Efnisyfirlit

• 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

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