Pre-Calculus Workbook For Dummies

Pre-Calculus Workbook for Dummies......Page 3
About the Authors......Page 5
Authors’ Acknowledgments......Page 7
Contents at a Glance......Page 9
Table of Contents......Page 10
About This Book......Page 15
How This Book Is Organized......Page 16
Icons Used in This Book......Page 17
Where to Go from Here......Page 18
Part I: Foundation (And We Don’t Mean Makeup!)......Page 19
Reviewing Order of Operations: The Fun in Fundamentals......Page 21
Keeping Your Balance While Solving Equalities......Page 24
A Picture Is Worth a Thousand Words: Graphing Equalities and Inequalities......Page 26
Using Graphs to Find Information (Distance, Midpoint, Slope)......Page 29
Answers to Problems on Fundamentals......Page 34
Solving Inequalities......Page 39
Expressing Inequality Solutions in Interval Notations......Page 42
Don’t Get Drastic with Radicals and Exponents — Just Simplify Them!......Page 44
Getting Out of a Sticky Situation, or Rationalizing......Page 47
Answers to Problems on Real Numbers......Page 50
Battling Out Even versus Odd......Page 55
Leaving the Nest: Transforming Parent Graphs......Page 57
Lucid Thinking? Graphing Rational Functions......Page 64
53 Picking Up the Pieces: Graphing Piece-Wise Functions......Page 67
Operating on Functions: No Scalpel Necessary......Page 68
Evaluating Composition of Functions......Page 70
Working Together: Domain and Range......Page 72
Finding the Inverse of a Function (Who Knew It Was Lost?)......Page 74
Answers to Questions on Functions......Page 76
Reason Through It: Factoring a Factorable Polynomial......Page 87
Get Your Roots Done while Solving a Quadratic Polynomial......Page 90
Climb the Mountains by Solving High Order Polynomials......Page 92
Strike That! Reverse It! Using Roots to Find an Equation......Page 95
Graphing Polynomials......Page 96
Answers to Questions on Finding Roots......Page 100
Things Get Bigger (Or Smaller) All the Time — Solving Exponential Functions......Page 105
The Only Logs You Won’t Cut: Solving Logarithms......Page 107
Putting Them Together: Solving Equations Using Exponents and Logs......Page 110
Solving Exponential Word Problems . . . Argh!......Page 112
Answers to Problems on Exponential and Logarithmic Functions......Page 114
Part II: Trig Is the Key: Basic Review, the Unit Circle, and Graphs......Page 119
It’s All Right-Triangle Trig — Finding the Six Trigonometric Ratios......Page 121
Solving Word Problems with Right Triangles......Page 124
Unit Circle and the Coordinate Plane: Finding Points and Angles......Page 126
Isn’t That Special? Finding Right Triangle Ratios on the Unit Circle......Page 129
Solving Trig Equations......Page 131
Making and Measuring Arcs......Page 133
Answers to Problems......Page 135
Getting a Grip on Period Graphs......Page 141
Sine and Cosine: Parent Graphs and Transformations......Page 142
Tangent and Cotangent: Mom, Pops, and Children......Page 145
Secant and Cosecant: Generations......Page 148
Answers to Problems on Graphing and Transforming Trig Functions......Page 151
Part III: Advanced Trig: Identities, Theorems, and Applications......Page 157
Using Reciprocal Identities to Simplify Trig Expressions......Page 159
Simplifying with Pythagorean Identities......Page 161
Discovering Even-Odd Identities......Page 162
Solving with Co-Function Identities......Page 163
Moving with Periodicity Identities......Page 164
Tackling Trig Proofs......Page 165
Answers to Problems on Basic Trig Identities......Page 167
Simplifying with Sum and Difference Identities......Page 175
Using Double Angle Identities......Page 177
Reducing with Half-Angle Identities......Page 179
Changing Products to Sums......Page 180
Expressing Sums as Products......Page 182
Powering Down: Power-Reducing Formulas......Page 183
Answers to Problems on Advanced Identities......Page 184
Solving a Triangle with the Law of Sines: ASA and AAS......Page 191
Tackling Triangles in the Ambiguous Case: SSA......Page 193
Conquering a Triangle with the Law of Cosines: SAS and SSS......Page 194
Using Oblique Triangles to Solve Word Problems......Page 196
Figuring Flatness (Area)......Page 198
Answers to Problems on Solving Triangles......Page 200
Part IV: And the Rest . . .......Page 207
Performing Operations with and Graphing Complex Numbers......Page 209
Round a Pole: Graphing Polar Coordinates......Page 213
Changing to and from Polar......Page 216
Graphing Polar Equations......Page 218
Answers to Problems on Complex Numbers and Polar Coordinates......Page 221
A Quick Conic Review......Page 225
Going Round and Round with Circles......Page 226
Graphing Parabolas: The Ups and Downs......Page 227
Graphing Ellipses: The Fat and the Skinny......Page 232
Graphing Hyperbolas: No Caffeine Required......Page 236
Identifying Conic Sections......Page 241
Converting from Parametric Form to Polar Coordinates and Back......Page 244
Answers to Problems on Conic Sections......Page 249
A Quick-and-Dirty Technique Overview......Page 257
Solving Two Linear Equations with Two Variables......Page 258
Not-So-Straight: Solving Nonlinear Systems......Page 261
Solving More than Two (Equations and/or Variables)......Page 263
Graphing Systems of Inequalities......Page 265
We’re Partial to . . . Decomposing Partial Fractions!......Page 267
There Is No Spoon: Working with a Matrix......Page 269
Getting It in the Right Form: Simplifying Matrices......Page 271
Solving Systems of Equations Using Matrices......Page 273
Answers to Problems on Systems of Equations......Page 278
Major General Sequences and Series: Calculating Terms......Page 289
Working Out the Common Difference: Arithmetic Sequences and Series......Page 291
Be Fruitful and Multiply: Simplifying Geometric Sequences and Series......Page 293
Expanding Polynomials Using the Binomial Theorem......Page 295
Answers to Problems on Sequences, Series, and Binomials......Page 297
Finding Limits: Graphically, Analytically, and Algebraically......Page 301
Knowing Your Limit Laws......Page 306
Determining Continuity......Page 307
Answers to Problems on Calculus......Page 310
Part V: The Part of Tens......Page 313
Squaring Up with Quadratics......Page 315
Rooting for Square Roots and Cube Roots......Page 316
Flipping over Rational Functions......Page 317
Exploring Exponential Graphs and Logarithmic Graphs......Page 318
Covering Cosecant and Secant......Page 319
Tripping over Tangent and Cotangent......Page 320
FOILed Again! FOILing Binomials Incorrectly......Page 323
Forgetting to Flip the Fraction......Page 324
Canceling Too Quickly......Page 325
Dealing with Distribution......Page 326
Index......Page 327