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More About This Textbook
Overview
Introductory Algebra is typically a 1semester course that provides a solid foundation in algebraic skills and reasoning for students who have little or no previous experience with the topic. The goal is to effectively prepare students to transition into Intermediate Algebra.
Editorial Reviews
Booknews
An introductory text covering equations, inequalities, polynomial, rational expressions, graphing, roots and radicals, and quadratic equations. Annotation c. by Book News, Inc., Portland, Or.Product Details
Related Subjects
Meet the Author
Elayn MartinGay, University of New Orleans
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.
Prentice Hall is pleased to announce the new Third Editions of Basic College Mathematics, Introductory Algebra, Intermediate Algebra, and Algebra A Combined Approach and two new first editions, Basic College Mathematics with Early Integers, and Developmental Mathematics. Elayn MartinGay also authors a bestselling ©2005 hardback series in developmental mathematics.
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 originated the Chapter Test Prep Video CDs to help students during their most “teachable moment” —as they prepare for a test.
Elayn’s experience has made her aware of how busy instructors are and what a difference quality supports make. For this reason, she created the InstructortoInstructor video series. These videos provide instructors with suggestions for presenting specific math topic 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 CDs useful for review. They are a great resource for suggestions regarding areas they may wish to emphasize, or common trouble areas students experience, that instructors my wish to highlight.
With her textbooks series, the Chapter Test Prep Video Cd, and CD Lecture series, Elayn has sought to put success within the reach of every student and instructor.
Table of Contents
Chapter R Prealgebra Review
R.1 Factors and the Least Common Multiple
R.2 Fractions
R.3 Decimals and Percents
Chapter 1 Real Numbers and Introduction to Algebra
1.1 Tips for Success in Mathematics
1.2 Symbols and Sets of Numbers
1.3 Exponents, Order of Operations, and Variable Expressions
1.4 Adding Real Numbers
1.5 Subtracting Real Numbers
Integrated Review–Operations on Real Numbers
1.6 Multiplying and Dividing Real Numbers
1.7 Properties of Real Numbers
1.8 Simplifying Expressions
Chapter 2 Equations, Inequalities, and Problem Solving
2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 Further 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 Solving Linear Inequalities
Chapter 3 Exponents and Polynomials
3.1 Exponents
3.2 Negative Exponents and Scientific Notation
3.3 Introduction to Polynomials
3.4 Adding and Subtracting Polynomials
3.5 Multiplying Polynomials
3.6 Special Products
Integrated Review–Exponents and Operations on Polynomials
3.7 Dividing Polynomials
Chapter 4 Factoring Polynomials
4.1 The Greatest Common Factor
4.2 Factoring Trinomials of the Form x² + bx + c
4.3 Factoring Trinomials of the Form ax² + bx + c
4.4 Factoring Trinomials of the Form ax² + bx + c, by Grouping
4.5 Factoring Perfect Square Trinomials and the Difference of Two Squares
Integrated Review–Choosing a Factoring Strategy
4.6 Solving Quadratic Equations by Factoring
4.7 Quadratic Equations and Problem Solving
Chapter 5 Rational Expressions
5.1 Simplifying Rational Expressions
5.2 Multiplying and Dividing Rational Expressions
5.3 Adding and Subtracting Rational Expressions with the Same Denominator and least Common Denominator
5.4 Adding and Subtracting Rational Expressions with Different Denominators
5.5 Solving Equations Containing Rational Expressions
Integrated Review–Summary on Rational Expressions
5.6 Proportion and Problem Solving
5.7 Simplifying Complex Fractions
Chapter 6 Graphing Equations and Inequalities
6.1 Reading Graphs and the Rectangular Coordinate System
6.2 Graphing Linear Equations
6.3 Intercepts
6.4 Slope and Rate of change
6.5 Equations of Lines
Integrated Review–Summary on Linear Equations
6.6 Introduction to Functions
6.7 Graphing Linear Inequalities in Two Variables
6.8 Direct and Inverse Variation
Chapter 7 Systems of Equations
7.1 Solving Systems of Linear Equations by Graphing
7.2 Solving Systems of Linear Equations by Substitution
7.3 Solving Systems of Linear Equations by Addition
Integrated Review–Summary on Solving Systems of Equations
7.4 Systems of Linear Equations and Problem Solving
Chapter 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
Integrated Review–Simplifying Radicals
8.5 Solving Equations Containing Radicals
8.6 Radical Equations and Problem Solving
Chapter 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
Integrated Review–Summary on Quadratic Equations
9.4 Graphing Quadratic Equations in Two Variables
