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