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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 (available separately). This revision of MartinGay's algebra series continues her focus on students and what they need to be successful.
Editorial Reviews
Booknews
Thirteen chapters discuss real numbers; equations, inequalities, and problem solving; graphs and functions; solving systems of linear equations; exponents and polynomials; factoring polynomials; rational expressions; transitions to intermediate algebra; radicals, rational exponents, and complex numbers; quadratic equations and functions; exponential and logarithmic functions; sequences, series, and the binomial theorem; and conic sections. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
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 THIS BOOK
Beginning and Intermediate Algebra, Second Edition, was written to provide a solid foundation in algebra as well as to develop students' problemsolving skills. 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 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 graphs and functions 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 edition 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 edition. 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 and Intermediate Algebra, Second Edition, is part of a series of texts that can include Basic College Mathematics and Prealgebra, Third Edition. Also available are Beginning Algebra, Third Edition, Intermediate Algebra,Third Edition, and Intermediate Algebra: A Graphing Approach, 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 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 every day life can help students gradually master both new and old information.
ProblemSolving 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 beginning 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, astronomy, automotive ownership, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, 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 xxiv.) 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 with and without using the internet are also included.
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. 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 90 and 365.
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 and circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now approximately 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 4. 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 remind students that these learning aids are available should they choose 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.
In addition, a reference to alternative or additional Real World Activities is given. This internet option invites students to find and retrieve real data for use in solving problems. Visit the Real World Activities Website by going to ...
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
Integrated Review–Operations on 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 and Multiplication Properties of Equality
2.3 Solving Linear Equations
Integrated Review–Solving Linear Equations
2.4 An Introduction to Problem Solving
2.5 Formulas and Problem Solving
2.6 Percent and Mixture Problem Solving
2.7 Further Problem Solving
2.8 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
Integrated Review–Summary on Slope and Graphing Linear Equations
3.5 Equation of Lines
3.6 Functions
4. Solving Systems of Linear Equations
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
Integrated Review–Solving Systems of Equations
4.4 Solving Systems of Linear Equations in Three Variables
4.5 Systems of Linear Equations and Problem Solving
5. Exponents and Polynomials
5.1 Exponents
5.2 Polynomial Functions and Adding and Subtracting Polynomials
5.3 Multiplying Polynomials
5.4 Special Products
Integrated Review–Exponents and Operations on Polynomials
5.5 Negative Exponents and Scientific Notation
5.6 Dividing Polynomials
5.7 Synthetic Division and the Remainder Theorem
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 by Perfect Square Trinomials
6.4 Factoring Trinomials of the Form ax ^{2} + bx + c by Grouping
6.5 Factoring Binomials
Integrated Review–Choosing a Factoring Strategy
6.6 Solving Quadratic Equations by Factoring
6.7 Quadratic Equations and Problem Solving
7. Rational Expressions
7.1 Rational Functions and Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator
7.4 Adding and Subtracting Rational Expressions with Unlike Denominators
7.5 Solving Equations Containing Rational Expressions
Integrated Review–Summary on Rational Expressions
7.6 Proportion and Problem Solving with Rational Equations
7.7 Simplifying Complex Fractions
8. More on Functions and Graphs
8.1 Graphing and Writing Linear Functions
8.2 Reviewing Function Notation and Graphing Nonlinear Functions
Integrated Review–Summary on Functions and Equations of Lines
8.3 Graphing PiecewiseDefined Functions and Shifting and Reflecting Graphs of Functions
8.4 Variation and Problem Solving
9. Inequalities and Absolute Value
9.1 Compound Inequalities
9.2 Absolute Value Equations
9.3 Absolute Value Inequalities
Integrated Review–Solving Compound Inequalities and Absolute Value Equations and Inequalities
9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities
10. Rational Exponents, Radicals, and Complex Numbers
10.1 Radicals and Radical Functions
10.2 Rational Exponents
10.3 Simplifying Radical Expressions
10.4 Adding, Subtracting, and Multiplying Radical Expressions
10.5 Rationalizing Denominators and Numerators of Radical Expressions
Integrated Review–Radicals and Rational Exponents
10.6 Radical Equations and Problem Solving
10.7 Complex Numbers
11. Quadratic Equations and Functions
11.1 Solving Quadratic Equations by Completing the Square
11.2 Solving Quadratic Equations by the Quadratic Formula
11.3 Solving Equations by Using Quadratic Methods
Integrated Review–Summary on Solving Quadratic Equations
11.4 Nonlinear Inequalities in One Variable
11.5 Quadratic Functions and Their Graphs
11.6 Further Graphing of Quadratic Functions
12. Exponential and Logarithmic Functions
12.1 The Algebra of Functions; Composite Functions
12.2 Inverse Functions