Appendices
A The Bigger Picture
B Factoring Sums and Differences of Cubes
C Mean, Median, Mode
D Sets
E Review of Angles, Lines, and special Triangles
F Tables
Answers To Selected Exercises
Solutions to Selected Exercises
Introduction
About This Book
Introductory Algebra, was written to provide a solid foundation in algebra for students who might have had no previous experience in algebra. Specific care was taken to ensure that students have the most uptodate relevant text preparation for their next mathematics course or for nonmathematical courses that require an understanding of algebraic fundamentals. I have tried to achieve this by writing a userfriendly text that is keyed to objectives and contains many workedout examples. As suggested by the AMATYC Crossroads Document and the NCTM Standards (plus Addenda), reallife and realdata applications, data interpretation, conceptual understanding, problem solving, writing, cooperative learning, appropriate use of technology, mental .mathematics, number sense, critical thinking, and geometric concepts are emphasized and integrated throughout the book.
The many factors that contributed to the success of the first edition have been retained. In preparing the Second Edition, I considered comments and suggestions of colleagues, students, and many users of the prior edition throughout the country.
Introductory Algebra, Second Edition is part of a series of texts that can include Basic College Mathematics, Second Edition; Prealgebra, Third Edition; Intermediate Algebra, Second Edition; and a combined text, Algebra A Combined 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 and Changes in the Second Edition
Readability and Connections. I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to relate the new ideas to those that students may already know. Constant reinforcement and connections within problemsolving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information. In addition, each section begins with a list of objectives covered in the section. Clear organization of section material based on objectives further enhances readability.
ProblemSolving Process. This is formally introduced in Chapter 2 with a fourstep process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' comfort level and confidence in tackling problems.
Applications and Connections. Every effort was made to include as many interesting and relevant reallife applications as possible throughout the text in both workedout examples and exercise sets. In the Second Edition, the applications have been thoroughly revised and updated, and the number of applications has increased. The applications help to motivate students and strengthen their understanding of mathematics in the real world. They show connections to a wide range of fields including agriculture, allied health, anthropology, art, astronomy, biology, business, chemistry, construction, consumer affairs, earth science, education, entertainment, environmental issues, finance, geography, government, history, medicine, music, nutrition, physics, sports, travel, and weather. Many of the applications are based on recent real data. Sources for data include newspapers, magazines, publicly held companies, government agencies, specialinterest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included. See the Applications Index on page xx.
Practice Problems. Throughout the text, each workedout example has a parallel Practice Problem placed next to the example in the margin. These invite students to be actively involved in the learning process before beginning the endofsection exercise set. Practice Problems immediately reinforce a skill after it is developed. Answers appear at the bottom of the page for quick reference.
Concept Checks. These margin exercises are appropriately placed throughout the text. They allow students to gauge their grasp of an idea as it is being explained in the text. Concept Checks stress conceptual understanding at the point of use and help suppress misconceived notions before they start. Answers appear at the bottom of the page.
Increased Integration of Geometry Concepts. In addition to the traditional topics in introductory and intermediate algebra courses, this text contains a strong emphasis on problem solving and geometric concepts, which are integrated throughout. The geometry concepts presented are those most important to a student's understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with the geometry icon. Also, geometric figures, and a review of angles, lines, and special triangles are covered in the appendices.
Helpful Hints. Helpful Hints contain practical advice on applying mathematical concepts. These are found throughout the text and strategically placed where students are most likely to need immediate reinforcement. Helpful Hunts are highlighted for quick reference.
