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More About This Textbook
Overview
Elayn MartinGay's developmental math textbooks and video resources are motivated by her firm belief that every student can succeed. MartinGay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of MartinGay's algebra series continues her focus on students and what they need to be successful.
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Meet the Author
An awardwinning instructor and bestselling author, Elayn MartinGay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the MartinGay series. Elayn also pioneered the Chapter Test Prep Video to help students as they prepare for a test–their most “teachable moment!”
Elayn’s experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the InstructortoInstructor video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the videos useful for review.
Her textbooks and acclaimed video program support Elayn's passion of helping every student to succeed.
Read an Excerpt
PREFACE
ABOUT THE BOOK
Beginning Algebra, Third Edition was written to provide a solid foundation in algebra for students who might have had no previous experience in algebra. Specific care has been taken to ensure that students have the most uptodate and relevant text preparation for their next mathematics course, as well as to help students to succeed in nonmathematical courses that require a grasp of algebraic fundamentals. I have tried to achieve this by writing a userfriendly text that is keyed to objectives and contains many workedout examples. The basic concepts of graphing are introduced early, and problem solving techniques, reallife and realdata applications, data interpretation, appropriate use of technology, mental mathematics, number sense, critical thinking, decisionmaking, and geometric concepts are emphasized and integrated throughout the book..
The many factors that contributed to the success of the first two editions have been retained. In preparing this edition, I considered the comments and suggestions of colleagues throughout the country, students, and many users of the prior editions. The AMATYC Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus and the MAA and NCTM standards (plus Addenda), together with advances in technology, also influenced the writing of this text.
Beginning Algebra, Third Edition is part of a series of texts that can include Basic College Mathematics, Prealgebra, Third Edition, Intermediate Algebra, Third Edition, or Intermediate Algebra: A Graphing Approach, Second Edition, andBeginning and Intermediate Algebra, Second Edition, a combined algebra text. 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 IN THE THIRD 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.
Problem Solving Process. This is formally introduced in Chapter 2 with a new fourstep process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps throughout the text in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' confidence in tackling problems.
Applications and Connections. Every effort was made to include as many accessible, interesting, and relevant reallife applications as possible throughout the text in both workedout examples and exercise sets. The applications strengthen students' understanding of mathematics in the real world and help to motivate students. They show connections to a wide range of fields including agriculture, allied health, art, astronomy, automotive ownership, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry and statistics. (See the Index of Applications on page xxi.) Many of the applications are based on recent and interesting reallife data. Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included.
Helpful Hints. Helpful Hints, formerly Reminders, 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. They are highlighted in a box for quick reference and, as appropriate, an indicator line is used to precisely identify the particular part of a problem or concept being discussed. For instance, see pages 96 and 408.
Visual Reinforcement of Concepts. The text contains numerous graphics, models, and illustrations to visually clarify and reinforce concepts. These include new and updated bar graphs, circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now over 1,000 figures.
Real World Chapter Openers. The new twopage chapter opener focuses on how math is used in a specific career, provides links to the World Wide Web, and references a "Spotlight on Decision Making" feature within the chapter for further exploration of the career and the relevance of algebra. For example, look at the opener for Chapter 8. The opening pages also contain a list of section titles, and an introduction to the mathematics to be studied together with mathematical connections to previous chapters in the text.
Student Resource Icons. At the beginning of each section, videotape, tutorial software CD Rom, Student Solutions Manual, and Study Guide icons are displayed. These icons help reinforce that these learning aids are available should students wish to use them to review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.
Chapter Highlights. Found at the end of each chapter, the Chapter Highlights contain key definitions, concepts, and examples to help students understand and retain what they have learned.
Chapter Project. This feature occurs at the end of each chapter, often serving as a chapter wrapup. For individual or group completion, the multipart Chapter Project, usually handson or data based, allows students to problem solve, make interpretations, and to think and write about algebra.
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. For example, look at pages 190 and 191 in Section 3.4.
