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Prentice Hall Professional Technical Reference
Algebra: A Combined Approach / Edition 1

Algebra: A Combined Approach / Edition 1

by K. Elayn Martin-Gay
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The engaging Martin-Gay workbook series presents a reader-friendly approach to the concepts of basic math and algebra, giving readers ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the workbooks are to build confidence, increase motivation, and encourage mastery of basic skills and concepts. Martin-Gay enhances users' perception of math by exposing them to real-life situations through graphs and applications; and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book includes key topics in algebra such as linear equations and inequalities with one and two variables, systems of equations, polynomial functions and equations, quadratic functions and equations, exponential functions and equations, logarithmic functions an equations, rational and radical expressions, and conic sections. For professionals who wish to brush up on their algebra skills.

Product Details

ISBN-13: 9780130853738
Publisher: Prentice Hall Professional Technical Reference
Publication date: 08/28/1999
Edition description: Older Edition
Product dimensions: 6.00(w) x 1.25(h) x 9.00(d)

Table of Contents

R. Prealgebra Preview.
1. Real Numbers and Introduction to Algebra.
2. Equations, Inequalities and Problem Solving.
3. Graphing Equations and Inequalities.
4. Exponents and Polynomials.
5. Factoring Polynomials.
6. Rational Expressions.
7. Graphs and Functions.
8. Systems of Equations and Inequalities.
9. Rational Exponents, Radicals, and Complex Numbers.
10. Quadratic Equations and Functions.
11. Exponential and Logarithmic Functions.
12. Conic Sections.
Appendix A: An Introduction to Using a Graphing Utility.
Appendix B: Tables of Squares and Square Roots.
Appendix C: Review of Angles, Lines, and Special Triangles.
Appendix D: Review of Geometric Figures.
Appendix E: Mean, Median, and Mode.
Appendix F: Sets and Compound Inequalities.
Appendix G: Absolute Value Equations and Inequalities.
Answers to Selected Exercises.
Solutions to Selected Exercises.


About This Book

Algebra A Combined Approach, Second Edition is intended for a two semester course in introductory and intermediate algebra. It was written to provide a solid foundation in algebra for students who might have had no previous experience in algebra. Specific care was taken to ensure that students have the most up-to-date relevant text preparation for their next mathematics course or for nonmathematical courses that require an understanding of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples. As suggested by the AMATYC Crossroads Document and the NCTM Standards (plus Addenda), real-life and real-data applications, data interpretation, conceptual understanding, problem solving, writing, cooperative learning, appropriate use of technology, mental .mathematics, number sense, critical thinking, and geometric concepts are emphasized and integrated throughout the book.

The many factors that contributed to the success of the first edition have been retained. In preparing the Second Edition, I considered comments and suggestions of colleagues, students, and many users of the prior edition throughout the country.

Algebra A Combined Approach, Second Edition is part of a series of texts that can include Basic College Mathematics, Second Edition; Prealgebra, Third Edition; Introductory Algebra, Second Edition; and Intermediate Algebra, Second Edition. Throughout the series pedagogical features are designed to develop student proficiency in algebra and problem solving, and to prepare students for future courses.

Key Pedagogical Features and Changes in the Second Edition

Readability and Connections. I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to relate the new ideas to those that students may already know. Constant reinforcement and connections within problem-solving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information. In addition, each section begins with a list of objectives covered in the section. Clear organization of section material based on objectives further enhances readability.

Problem-Solving Process. This is formally introduced in Chapter 2 with a four-step process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' comfort level and confidence in tackling problems.

Applications and Connections. Every effort was made to include as many interesting and relevant real-life applications as possible throughout the text in both worked-out examples and exercise sets. In the Second Edition, the applications have been thoroughly revised and updated, and the number of applications has increased. The applications help to motivate students and strengthen their understanding of mathematics in the real world. They show connections to a wide range of fields including agriculture, allied health, anthropology, art, astronomy, biology, business, chemistry, construction, consumer affairs, earth science, education, entertainment, environmental issues, finance, geography, government, history, medicine, music, nutrition, physics, sports, travel, and weather. Many of the applications are based on recent real data. Sources for data include newspapers, magazines, publicly held companies, government agencies, special-interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included. See the Applications Index on page xx.