Visual Reinforcement of Concepts. The Second Edition contains a wealth of graphics, models, photographs, and illustrations to visually clarify and reinforce concepts. These include new and updated bar graphs, line graphs, calculator screens, application illustrations, and geometric figures.
Calculator and Graphing Calculator Explorations. These optional explorations offer pointofuse instruction, through examples and exercises, on the proper use of scientific and graphing calculators as tools in the mathematical problemsolving process. Placed appropriately throughout the text, Calculator and Graphing Calculator Explorations also reinforce concepts learned in the corresponding section and motivate discoverybased learning.
Additional exercises building on the skill developed in the Explorations may be found in exercise sets throughout the text. Exercises requiring a calculator are marked with the calculator icon. Exercises requiring a graphing calculator are marked with the calculator icon. An Introduction to Using a Graphing Utility is included in the appendix.
Study Skills Reminders. New Study Skills Reminder boxes are integrated throughout the text. They are strategically placed to constantly remind and encourage students as they hone their study skills. A new Section 1.1, Tips on Success in Mathematics, provides an overview of the Study Skills needed to succeed in math. These are reinforced by the Study Skills Reminder boxes throughout the text.
Focus On. Appropriately placed throughout each chapter, these are divided into Focus on Mathematical Connections, Focus on Business and Career, Focus on the Real World, and Focus on History. They are written to help students develop effective habits for engaging in investigations of other branches of mathematics, understanding the importance of mathematics in various careers and in the world of business, and seeing the relevance of mathematics in both the present and past through critical thinking exercises and group activities.
Chapter Highlights. Found at the end of each chapter, these contain key definitions, concepts, and examples to help students understand and retain what they have learned and help them organize their notes and study for tests.
Chapter Activity. These features occur once per chapter at the end of the chapter, often serving as a chapter wrapup. For individual or group completion, the Chapter Activity, usually handson or databased, complements and extends to concepts of the chapter, allowing students to make decisions and interpretations and to think and write about algebra.
Integrated Reviews. These "midchapter reviews" are appropriately placed once per chapter. Integrated Reviews allow students to review and assimilate the many different skills learned separately over several sections before moving on to related material in the chapter.
Pretests. Each chapter begins with a pretest that is designed to help students identify areas where they need to pay special attention in the upcoming chapter.
Chapter Review and Test. The end of each chapter contains a review of topics introduced in the chapter. The Chapter Review offers exercises that are keyed to sections of the chapter. The Chapter Test is a practice test and is not keyed to sections of the chapter.
Cumulative Review. These features are found at the end of each chapter (except Chapters R and 1). Each problem contained in the Cumulative Review is an earlier worked example in the text that is referenced in the back of the book along with the answer. Students who need to see a complete workedout solution, with explanation, can do so by turning to the appropriate example in the text.
Student Resource Icons. At the beginning of each section, videotape and CD, tutorial software, Prentice Hall Tutor Center, and solutions manual icons are displayed. These icons help reinforce that these learning aids are available should students wish to use them to help them review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.
Functional Use of Color and New Design. Elements of this text are highlighted with color or design to make it easier for students to read and study. Special care has been taken to use color within solutions to examples or in the art to help clarify, distinguish, or connect concepts.
Exercise Sets. Each text section ends with an Exercise Set. Each exercise in the set, except those found in parts labeled Review and Preview or Combining Concepts, is keyed to one of the objectives of the section. Wherever possible, a specific example is also referenced. In addition to the approximately 4400 exercises in endofsection exercise sets, exercises may also be found in the Pretests, Integrated Reviews, Chapter Reviews, Chapter Tests, and Cumulative Reviews.
Exercises and examples marked with a video icon have been worked out stepbystep by the author in the videos that accompany this text.
Throughout the exercises in the text there is an emphasis on data and graphical interpretation via tables, charts, and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it. Similarly, geometric concepts—such as perimeter and area—are integrated throughout the text. Exercises and examples marked with a geometry icon have been identified for convenience.
Each exercise set contains one or more of the following features.
