Algebra II Workbook For Dummies E-Book

Mary Jane Sterling

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2014

Seitenzahl: 469

Beschreibung

To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you fortrigonometry, calculus, and a of myriad STEM topics. Workingthrough practice problems helps students better ingest and retainlesson content, creating a solid foundation to build on for futuresuccess. Algebra II Workbook For Dummies, 2nd Edition helps youlearn Algebra II by doing Algebra II. Author and math professorMary Jane Sterling walks you through the entire course, showing youhow to approach and solve the problems you encounter in class.You'll begin by refreshing your Algebra I skills, because you'llneed a strong foundation to build upon. From there, you'll workthrough practice problems to clarify concepts and improveunderstanding and retention. * Revisit quadratic equations, inequalities, radicals, and basicgraphs * Master quadratic, exponential, and logarithmic functions * Tackle conic sections, as well as linear and nonlinearsystems * Grasp the concepts of matrices, sequences, and imaginarynumbers Algebra II Workbook For Dummies, 2nd Edition includessections on graphing and special sequences to familiarize you withthe key concepts that will follow you to trigonometry and beyond.Don't waste any time getting started. Algebra II Workbook ForDummies, 2nd Edition is your complete guide to success.

Leseprobe

Algebra II Workbook For Dummies®, 2nd Edition

Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com

Copyright © 2014 by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Control Number: 2013956855

ISBN 978-1-118-86703-7 (pbk); ISBN 978-1-118-86708-2 (ebk); ISBN 978-1-118-86685-6 (ebk)

Manufactured in the United States of America

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Algebra II Workbook For Dummies

Visit www.dummies.com/cheatsheet/algebraiiwb to view this book's cheat sheet.

Table of Contents

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Part I: Getting Started with Algebra II

Chapter 1: Going Beyond Beginning Algebra

Good Citizenship: Following the Order of Operations and Other Properties

Specializing in Products and FOIL

Variables on the Side: Solving Linear Equations

Dealing with Linear Absolute Value Equations

Greater Math Skills: Equalizing Linear Inequalities

Answers to Problems on Going Beyond Beginning Algebra

Chapter 2: Handling Quadratic (and Quadratic-Like) Equations and Inequalities

Finding Reasonable Solutions with Radicals

UnFOILed Again! Successfully Factoring for Solutions

Your Bag of Tricks: Factoring Multiple Ways

Keeping Your Act Together: Factoring by Grouping

Resorting to the Quadratic Formula

Solving Quadratics by Completing the Square

Working with Quadratic-Like Equations

Checking Out Quadratic Inequalities

Answers to Problems on Quadratic (and Quadratic-Like) Equations and Inequalities

Chapter 3: Rooting Out the Rational, the Radical, and the Negative

Doing Away with Denominators with an LCD

Simplifying and Solving Proportions

Wrangling with Radicals

Changing Negative Attitudes toward Negative Exponents

Divided Powers: Solving Equations with Fractional Exponents

Answers to Problems on Rooting Out the Rational, the Radical, and the Negative

Chapter 4: Graphing for the Good Life

Coordinating Axes, Coordinates of Points, and Quadrants

Crossing the Line: Using Intercepts and Symmetry to Graph

Graphing Lines Using Slope-Intercept and Standard Forms

Graphing Basic Polynomial Curves

Grappling with Radical and Absolute Value Functions

Enter the Machines: Using a Graphing Calculator

Answers to Problems on Graphing for the Good Life

Part II: Functions

Chapter 5: Formulating Functions

Evaluating Functions

Determining the Domain and Range of a Function

Recognizing Even, Odd, and One-to-One Functions

Composing Functions and Simplifying the Difference Quotient

Solving for Inverse Functions

Answers to Problems on Formulating Functions

Chapter 6: Specializing in Quadratic Functions

Finding Intercepts and the Vertex of a Parabola

Applying Quadratics to Real-Life Situations

Graphing Parabolas

Answers to Problems on Quadratic Functions

Chapter 7: Plugging In Polynomials

Finding Basic Polynomial Intercepts

Digging Up More-Difficult Polynomial Roots with Factoring

Determining Where a Function Is Positive or Negative

Graphing Polynomials

Possible Roots and Where to Find Them: The Rational Root Theorem and Descartes’s Rule

