Algebra and Functions Workbook

Welcome

to the Ready Set, Go! Algebra & Functions Workbook!

About This Book

This book will help high school math students at all learning levels understand basic algebra. Students will develop the skills, confidence, and knowledge they need to succeed on high school math exams with emphasis on passing high school graduation exams.

More than 20 easy-to-follow lessons break down the material into the basics. In-depth, step-by-step examples and solutions reinforce student learning, while the Math Flash feature provides useful tips and strategies, including advice on common mistakes to avoid.

Students can take drills and quizzes to test themselves on the subject matter, then review any areas in which they need improvement or additional reinforcement. The book conclude with a final exam, designed to comprehensively test what students have learned.

The Ready, Set, Go! Algebra & Functions Workbook will help students master the basics of mathematics—and help them face their next math test—with confidence!

Icons Explained

Icons make navigating through the book easier. The icons, explained below, highlight tips and strategies, where to review a topic, and the drills found at the end of each lesson.

Math Flash!

Look for the Math Flash feature for helpful tips and strategies, including advice on how to avoid common mistakes.

When you see the Let’s Review icon, you know just where to look for more help with the topic on which you are currently working.

Test Yourself!

The Test Yourself! icon, found at the end of every lesson, signals a short drill that reviews the skills you have studied in that lesson.

To the Student

This workbook will help you master the fundamentals of Algebra & Functions. It offers you the support you need to boost your skills and helps you succeed in school and beyond!

It takes the guesswork out of math by explaining what you most need to know in a step-by-step format. When you apply what you learn from this workbook, you can

do better in class;

raise your grades, and

score higher on your high school math exams.

Each compact lesson in this book introduces a math concept and explains the method behind it in plain language. This is followed with lots of examples with fully worked-out solutions that take you through the key points of each problem.

The book gives you two tools to measure what you learn along the way:

e9780738667409_img_10003.gif Short drills that follow each lesson

e9780738667409_img_10004.gif Quizzes that test you on multiple lessons

These tools are designed to comfortably build your test-taking confidence.

Meanwhile, the Math Flash feature throughout the book offers helpful tips and strategies—including advice on how to avoid common mistakes.

When you complete the lessons, take the final exam at the end of the workbook to see how far you’ve come. If you still need to strengthen your grasp on any concept, you can always go back to the related lesson and review at your own pace.

To the Parent

For many students, math can be a challenge—but with the right tools and support, your child can master the basics of algebra. As educational publishers, our goal is to help all students develop the crucial math skills they’ll need in school and beyond.

This Ready, Set, Go! Workbook is intended for students who need to build their basic algebra skills. It was specifically created and designed to assist students who need a boost in understanding and learning the math concepts that are most tested along the path to graduation. Through a series of easy-to-follow lessons, students are introduced to the essential mathematical ideas and methods, and then take short quizzes to test what they are learning.

Each lesson is devoted to a key mathematical building block. The concepts and methods are fully explained, then reinforced with examples and detailed solutions. Your child will be able to test what he or she has learned along the way, and then take a cumulative exam found at the end of the book.

Whether used in school with teachers, for home study, or with a tutor, the Ready, Set, Go! Workbook is a great support tool. It can help improve your child’s math proficiency in a way that’s fun and educational!

To the Teacher

As you know, not all students learn the same, or at the same pace. And most students require additional instruction, guidance, and support in order to do well academically.

Using the Curriculum Focal Points of the National Council of Teachers of Mathematics, this workbook was created to help students increase their math abilities and succeed on high school exams with special emphasis on high school proficiency exams. The book’s easy-to-follow lessons offer a review of the basic material, supported by examples and detailed solutions that illustrate and reinforce what the students have learned.

To accommodate different pacing for students, we provide drills and quizzes throughout the book to enable students to mark their progress. This approach allows for the mastery of smaller chunks of material and provides a greater opportunity to build mathematical competence and confidence.

When we field-tested this series in the classroom, we made every effort to ensure that the book would accommodate the common need to build basic math skills as effectively and flexibly as possible. Therefore, this book can be used in conjunction with lesson plans, stand alone as a single teaching source, or be used in a group-learning environment. The practice quizzes and drills can be given in the classroom as part of the overall curriculum or used for independent study. A cumulative exam at the end of the workbook helps students (and their instructors) gauge their mastery of the subject matter.

We are confident that this workbook will help your students develop the necessary skills and build the confidence they need to succeed on high school math exams.

Lesson One

Variables and Algebraic Expressions in One Variable

In this lesson, we will explore the meaning of algebraic expressions or an equation that has one unknown. This is represented by a letter. These letters are called variables. You will see that an expression with a variable can be solved when you are given the value of the variable.

Your Goal: When you have completed this lesson, you should be able to determine the value of any algebraic expression involving one variable.

Algebraic expressions contain a combination of letters (called variables) and numbers (called constants). These variables and constants are joined together using any or all of the arithmetic operations. These include addition, subtraction, multiplication, division, and exponents. The variables represent unknown quantities. Usually, letters such as x, y, and z are used to represent unknown quantities; however, there is no strict rule as to which letters may be used. In this lesson, we will just use either x, y, or z to represent the unknown quantity. Remember that whenever you see a variable such as x, it means 1 · x, usually written as 1x. Caution: This does not mean that the value of x is 1.

Math Flash

(6w)² ≠ 6w²

On the left side, we first multiply 6 by w, then square this result; on the right side, we square w first, then multiply this number by 6. Suppose w = 2. (6 × 2)² = 12² = 144. However, 6(2)² = 6 × 4 = 24. They are not equal!

Test Yourself!

Evaluate each algebraic expression with the given value of the variable.

Lesson Two

Linear Equations in One Variable—Part 1

In this lesson, we will explore the methods to solve a linear equation in one variable. Each of these equations will have a single answer, also called a solution. As in Lesson 1, we will use the letters x, y, or z to represent the unknown quantity; however, you need to understand that any letter may be used.

Your Goal: When you have completed this lesson, you should be able to determine the solution of a linear equation for which there is exactly one solution. In a later lesson, we will work on linear equations for which there is either no solution or infinitely many solutions.

As we proceed through this lesson, you need to know that an equation represents a balance of two equal quantities. Basically, this means that the left side must be equal to the right side. For a linear equation, the highest exponent of the given variable will be 1. In each equation, the letter x will be used. (Any letter would be allowed.)