Elementary Algebra (2e)

The Sullivan/Struve/Mazzarella Algebra Series was written to motivate students to “do the math” outside of the classroom through a design and organization that models what you do inside the classroom. The left-to-right annotations in the examples provide a teacher’s voice through every step of the problem-solving process. The Sullivan exercise sets, which begin with Quick Checks to reinforce each example, present problem types of every possible derivation with a gradual increase in difficulty level. The new “Do the Math” Workbook acts as a companion to the text and to MyMathLab^® by providing short warm-up exercises, guided practice examples, and additional “Do the Math” practice exercises for every section of the text.

1. Operations on Real Numbers and Algebraic Expressions

1.1 Success in Mathematics

1.2 Fractions, Decimals, and Percents

1.3 The Number Systems and the Real Number Line

1.4 Adding, Subtracting, Multiplying, and Dividing Integers

1.5 Adding, Subtracting, Multiplying, and Dividing Rational Numbers Expressed as Fractions and Decimals

            Putting the Concepts Together (Sections 1.2—1.5)

1.6 Properties of Real Numbers

1.7 Exponents and the Order of Operations

1.8 Simplifying Algebraic Expressions

            Chapter 1 Activity: The Math Game

            Chapter 1 Review

            Chapter 1 Test

 

2. Equations and Inequalities in One Variable

2.1 Linear Equations: The Addition and Multiplication Properties of Equality

2.2 Linear Equations: Using the Properties Together

2.3 Solving Linear Equations Involving Fractions and Decimals; Classifying Equations

2.4 Evaluating Formulas and Solving Formulas for a Variable

            Putting the Concepts Together (Sections 2.1—2.4)

2.5 Introduction to Problem Solving: Direct Translation Problems

2.6 Problem Solving: Direct Translation Problems Involving Percent

2.7 Problem Solving: Geometry and Uniform Motion

2.8 Solving Linear Inequalities in One Variable

            Chapter 2 Activity: Pass to the Right

            Chapter 2 Review

            Chapter 2 Test

 

3. Introduction to Graphing and Equations of Lines

3.1 The Rectangular Coordinate System and Equations in Two Variables

3.2 Graphing Equations in Two Variables

3.3 Slope

3.4 Slope-Intercept Form of a Line

3.5 Point-Slope Form of a Line

3.6 Parallel and Perpendicular Lines

            Putting the Concepts Together (Sections 3.1—3.6)

3.7 Linear Inequalities in Two Variables

            Chapter 3 Activity: Graphing Practice

            Chapter 3 Review

            Chapter 3 Test

            Cumulative Review Chapters 1—3

 

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations Using Substitution

4.3 Solving Systems of Linear Equations Using Elimination

            Putting the Concepts Together (Sections 4.1—4.3)

4.4 Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations

4.5 Solving Mixture Problems Using Systems of Linear Equations

4.6 Systems of Linear Inequalities

            Chapter 4 Activity: Find the Numbers

            Chapter 4 Review

            Chapter 4 Test

 

5. Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 Multiplying Monomials: The Product and Power Rules

5.3 Multiplying Polynomials

5.4 Dividing Monomials: The Quotient Rule and Integer Exponents

            Putting the Concepts Together (Sections 5.1—5.4)

5.5 Dividing Polynomials

5.6 Applying the Exponent Rules: Scientific Notation

            Chapter 5 Activity: What Is the Question?

            Chapter 5 Review

            Chapter 5 Test

            Cumulative Review Chapters 1—5

 

6. Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x² + bx + c

6.3 Factoring Trinomials of the Form ax² + bx + c, a ≠ 1

6.4 Factoring Special Products

6.5 Summary of Factoring Techniques

            Putting the Concepts Together (Sections 6.1—6.5)

6.6 Solving Polynomial Equations by Factoring

6.7 Modeling and Solving Problems with Quadratic Equations

            Chapter 6 Activity: Which One Does Not Belong?

            Chapter 6 Review

            Chapter 6 Test

 

7. Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with a Common Denominator

7.4 Finding the Least Common Denominator and Forming Equivalent Rational Expressions

7.5 Adding and Subtracting Rational Expressions with Unlike Denominators

7.6 Complex Rational Expressions

            Putting the Concepts Together (Sections 7.1—7.6)

7.7 Rational Equations

7.8 Models Involving Rational Equations

7.9 Variation

            Chapter 7 Activity: Correct the Quiz

            Chapter 7 Review

            Chapter 7 Test

            Cumulative Review Chapters 1—7

 

8. Roots and Radicals

8.1 Introduction to Square Roots

8.2 Simplifying Square Roots

8.3 Adding and Subtracting Square Roots

8.4 Multiplying Expressions with Square Roots

8.5 Dividing Expressions with Square Roots

            Putting the Concepts Together (Sections 8.1—8.5)

8.6 Solving Equations Containing Square Roots

8.7 Higher Roots and Rational Exponents

            Chapter 8 Activity: Working Together with Radicals

            Chapter 8 Review

            Chapter 8 Test

 

9. Quadratic Equations

9.1 Solving Quadratic Equations Using the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations Using the Quadratic Formula

            Putting the Concepts Together (Sections 9.1—9.3)

9.4 Problem Solving Using Quadratic Equations

9.5 The Complex Number System

            Chapter 9 Activity: The Math Game

            Chapter 9 Review

            Chapter 9 Test

            Cumulative Review Chapters 1—9

 

