Pre-Calculus Workbook For Dummies

Title Page
Copyright Page
Table of Contents
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
			Graphing with two points
			Graphing by using the slope-intercept form
			Graphing inequalities
		Using Graphs to Find Distance, Midpoint, and Slope
			Finding the distance
			Calculating the midpoint
			Discovering the 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
			Quadratic functions
			Square root functions
			Absolute value functions
			Cubic functions
			Cube root functions
			Steeper or flatter
			Translations
			Reflections
			Combinations of transformations
		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
			Completing the square
			Quadratic formula
		Solving High-Order Polynomials
			Factoring by grouping
			Determining positive and negative roots: Descartes’ Rule of Signs
			Counting on imaginary roots
			Getting the rational roots
			Finding roots through synthetic division
		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
			Archimedean spiral
			Cardioid
			Rose
			Circle
			Lemniscate
			Limaçon
		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
			Standing tall: Vertical parabolas
			Lying down on the job: Horizontal parabolas
		The Fat and the Skinny: Graphing Ellipses
			Short and fat: The horizontal ellipse
			Tall and skinny: The vertical ellipse
		No Caffeine Required: Graphing Hyperbolas
			Horizontal hyperbolas
			Vertical hyperbolas
		Identifying Conic Sections
		Conic Sections in Parametric Form and Polar Coordinates
			Parametric form for conic sections
			Changing from parametric form to rectangular form
			Conic sections on the polar coordinate plane
		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
			The substitution method
			The elimination method
		Not-So-Straight: Solving Nonlinear Systems
			One equation that’s linear and one that isn’t
			Two nonlinear equations
			Systems of rational equations
		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
			Gaussian elimination
			Inverse matrices
			Cramer’s Rule
		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
			Graphically
			Analytically
			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
EULA