EXERCISE SETS
Each text section ends with an exercise set, usually divided into two parts. Both parts contain graded exercises. The first part is carefully keyed to at least one worked example in the text. Once a student has gained confidence in a skill, the second part contains exercises not keyed to examples. Exercises and examples marked with a video icon have been worked out stepbystep by the author in the videos that accompany this text.
Throughout the text exercises 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, throughout the text there is integration of geometric concepts, such as perimeter and area. Exercises and examples marked with a geometry icon have been identified for convenience.
Each exercise set contains one or more of the following features.
Spotlight on Decision Making. These unique new, specially designed applications help students develop their decisionmaking and problem solving abilities, skills useful in mathematics and in life. Appropriately placed before an exercise set begins, students have an opportunity to immediately practice and reinforce basic algebraic concepts found in the accompanying section in relevant, accessible contexts. There is an emphasis on workplace or jobrelated career situations (such as the decisions of a small business owner in Section 3.1, a physical therapist in Section 7.2, or a registered nurse in Section 8.5) as well as decisionmaking in general (such as choosing a homeowner's insurance policy in Section 2.8 or choosing a credit card in Section 5.5 or deciding when to plant flower bulbs in Section 10.6).
Mental Mathematics. These problems are found at the beginning of many exercise sets. They are mental warmups that 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.
Writing Exercises. These exercises now found in almost every exercise set are marked with the pencil 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. Writing opportunities also occur within features such as Spotlight on Decision Making and Chapter Projects.
Data and Graphical Interpretation. Throughout the text there is an emphasis on data interpretation in exercises via tables, bar charts, line graphs, or circle graphs. The ability to interpret data and read and create a variety of graphs is developed gradually so students become comfortable with it. In addition, there is an appendix on mean, median, and mode together with exercises.
Calculator Explorations and Exercises. These optional explorations offer guided instruction, through examples and exercises, on the proper use of scientific and graphing calculators or computer graphing utilities as tools in the mathematical problemsolving process. Placed appropriately throughout the text, these explorations reinforce concepts or motivate discovery learning.
Additional exercises building on the skills developed in the Explorations may be found in exercise sets throughout the text, and are marked with the icon for scientific calculator use and with the icon for graphing calculator use.
Review Exercises. These exercises occur in each exercise set (except for those in Chapter 1). These problems are keyed to earlier 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.
A Look Ahead. These exercises occur at the end of some exercise sets. This section contains examples and problems similar to those found in a subsequent algebra course. "A Look Ahead" is presented as a natural extension of the material and contains an example followed by advanced exercises.
In addition to the approximately 5,500 exercises within chapters, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, as Cumulative Reviews.
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 verbal skills.
Chapter Review and Chapter Test. The end of each chapter contains a 'review of topics introduced in the chapter. The review problems are keyed to sections. The chapter test is not keyed to sections.
Cumulative Review. Each chapter after the first contains a cumulative review of all chapters beginning with the first up through the chapter at hand. Each problem contained in the cumulative review is actually 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 workedout solution, with explanation, can do so by turning to the appropriate example in the text.
KEY CONTENT FEATURES IN THE THIRD 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 reallife applications and exercises. For example, look at Sections 1.9, 2.5, or 7.2. Some sections have internal reorganization to better clarify and enhance the presentation.
Increased Integration of Geometry Concepts. In addition to the traditional topics in beginning algebra courses, this text contains a strong emphasis on problem solving, and geometric concepts are integrated throughout. The geometry concepts presented are those most important to a students' understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with the triangle icon. Also, geometric figures, a review of angles, lines, and special triangles, as well as a new review of volume and surface area are covered in the appendices. The inside front cover provides a quick reference of geometric formulas.
Review of Real Numbers. Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. Former Sections 1.3 and 1.4 were merged to form new Section 1.4 for a smoother, more efficient flow. Chapter 1 now begins with Study Tips for Success in Mathematics (Section 1.1). New applications and real data enhance the chapter, especially in the reading graphs section.
