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.

About This Book

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

• You’re fresh off Algebra I and feel eager to start on this new venture.
• You’ve been away from algebra for a while, but math has always been your main interest, so you don’t want to start too far back.
• You’re a parent of a student embarking on or having some trouble with an Algebra II class and you want to help.
• You’re just naturally curious about science and mathematics and you want to get to the good stuff that’s in Algebra II.

Whichever category you represent (and I may have missed one or two), you’ll find what you need in this book. You can find some advanced algebraic topics, but I also cover the necessary basics, too. You can also find plenty of connections — the ways different algebraic topics connect with each other and the ways the algebra connects with other areas of mathematics.

After all, the many other math areas drive Algebra II. Algebra is the passport to studying calculus, trigonometry, number theory, geometry, all sorts of good mathematics, and much of science. Algebra is basic, and the algebra you find here will help you grow your skills and knowledge so you can do well in math courses and possibly pursue other math topics.

To help you navigate this book, I use the following conventions:

• I italicize special mathematical terms and define them right then and there so you don’t have to search around.
• I use boldface text to indicate keywords in bulleted lists or the action parts of numbered steps. I describe many algebraic procedures in a step-by-step format and then use those steps in an example or two.
• Sidebars are shaded boxes that contain text you may find interesting, but this text isn’t necessarily critical to your understanding of the chapter or topic.

Foolish Assumptions

Algebra II is essentially a continuation of Algebra I, so I have some assumptions I need to make about anyone who wants (or has) to take algebra one step further.

I assume that a person reading about Algebra II has a grasp of the arithmetic of signed numbers — how to combine positive and negative numbers and come out with the correct sign. Another assumption I make is that your order of operations is in order. Working your way through algebraic equations and expressions requires that you know the rules of order. Imagine yourself at a meeting or in a courtroom. You don’t want to be called out of order!  

I assume that people who complete Algebra I successfully know how to solve equations and do basic graphs. Even though I lightly review these topics in this book, I assume that you have a general knowledge of the necessary procedures. I also assume that you have a handle on the basic terms you run across in Algebra I, such as

• binomial: An expression with two terms
• coefficient: The multiplier or factor of a variable
• constant: A number that doesn’t change in value
• expression: Combination of numbers and variables grouped together — not an equation or inequality
• factor (n.): Something multiplying something else
• factor (v.): To change the format of several terms added together into a product
• linear: An expression in which the highest power of any variable term is one
• monomial: An expression with only one term
• polynomial: An expression with several terms
• quadratic: An expression in which the highest power of any variable term is two
• simplify: To change an expression into an equivalent form that you combined, reduced, factored, or otherwise made more useable
• solve: To find the value or values of the variable that makes a statement true
• term: A grouping of constants and variables connected by multiplication, division, or grouping symbols and separated from other constants and variables by addition or subtraction
• trinomial: An expression with three terms
• variable: Something that can have many values (usually represented by a letter to indicate that you have many choices for its value)

If you feel a bit over your head after reading through some chapters, you may want to refer to Algebra I For Dummies (Wiley) for a more complete explanation of the basics. My feelings won’t be hurt; I wrote that one, too!

Icons Used in This Book

The icons that appear in this book are great for calling attention to what you need to remember or what you need to avoid when doing algebra. Think of the icons as signs along the Algebra II Highway; you pay attention to signs — you don’t run them over!

This icon provides you with the rules of the road. You can’t go anywhere without road signs — and in algebra, you can’t get anywhere without following the rules that govern how you deal with operations. In place of “Don’t cross the solid yellow line,” you see “Reverse the sign when multiplying by a negative.” Not following the rules gets you into all sorts of predicaments with the Algebra Police (namely, your instructor).

This icon is like the sign alerting you to the presence of a sports arena, museum, or historical marker. Use this information to improve your mind, and put the information to work to improve your algebra problem-solving skills.

This icon lets you know when you’ve come to a point in the road where you should soak in the information before you proceed. Think of it as stopping to watch an informative sunset. Don’t forget that you have another 30 miles to Chicago. Remember to check your answers when working with rational equations.

This icon alerts you to common hazards and stumbling blocks that could trip you up — much like “Watch for Falling Rock” or “Railroad Crossing.” Those who have gone before you have found that these items can cause a huge failure in the future if you aren’t careful.

Yes, Algebra II does present some technical items that you may be interested to know. Think of the temperature or odometer gauges on your dashboard. The information they present is helpful, but you can drive without it, so you can simply glance at it and move on if everything is in order.

Beyond the Book

In addition to all the great content provided in this book, you can find even more of it online. Check out www.dummies.com/cheatsheet/algebraii for a free Cheat Sheet that provides you with a quick reference to some standard forms, such as special products and equations of conics; some formulas, such as those needed for counting techniques and sequences and series; and, yes, those ever-important laws of logarithms.

You can also find several bonus articles on topics such as just what a normal line is (as opposed to abnormal?) and how mathematics helped a young man become king at www.dummies.com/extras/algebraii.

Where to Go from Here

I’m so pleased that you’re willing, able, and ready to begin an investigation of Algebra II. If you’re so pumped up that you want to tackle the material cover to cover, great! But you don’t have to read the material from page 1 to page 2 and so on. You can go straight to the topic or topics you want or need and refer to earlier material if necessary. You can also jump ahead if so inclined. I include clear cross-references in chapters that point you to the chapter or section where you can find a particular topic — especially if it’s something you need for the material you’re looking at or if it extends or furthers the discussion at hand.

You can use the table of contents at the beginning of the book and the index in the back to navigate your way to the topic that you need to brush up on. Or, if you’re more of a freewheeling type of guy or gal, take your finger, flip open the book, and mark a spot. No matter your motivation or what technique you use to jump into the book, you won’t get lost because you can go in any direction from there.

Enjoy!