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• Cover
• Introduction
• About This Book
• Foolish Assumptions
• Icons Used in This Book
• Beyond the Book
• Where to Go from Here
• Part 1: Getting Started with Pre-Calculus
• Chapter 1: Pre-Pre-Calculus
• Pre-Calculus: An Overview
• All the Number Basics (No, Not How to Count Them!)
• Visual Statements: When Math Follows Form with Function
• Get Yourself a Graphing Calculator
• Chapter 2: Playing with Real Numbers
• Solving Inequalities
• Variations on Dividing and Multiplying: Working with Radicals and Exponents
• Chapter 3: The Building Blocks of Pre-Calculus Functions
• Qualities of Special Function Types and Their Graphs
• Dealing with Parent Functions and Their Graphs
• Graphing Functions That Have More Than One Rule: Piece-Wise Functions
• Setting the Stage for Rational Functions
• Putting the Results to Work: Graphing Rational Functions
• Chapter 4: Operating on Functions
• Transforming the Parent Graphs
• Sharpen Your Scalpel: Operating on Functions
• Turning Inside Out with Inverse Functions
• Chapter 5: Digging Out and Using Roots to Graph Polynomial Functions
• Understanding Degrees and Roots
• Factoring a Polynomial Expression
• Finding the Roots of a Factored Equation
• Cracking a Quadratic Equation When It Won’t Factor
• Solving Unfactorable Polynomials with a Degree Higher Than Two
• Put It in Reverse: Using Solutions to Find Factors
• Graphing Polynomials
• Chapter 6: Exponential and Logarithmic Functions
• Exploring Exponential Functions
• Logarithms: The Inverse of Exponential Functions
• Base Jumping to Simplify and Solve Equations
• Growing Exponentially: Word Problems in the Kitchen
• Part 2: The Essentials of Trigonometry
• Chapter 7: Circling in on Angles
• Introducing Radians: Circles Weren’t Always Measured in Degrees
• Trig Ratios: Taking Right Triangles a Step Further
• Understanding How Trig Ratios Work on the Coordinate Plane
• Building the Unit Circle by Dissecting the Right Way
• Digesting Special Triangle Ratios
• Triangles and the Unit Circle: Working Together for the Common Good
• Measuring Arcs: When the Circle Is Put in Motion
• Chapter 8: Simplifying the Graphing and Transformation of Trig Functions
• Drafting the Sine and Cosine Parent Graphs
• Graphing Tangent and Cotangent
• Putting Secant and Cosecant in Pictures
• Transforming Trig Graphs
• Chapter 9: Identifying with Trig Identities: The Basics
• Keeping the End in Mind: A Quick Primer on Identities
• Lining Up the Means to the End: Basic Trig Identities
• Tackling Difficult Trig Proofs: Some Techniques to Know
• Chapter 10: Advanced Identities: Your Keys to Success
• Finding Trig Functions of Sums and Differences
• Doubling an Angle and Finding Its Trig Value
• Taking Trig Functions of Common Angles Divided in Two
• A Glimpse of Calculus: Traveling from Products to Sums and Back
• Eliminating Exponents with Power-Reducing Formulas
• Chapter 11: Taking Charge of Oblique Triangles with the Laws of Sines and Cosines
• Solving a Triangle with the Law of Sines
• Conquering a Triangle with the Law of Cosines
• Filling in the Triangle by Calculating Area
• Part 3: Analytic Geometry and System Solving
• Chapter 12: Plane Thinking: Complex Numbers and Polar Coordinates
• Understanding Real versus Imaginary
• Combining Real and Imaginary: The Complex Number System
• Graphing Complex Numbers
• Plotting Around a Pole: Polar Coordinates
• Chapter 13: Creating Conics by Slicing Cones
• Cone to Cone: Identifying the Four Conic Sections
• Going Round and Round: Graphing Circles
• Riding the Ups and Downs with Parabolas
• The Fat and the Skinny on the Ellipse
• Pair Two Curves and What Do You Get? Hyperbolas
• Expressing Conics Outside the Realm of Cartesian Coordinates
• Chapter 14: Streamlining Systems, Managing Variables
• A Primer on Your System-Solving Options
• Algebraic Solutions of Two-Equation Systems
• Solving Systems with More than Two Equations
• Decomposing Partial Fractions
• Surveying Systems of Inequalities
• Introducing Matrices: The Basics
• Simplifying Matrices to Ease the Solving Process
• Making Matrices Work for You
• Chapter 15: Sequences, Series, and Expanding Binomials for the Real World
• Speaking Sequentially: Grasping the General Method
• Difference between Terms: Arithmetic Sequences
• Ratios and Consecutive Paired Terms: Geometric Sequences
• Creating a Series: Summing Terms of a Sequence
• Expanding with the Binomial Theorem
• Chapter 16: Onward to Calculus
• Scoping Out the Differences between Pre-Calculus and Calculus
• Understanding Your Limits
• Finding the Limit of a Function
• Operating on Limits: The Limit Laws
• Calculating the Average Rate of Change
• Exploring Continuity in Functions
• Part 4: The Part of Tens
• Chapter 17: Ten Polar Graphs
• Spiraling Outward
• Falling in Love with a Cardioid
• Cardioids and Lima Beans
• Leaning Lemniscates
• Lacing through Lemniscates
• Roses with Even Petals
• A Rose Is a Rose Is a Rose
• Limaçon or Escargot?
• Limaçon on the Side
• Bifolium or Rabbit Ears?
• Chapter 18: Ten Habits to Adjust before Calculus
• Figure Out What the Problem Is Asking
• Draw Pictures (the More the Better)
• Plan Your Attack — Identify Your Targets
• Write Down Any Formulas
• Show Each Step of Your Work
• Know When to Quit
• Check Your Answers
• Practice Plenty of Problems
• Keep Track of the Order of Operations
• Use Caution When Dealing with Fractions
• Index
• About the Author
• Advertisement Page
• Connect with Dummies
• End User License Agreement