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Pre-Calculus For Dummies, 2nd Edition

Book Description

The fun and easy way to learn pre-calculus

Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations.

With this guide's help you'll quickly and painlessly get a handle on all of the concepts — not just the number crunching — and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for how these concepts are used in the real world, and find out that getting a decent grade in pre-calc isn't as impossible as you thought.

  • Updated with fresh example equations and detailed explanations

  • Tracks to a typical pre-calculus class

  • Serves as an excellent supplement to classroom learning

  • If "the fun and easy way to learn pre-calc" seems like a contradiction, get ready for a wealth of surprises in Pre-Calculus For Dummies!

Table of Contents

  1. Cover
  2. Table of Contents
  3. Title Page
  4. Introduction
  5. Part I: Set It Up, Solve It, Graph It
    1. Chapter 1: Pre-Pre-Calculus
      1. Pre-Calculus: An Overview
      2. All the Number Basics (No, Not How to Count Them!)
      3. Visual Statements: When Math Follows Form with Function
      4. Get Yourself a Graphing Calculator
    2. Chapter 2: Playing with Real Numbers
      1. Solving Inequalities
      2. Variations on Dividing and Multiplying: Working with Radicals and Exponents
    3. Chapter 3: The Building Blocks of Pre-Calc: Functions
      1. Qualities of Even and Odd Functions and Their Graphs
      2. Dealing with Parent Functions and Their Graphs
      3. Transforming the Parent Graphs
      4. Graphing Functions that Have More than One Rule: Piece-Wise Functions
      5. Calculating Outputs for Rational Functions
      6. Putting the Output to Work: Graphing Rational Functions
      7. Sharpen Your Scalpel: Operating on Functions
      8. Turning Inside Out with Inverse Functions
    4. Chapter 4: Digging Out and Using Roots to Graph Polynomial Functions
      1. Understanding Degrees and Roots
      2. Factoring a Polynomial Expression
      3. Finding the Roots of a Factored Equation
      4. Cracking a Quadratic Equation When It Won’t Factor
      5. Solving Unfactorable Polynomials with a Degree Higher than Two
      6. Put It in Reverse: Using Solutions to Find Factors
      7. Graphing Polynomials
    5. Chapter 5: Exponential and Logarithmic Functions
      1. Exploring Exponential Functions
      2. Logarithms: The Inverse of Exponential Functions
      3. Base Jumping to Simplify and Solve Equations
      4. Growing Exponentially: Word Problems in the Kitchen
  6. Part II: The Essentials of Trigonometry
    1. Chapter 6: Circling in on Angles
      1. Introducing Radians: Circles Weren’t Always Measured in Degrees
      2. Trig Ratios: Taking Right Triangles a Step Further
      3. Understanding How Trig Ratios Work on the Coordinate Plane
      4. Building the Unit Circle by Dissecting the Right Way
      5. Digesting Special Triangle Ratios
      6. Triangles and the Unit Circle: Working Together for the Common Good
      7. Measuring Arcs: When the Circle Is Put in Motion
    2. Chapter 7: Simplifying the Graphing and Transformation of Trig Functions
      1. Drafting the Sine and Cosine Parent Graphs
      2. Graphing Tangent and Cotangent
      3. Putting Secant and Cosecant in Pictures
      4. Transforming Trig Graphs
    3. Chapter 8: Identifying with Trig Identities: The Basics
      1. Keeping the End in Mind: A Quick Primer on Identities
      2. Lining Up the Means to the End: Basic Trig Identities
      3. Tackling Difficult Trig Proofs: Some Techniques to Know
    4. Chapter 9: Advanced Identities: Your Keys to Pre-Calc Success
      1. Finding Trig Functions of Sums and Differences
      2. Doubling an Angle’s Trig Value without Knowing the Angle
      3. Taking Trig Functions of Common Angles Divided in Two
      4. A Glimpse of Calculus: Traveling from Products to Sums and Back
      5. Eliminating Exponents with Power-Reducing Formulas
    5. Chapter 10: Taking Charge of Oblique Triangles with the Laws of Sines and Cosines
      1. Solving a Triangle with the Law of Sines
      2. Conquering a Triangle with the Law of Cosines
      3. Filling in the Triangle by Calculating Area
  7. Part III: Analytic Geometry and System Solving
    1. Chapter 11: Plane Thinking: Complex Numbers and Polar Coordinates
      1. Understanding Real versus Imaginary (According to Mathematicians)
      2. Combining Real and Imaginary: The Complex Number System
      3. Graphing Complex Numbers
      4. Plotting Around a Pole: Polar Coordinates
    2. Chapter 12: Slicing Cones or Measuring the Path of a Comet - with Confidence
      1. Cone to Cone: Identifying the Four Conic Sections
      2. Going Round and Round: Graphing Circles
      3. Riding the Ups and Downs with Parabolas
      4. The Fat and the Skinny on the Ellipse (A Fancy Word for Oval)
      5. Pair Two Parabolas and What Do You Get? Hyperbolas
      6. Expressing Conics Outside the Realm of Cartesian Coordinates
    3. Chapter 13: Streamlining Systems, Managing Variables
      1. A Primer on Your System-Solving Options
      2. Finding Solutions of Two-Equation Systems Algebraically
      3. Solving Systems with More than Two Equations
      4. Decomposing Partial Fractions
      5. Surveying Systems of Inequalities
      6. Introducing Matrices: The Basics
      7. Simplifying Matrices to Ease the Solving Process
      8. Conquering Matrices
    4. Chapter 14: Sequences, Series, and Expanding Binomials for the Real World
      1. Speaking Sequentially: Grasping the General Method
      2. Covering the Distance between Terms: Arithmetic Sequences
      3. Sharing Ratios with Consecutive Paired Terms: Geometric Sequences
      4. Creating a Series: Summing Terms of a Sequence
      5. Expanding with the Binomial Theorem
    5. Chapter 15: Scouting the Road Ahead to Calculus
      1. Scoping Out the Differences between Pre-Calc and Calc
      2. Understanding and Communicating about Limits
      3. Finding the Limit of a Function
      4. Operating on Limits: The Limit Laws
      5. Exploring Continuity in Functions
  8. Part IV: The Part of Tens
    1. Chapter 16: Ten Habits to Develop as You Prepare for Calculus
      1. Figure Out What the Problem Is Asking
      2. Draw Pictures (And Plenty of ’Em)
      3. Plan Your Attack
      4. Write Down Any Formulas
      5. Show Each Step of Your Work
      6. Know When to Quit
      7. Check Your Answers
      8. Practice Plenty of Problems
      9. Make Sure You Understand the Concepts
      10. Pepper Your Teacher with Questions
    2. Chapter 17: Ten Habits to Quit Before Calculus
      1. Operating Out of Order
      2. Squaring without FOILing
      3. Splitting Up Terms in Denominators
      4. Combining the Wrong Terms
      5. Forgetting the Reciprocal
      6. Losing Track of Minus Signs
      7. Oversimplifying Radicals
      8. Erring in Exponential Dealings
      9. Canceling Out Too Quickly
      10. Distributing Improperly
  9. Cheat Sheet