10. Graphs of Quadratic Equations in Two Variables and an Introduction to Functions

10.1 Quadratic Equations in Two Variables

10.2 Relations

            Putting the Concepts Together (Sections 10.1—10.2)

10.3 An Introduction to Functions

            Chapter 10 Activity: Discovering Shifting

            Chapter 10 Review

            Chapter 10 Test

 

Appendix A: Table of Square Roots

Appendix B: Geometry Review

Answers to Selected Exercises

Graphing Answers Section

Applications Index

Subject Index

Photo Credits

New and Updated Features

• Quick Check Exercises, which follow every example, are now numbered as the first problems in each section's exercise set to make them easier to assign as homework. Quick Checks provide the platform for student to get “into the text.” By starting their homework with these Exercises, students will be directed to the instructional material in that section, increasing their confidence and ability to work any math problem–particularly when they are away from the classroom. Answers to the Quick Check exercises have been included in the back of the text.
• The exercise sets have been updated and re-designed in a 2-column format for better organization and more visual appeal.
• The Annotated Instructor’s Edition contains annotated answers placed next to their respective exercises.

Content Changes

• The former Chapter 8, Introduction to Graphing and Equations of Lines, and Chapter 9, Systems of Linear Equations and Inequalities, have been moved to Chapters 3 and 4, allowing instructors to cover ”everything linear” early in the course.
• The former Section 8.7, Variation, is now Section 7.9, so that content on variation appears in the same chapter as rational expressions.

New to the Supplements Package

• The Do the Math Workbook offers a collection of 5-Minute Warm-Up exercises, Guided Practice exercises, and Do the Math exercises for each section in the text. These worksheets can be used as in-class assignments, as an in-lab study assignment or for homework.
• The Videos on DVD offer a lecture for every section of the text. All videos include optional subtitles in English and Spanish.
• MyMathLab enhancements include:

• Substantially increased coverage of exercises (including Chapter Review exercises) to give students more opportunity for practice.
• Authors in Action Videos, made with Camtasia, take students into the classrooms of authors Michael Sullivan, Katherine Struve, and Janet Mazzarella.
• Video lectures and chapter test solutions on video, now with optional subtitles in English and Spanish.
• Translating Word Problems Animations to help students practice the translation step of solving word problems.
• An Interactive English/Spanish glossary that offers definitions of important mathematical terms in both English and Spanish.

• Sullivan Examples and Showcase Examples provide students with superior guidance and instruction when they need it most–when they are away from the instructor and the classroom.

• Sullivan examples feature an active two-column format in which annotations are provided to the left of the algebra, mirroring the way that we read. The annotations explain what the authors are about to do in each step instead of what was just done.
• Showcase Examples provide how-to instruction in an easy-to-understand, 3-column format. The left column describes a step, the middle column provides a brief annotation, as needed, to explain the step, and the right column presents the algebra.
• Placed at the conclusion of most examples, the Quick Check exercises provide students with immediate reinforcement and instant feedback to determine their understanding of the concepts presented in the examples.
• Students learn algebra by doing algebra. Throughout the textbook, the exercise sets are grouped into eight categories–some of which appear only as needed:
• “Preparing For...”problems are located at the opening of a section. These test students’ grasp of the prerequisite material for each new section.
• Quick Check Exercises immediately follow the examples, allowing students to practice and apply what they have just learned. These exercises are also assignable as homework, so students can easily refer back to the relevant example for extra help.

• Building Skills exercises are drill problems that develop the students' understanding of the procedures and skills in working with the methods presented in the section. These exercises are tied to the section objectives and are often linked back to an example.
• Mixed Practice exercises offer comprehensive skill assessment by asking students to relate multiple concepts or objectives. These exercise sets may also include problems from previous sections so that students must first recognize the problem-type before using the appropriate technique to solve it.
• Applying the Concepts exercises ask students to apply the mathematical concepts to real-world situations.
• Extending the Concepts exercises go beyond the basics, using a variety of problems to sharpen students' critical-thinking skills.
• Explaining the Concepts problems ask students to explain the concepts in their own words.
• Graphing calculator exercises are optional and may appear at the end of a section's exercise set.
• Study Skills features are a regular theme throughout the book, anticipating students’ needs and providing the voice of an instructor.
• Section 1.1: Success in Mathematics introduces the basics of study skills, such as what to do during the first week of the semester; what to do before, during and after class; how to use the text effectively; and prepare for an exam.
• In Words features help students understand definitions and theorems by putting them in plain English, just like an instructor would do in class.
• Work Smart features identify common errors to avoid and encourage students to work more efficiently.
• Work Smart: Study Skills boxes appear throughout the book to remind students to stay organized and to manage their time in the most effective way possible.
• Test preparation features help students make the most of their study time.
• Chapter Tests reflect the levels and types of exercises that students are likely to see on an exam, providing a valuable study tool that decreases anxiety and stress.
• The Chapter Test Prep Video CD provides step-by-step solutions to every problem from the Chapter Tests, and is included with every new copy of the book. These videos provide guidance and support when students need the most help: the night before an exam.
• The Big Picture: Putting It Together chapter openers summarize the concepts and techniques previously presented and then relate this material to the concepts about to be presented.

Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.