Early and Intuitive Introduction to Graphing. As bar and line graphs are gradually introduced in Chapters 1 and 2, an emphasis is placed on the notion of paired data. This leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 3. Chapter 3 is devoted to graphing and concepts of graphing linear equations such as slope and intercepts. These concepts are reinforced throughout exercise sets in subsequent chapters, helping prepare students for more work with equations in Chapter 7.
Chapter 3 has been updated, and the overall emphasis was to better reinforce key concepts. Reviewers have been pleased. Following user recommendations, a few of the changes are: Section 3.1 contains scattergrams of real data. Section 3.2 contains a new example and exercises on graphing and interpreting linear equations that model real data. Section 3.4 contains a new example and exercises interpreting slope as a rate of change. As usual, exercise sets progress gradually from easier to more difficult exercises.
Increased Attention to Problem Solving. Building on the strengths of the prior editions, a special emphasis and strong commitment is given to contemporary, accessible, and practical applications of algebra. Real data was drawn from a variety of sources including internet sources, magazines, newspapers, government publications, and reference books. New Spotlight on Decision Making exercises and a new fourstep problem solving process are incorporated throughout to focus on helping to build students problemsolving skills.
Increased Opportunities for Using Technology. Optional explorations for a calculator or graphing calculator (or graphing utility such as Texas Instruments Interactive), are integrated appropriately throughout the text in Calculator Explorations features and in exercises marked with a calculator icon. The MartinGay companion website includes links to internet sites to allow opportunities for finding data and researching potential mathematically related careers branching from the chapter openers.
New Examples. Detailed stepbystep examples were added, deleted, replaced, or updated as needed. Many of these reflect real life. Examples are used in two ways. Often there are numbered, formal examples, and occasionally an example or application is used to introduce a topic or informally discuss the topic.
New Exercises. A significant amount of time was spent on the exercise sets. New exercises and examples help address a wide range of student learning styles and abilities. The text now includes the following types of exercises: spotlight on decision making exercises, mental math, computational exercises, reallife applications, wring exercises, multipart exercises, review exercises, a look ahead exercises, optional calculator or graphing calculator exercises, data analysis from tables and graphs, vocabulary checks, and projects for individual or group assignment.
Enhanced Supplements Package. The new Third Edition is supported by a wealth of supplements designed for added effectiveness and efficiency. New items include the MathPro 4.0 Explorer tutorial software together with a unique video clip feature" new computerized testing system TestGenEQ, and an expanded and improve MartinGay companion website. Some highlights in print materials include the addition of teaching tips in the Annotated Instructor's Edition, and an expander Instructor's Resource Manual with Tests including additional exercises and short grout activities in a readytouse format. Please see the list of supplements for descriptions.
OnLine Options for Distance Learning
For maximum convenience, Prentice Hall offers online interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text, Beginning Algebra.
Companion Website
Visit ...