Mental Math. Found at the beginning of an exercise set, these mental warmups reinforce concepts found in the accompanying section and increase students' confidence before they tackle an exercise set. By relying on their own mental skills, students increase not only their confidence in themselves but also their number sense and estimation ability.
Review and Preview. These exercises occur in each exercise set (except for those in Chapters R and 1) after the exercises keyed to the objectives of the section. Review and Preview problems are keyed to previous sections and review concepts learned earlier in the text that are needed in the next section or in the next chapter. These exercises show the links between earlier topics and later material.
Combining Concepts. These exercises are found at the end of each exercise set after the Review and Preview exercises. Combining Concepts exercises require students to combine several concepts from that section or to take the concepts of the section a step further by combining them with concepts learned in previous sections. For instance, sometimes students are required to combine the concepts of the section with the problemsolving process they learned in Chapter 2 to try their hand at solving an application problem.
Writing Exercises. These exercises occur in almost every exercise set and are marked with an icon. They require students to assimilate information and provide a written response to explain concepts or justify their thinking. Guidelines recommended by the American Mathematical Association of Two Year Colleges (AMATYC) and other professional groups recommend incorporating writing in mathematics courses to reinforce concepts.
Vocabulary Checks. Vocabulary Checks, new to this edition, provide an opportunity for students to become more familiar with the use of mathematical terms as they strengthen their verbal skills. These appear at the end of the chapter before the Chapter Highlights.
Data and Graphical Interpretation. There is an emphasis on data interpretation in exercises via tables and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it.
Internet Excursions. These exercises occur once per chapter. Internet Excursions require students to use the Internet as a datacollection tool to complete the exercises, allowing students firsthand experience with manipulating and working with real data.
Key Content Features in the Second Edition
Overview. This new edition retains many of the factors that have contributed to its success. Even so, every section of the text was carefully reexamined. Throughout the new edition you will find numerous new applications, examples, and many reallife applications and exercises. For example, look at the exercise sets of Sections 1.8, 2.5, 2.6, 6.1, 6.4, or 8.2. Some sections have internal reorganization to better clarify and enhance the presentation.
Chapter 1 now begins with Tips for Success in Mathematics (Section 1.1). New applications, and real data enhance the chapter.
New Study Skills Reminder boxes have been inserted throughout the text. These boxes reinforce the tips from Section 1.1. They are placed strategically to encourage students to hone their study skills.
Increased Integration of Geometry Concepts. The geometry concepts presented are those most important to a student's understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with a geometry icon. Also, geometric figures and a review of angles, lines, and special triangles are covered in the appendices.
New Examples. Detailed stepbystep examples were added, deleted, replaced, or updated as needed. Many of these reflect real life.
Exercise Sets Revised and Updated. The exercise sets have been carefully examined and extensively revised. The realworld and realdata applications have been thoroughly updated and many new applications are included. In addition, an increased number of challenging problems have been included in the new edition. Writing exercises are now included in most exercise sets and new Vocabulary Checks have been added to the end of the chapter to help students become proficient in the language of mathematics.
Enhanced Supplements Package. The Second Edition is supported by a wealth of supplements designed for added effectiveness and efficiency. New items include the MathPro 5 online tutorial with diagnostic and unique video clip feature, a new computerized testing system (TestGenEQ with QuizMaster), Prentice Hall Tutor Center, digitized videos on CD, and Instructor to Instructor, Teaching Mathematics CD Series. Please see the list of supplements for descriptions.
Options for 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.
The Companion Web site includes basic distance learning access to provide links to the text's Internet Excursions and a selection of online self quizzes. Email is available.
WebCT. WebCT includes distance learning access to content found in the MartinGay companion Web site 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.
Annotated Instructor's Edition (0130676845)
Answers to all exercises printed on the same text page.
Teaching Tips throughout the text placed at key points in the margin.
Instructor's Solution Manual (0130676853)
Solutions to evennumbered section exercises.
Solutions to every (even and odd) Mental Math exercise.
Solutions to every (even and odd) Practice Problem (margin exercise).
Solutions to every (even and odd) exercise found in the Pretests, Integrated Reviews (midchapter reviews), Chapter Reviews, Chapter Tests, and Cumulative Reviews.
