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Where to Go for Additional Help

The written directions given with the individual problems are designed to tell you what you need to do to get the correct answer. Sometimes the directions may seem vague if you aren’t familiar with the words or the context of the words. Go ahead and look at the solution to see whether that helps you with the meaning. But if the vocabulary is still unrecognizable, you may want to refer to the glossaries in algebra books, such as Algebra I For Dummies or Algebra II For Dummies, written by yours truly and published by John Wiley & Sons, Inc.

      This book is designed to provide you with enough practice to become very efficient in algebra, but it isn’t intended to give the step-by-step explanation on how and why each step is necessary. You may need to refer to Algebra II For Dummies or Algebra II Essentials For Dummies (also written by me) to get more background on a problem or to understand why a particular step is taken in the solution of the problem.

      Algebra is sometimes seen as being a bunch of rules without a particular purpose. Why do you have to solve for the solutions of a quadratic equation? Where will you use that again? The answers to all these questions are more apparent when you see them tied together and when more background information is available. Don’t be shy about seeking out that kind of information.

      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 1

      The Questions

IN THIS PART …

      You get to tackle 1,001 Algebra II problems. Have fun! Here are the general types of questions you’ll be dealing with:

      1  Algebra basics, quadratic equations, and graphing lines (Chapters 1 through 4)

      2  All kinds of functions (Chapters 5 through 9)

      3  Conic sections and linear and nonlinear equations (Chapters 10 through 12)

      4  Complex numbers, matrices, sequences, series, and sets (Chapters 13 through 17)

Chapter 1

      Reviewing Algebra Basics

      The basics of Algebra II consist of the processes learned in earlier exposures to algebra — in this case, all lumped together in one chapter. It’s hard to cover every little thing that you’ll need to continue your algebra study in this one book, but this is a really good place to start. Under the guise of solving some equations and inequalities, you get to review many of the most important properties and procedures needed to be successful. Anything missing in this discussion is covered in later chapters as part of the problems’ explanations.

The Problems You’ll Work On

      In this chapter, you’ll work with simplifying expressions and solving equations and inequalities in the following ways:

       Multiplying binomials and trinomials

       Expanding higher powers of binomials

       Solving linear equations and absolute value equations

       Solving linear inequalities

       Simplifying radical expressions

       Rewriting expressions involving imaginary numbers

What to Watch Out For

      Don’t let common mistakes trip you up; watch for the following when working with simplifying expressions and solving equations and inequalities:

       Distributing the factor over every term in the parentheses

       Multiplying terms by a negative factor

       Reversing the inequality sense when multiplying or dividing by a negative factor

       Correctly multiplying a binomial and its conjugate

       Simplifying expressions involving powers of i

Multiplying Binomials and Trinomials

       1–8 Simplify the expressions by performing the operations and combining like terms.

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