Getting Real Results with Synthetic Division and the Remainder Theorem

Connecting the Factor Theorem with a Polynomial’s Roots

Answers to Problems on Plugging In Polynomials

Chapter 8: Acting Rationally with Functions

Determining Domain and Intercepts of Rational Functions

Introducing Vertical and Horizontal Asymptotes

Getting a New Slant with Oblique Asymptotes

Removing Discontinuities

Going the Limit: Limits at a Number and Infinity

Graphing Rational Functions

Answers to Problems on Rational Functions

Chapter 9: Exposing Exponential and Logarithmic Functions

Evaluating e-Expressions and Powers of e

Solving Exponential Equations

Making Cents: Applying Compound Interest and Continuous Compounding

Checking Out the Properties of Logarithms

Presto-Chango: Expanding and Contracting Expressions with Log Functions

Solving Logarithmic Equations

They Ought to Be in Pictures: Graphing Exponential and Logarithmic Functions

Answers to Problems on Exponential and Logarithmic Functions

Part III: Conics and Systems of Equations

Chapter 10: Any Way You Slice It: Conic Sections

Putting Equations of Parabolas in Standard Form

Shaping Up: Determining the Focus and Directrix of a Parabola

Back to the Drawing Board: Sketching Parabolas

Writing the Equations of Circles and Ellipses in Standard Form

Determining Foci and Vertices of Ellipses

Rounding Out Your Sketches: Circles and Ellipses

Hyperbola: Standard Equations and Foci

Determining the Asymptotes and Intercepts of Hyperbolas

Sketching the Hyperbola

Answers to Problems on Conic Sections

Chapter 11: Solving Systems of Linear Equations

Solving Two Linear Equations Algebraically

Using Cramer’s Rule to Defeat Unruly Fractions

A Third Variable: Upping the Systems to Three Linear Equations

A Line by Any Other Name: Writing Generalized Solution Rules

Decomposing Fractions Using Systems

Answers to Problems on Systems of Equations

Chapter 12: Solving Systems of Nonlinear Equations and Inequalities

Finding the Intersections of Lines and Parabolas

Crossing Curves: Finding the Intersections of Parabolas and Circles

Appealing to a Higher Power: Dealing with Exponential Systems

Solving Systems of Inequalities

Answers to Problems on Solving Systems of Nonlinear Equations and Inequalities

Part IV: Other Good Stuff: Lists, Arrays, and Imaginary Numbers

Chapter 13: Getting More Complex with Imaginary Numbers

Simplifying Powers of i

Not Quite Brain Surgery: Doing Operations on Complex Numbers

“Dividing” Complex Numbers with a Conjugate

Solving Equations with Complex Solutions

Answers to Problems on Imaginary Numbers

Chapter 14: Getting Squared Away with Matrices

Describing Dimensions and Types of Matrices

Adding, Subtracting, and Doing Scalar Multiplication on Matrices

Trying Times: Multiplying Matrices by Each Other

The Search for Identity: Finding Inverse Matrices

Using Matrices to Solve Systems of Equations

Answers to Problems on Matrices

Chapter 15: Going Out of Sequence with Sequences and Series

Writing the Terms of a Sequence

Differences and Multipliers: Working with Special Sequences

Backtracking: Constructing Recursively Defined Sequences

Using Summation Notation

Finding Sums with Special Series

Answers to Problems on Sequences and Series

Chapter 16: Everything You Ever Wanted to Know about Sets and Counting

Writing the Elements of a Set from Rules or Patterns

Get Together: Combining Sets with Unions, Intersections, and Complements

Multiplication Countdowns: Simplifying Factorial Expressions

Checking Your Options: Using the Multiplication Property

Counting on Permutations When Order Matters

Mixing It Up with Combinations

Raising Binomials to Powers: Investigating the Binomial Theorem

Answers to Problems on Sets and Counting

Part V: The Part of Tens

Chapter 17: Ten Basic Graphs

Putting Polynomials in Their Place

Lining Up Front and Center

Being Absolutely Sure with Absolute Value

Graphing Reciprocals of x and x

2

Rooting Out Square Root and Cube Root

Growing Exponentially with a Graph

Logging In on Logarithmic Graphing

Chapter 18: Ten Special Sequences and Their Sums

Adding As Easy As One, Two, Three

Summing Up the Squares

Finding the Sum of the Cubes

Not Being at Odds with Summing Odd Numbers

Evening Things Out by Adding Up Even Numbers

Adding Everything Arithmetic

Geometrically Speaking

Easing into a Sum for e

Signing In on the Sine

Powering Up on Powers of 2

Adding Up Fractions with Multiples for Denominators

About the Author

Cheat Sheet

More Dummies Products

End User License Agreement

Guide

Table of Contents

Begin Reading

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Introduction

Here you are, pencil in hand, ready to take on the challenges of working on Algebra II problems. How did you get here? Are you taking an Algebra II class and just not getting enough homework assigned? Or have you found a few gaps in the instruction and want to fill them in before you end up with a flood of questions? Maybe you’ve been away from algebra for a while and you want a review. Or perhaps you’re getting ready to tackle another mathematics course, such as Calculus. If you’re looking for some good-natured, clear explanations on how to do some standard and challenging algebra problems, then you’ve come to the right place.