Table of Contents
1. Review of Real Numbers
1.1 Tips for Success in Mathematics
1.2 Symbols and Sets of Numbers
1.3 Fractions and Mixed Numbers
1.4 Exponents, Order of Operations, Variable Expressions and Equations
1.5 Adding Real Numbers
1.6 Subtracting Real Numbers
1.7 Multiplying and Dividing Real Numbers
1.8 Properties of Real Numbers
2. Equations, Inequalities, and Problem Solving
2.1 Simplifying Algebraic Expressions
2.2 The Addition Property of Equality
2.3 The Multiplication Property of Equality
2.4 Solving Linear Equations
2.5 An Introduction to Problem Solving
2.6 Formulas and Problem Solving
2.7 Percent and Mixture Problem Solving
2.8 Further Problem Solving
2.9 Solving Linear Inequalities
3. Graphing
3.1 Reading Graphs and the Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 Intercepts
3.4 Slope and Rate of Change
3.5 Equations of Lines
3.6 Functions
4. Solving Systems of Linear Equations and Inequalities
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Addition
4.4 Systems of Linear Equations and Problem Solving
4.5 Graphing Linear Inequalities
4.6 Systems of Linear Inequalities
5. Exponents and Polynomials
5.1 Exponents
5.2 Adding and Subtracting Polynomials
5.3 Multiplying Polynomials
5.4 Special Products
5.5 Negative Exponents and Scientific Notation
5.6 Dividing Polynomials
6. Factoring Polynomials
6.1 The Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x ^{2} + bx + c
6.3 Factoring Trinomials of the Form ax ^{2} + bx + c and Perfect Square Trinomial
6.4 Factoring Trinomials of the Form ax ^{2} + bx + c by Grouping
6.5 Factoring Binomials
6.6 Solving Quadratic Equations by Factoring
6.7 Quadratic Equations and Problems Solving
7. Rational Expressions
7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominators
7.4 Adding and Subtracting Rational Expressions with Unlike Denominators
7.5 Solving Equations Containing Rational Expressions
7.6 Proportion and Problem Solving with Rational Equations
7.7 Variation and Problem Solving
7.8 Simplifying Complex Fractions
8. Roots and Radicals
8.1 Introduction to Radicals
8.2 Simplifying Radicals
8.3 Adding and Subtracting Radicals
8.4 Multiplying and Dividing Radicals
8.5 Solving Equations Containing Radicals
8.6 Radical Equations and Problem Solving
8.7 Rational Exponents
9. Quadratic Equations
9.1 Solving Quadratic Equations by the Square Root Property
9.2 Solving Quadratic Equations by Completing the Square
9.3 Solving Quadratic Equations by the Quadratic Formula
9.4 Complex Solutions of Quadratic Equations
9.5 Graphing Quadratic Equations
Appendix A. Geometry
Appendix B. Additional Exercises on Proportion and Proportion Applications
Appendix C. Operations on Decimals
Appendix D. Mean, Median, and Mode
Appendix E. Tables
Preface
PREFACE
ABOUT THE BOOK
Beginning Algebra, Third Edition was written to provide a solid foundation in algebra for students who might have had no previous experience in algebra. Specific care has been taken to ensure that students have the most uptodate and relevant text preparation for their next mathematics course, as well as to help students to succeed in nonmathematical courses that require a grasp of algebraic fundamentals. I have tried to achieve this by writing a userfriendly text that is keyed to objectives and contains many workedout examples. The basic concepts of graphing are introduced early, and problem solving techniques, reallife and realdata applications, data interpretation, appropriate use of technology, mental mathematics, number sense, critical thinking, decisionmaking, and geometric concepts are emphasized and integrated throughout the book..
The many factors that contributed to the success of the first two editions have been retained. In preparing this edition, I considered the comments and suggestions of colleagues throughout the country, students, and many users of the prior editions. The AMATYC Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus and the MAA and NCTM standards (plus Addenda), together with advances in technology, also influenced the writing of this text.
Beginning Algebra, Third Edition is part of a series of texts that can include Basic College Mathematics, Prealgebra, Third Edition, Intermediate Algebra, Third Edition, or Intermediate Algebra: A Graphing Approach, Second Edition,andBeginning and Intermediate Algebra, Second Edition, a combined algebra text. 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 IN THE THIRD 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.
Problem Solving Process. This is formally introduced in Chapter 2 with a new fourstep process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps throughout the text in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' confidence in tackling problems.
Applications and Connections. Every effort was made to include as many accessible, interesting, and relevant reallife applications as possible throughout the text in both workedout examples and exercise sets. The applications strengthen students' understanding of mathematics in the real world and help to motivate students. They show connections to a wide range of fields including agriculture, allied health, art, astronomy, automotive ownership, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry and statistics. (See the Index of Applications on page xxi.) Many of the applications are based on recent and interesting reallife data. Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included.
Helpful Hints. Helpful Hints, formerly Reminders, 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. They are highlighted in a box for quick reference and, as appropriate, an indicator line is used to precisely identify the particular part of a problem or concept being discussed. For instance, see pages 96 and 408.