Practice Problems. Throughout the text, each worked-out example has a parallel Practice Problem placed next to the example in the margin. These invite students to be actively involved in the learning process before beginning the end-of-section exercise set. Practice Problems immediately reinforce a skill after it is developed. Answers appear at the bottom of the page for quick reference.

Concept Checks. These margin exercises are appropriately placed throughout the text. They allow students to gauge their grasp of an idea as it is being explained in the text. Concept Checks stress conceptual understanding at the point of use and help suppress misconceived notions before they start. Answers appear at the bottom of the page.

Increased Integration of Geometry Concepts. In addition to the traditional topics in introductory and intermediate algebra courses, this text contains a strong emphasis on problem solving and geometric concepts, which are integrated throughout. The geometry concepts presented are those most important to a student's understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with the geometry icon. Also, geometric figures, and a review of angles, lines, and special triangles are covered in the appendices.

Helpful Hints. Helpful Hints contain practical advice on applying mathematical concepts. These are found throughout the text and strategically placed where students are most likely to need immediate reinforcement. Helpful Hunts are highlighted for quick reference.

Visual Reinforcement of Concepts. The Second Edition contains a wealth of graphics, models, photographs, and illustrations to visually clarify and reinforce concepts. These include new and updated bar graphs, line graphs, calculator screens, application illustrations, and geometric figures.

Calculator and Graphing Calculator Explorations. These optional explorations offer point-of-use instruction, through examples and exercises, on the proper use of scientific and graphing calculators as tools in the mathematical problem-solving process. Placed appropriately throughout the text, Calculator and Graphing Calculator Explorations also reinforce concepts learned in the corresponding section and motivate discovery-based learning.

Additional exercises building on the skill developed in the Explorations may be found in exercise sets throughout the text. Exercises requiring a calculator are marked with the calculator icon. Exercises requiring a graphing calculator are marked with the calculator icon. An Introduction to Using a Graphing Utility is included in the appendix.

Study Skills Reminders. New Study Skills Reminder boxes are integrated throughout the text. They are strategically placed to constantly remind and encourage students as they hone their study skills. A new Section 1.1, Tips on Success in Mathematics, provides an overview of the Study Skills needed to succeed in math. These are reinforced by the Study Skills Reminder boxes throughout the text.

Focus On. Appropriately placed throughout each chapter, these are divided into Focus on Mathematical Connections, Focus on Business and Career, Focus on the Real World, and Focus on History. They are written to help students develop effective habits for engaging in investigations of other branches of mathematics, understanding the importance of mathematics in various careers and in the world of business, and seeing the relevance of mathematics in both the present and past through critical thinking exercises and group activities.

Chapter Highlights. Found at the end of each chapter, these contain key definitions, concepts, and examples to help students understand and retain what they have learned and help them organize their notes and study for tests.

Chapter Activity. These features occur once per chapter at the end of the chapter, often serving as a chapter wrap-up. For individual or group completion, the Chapter Activity, usually hands-on or data-based, complements and extends to concepts of the chapter, allowing students to make decisions and interpretations and to think and write about algebra.

Integrated Reviews. These "mid-chapter reviews" are appropriately placed once per chapter. Integrated Reviews allow students to review and assimilate the many different skills learned separately over several sections before moving on to related material in the chapter.

Pretests. Each chapter begins with a pretest that is designed to help students identify areas where they need to pay special attention in the upcoming chapter.

Chapter Review and Test. The end of each chapter contains a review of topics introduced in the chapter. The Chapter Review offers exercises that are keyed to sections of the chapter. The Chapter Test is a practice test and is not keyed to sections of the chapter.