12.3 Exponential Functions
12.4 Exponential Growth and Decay Functions
12.5 Logarithmic Functions
12.6 Properties of Logarithms
Integrated Review–Functions and Properties of Logarithms
12.7 Common Logarithms, Natural Logarithms, and Change of Base
12.8 Exponential and Logarithmic Equations and Problem Solving
13. Conic Sections
13.1 The Parabola and the Circle
13.2 The Ellipse and the Hyperbola
Integrated Review–Graphing Conic Sections
13.3 Solving Nonlinear Systems of Equations
13.4 Nonlinear Inequalities and Systems of Inequalities
14. Sequences, Series, and the Binomial Theorem
14.1 Sequences
14.2 Arithmetic and Geometric Sequences
14.3 Series
Integrated Review–Sequences and Series
14.4 Partial Sums of Arithmetic and Geometric Sequences
14.5 The Binomial Theorem
Appendix A. Operations on Decimals/Percent, Decimal, and Fraction Table
Appendix B. Review of Algebra Topics
Appendix C. An Introduction to Using a Graphic Utility
Appendix D. Solving Systems of Equations by Matrices
Appendix E. Solving Systems of Equations by Determinants
Appendix F. Mean, Median, and Mode
Appendix G. Review of Angles, Lines, and Special Triangles
Preface
PREFACE
ABOUT THIS BOOK
Beginning and Intermediate Algebra, Second Edition, was written to provide a solid foundation in algebra as well as to develop students' problemsolving skills. 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 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 graphs and functions 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 edition 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 edition. 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 and Intermediate Algebra, Second Edition, is part of a series of texts that can include Basic College Mathematics and Prealgebra, Third Edition. Also available are Beginning Algebra, Third Edition, Intermediate Algebra, ThirdEdition, and Intermediate Algebra: A Graphing Approach, 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 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 every day life can help students gradually master both new and old information.
ProblemSolving 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 beginning 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, astronomy, automotive ownership, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, 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 xxiv.) 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 with and without using the internet are also included.
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. 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 90 and 365.
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 and circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now approximately 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 4. 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 remind students that these learning aids are available should they choose 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.
In addition, a reference to alternative or additional Real World Activities is given. This internet option invites students to find and retrieve real data for use in solving problems. Visit the Real World Activities Website by going to http://www.prenhall.com/martingay.
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 page 301 in Section 5.3.
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 problemsolving 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 Meteorologist in Section 3.1, a phychologist in Section 9.6, or a Webmaster in Section 11.4) as well as decision making in general (such as choosing a credit card in Section 6.5 or deciding between two job offers in Section 4.3).
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 a 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.
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 or 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 7000 exercises within sections, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, and 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 their 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 TIDE 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 reallife applications and exercises. Some sections have internal reorganization to better clarify and enhance the presentation.
Table of Content Changes in the Second Edition. The second edition includes a new Chapter 8, Transitions to Intermediate Algebra. Although intermediate algebra topics are woven into earlier chapters where appropriate, the purpose of this chapter is to help students make the transition from beginning algebra to intermediate algebra. For example, Chapter 8 contains types of equations and inequalities normally found in intermediate algebra, such as absolute value equations and inequalities, system of equations in three variables as well as matrices and determinants.
By moving these intermediate algebra topics to Chapter 8, Chapters 2 and 3 were combined to form a new Chapter 2, Equations, Inequalities, and Problem Solving. As a result, graphing is now covered in Chapter 3, Graphs and Functions. A new Section 3.1 is devoted to introducing the rectangular coordinate system and creating scatter diagrams from real data. Functions are introduced in Section 3.3 and continually revisited to help students fully understand and see the importance of this topic. For example, see Sections 3.4, 5.3, 6.8, and 7.1 just to name a few.
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 geometry icon. Also, geometric figures, a review of angles, lines, and special triangles, are covered in the appendices. The inside front cover provides a quick reference of geometric formulas.
Real Numbers and Algebraic Expressions. Chapter 1 now begins with Tips for Success in Mathematics (Section 1.1). Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. New applications and real data enhance the chapter.
Early and Intuitive Introduction to Graphs and Functions. As bar and line graphs are gradually introduced in Chapters 1 and 2, an emphasis are 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. This edition offers more real data and conceptual type applications and further strengthens the introduction to slope.
