Introduction - Idiot's Guides - Algebra I

Idiot's Guides: Algebra I (2015)


Do you have a favorite type of reading? Do you love romance or biography? What about movies and television? Is there a genre that you prefer? Are you a science fiction buff, or a reality show junkie? I enjoy a lot of those, but if I have to pick a favorite type of story to read or watch, I’ll go for mysteries every time. Within the general heading of mysteries, my true passion is police procedurals, or in common language, cop shows. The ones that involve great forensic science are particular favorites but anything that involves investigation will get my attention.

You might be wondering why I’m talking about books and movies in an algebra book. You can probably find quite a few people who would describe algebra as a mystery, and of course, with all the problems that instruct us to “find x,” algebra can feel like an endless search. The real connection, I think, is between the structure of the story and the structure of this book.

How This Book Is Organized

This book is presented in five parts. Each part contains from one to five chapters, grouped together around some common aspects of the work.

Part 1, Introduction to Algebra, takes you from arithmetic to the fundamentals of algebra. This part provides a foundation by looking at numbers, introducing variables, and showing how your knowledge of arithmetic can transfer to algebra. This part also introduces functions, the relationships at the center of much of our work in algebra. That’s the set up to our mystery story. We get a little background and an introduction to our task.

Part 2, Linear Relationships, gets you started on the straight and narrow. Mysteries always begin with a smooth start to the investigation, and our study of algebra begins with linear functions that operate in clear, predictable ways. We graph lines, find the equations of lines from their graphs, and solve linear equations and inequalities. It’s all connected and tied up with a few clear rules, but it’s enough for us to solve quite a few problems.

Part 3, Variations on the Line, introduces the lines that don’t behave like other lines, the horizontal and vertical lines. You’ll meet absolute value functions, made up of parts of two different lines, and learn to solve systems, problems that simultaneously solve two linear equations.

Part 4, Polynomials, is that crucial part of the mystery story where everything starts to look complicated but the heroes untangle it all. When we first meet polynomials, they look complicated, but we’ll bring our algebra skills to bear, and learn to add, subtract, multiply, and divide them, and even disassemble them into products of simpler expressions.

Part 5, Radical, Quadratic, and Rational Functions, gives you the tools to amaze all onlookers by using your previously acquired skills to unravel the mysteries of functions, which that seem dramatically different from the linear relationships with which we began.


As you make your way through this investigation of algebra, you’ll see some items set off in ways meant to catch your attention. Here’s a summary of what you’ll see.


All the evidence in the world won’t help you solve a mystery if you don’t know what it means. Clear definitions are important to understanding. The Definition sidebars throughout this book will show you critical words and phrases that you’ll want to know and use.


Like most things, algebra is full of spots where it’s easy to trip up. Don’t get caught making a rookie mistake! These sidebars serve as a caution and try to help you think and act like an algebra detective.


Algebra is full of little bits of information that are helpful to know, but many times we don’t learn them until we’ve had some experience. Watch for sidebars throughout the book that point out those bits of information to give you the benefit of others’ experience.


These sidebars will encourage you to stop for a moment to think about why the techniques you’re learning work. You’ll find that when you understand the “whys,” you’ll have a better grasp of the concepts and of when and how to use them.


As you investigate the various mysteries that algebra presents, you’ll want to stop from time to time and take stock of what you know. Check Points ask you to answer a few questions to see if you’re ready to move on. You’ll find the answers for these Check Point questions in Appendix B.

But Wait! There’s More!

Have you logged on to lately? If you haven’t, go there now! As a bonus to the book, we’ve included 400 practice problems to help you practice your new algebra skills. You can find them at