Cumulative Review. These features are found at the end of each chapter (except Chapters R and 1). Each problem contained in the Cumulative Review is an earlier worked example in the text that is referenced in the back of the book along with the answer. Students who need to see a complete worked-out solution, with explanation, can do so by turning to the appropriate example in the text.

Student Resource Icons. At the beginning of each section, videotape and CD, tutorial software, Prentice Hall Tutor Center, and solutions manual icons are displayed. These icons help reinforce that these learning aids are available should students wish to use them to help them review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.

Functional Use of Color and New Design. Elements of this text are highlighted with color or design to make it easier for students to read and study. Special care has been taken to use color within solutions to examples or in the art to help clarify, distinguish, or connect concepts.

Exercise Sets. Each text section ends with an Exercise Set. Each exercise in the set, except those found in parts labeled Review and Preview or Combining Concepts, is keyed to one of the objectives of the section. Wherever possible, a specific example is also referenced. In addition to the approximately 5500 exercises in end-of-section exercise sets, exercises may also be found in the Pretests, Integrated Reviews, Chapter Reviews, Chapter Tests, and Cumulative Reviews.

Exercises and examples marked with a video icon have been worked out step-by-step by the author in the videos that accompany this text.

Throughout the exercises in the text there is an emphasis on data and graphical interpretation via tables, charts, and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it. Similarly, geometric concepts--such as perimeter and area--are integrated throughout the text. Exercises and examples marked with a geometry icon have been identified for convenience.

Each exercise set contains one or more of the following features.

Mental Math. Found at the beginning of an exercise set, these mental warmups reinforce concepts found in the accompanying section and increase students' confidence before they tackle an exercise set. By relying on their own mental skills, students increase not only their confidence in themselves but also their number sense and estimation ability.

Review and Preview. These exercises occur in each exercise set (except for those in Chapters R and 1) after the exercises keyed to the objectives of the section. Review and Preview problems are keyed to previous sections and review concepts learned earlier in the text that are needed in the next section or in the next chapter. These exercises show the links between earlier topics and later material.

Combining Concepts. These exercises are found at the end of each exercise set after the Review and Preview exercises. Combining Concepts exercises require students to combine several concepts from that section or to take the concepts of the section a step further by combining them with concepts learned in previous sections. For instance, sometimes students are required to combine the concepts of the section with the problem-solving process they learned in Chapter 2 to try their hand at solving an application problem.

Writing Exercises. These exercises occur in almost every exercise set and are marked with an icon. They require students to assimilate information and provide a written response to explain concepts or justify their thinking. Guidelines recommended by the American Mathematical Association of Two Year Colleges (AMATYC) and other professional groups recommend incorporating writing in mathematics courses to reinforce concepts.

Vocabulary Checks. Vocabulary Checks, new to this edition, provide an opportunity for students to become more familiar with the use of mathematical terms as they strengthen their verbal skills. These appear at the end of the chapter before the Chapter Highlights.

Data and Graphical Interpretation. There is an emphasis on data interpretation in exercises via tables and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it.

Internet Excursions. These exercises occur once per chapter. Internet Excursions require students to use the Internet as a data-collection tool to complete the exercises, allowing students first-hand experience with manipulating and working with real data.

Key Content Features in the Second Edition

Overview. This new edition retains many of the factors that have contributed to its success. Even so, every section of the text was carefully reexamined. Throughout the new edition you will find numerous new applications, examples, and many real-life applications and exercises. For example, look at the exercise sets of Sections 2.5, 2.6, 3.1, 3.4, 7.4, 8.4, and 9.6. Some sections have internal re-organization to better clarify and enhance the presentation.

Chapter 1 now begins with Tips for Success in Mathematics (Section 1.1). New applications, and real data enhance the chapter.

