Pre-Calculus Workbook For Dummies, 3rd Edition

Pre-Calculus Workbook For Dummies, 3rd Edition

by Mary Jane Sterling
Released April 2019
Publisher(s): For Dummies
ISBN: 9781119508809

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Book description

Get a handle on pre-calculus in a pinch!

If you’re tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you’ll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem. 

In Pre-Calculus Workbook For Dummies, you’ll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you’ll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations. 

  • Get ample review before jumping into a calculus course
  • Supplement your classroom work with easy-to-follow guidance
  • Make complex formulas and concepts more approachable
  • Be prepared to further your mathematics studies

Whether you’re enrolled in a pre-calculus class or you’re looking for a refresher as you prepare for a calculus course, this is the perfect study companion to make it easier.

Table of contents

  1. Cover
  2. Introduction
    1. About This Book
    2. Foolish Assumptions
    3. Icons Used in This Book
    4. Beyond the Book
    5. Where to Go from Here
  3. Part 1: Setting the Foundation: The Nuts and Bolts of Pre-Calculus
    1. Chapter 1: Preparing for Pre-Calculus
      1. Reviewing Order of Operations: The Fun in Fundamentals
      2. Keeping Your Balance While Solving Equalities
      3. When Your Image Really Counts: Graphing Equalities and Inequalities
      4. Using Graphs to Find Distance, Midpoint, and Slope
      5. Answers to Problems on Fundamentals
    2. Chapter 2: Real Numbers Come Clean
      1. Solving Inequalities
      2. Expressing Inequality Solutions in Interval Notation
      3. Radicals and Exponents — Just Simplify!
      4. Getting Out of a Sticky Situation, or Rationalizing
      5. Answers to Problems on Real Numbers
    3. Chapter 3: Controlling Functions by Knowing Their Function
      1. Using Both Faces of the Coin: Even and Odd
      2. Leaving the Nest: Transforming Parent Graphs
      3. Graphing Rational Functions
      4. Piecing Together Piecewise Functions
      5. Combining Functions
      6. Evaluating Composition of Functions
      7. Working Together: Domain and Range
      8. Unlocking the Inverse of a Function: Turning It Inside Out
      9. Answers to Problems on Functions
    4. Chapter 4: Searching for Roots
      1. Factoring a Factorable Quadratic
      2. Solving a Quadratic Polynomial Equation
      3. Solving High-Order Polynomials
      4. Using Roots to Create an Equation
      5. Graphing Polynomials
      6. Answers to Problems on Roots and Degrees
    5. Chapter 5: Exponential and Logarithmic Functions
      1. Working with Exponential Functions
      2. Eagerly Engaging Edgy Logarithmic Solutions
      3. Making Exponents and Logs Work Together
      4. Using Exponents and Logs in Practical Applications
      5. Answers to Problems on Exponential and Logarithmic Functions
  4. Part 2: Trig Is the Key: Basic Review, the Unit Circle, and Graphs
    1. Chapter 6: Basic Trigonometry and the Unit Circle
      1. Finding the Six Trigonometric Ratios
      2. Solving Word Problems with Right Triangles
      3. Unit Circle and the Coordinate Plane: Finding Points and Angles
      4. Finding Ratios from Angles on the Unit Circle
      5. Solving Trig Equations
      6. Making and Measuring Arcs
      7. Answers to Problems on Basic Trig and the Unit Circle
    2. Chapter 7: Graphing and Transforming Trig Functions
      1. Getting a Grip on Periodic Graphs
      2. Parent Graphs and Transformations: Sine and Cosine
      3. Tangent and Cotangent: More Family Members
      4. Generations: Secant and Cosecant
      5. Answers to Problems on Graphing and Transforming Trig Functions
  5. Part 3: Digging into Advanced Trig: Identities, Theorems, and Applications
    1. Chapter 8: Basic Trig Identities
      1. Using Reciprocal Identities to Simplify Trig Expressions
      2. Simplifying with Pythagorean Identities
      3. Discovering Even-Odd Identities
      4. Simplifying with Co-Function Identities