Instructor's Resource Manual with Tests (0130676926)
Notes to the Instructor that include an introduction to Interactive Learning, Interpreting Graphs and Data, Alternative Assessment, Using Technology, and Helping Students Succeed.
Two freeresponse Pretests per chapter.
Eight Chapter Tests per chapter (3 multiplechoice, 5 freeresponse).
Two Cumulative Review Tests (one multiplechoice, one freeresponse) every two chapters (after chapters 2,4,6,9).
Eight Final Exams (3 multiplechoice, 5 freeresponse).
Twenty additional exercises per section for added test exercises if needed.
Group Activities (an average of two per chapter; providing short group activities in a convenient, readytouse format).
Answers to all items.
Media Supplements
TestGenEQ with QuizMaster CDROM (Windows/Macintosh) (0130676977)
Algorithmically driven, textspecific testing program.
Networkable for administering tests and capturing grades online.
Edit and add your own questions to create a nearly unlimited number of tests and worksheets.
Use the new "Function Plotter" to create graphs.
Tests can be easily exported to HTML so they can be posted to the Web for student practice.
Includes an email function for network users, enabling instructors to send a message to a specific student or an entire group.
Networkbased reports and summaries for a class or student and for cumulative or selected scores are available.
MathPro 5 Instructor Version
Online, customizable tutorial, diagnostic, and assessment program for anytime, anywhere tutorial support.
Text specific at the learning objective level.
Diagnostic option identifies student skills, provides individual learning plan, and tutorial reinforcement.
Integration of TestGenEQ allows for testing to operate within the tutorial environment.
Course management tracking of tutorial and testing activity.
MathPro Explorer 4.0
Network Version IBM/Mac 0130676969.
Enables instructors to create either customized or algorithmically generated practice quizzes from any section of a chapter.
Includes email function for network users, enabling instructors to send a message to a specific student or to an entire group.
Networkbased reports and summaries for a class or student and for cumulative or selected scores.
Instructor's CD Series (0130473529)
Written and presented by Elayn MartinGay.
Contains suggestions for presenting course material, utilizing the integrated resource package, timesaving tips, and much more.
Companion Web Site
Create a customized online syllabus with Syllabus Manager.
Links related to the Internet Excursions in each chapter allow students to find and retrieve real data for use in guided problem solving.
Assign quizzes or monitor student self quizzes by having students email results, such as true/false reading quizzes or vocabulary check quizzes.
Destination links provide additional opportunities to explore related sites.
Supplements for the Student
Printed Supplements
Student's Solution Manual (0130350680)
Solutions to oddnumbered section exercises.
Solutions to every (even and odd) Mental Math exercise.
Solutions to every (even and odd) Practice Problem (margin exercise).
Solutions to every (even and odd) exercise found in the Pretests, Integrated Reviews (midchapter reviews), Chapter Reviews, Chapter Tests, and Cumulative Reviews.
Study Skills Notebook (0130473235)
Media Supplements
MathPro 5 (Student Version)
Online, customizable tutorial, diagnostic, and assessment software.
Text specific to the learning objective level, providing anytime, anywhere tutorial support.
Algorithmically driven for virtually unlimited practice problems with immediate feedback.
"Watch" screen videoclips by K. Elayn MartinGay.
Stepby Step solutions.
Summary of Progress.
MathPro 4.0 Student Version (0130676888)
Available on CDROM for stand alone use or can be networked in the school laboratory.
Text specific tutorial exercises and instructions at the objective level.
Algorithmically generated Practice Problems.
"Watch" screen videoclips by K. Elayn MartinGay.
Videotape Series (0130676861)
Written and presented by Elayn MartinGay.
Keyed to each section of the text.
Stepbystep solutions to exercises from each section of the text. Exercises that are worked in the videos are marked with a video icon.
New Digitized Lecture Videos on CDROM (0130676918)
The entire set of Introductory Algebra, Second Edition lecture videotapes in digital form.
Convenient access anytime to video tutorial support from a computer at home or on campus.
Available shrinkwrapped with the text or standalone.