New Study Skills Reminder boxes have been inserted throughout the text. These boxes reinforce the tips from Section 1.1. They are placed strategically to encourage students to hone their study skills.

Increased Integration of Geometry Concepts. The geometry concepts presented are those most important to a student's understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with a geometry icon. Also, geometric figures and a review of angles, lines, and special triangles are covered in the appendices.

New Examples. Detailed step-by-step examples were added, deleted, replaced, or updated as needed. Many of these reflect real life.

Exercise Sets Revised and Updated. The exercise sets have been carefully examined and extensively revised. The real-world and real-data applications have been thoroughly updated and many new applications are included. In addition, an increased number of challenging problems have been included in the new edition. Writing exercises are now included in most exercise sets and new Vocabulary Checks have been added to the end of the chapter to help students become proficient in the language of mathematics.

Additional changes in content include:

  • Determinants and Cramer's Rule is now covered in Appendix F.
  • To facilitate the transition from introductory to intermediate algebra, two new review appendices have been added. These are: Appendix A, Transition Review: Exponents, Polynomials, and Factoring Strategies and Appendix B, Transition Review: Solving Linear and Quadratic Equations.
  • Reading Graphs, formerly Section 1.8, has been combined into Chapter 3 to streamline the presentation.

Enhanced Supplements Package. The Second Edition is supported by a wealth of supplements designed for added effectiveness and efficiency. New items include the MathPro 5 on-line tutorial with diagnostic and unique video clip feature, a new computerized testing system (TestGen-EQ with QuizMaster), Prentice Hall Tutor Center, digitized videos on CD, and Instructor to Instructor, Teaching Mathematics CD Series. Please see the list of supplements for descriptions.

Options for On-line and Distance Learning

For maximum convenience, Prentice Hall offers on-line interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text.

The Companion Web site includes basic distance learning access to provide links to the text's Internet Excursions and a selection of on-line self quizzes. Email is available.

WebCT. WebCT includes distance learning access to content found in the Martin-Gay companion Web site plus more. WebCT provides tools to create, manage, and use on-line course materials. Save time and take advantage of items such as on-line help, communication tools, and access to instructor and student manuals. Your college may already have WebCT's software installed on their server or you may choose to download it. Contact your local Prentice Hall sales representative for details.

BlackBoard. Visit For distance learning access to content and features from the Martin-Gay companion Web site plus more, Blackboard provides simple templates and tools.

Course Compass. Powered by BlackBoard. Visit

Supplements for the Instructor

Printed Supplements

Annotated Instructor's Edition (0-13-067450-8)
• Answers to all exercises printed on the same text page.
• Teaching Tips throughout the text placed at key points in the margin.

Instructor's Solution Manual (0-13-067461-3)
• Solutions to even-numbered section exercises.
• Solutions to every (even and odd) Mental Math exercise.
• Solutions to every (even and odd) Practice Problem (margin exercise).
• Solutions to every (even and odd) exercise found in the Pretests, Integrated Reviews (mid-chapter reviews), Chapter Reviews, Chapter Tests, and Cumulative Reviews.

Instructor's Resource Manual with Tests (0-13-067462-1)
• Notes to the Instructor that include an introduction to Interactive Learning, Interpreting Graphs and Data, Alternative Assessment, Using Technology, and Helping Students Succeed.
• Two free-response Pretests per chapter.
• Eight Chapter Tests per chapter (3 multiple-choice, 5 free-response).
• Two Cumulative Review Tests (one multiple-choice, one free-response) every two chapters.
• Eight Final Exams (3 multiple-choice, 5 free-response).
• Twenty additional exercises per section for added test exercises if needed.
• Group Activities (an average of two per chapter; providing short group activities in a convenient, ready-to-use format).
• Answers to all items.