      5. Moving with Periodicity Identities
      6. Tackling Trig Proofs (Identities)
      7. Answers to Problems on Basic Trig Identities
    2. Chapter 9: Advanced Trig Identities
      1. Simplifying with Sum and Difference Identities
      2. Using Double-Angle Identities
      3. Reducing with Half-Angle Identities
      4. Changing Products to Sums
      5. Expressing Sums as Products
      6. Powering Down: Power-Reducing Formulas
      7. Answers to Problems on Advanced Trig Identities
    3. Chapter 10: Solving Oblique Triangles
      1. Solving a Triangle with the Law of Sines: ASA and AAS
      2. Tackling Triangles in the Ambiguous Case: SSA
      3. Conquering a Triangle with the Law of Cosines: SAS and SSS
      4. Using Oblique Triangles to Solve Practical Applications
      5. Figuring Area
      6. Answers to Problems on Solving Triangles
  6. Part 4: Polar Coordinates, Cones, Solutions, Sequences, and Finding Your Limits
    1. Chapter 11: Exploring Complex Numbers and Polar Coordinates
      1. Performing Operations with and Graphing Complex Numbers
      2. Round a Pole: Graphing Polar Coordinates
      3. Changing to and from Polar
      4. Graphing Polar Equations
      5. Answers to Problems on Complex Numbers and Polar Coordinates
    2. Chapter 12: Conquering Conic Sections
      1. A Quick Conic Review
      2. Going Round and Round with Circles
      3. The Ups and Downs: Graphing Parabolas
      4. The Fat and the Skinny: Graphing Ellipses
      5. No Caffeine Required: Graphing Hyperbolas
      6. Identifying Conic Sections
      7. Conic Sections in Parametric Form and Polar Coordinates
      8. Answers to Problems on Conic Sections
    3. Chapter 13: Finding Solutions for Systems of Equations
      1. A Quick-and-Dirty Technique Overview
      2. Solving Two Linear Equations with Two Variables
      3. Not-So-Straight: Solving Nonlinear Systems
      4. Systems of More Than Two Equations
      5. Graphing Systems of Inequalities
      6. Breaking Down Decomposing Partial Fractions
      7. Working with a Matrix
      8. Getting It in the Right Form: Simplifying Matrices
      9. Solving Systems of Equations Using Matrices
      10. Answers to Problems on Systems of Equations
    4. Chapter 14: Spotting Patterns in Sequences and Series
      1. General Sequences and Series: Determining Terms
      2. Working Out the Common Difference: Arithmetic Sequences and Series
      3. Simplifying Geometric Sequences and Series
      4. Expanding Polynomials Using the Binomial Theorem
      5. Answers to Problems on Sequences, Series, and Binomials
    5. Chapter 15: Previewing Calculus
      1. Finding Limits: Graphically, Analytically, and Algebraically
      2. Knowing Your Limits
      3. Calculating the Average Rate of Change
      4. Determining Continuity
      5. Answers to Problems on Calculus
  7. Part 5: The Part of Tens
    1. Chapter 16: Ten Plus Parent Graphs
      1. Squaring Up with Quadratics
      2. Cueing Up for Cubics
      3. Rooting for Square Roots and Cube Roots
      4. Graphing Absolutely Fabulous Absolute Value Functions
      5. Flipping over Rational Functions
      6. Exploring Exponential Graphs and Logarithmic Graphs
      7. Seeing the Sine and Cosine
      8. Covering Cosecant and Secant
      9. Tripping over Tangent and Cotangent
      10. Lining Up and Going Straight with Lines
    2. Chapter 17: Ten Missteps to Avoid
      1. Going Out of Order (of Operations)
      2. FOILing Binomials Incorrectly
      3. Breaking Up Fractions Badly
      4. Combining Terms That Can’t Be Combined
      5. Forgetting to Flip the Fraction
      6. Losing the Negative (Sign)
      7. Oversimplifying Roots
      8. Executing Exponent Errors
      9. Ignoring Extraneous
      10. Misinterpreting Trig Notation
  8. Index
  9. About the Author
  10. Connect with Dummies
  11. End User License Agreement

Product information

  • Title: Pre-Calculus Workbook For Dummies, 3rd Edition
  • Author(s): Mary Jane Sterling
  • Release date: April 2019
  • Publisher(s): For Dummies
  • ISBN: 9781119508809