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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: Setting the Foundation: The Nuts and Bolts of Pre-Calculus
• Chapter 1: Preparing for Pre-Calculus
• Reviewing Order of Operations: The Fun in Fundamentals
• Keeping Your Balance While Solving Equalities
• When Your Image Really Counts: Graphing Equalities and Inequalities
• Using Graphs to Find Distance, Midpoint, and Slope
• Answers to Problems on Fundamentals
• Chapter 2: Real Numbers Come Clean
• Solving Inequalities
• Expressing Inequality Solutions in Interval Notation
• Radicals and Exponents — Just Simplify!
• Getting Out of a Sticky Situation, or Rationalizing
• Answers to Problems on Real Numbers
• Chapter 3: Controlling Functions by Knowing Their Function
• Using Both Faces of the Coin: Even and Odd
• Leaving the Nest: Transforming Parent Graphs
• Graphing Rational Functions
• Piecing Together Piecewise Functions
• Combining Functions
• Evaluating Composition of Functions
• Working Together: Domain and Range
• Unlocking the Inverse of a Function: Turning It Inside Out
• Answers to Problems on Functions
• Chapter 4: Searching for Roots
• Factoring a Factorable Quadratic
• Solving a Quadratic Polynomial Equation
• Solving High-Order Polynomials
• Using Roots to Create an Equation
• Graphing Polynomials
• Answers to Problems on Roots and Degrees
• Chapter 5: Exponential and Logarithmic Functions
• Working with Exponential Functions
• Eagerly Engaging Edgy Logarithmic Solutions
• Making Exponents and Logs Work Together
• Using Exponents and Logs in Practical Applications
• Answers to Problems on Exponential and Logarithmic Functions
• Part 2: Trig Is the Key: Basic Review, the Unit Circle, and Graphs
• Chapter 6: Basic Trigonometry and the Unit Circle
• Finding the Six Trigonometric Ratios
• Solving Word Problems with Right Triangles
• Unit Circle and the Coordinate Plane: Finding Points and Angles
• Finding Ratios from Angles on the Unit Circle
• Solving Trig Equations
• Making and Measuring Arcs
• Answers to Problems on Basic Trig and the Unit Circle
• Chapter 7: Graphing and Transforming Trig Functions
• Getting a Grip on Periodic Graphs
• Parent Graphs and Transformations: Sine and Cosine
• Tangent and Cotangent: More Family Members
• Generations: Secant and Cosecant
• Answers to Problems on Graphing and Transforming Trig Functions
• Part 3: Digging into 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
• Simplifying with Co-Function Identities
• Moving with Periodicity Identities
• Tackling Trig Proofs (Identities)
• Answers to Problems on Basic Trig Identities
• Chapter 9: Advanced Trig 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 Trig 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 Practical Applications
• Figuring Area
• Answers to Problems on Solving Triangles
• Part 4: Polar Coordinates, Cones, Solutions, Sequences, and Finding Your Limits
• Chapter 11: Exploring 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
• The Ups and Downs: Graphing Parabolas
• The Fat and the Skinny: Graphing Ellipses
• No Caffeine Required: Graphing Hyperbolas
• Identifying Conic Sections
• Conic Sections in Parametric Form and Polar Coordinates
• 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
• Systems of More Than Two Equations
• Graphing Systems of Inequalities
• Breaking Down Decomposing Partial Fractions
• 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: Spotting Patterns in Sequences and Series
• General Sequences and Series: Determining Terms
• Working Out the Common Difference: Arithmetic Sequences and Series
• Simplifying Geometric Sequences and Series
• Expanding Polynomials Using the Binomial Theorem
• Answers to Problems on Sequences, Series, and Binomials
• Chapter 15: Previewing Calculus
• Finding Limits: Graphically, Analytically, and Algebraically
• Knowing Your Limits
• Calculating the Average Rate of Change
• Determining Continuity
• Answers to Problems on Calculus
• Part 5: The Part of Tens
• Chapter 16: Ten Plus 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
• Lining Up and Going Straight with Lines
• Chapter 17: Ten Missteps to Avoid
• Going Out of Order (of Operations)
• FOILing Binomials Incorrectly
• Breaking Up Fractions Badly
• Combining Terms That Can’t Be Combined
• Forgetting to Flip the Fraction
• Losing the Negative (Sign)
• Oversimplifying Roots
• Executing Exponent Errors
• Ignoring Extraneous
• Misinterpreting Trig Notation
• Index
• About the Author
• Connect with Dummies
• End User License Agreement