Algebra II For Dummies

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Sterling Mary Jane. Algebra II For Dummies

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Part I. Homing in on Basic Solutions

Chapter 1. Going Beyond Beginning Algebra

Outlining Algebraic Properties

Ordering Your Operations

Zeroing in on the Multiplication Property of Zero

Expounding on Exponential Rules

Implementing Factoring Techniques

Chapter 2. Toeing the Straight Line: Linear Equations

Linear Equations: Handling the First Degree

Linear Inequalities: Algebraic Relationship Therapy

Absolute Value: Keeping Everything in Line

Chapter 3. Conquering Quadratic Equations

Implementing the Square Root Rule

Dismantling Quadratic Equations into Factors

Resorting to the Quadratic Formula

Completing the Square: Warming Up for Conics

Tackling Higher-Powered Polynomials

Solving Quadratic Inequalities

Chapter 4. Rooting Out the Rational, Radical, and Negative

Acting Rationally with Fraction-Filled Equations

Ridding Yourself of a Radical

Changing Negative Attitudes about Exponents

Fooling Around with Fractional Exponents

Chapter 5. Graphing Your Way to the Good Life

Coordinating Your Graphing Efforts

Streamlining the Graphing Process with Intercepts and Symmetry

Graphing Lines

Looking at 10 Basic Forms

Solving Problems with a Graphing Calculator

Part II. Facing Off with Functions

Chapter 6. Formulating Function Facts

Defining Functions

Homing In on Domain and Range

Betting on Even or Odd Functions

Facing One-to-One Confrontations

Going to Pieces with Piecewise Functions

Composing Yourself and Functions

Singing Along with Inverse Functions

Chapter 7. Sketching and Interpreting Quadratic Functions

Interpreting the Standard Form of Quadratics

Investigating Intercepts in Quadratics

Going to the Extreme: Finding the Vertex

Lining Up along the Axis of Symmetry

Sketching a Graph from the Available Information

Applying Quadratics to the Real World

Chapter 8. Staying Ahead of the Curves: Polynomials

Taking a Look at the Standard Polynomial Form

Exploring Polynomial Intercepts and Turning Points

Determining Positive and Negative Intervals

Finding the Roots of a Polynomial

Synthesizing Root Findings

Chapter 9. Reasoning with Rational Functions

Exploring Rational Functions

Adding Asymptotes to the Rational Pot

Accounting for Removable Discontinuities

Pushing the Limits of Rational Functions

Putting It All Together: Sketching Rational Graphs from Clues

Chapter 10. Exposing Exponential and Logarithmic Functions

Evaluating Exponential Expressions

Exponential Functions: It’s All About the Base, Baby

Solving Exponential Equations

Showing an “Interest” in Exponential Functions

Logging On to Logarithmic Functions

Solving Logarithmic Equations

Graphing Exponential and Logarithmic Functions

Part III. Conquering Conics and Systems of Equations

Chapter 11. Cutting Up Conic Sections

Cutting Up a Cone

Opening Every Which Way with Parabolas

Going Round and Round in Conic Circles

Preparing Your Eyes for Solar Ellipses

Feeling Hyper about Hyperbolas

Identifying Conics from Their Equations, Standard or Not

Chapter 12. Solving Systems of Linear Equations

Looking at the Standard Linear-Systems Form and Its Possible Solutions

Graphing Solutions of Linear Systems

Solving Systems of Two Linear Equations by Using Elimination

Making Substitution the Choice

Using Cramer’s Rule to Defeat Unwieldy Fractions

Tackling Linear Systems with Three Linear Equations

Upping the Ante with Larger Systems

Applying Linear Systems to Our 3-D World

Using Systems to Decompose Fractions

Chapter 13. Solving Systems of Nonlinear Equations and Inequalities

Crossing Parabolas with Lines

Intertwining Parabolas and Circles

Planning Your Attack on Other Systems of Equations

Playing Fair with Inequalities

Part IV. Shifting into High Gear with Advanced Concepts

Chapter 14. Simplifying Complex Numbers in a Complex World

Using Your Imagination to Simplify Powers of i

Understanding the Complexity of Complex Numbers

Solving Quadratic Equations with Complex Solutions

Working Polynomials with Complex Solutions

Chapter 15. Making Moves with Matrices

Describing the Different Types of Matrices

Performing Operations on Matrices

Defining Row Operations

Finding Inverse Matrices

Dividing Matrices by Using Inverses

Using Matrices to Find Solutions for Systems of Equations

Chapter 16. Making a List: Sequences and Series

Understanding Sequence Terminology

Taking Note of Arithmetic and Geometric Sequences

Recursively Defining Functions

Making a Series of Moves

Applying Sums of Sequences to the Real World

Highlighting Special Formulas

Chapter 17. Everything You Wanted to Know about Sets

Revealing Set Notation

Operating on Sets

Drawing Venn You Feel Like It

Focusing on Factorials

How Do I Love Thee? Let Me Count Up the Ways

Branching Out with Tree Diagrams

Part V. The Part of Tens

Chapter 18. Ten Multiplication Tricks

Squaring Numbers that End in 5

Finding the Next Perfect Square

Recognizing the Pattern in Multiples of 9 and 11

Casting Out 9s

Casting Out 9s: The Multiplication Moves

Multiplying by 11

Multiplying by 5

Finding Common Denominators

Determining Divisors

Multiplying Two-Digit Numbers

Chapter 19. Ten Special Types of Numbers

Triangular Numbers

Square Numbers

Hexagonal Numbers

Perfect Numbers

Amicable Numbers

Happy Numbers

Abundant Numbers

Deficient Numbers

Narcissistic Numbers

Prime Numbers

About the Author

Dedication

Author’s Acknowledgments

WILEY END USER LICENSE AGREEMENT

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Here you are, contemplating reading a book on Algebra II. It isn’t a mystery novel, although you can find people who think mathematics in general is a mystery. It isn’t a historical account, even though you find some historical tidbits scattered here and there. Science fiction it isn’t; mathematics is a science, but you find more fact than fiction. As Joe Friday (star of the old Dragnet series) says, “The facts, ma’am, just the facts.” This book isn’t light reading, although I attempt to interject humor whenever possible. What you find in this book is a glimpse into the way I teach: uncovering mysteries, working in historical perspectives, providing information, and introducing the topic of Algebra II with good-natured humor. This book has the best of all literary types! Over the years, I’ve tried many approaches to teaching algebra, and I hope that with this book I’m helping you cope with and incorporate other teaching methods.

Because you’re interested in this book, you probably fall into one of four categories:

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So, you can say and so on, along with .

To simplify a radical expression such as , you change the radicals to exponents and apply the rules for multiplication and division of values with the same base (see the previous section):

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