b></p> <p><b>Chapter 8: Basic Trig Identities</b><b> 157</b></p> <p>Using Reciprocal Identities to Simplify Trig Expressions 157</p> <p>Simplifying with Pythagorean Identities 159</p> <p>Discovering Even-Odd Identities 160</p> <p>Simplifying with Co-Function Identities 162</p> <p>Moving with Periodicity Identities 163</p> <p>Tackling Trig Proofs (Identities) 165</p> <p>Answers to Problems on Basic Trig Identities 167</p> <p><b>Chapter 9: Advanced Trig Identities</b><b> 175</b></p> <p>Simplifying with Sum and Difference Identities 175</p> <p>Using Double-Angle Identities 178</p> <p>Reducing with Half-Angle Identities 180</p> <p>Changing Products to Sums 181</p> <p>Expressing Sums as Products 182</p> <p>Powering Down: Power-Reducing Formulas 184</p> <p>Answers to Problems on Advanced Trig Identities 186</p> <p><b>Chapter 10: Solving Oblique Triangles</b><b> 193</b></p> <p>Solving a Triangle with the Law of Sines: ASA and AAS 194</p> <p>Tackling Triangles in the Ambiguous Case: SSA 195</p> <p>Conquering a Triangle with the Law of Cosines: SAS and SSS 197</p> <p>Using Oblique Triangles to Solve Practical Applications 198</p> <p>Figuring Area 201</p> <p>Answers to Problems on Solving Triangles 202</p> <p><b>Part 4: Polar Coordinates, Cones, Solutions, Sequences, and Finding Your Limits</b><b> 209</b></p> <p><b>Chapter 11: Exploring Complex Numbers and Polar Coordinates</b><b> 211</b></p> <p>Performing Operations with and Graphing Complex Numbers 212</p> <p>Round a Pole: Graphing Polar Coordinates 215</p> <p>Changing to and from Polar 217</p> <p>Graphing Polar Equations 220</p> <p>Archimedean spiral 220</p> <p>Cardioid 220</p> <p>Rose 220</p> <p>Circle 220</p> <p>Lemniscate 220</p> <p>Limaçon 221</p> <p>Answers to Problems on Complex Numbers and Polar Coordinates 223</p> <p><b>Chapter 12: Conquering Conic Sections</b><b> 229</b></p> <p>A Quick Conic Review 230</p> <p>Going Round and Round with Circles 230</p> <p>The Ups and Downs: Graphing Parabolas 232</p> <p>Standing tall: Vertical parabolas 233</p> <p>Lying down on the job: Horizontal parabolas 235</p> <p>The Fat and the Skinny: Graphing Ellipses 237</p> <p>Short and fat: The horizontal ellipse 237</p> <p>Tall and skinny: The vertical ellipse 239</p> <p>No Caffeine Required: Graphing Hyperbolas 241</p> <p>Horizontal hyperbolas 241</p> <p>Vertical hyperbolas 244</p> <p>Identifying Conic Sections 246</p> <p>Conic Sections in Parametric Form and Polar Coordinates 248</p> <p>Parametric form for conic sections 248</p> <p>Changing from parametric form to rectangular form 250</p> <p>Conic sections on the polar coordinate plane 251</p> <p>Answers to Problems on Conic Sections 253</p> <p><b>Chapter 13: Finding Solutions for Systems of Equations</b><b> 265</b></p> <p>A Quick-and-Dirty Technique Overview 266</p> <p>Solving Two Linear Equations with Two Variables 266</p> <p>The substitution method 267</p> <p>The elimination method 268</p> <p>Not-So-Straight: Solving Nonlinear Systems 269</p> <p>One equation that’s linear and one that isn’t 269</p> <p>Two nonlinear equations 270</p> <p>Systems of rational equations 271</p> <p>Systems of More Than Two Equations 272</p> <p>Graphing Systems of Inequalities 274</p> <p>Breaking Down Decomposing Partial Fractions 276</p> <p>Working with a Matrix 278</p> <p>Getting It in the Right Form: Simplifying Matrices 281</p> <p>Solving Systems of Equations Using Matrices 283</p> <p>Gaussian elimination 283</p> <p>Inverse matrices 285</p> <p>Cramer’s Rule 287</p> <p>Answers to Problems on Systems of Equations 289</p> <p><b>Chapter 14: Spotting Patterns in Sequences and Series</b><b> 301</b></p> <p>General Sequences and Series: Determining Terms 301</p> <p>Working Out the Common Difference: Arithmetic Sequences and Series 303</p> <p>Simplifying Geometric Sequences and Series 305</p> <p>Expanding Polynomials Using the Binomial Theorem 308</p> <p>Answers to Problems on Sequences, Series, and Binomials 310</p> <p><b>Chapter 15: Previewing Calculus</b><b> 315</b></p> <p>Finding Limits: Graphically, Analytically, and Algebraically 316</p> <p>Graphically 316</p> <p>Analytically 318</p> <p>Algebraically 319</p> <p>Knowing Your Limits 321</p> <p>Calculating the Average Rate of Change 322</p> <p>Determining Continuity 323</p> <p>Answers to Problems on Calculus 326</p> <p><b>Part 5: The Part of Tens</b><b> 329</b></p> <p><b>Chapter 16: Ten Plus Parent Graphs</b><b> 331</b></p> <p>Squaring Up with Quadratics 331</p> <p>Cueing Up for Cubics 332</p> <p>Rooting for Square Roots and Cube Roots 333</p> <p>Graphing Absolutely Fabulous Absolute Value Functions 334</p> <p>Flipping over Rational Functions 334</p> <p>Exploring Exponential Graphs and Logarithmic Graphs 335</p> <p>Seeing the Sine and Cosine 336</p> <p>Covering Cosecant and Secant 337</p> <p>Tripping over Tangent and Cotangent 338</p> <p>Lining Up and Going Straight with Lines 339</p> <p><b>Chapter 17: Ten Missteps to Avoid</b><b> 341</b></p> <p>Going Out of Order (of Operations) 341</p> <p>FOILing Binomials Incorrectly 342</p> <p>Breaking Up Fractions Badly 342</p> <p>Combining Terms That Can’t Be Combined 342</p> <p>Forgetting to Flip the Fraction 342</p> <p>Losing the Negative (Sign) 343</p> <p>Oversimplifying Roots 343</p> <p>Executing Exponent Errors 343</p> <p>Ignoring Extraneous 344</p> <p>Misinterpreting Trig Notation 344</p> <p>Index 345</p>

<p><b>Mary Jane Sterling</b> taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of <i>Trigonometry For Dummies</i> and <i>Finite Math For Dummies.</i>

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