I hope you can find everything you need in this book to practice the concepts of Algebra II. You’ll find some basic (to get you in the mood) and advanced algebra topics. But not all the basics are here — that’s where Algebra I comes in. The topics that aren’t here are referenced for your investigation or further study.

Calculus and other more-advanced math drive Algebra II. Algebra is the passport to studying calculus and trigonometry and number theory and geometry and all sorts of good mathematics and science. Algebra is basic, and the algebra here can help you grow in your skills and knowledge.

About This Book

You don’t have to do the problems in this book in the order in which they’re presented. You can go to the topics you want or need and refer back to earlier problems if necessary. You can jump back and forth and up and down, if so inclined (but please, not on the furniture). The organization allows you to move freely about and find what you need.

Use this book as a review or to supplement your study of Algebra II. Each section has a short explanation and an example or two — enough information to allow you to do the problems.

If you want more background or historical information on a topic, you can refer to the companion book, Algebra II For Dummies, where I go into more depth on what’s involved with each type of problem. (If you need more-basic information, you can try Algebra I For Dummies and Algebra I Workbook For Dummies). In this workbook, I get to the point quickly but with enough detail to see you through. The answers to the problems, at the end of each chapter, provide even more step-by-step instruction.

Foolish Assumptions

You’re interested in doing algebra problems. Is that a foolish thing for me to assume? No! Of course, you’re interested and excited and, perhaps, just a slight bit tentative. No need to worry. In this book, I assume that you have a decent background in the basics of algebra and want to investigate further. If so, this is the place to be. I take those basic concepts and expand your horizons in the world of algebra.

Are you a bit rusty with your algebra skills? Then the worked-out solutions in this book will act as refreshers as you investigate the different topics. You may be preparing for a more advanced mathematics course such as trigonometry or calculus. Again, the material in this book will be helpful.

Or maybe it’s just my first assumption that fits your situation: You’re interested in doing algebra and couldn’t pass up doing the problems in this book!

Icons Used in This Book

Throughout this book, I highlight some of the most important information with icons. Here’s what the icons mean:

You can read the word rules as a noun or a verb. Sometimes it’s hard to differentiate. But usually, in this book, rules is a noun. This icon marks a formula or theorem or law from algebra that pertains to the subject at hand. The rule applies at that moment and at any moment in algebra.

You see this icon when I present an example problem whose solution I walk you through step by step. You get a problem and a detailed answer.

This icon refers back to information that I think you may already know. It needs to be pointed out or repeated so that the current explanation makes sense.

Tips show you a quick and easy way to do a problem. Try these tricks as you’re solving problems.

There are always things that are tricky or confusing or problems that just ask for an error to happen. This icon is there to alert you, hoping to help you avoid a mathematical pitfall.

Beyond the Book

In addition to the material in the print or e-book you’re reading right now, this product also comes with some access-anywhere goodies on the web. No matter how diligent you are about reading through this material, you’ll likely come across a few questions where you don’t have a clue. Check out the free Cheat Sheet at www.dummies.com/cheatsheet/algebraiiwb for helpful information, all provided in a concise, quick-access format.

Finally, you can find some articles online that tie together and offer new insights to the material you find in this book. Go to www.dummies.com/extras/algebraiiwb for these informative articles.

Where to Go from Here

You may become intrigued with a particular topic or particular type of problem. Where do you find more problems like those found in a section? Where do you find the historical background of a favorite algebra process? There are many resources out there, including a couple that I wrote:

Do you like the applications? Try Math Word Problems For Dummies.Are you more interested in the business-type uses of algebra? Take a look at Business Math For Dummies.

If you’re ready for another area of mathematics, look for a couple more of my titles: Trigonometry For Dummies and Linear Algebra For Dummies.

Part I

Getting Started with Algebra II

For Dummies can help you get started with lots of subjects. Visit www.dummies.com to learn more and do more with For Dummies.

In this part …

Find order in the order of operations and relate algebraic properties to processes used when solving equations.Solve linear equations and inequalities and rewrite absolute value equations before solving.Take on radical equations, rational equations, and fractional exponents.Use one or more factorization methods to ready equations for the multiplication property of zero.Solve equations with the quadratic formula or complete the square.Graph basic curves using intercepts and properties of functions.