Media Supplements

TestGen-EQ with QuizMaster CD-ROM (Windows/Macintosh) (0-13-067454-0)
• Algorithmically driven, text-specific testing program.
• Networkable for administering tests and capturing grades on-line.
• Edit and add your own questions to create a nearly unlimited number of tests and worksheets.
• Use the new "Function Plotter" to create graphs.
• Tests can be easily exported to HTML so they can be posted to the Web for student practice.
• Includes an email function for network users, enabling instructors to send a message to a specific student or an entire group.
• Network-based reports and summaries for a class or student and for cumulative or selected scores are available.

MathPro 5 Instructor Version
• On-line, customizable tutorial, diagnostic, and assessment program for anytime, anywhere tutorial support.
• Text specific at the learning objective level.
• Diagnostic option identifies student skills, provides individual learning plan, and tutorial reinforcement.
• Integration of TestGen-EQ allows for testing to operate within the tutorial environment.
• Course management tracking of tutorial and testing activity.

MathPro Explorer 4.0
• Network Version IBM/Mac 0-13-067457-5.
• Enables instructors to create either customized or algorithmically generated practice quizzes from any section of a chapter.
• Includes email function for network users, enabling instructors to send a message to a specific student or to an entire group.
• Network-based reports and summaries for a class or student and for cumulative or selected scores.

Instructor to Instructor Teaching Mathematics CD Series
• Written and presented by Elayn Martin-Gay.
• Contains suggestions for presenting course material, utilizing the integrated resource package, time-saving tips, and much more.

Companion Web Site prenhall.con/martin-gay_algebra
• Create a customized on-line syllabus with Syllabus Manager.
• Links related to the Internet Excursions in each chapter allow students to find and retrieve real data for use in guided problem solving.
• Assign quizzes or monitor student self quizzes by having students email results, such as true/false reading quizzes or vocabulary check quizzes.
• Destination links provide additional opportunities to explore related sites.

Supplements for the Student

Printed Supplements

Student's Solution Manual (0-13-067459-1) • Solutions to odd-numbered section exercises.
• Solutions to every (even and odd) Mental Math exercise.
• Solutions to every (even and odd) Practice Problem (margin exercise).
• Solutions to every (even and odd) exercise found in the Pretests, Integrated Reviews (mid-chapter reviews), Chapter Reviews, Chapter Tests, and Cumulative Reviews.

Media Supplements

MathPro 5 (Student Version)
• Online, customizable tutorial, diagnostic, and assessment software.
• Text specific to the learning objective level, providing anytime, anywhere tutorial support.
• Algorithmically driven for virtually unlimited practice problems with immediate feedback.
• "Watch" screen videoclips by K. Elayn Martin-Gay.
• Step-by Step solutions.
• Summary of Progress.

MathPro 4.0 Student Version (0-13-067456-7)
• Available on CD-ROM for stand alone use or can be networked in the school laboratory.
• Text specific tutorial exercises and instructions at the objective level.
• Algorithmically generated Practice Problems.
• "Watch" screen videoclips by K. Elayn Martin-Gay.

Videotape Series (0-13-067453-2)
• Written and presented by Elayn Martin-Gay.
• Keyed to each section of the text.
• Step-by-step solutions to exercises from each section of the text. Exercises that are worked in the videos are marked with a video icon.

New Digitized Lecture Videos on CD-ROM (0-13-047345-6)
• The entire set of Algebra A Combined Approach, Second Edition lecture videotapes in digital form.
• Convenient access anytime to video tutorial support from a computer at home or on campus.
• Available shrink-wrapped with the text or stand-alone.

New Prentice Hall Tutor Center
• Staffed with developmental math instructors and open 5 days a week, 7 hours per day.
• Obtain help for examples and exercises in Martin-Gay, Algebra A Combined Approach, Second Edition via toll-free telephone, fax, or email.
• The Prentice Hall Tutor Center is accessed through a registration number that may be bundled with a new text or purchased separately with a used book. Visit to learn more.

Companion Web Site
• Links related to the Internet Excursions in each chapter allow you to collect data to solve specific internet exercises.

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