Once students are comfortable with graphing equations, functions are introduced in Chapter 3. The concept of function is illustrated in numerous ways to ensure student understanding: by listing ordered pairs of data, showing rectangular coordinate system graphs, visually representing set correspondences, and including numerous realdata and conceptual examples. The importance of a function is continuously reinforced by not treating it as a single, standalone topic but by constantly integrating functions in appropriate sections of this text.
Increased Attention to Problem Solving. Building on the strengths of the prior edition, a special emphasis and strong commitment are 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. Unique Spotlight on Decision Making exercises and a new fourstep problemsolving 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 using it for problem solving such as with the accompanying online Real World Activities. The Website also includes links to search potential mathematically related careers branching from the chapter openers. Instructors may also choose from a variety of distance learning or online delivery options including Blackboard or Web CT.
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, writing 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. Also available are new online Real World Activities accessed via this textbook's companion website, and a selection of group activities in a worksheet ready, easy to use format, found in the Instructor's Resource Manual with Tests.
Enhanced Supplements Package. The new Second 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, a new computerized testing system TestGenEQ, and an expanded and improved MartinGay companion website. Some highlights in print materials include the addition of teaching tips in the Annotated Instructor's Edition, and an expanded Instructor's Resource Manual with Tests including additional exercises and short group activities in a readyto useformat. Please see the list of supplements for descriptions.
OPTIONS FOR ONLINE AND 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 and Intermediate Algebra.
Companion Website
Visit http:llwww.prenhall.com/martingay
The companion Website includes basic distance learning access to provide links to the text's Real World Activities, careerrelated sites referenced in the chapter opening pages and a selection of online self quizzes. Email is available. For quick reference, the inside front cover of this text also lists the companion Website URL.
WebCT
WebCT includes distance learning access to content found in the MartinGay Companion Website plus more: WebCT provides tools to create, manage, and use online course materials. Save time and take advantage of items such as online 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 http://www.prenhall.com/demo
For distance learning access to content and features from the MartinGay Companion Website plus more, Blackboard provides simple templates and tools to create, manage, and use online course materials. Save time and take advantage of items such as online help, course management tools, communication tools, and access to instructor and student manuals. No technical experience required. Contact your local Prentice Hall sales representative for details.
For a complete computerbased internet course
Prentice Hall Interactive Math
Visit http://www.prenhall.com/interactive_math
Prentice Hall Interactive Math is an exciting, proven choice to help students succeed in math. Created for a computerbased course, it provides the effective teaching philosophy of K. Elayn MartinGay in an Internetbased course format. Interactive Math, Introductory and Intermediate Algebra, takes advantage of stateoftheart technology to provide highly flexible and userfriendly course management tools and an engaging, highly interactive student learning program that easily accommodates the variety of learning styles and broad spectrum of students presented by the typical beginning and intermediate algebra class. Personalized learning includes reading, writing, watching video clips, and exploring concepts through interactive questions and activities. Contact your local Prentice Hall sales representative for details.
SUPPLEMENTS FOR THE INSTRUCTOR
Printed Supplements
Annotated Instructor's Edition (ISBN 0130166375)
Instructor's Solutions Manual (ISBN 0130173398)
Instructor's Resource Manual with Tests (ISBN 0130173304)
Media Supplements
TestGen EQ CDROM (Windows/Macintosh) (ISBN 0130185914)
Computerized Tutorial Software Course Management Tools
MathPro 4.0 Explorer Network CDROM (ISBN 0130185930)
Companion Website: http://www.prenhall.com/martingay
SUPPLEMENTS FOR THE STUDENT
Printed Supplements
Student Solutions Manual (ISBN 013017338X)
Student Study Guide (ISBN 013017341X)
How to Study Mathematics
Media Supplements
Computerized Tutorial Software
MathPro 4.0 Explorer Network CDRom (ISBN 0130185930)
MathPro 4.0 Explorer Student CDRom (ISBN 0130185949)
Videotape Series (ISBN 0130185981)
Companion Website: www.prenhall.comlmartingay
Introduction
PREFACE
ABOUT THIS BOOK
Beginning and Intermediate Algebra, Second Edition, was written to provide a solid foundation in algebra as well as to develop students' problemsolving skills. 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 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 graphs and functions 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 edition 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 edition. 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 and Intermediate Algebra, Second Edition, is part of a series of texts that can include Basic College Mathematics and Prealgebra, Third Edition. Also available are Beginning Algebra, Third Edition, Intermediate Algebra, ThirdEdition, and Intermediate Algebra: A Graphing Approach, 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 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 every day life can help students gradually master both new and old information.
ProblemSolving 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 beginning 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, astronomy, automotive ownership, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, 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 xxiv.) 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 with and without using the internet are also included.
