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by Elleyne Kase, Yang Kuang PhD
Pre-Calculus For Dummies, 2nd Edition
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Table of Contents
Title Page
Introduction
Part I: Set It Up, Solve It, Graph It
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-Calc: Functions
Qualities of Even and Odd Functions and Their Graphs
Dealing with Parent Functions and Their Graphs
Transforming the Parent Graphs
Graphing Functions that Have More than One Rule: Piece-Wise Functions
Calculating Outputs for Rational Functions
Putting the Output to Work: Graphing Rational Functions
Sharpen Your Scalpel: Operating on Functions
Turning Inside Out with Inverse Functions
Chapter 4: 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 5: 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 II: The Essentials of Trigonometry
Chapter 6: 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 7: 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 8: 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 9: Advanced Identities: Your Keys to Pre-Calc Success
Finding Trig Functions of Sums and Differences
Doubling an Angle’s Trig Value without Knowing the Angle
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 10: 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 III: Analytic Geometry and System Solving
Chapter 11: Plane Thinking: Complex Numbers and Polar Coordinates
Understanding Real versus Imaginary (According to Mathematicians)
Combining Real and Imaginary: The Complex Number System
Graphing Complex Numbers
Plotting Around a Pole: Polar Coordinates
Chapter 12: Slicing Cones or Measuring the Path of a Comet - with Confidence
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 (A Fancy Word for Oval)
Pair Two Parabolas and What Do You Get? Hyperbolas
Expressing Conics Outside the Realm of Cartesian Coordinates
Chapter 13: Streamlining Systems, Managing Variables
A Primer on Your System-Solving Options
Finding Solutions of Two-Equation Systems Algebraically
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
Conquering Matrices
Chapter 14: Sequences, Series, and Expanding Binomials for the Real World
Speaking Sequentially: Grasping the General Method
Covering the Distance between Terms: Arithmetic Sequences
Sharing Ratios with Consecutive Paired Terms: Geometric Sequences
Creating a Series: Summing Terms of a Sequence
Expanding with the Binomial Theorem
Chapter 15: Scouting the Road Ahead to Calculus
Scoping Out the Differences between Pre-Calc and Calc
Understanding and Communicating about Limits
Finding the Limit of a Function
Operating on Limits: The Limit Laws
Exploring Continuity in Functions
Part IV: The Part of Tens
Chapter 16: Ten Habits to Develop as You Prepare for Calculus
Figure Out What the Problem Is Asking
Draw Pictures (And Plenty of ’Em)
Plan Your Attack
Write Down Any Formulas
Show Each Step of Your Work
Know When to Quit
Check Your Answers
Practice Plenty of Problems
Make Sure You Understand the Concepts
Pepper Your Teacher with Questions
Chapter 17: Ten Habits to Quit Before Calculus
Operating Out of Order
Squaring without FOILing
Splitting Up Terms in Denominators
Combining the Wrong Terms
Forgetting the Reciprocal
Losing Track of Minus Signs
Oversimplifying Radicals
Erring in Exponential Dealings
Canceling Out Too Quickly
Distributing Improperly
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