Pre-Calculus Workbook For Dummies

Pre-Calculus Workbook for Dummies
About the Authors
Dedication
Authors’ Acknowledgments
Contents at a Glance
Table of Contents
Introduction
About This Book
Conventions Used in This Book
Foolish Assumptions
How This Book Is Organized
Icons Used in This Book
Where to Go from Here
Part I: Foundation (And We Don’t Mean Makeup!)
Chapter 1: Beginning at the Very Beginning: Pre-Pre-Calculus
Reviewing Order of Operations: The Fun in Fundamentals
Keeping Your Balance While Solving Equalities
A Picture Is Worth a Thousand Words: Graphing Equalities and Inequalities
Using Graphs to Find Information (Distance, Midpoint, Slope)
Answers to Problems on Fundamentals
Chapter 2: Get Real!: Wrestling with Real Numbers
Solving Inequalities
Expressing Inequality Solutions in Interval Notations
Don’t Get Drastic with Radicals and Exponents — Just Simplify Them!
Getting Out of a Sticky Situation, or Rationalizing
Answers to Problems on Real Numbers
Chapter 3: Understanding the Function of Functions
Battling Out Even versus Odd
Leaving the Nest: Transforming Parent Graphs
Lucid Thinking? Graphing Rational Functions
53 Picking Up the Pieces: Graphing Piece-Wise Functions
Operating on Functions: No Scalpel Necessary
Evaluating Composition of Functions
Working Together: Domain and Range
Finding the Inverse of a Function (Who Knew It Was Lost?)
Answers to Questions on Functions
Chapter 4: Go Back to Your Roots to Get Your Degree
Reason Through It: Factoring a Factorable Polynomial
Get Your Roots Done while Solving a Quadratic Polynomial
Climb the Mountains by Solving High Order Polynomials
Strike That! Reverse It! Using Roots to Find an Equation
Graphing Polynomials
Answers to Questions on Finding Roots
Chapter 5: Exponential and Logarithmic Functions
Things Get Bigger (Or Smaller) All the Time — Solving Exponential Functions
The Only Logs You Won’t Cut: Solving Logarithms
Putting Them Together: Solving Equations Using Exponents and Logs
Solving Exponential Word Problems . . . Argh!
Answers to Problems on Exponential and Logarithmic Functions
Part II: Trig Is the Key: Basic Review, the Unit Circle, and Graphs
Chapter 6: Basic Trigonometry and the Unit Circle
It’s All Right-Triangle Trig — Finding the Six Trigonometric Ratios
Solving Word Problems with Right Triangles
Unit Circle and the Coordinate Plane: Finding Points and Angles
Isn’t That Special? Finding Right Triangle Ratios on the Unit Circle
Solving Trig Equations
Making and Measuring Arcs
Answers to Problems
Chapter 7: Graphing and Transforming Trig Functions
Getting a Grip on Period Graphs
Sine and Cosine: Parent Graphs and Transformations
Tangent and Cotangent: Mom, Pops, and Children
Secant and Cosecant: Generations
Answers to Problems on Graphing and Transforming Trig Functions
Part III: Advanced Trig: Identities, Theorems, and Applications
Chapter 8: Basic Trig Identities
Using Reciprocal Identities to Simplify Trig Expressions
Simplifying with Pythagorean Identities
Discovering Even-Odd Identities
Solving with Co-Function Identities
Moving with Periodicity Identities
Tackling Trig Proofs
Answers to Problems on Basic Trig Identities
Chapter 9: Advanced Identities
Simplifying with Sum and Difference Identities
Using Double Angle Identities
Reducing with Half-Angle Identities
Changing Products to Sums
Expressing Sums as Products
Powering Down: Power-Reducing Formulas
Answers to Problems on Advanced Identities
Chapter 10: Solving Oblique Triangles
Solving a Triangle with the Law of Sines: ASA and AAS
Tackling Triangles in the Ambiguous Case: SSA
Conquering a Triangle with the Law of Cosines: SAS and SSS
Using Oblique Triangles to Solve Word Problems
Figuring Flatness (Area)
Answers to Problems on Solving Triangles
Part IV: And the Rest . . .
Chapter 11: Complex Numbers and Polar Coordinates
Performing Operations with and Graphing Complex Numbers
Round a Pole: Graphing Polar Coordinates
Changing to and from Polar
Graphing Polar Equations
Answers to Problems on Complex Numbers and Polar Coordinates
Chapter 12: Conquering Conic Sections
A Quick Conic Review
Going Round and Round with Circles
Graphing Parabolas: The Ups and Downs
Graphing Ellipses: The Fat and the Skinny
Graphing Hyperbolas: No Caffeine Required
Identifying Conic Sections
Converting from Parametric Form to Polar Coordinates and Back
Answers to Problems on Conic Sections
Chapter 13: Finding Solutions for Systems of Equations
A Quick-and-Dirty Technique Overview
Solving Two Linear Equations with Two Variables
Not-So-Straight: Solving Nonlinear Systems
Solving More than Two (Equations and/or Variables)
Graphing Systems of Inequalities
We’re Partial to . . . Decomposing Partial Fractions!
There Is No Spoon: Working with a Matrix
Getting It in the Right Form: Simplifying Matrices
Solving Systems of Equations Using Matrices
Answers to Problems on Systems of Equations
Chapter 14: Sequences, Series, and Binomials — Oh My!
Major General Sequences and Series: Calculating Terms
Working Out the Common Difference: Arithmetic Sequences and Series
Be Fruitful and Multiply: Simplifying Geometric Sequences and Series
Expanding Polynomials Using the Binomial Theorem
Answers to Problems on Sequences, Series, and Binomials
Chapter 15: The Next Step Is Calculus
Finding Limits: Graphically, Analytically, and Algebraically
Knowing Your Limit Laws
Determining Continuity
Answers to Problems on Calculus
Part V: The Part of Tens
Chapter 16: Ten Uses for Parent Graphs
Squaring Up with Quadratics
Cueing Up for Cubics
Rooting for Square Roots and Cube Roots
Graphing Absolutely Fabulous Absolute Value Functions
Flipping over Rational Functions
Exploring Exponential Graphs and Logarithmic Graphs
Seeing the Sine and Cosine
Covering Cosecant and Secant
Tripping over Tangent and Cotangent
Chapter 17: Ten Pitfalls to Pass Up in Pre-Calc
Going Out of Order (Of Operations)
FOILed Again! FOILing Binomials Incorrectly
Gettin’ Down with Denominators
Combining Terms That Can’t Be Combined
Forgetting to Flip the Fraction
Losing the Negative (Sign)
Oversimplifying Roots
Avoiding Exponent Errors
Canceling Too Quickly
Dealing with Distribution
Index