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. 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 90 and 365.
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 and circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now approximately 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 4. 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 remind students that these learning aids are available should they choose 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.
In addition, a reference to alternative or additional Real World Activities is given. This internet option invites students to find and retrieve real data for use in solving problems.
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 page 301 in Section 5.3.
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 problemsolving 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 Meteorologist in Section 3.1, a phychologist in Section 9.6, or a Webmaster in Section 11.4) as well as decision making in general (such as choosing a credit card in Section 6.5 or deciding between two job offers in Section 4.3).
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 a 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.
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 or 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 7000 exercises within sections, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, and 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 their 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 TIDE 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 reallife applications and exercises. Some sections have internal reorganization to better clarify and enhance the presentation.
Table of Content Changes in the Second Edition. The second edition includes a new Chapter 8, Transitions to Intermediate Algebra. Although intermediate algebra topics are woven into earlier chapters where appropriate, the purpose of this chapter is to help students make the transition from beginning algebra to intermediate algebra. For example, Chapter 8 contains types of equations and inequalities normally found in intermediate algebra, such as absolute value equations and inequalities, system of equations in three variables as well as matrices and determinants.
By moving these intermediate algebra topics to Chapter 8, Chapters 2 and 3 were combined to form a new Chapter 2, Equations, Inequalities, and Problem Solving. As a result, graphing is now covered in Chapter 3, Graphs and Functions. A new Section 3.1 is devoted to introducing the rectangular coordinate system and creating scatter diagrams from real data. Functions are introduced in Section 3.3 and continually revisited to help students fully understand and see the importance of this topic. For example, see Sections 3.4, 5.3, 6.8, and 7.1 just to name a few.
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 geometry icon. Also, geometric figures, a review of angles, lines, and special triangles, are covered in the appendices. The inside front cover provides a quick reference of geometric formulas.
Real Numbers and Algebraic Expressions. Chapter 1 now begins with Tips for Success in Mathematics (Section 1.1). Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. New applications and real data enhance the chapter.
Early and Intuitive Introduction to Graphs and Functions. As bar and line graphs are gradually introduced in Chapters 1 and 2, an emphasis are 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. This edition offers more real data and conceptual type applications and further strengthens the introduction to slope.
Once students are comfortable with graphing equations, functions are introduced in Chapter 3. The concept of function is illustrated in numerous ways to ensure student understanding: by listing ordered pairs of data, showing rectangular coordinate system graphs, visually representing set correspondences, and including numerous realdata and conceptual examples. The importance of a function is continuously reinforced by not treating it as a single, standalone topic but by constantly integrating functions in appropriate sections of this text.
Increased Attention to Problem Solving. Building on the strengths of the prior edition, a special emphasis and strong commitment are 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. Unique Spotlight on Decision Making exercises and a new fourstep problemsolving 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 using it for problem solving such as with the accompanying online Real World Activities. The Website also includes links to search potential mathematically related careers branching from the chapter openers. Instructors may also choose from a variety of distance learning or online delivery options including Blackboard or Web CT.
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, writing 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. Also available are new online Real World Activities accessed via this textbook's companion website, and a selection of group activities in a worksheet ready, easy to use format, found in the Instructor's Resource Manual with Tests.
Enhanced Supplements Package. The new Second 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, a new computerized testing system TestGenEQ, and an expanded and improved MartinGay companion website. Some highlights in print materials include the addition of teaching tips in the Annotated Instructor's Edition, and an expanded Instructor's Resource Manual with Tests including additional exercises and short group activities in a readyto useformat. Please see the list of supplements for descriptions.
OPTIONS FOR ONLINE AND 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 and Intermediate Algebra.
SUPPLEMENTS FOR THE INSTRUCTOR
Printed Supplements
Annotated Instructor's Edition (ISBN 0130166375)
Instructor's Solutions Manual (ISBN 0130173398)
Instructor's Resource Manual with Tests (ISBN 0130173304)
Media Supplements
TestGen EQ CDROM (Windows/Macintosh) (ISBN 0130185914)
Computerized Tutorial Software Course Management Tools
MathPro 4.0 Explorer Network CDROM (ISBN 0130185930)
SUPPLEMENTS FOR THE STUDENT
Printed Supplements
Student Solutions Manual (ISBN 013017338X)
Student Study Guide (ISBN 013017341X)
How to Study Mathematics
Media Supplements
Computerized Tutorial Software
MathPro 4.0 Explorer Network CDRom (ISBN 0130185930)
MathPro 4.0 Explorer Student CDRom (ISBN 0130185949)
Videotape Series (ISBN 0130185981)