Visual Reinforcement of Concepts. The text contains numerous graphics, models, and illustrations to visually clarify and reinforce concepts. These include new and updated bar graphs, circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now over 1,000 figures.
Real World Chapter Openers. The new twopage chapter opener focuses on how math is used in a specific career, provides links to the World Wide Web, and references a "Spotlight on Decision Making" feature within the chapter for further exploration of the career and the relevance of algebra. For example, look at the opener for Chapter 8. The opening pages also contain a list of section titles, and an introduction to the mathematics to be studied together with mathematical connections to previous chapters in the text.
Student Resource Icons. At the beginning of each section, videotape, tutorial software CD Rom, Student Solutions Manual, and Study Guide icons are displayed. These icons help reinforce that these learning aids are available should students wish to use them to review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.
Chapter Highlights. Found at the end of each chapter, the Chapter Highlights contain key definitions, concepts, and examples to help students understand and retain what they have learned.
Chapter Project. This feature occurs at the end of each chapter, often serving as a chapter wrapup. For individual or group completion, the multipart Chapter Project, usually handson or data based, allows students to problem solve, make interpretations, and to think and write about algebra.
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. For example, look at pages 190 and 191 in Section 3.4.
EXERCISE SETS
Each text section ends with an exercise set, usually divided into two parts. Both parts contain graded exercises. The first part is carefully keyed to at least one worked example in the text. Once a student has gained confidence in a skill, the second part contains exercises not keyed to examples. Exercises and examples marked with a video icon have been worked out stepbystep by the author in the videos that accompany this text.
Throughout the text exercises 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, throughout the text there is integration of geometric concepts, such as perimeter and area. Exercises and examples marked with a geometry icon have been identified for convenience.
Each exercise set contains one or more of the following features.
Spotlight on Decision Making. These unique new, specially designed applications help students develop their decisionmaking and problem solving abilities, skills useful in mathematics and in life. Appropriately placed before an exercise set begins, students have an opportunity to immediately practice and reinforce basic algebraic concepts found in the accompanying section in relevant, accessible contexts. There is an emphasis on workplace or jobrelated career situations (such as the decisions of a small business owner in Section 3.1, a physical therapist in Section 7.2, or a registered nurse in Section 8.5) as well as decisionmaking in general (such as choosing a homeowner's insurance policy in Section 2.8 or choosing a credit card in Section 5.5 or deciding when to plant flower bulbs in Section 10.6).
Mental Mathematics. These problems are found at the beginning of many exercise sets. They are mental warmups that 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.
Writing Exercises. These exercises now found in almost every exercise set are marked with the pencil 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. Writing opportunities also occur within features such as Spotlight on Decision Making and Chapter Projects.
Data and Graphical Interpretation. Throughout the text there is an emphasis on data interpretation in exercises via tables, bar charts, line graphs, or circle graphs. The ability to interpret data and read and create a variety of graphs is developed gradually so students become comfortable with it. In addition, there is an appendix on mean, median, and mode together with exercises.
Calculator Explorations and Exercises. These optional explorations offer guided instruction, through examples and exercises, on the proper use of scientific and graphing calculators or computer graphing utilities as tools in the mathematical problemsolving process. Placed appropriately throughout the text, these explorations reinforce concepts or motivate discovery learning.
Additional exercises building on the skills developed in the Explorations may be found in exercise sets throughout the text, and are marked with the icon for scientific calculator use and with the icon for graphing calculator use.
Review Exercises. These exercises occur in each exercise set (except for those in Chapter 1). These problems are keyed to earlier 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.
A Look Ahead. These exercises occur at the end of some exercise sets. This section contains examples and problems similar to those found in a subsequent algebra course. "A Look Ahead" is presented as a natural extension of the material and contains an example followed by advanced exercises.
In addition to the approximately 5,500 exercises within chapters, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, as Cumulative Reviews.
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 verbal skills.
Chapter Review and Chapter Test. The end of each chapter contains a 'review of topics introduced in the chapter. The review problems are keyed to sections. The chapter test is not keyed to sections.
Cumulative Review. Each chapter after the first contains a cumulative review of all chapters beginning with the first up through the chapter at hand. Each problem contained in the cumulative review is actually 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 workedout solution, with explanation, can do so by turning to the appropriate example in the text.
KEY CONTENT FEATURES IN THE THIRD 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 reallife applications and exercises. For example, look at Sections 1.9, 2.5, or 7.2. Some sections have internal reorganization to better clarify and enhance the presentation.
Increased Integration of Geometry Concepts. In addition to the traditional topics in beginning algebra courses, this text contains a strong emphasis on problem solving, and geometric concepts are integrated throughout. The geometry concepts presented are those most important to a students' understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with the triangle icon. Also, geometric figures, a review of angles, lines, and special triangles, as well as a new review of volume and surface area are covered in the appendices. The inside front cover provides a quick reference of geometric formulas.
Review of Real Numbers. Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. Former Sections 1.3 and 1.4 were merged to form new Section 1.4 for a smoother, more efficient flow. Chapter 1 now begins with Study Tips for Success in Mathematics (Section 1.1). New applications and real data enhance the chapter, especially in the reading graphs section.
Early and Intuitive Introduction to Graphing. As bar and line graphs are gradually introduced in Chapters 1 and 2, an emphasis is placed on the notion of paired data. This leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 3. Chapter 3 is devoted to graphing and concepts of graphing linear equations such as slope and intercepts. These concepts are reinforced throughout exercise sets in subsequent chapters, helping prepare students for more work with equations in Chapter 7.
Chapter 3 has been updated, and the overall emphasis was to better reinforce key concepts. Reviewers have been pleased. Following user recommendations, a few of the changes are: Section 3.1 contains scattergrams of real data. Section 3.2 contains a new example and exercises on graphing and interpreting linear equations that model real data. Section 3.4 contains a new example and exercises interpreting slope as a rate of change. As usual, exercise sets progress gradually from easier to more difficult exercises.
Increased Attention to Problem Solving. Building on the strengths of the prior editions, a special emphasis and strong commitment is given to contemporary, accessible, and practical applications of algebra. Real data was drawn from a variety of sources including internet sources, magazines, newspapers, government publications, and reference books. New Spotlight on Decision Making exercises and a new fourstep problem solving process are incorporated throughout to focus on helping to build students problemsolving skills.
Increased Opportunities for Using Technology. Optional explorations for a calculator or graphing calculator (or graphing utility such as Texas Instruments Interactive), are integrated appropriately throughout the text in Calculator Explorations features and in exercises marked with a calculator icon. The MartinGay companion website includes links to internet sites to allow opportunities for finding data and researching potential mathematically related careers branching from the chapter openers.
New Examples. Detailed stepbystep examples were added, deleted, replaced, or updated as needed. Many of these reflect real life. Examples are used in two ways. Often there are numbered, formal examples, and occasionally an example or application is used to introduce a topic or informally discuss the topic.
New Exercises. A significant amount of time was spent on the exercise sets. New exercises and examples help address a wide range of student learning styles and abilities. The text now includes the following types of exercises: spotlight on decision making exercises, mental math, computational exercises, reallife applications, wring exercises, multipart exercises, review exercises, a look ahead exercises, optional calculator or graphing calculator exercises, data analysis from tables and graphs, vocabulary checks, and projects for individual or group assignment.
Enhanced Supplements Package. The new Third Edition is supported by a wealth of supplements designed for added effectiveness and efficiency. New items include the MathPro 4.0 Explorer tutorial software together with a unique video clip feature" new computerized testing system TestGenEQ, and an expanded and improve MartinGay companion website. Some highlights in print materials include the addition of teaching tips in the Annotated Instructor's Edition, and an expander Instructor's Resource Manual with Tests including additional exercises and short grout activities in a readytouse format. Please see the list of supplements for descriptions.
OnLine Options for Distance Learning
For maximum convenience, Prentice Hall offers online interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text, Beginning Algebra.
Companion Website
Visit ...