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More About This Textbook
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Meet the Author
Allen R. Angel received his AAS in Electrical Technology from New York City Community College. He then received his BS in Physics and his MS in Mathematics from SUNY at New Paltz, and he took additional graduate work at Rutgers University. He is Professor Emeritus at Monroe Community College in Rochester, New York where he served for many years as the chair of the Mathematics Department. He also served as the Assistant Director of the National Science Foundation Summer Institutes at Rutgers University from 1967–73. He served as the President of the New York State Mathematics Association of Two Year Colleges (NYSMATYC) and the Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). He is the recipient of many awards including a number of NISOD Excellence in Teaching Awards, NYSMATYC's Outstanding Contributions to Mathematics Education Award, and AMATYC's President Award. Allen enjoy tennis, worldwide travel, and visiting with his children and granddaughter.
Dennis Runde received his BS and MS in mathematics from the University of Wisconsin—Platteville and Milwaukee, respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for twenty years at State College of Florida, Manatee, and Sarasota Counties and for ten years at Saint Stephen's Episcopal School. Besides coaching little league baseball, his other interests include history, politics, fishing, canoeing, and cooking. He and his wife Kristin stay busy keeping up with their three sons–Alex, Nick, and Max.
Table of Contents
1. Basic Concepts
1.1 Study Skills for Success in Mathematics, and Using a Calculator
1.2 Sets and Other Basic Concepts
1.3 Properties of and Operations with Real Numbers
1.4 Order of Operations
1.5 Exponents
1.6 Scientific Notation
2. Equations and Inequalities
2.1 Solving Linear Equations
2.2 Problem Solving and Using Formulas
2.3 Applications of Algebra
2.4 Additional Application Problems
2.5 Solving Linear Inequalities
2.6 Solving Equations and Inequalities Containing Absolute Values
3. Graphs and Functions
3.1 Graphs
3.2 Functions
3.3 Linear Functions: Graphs and Applications
3.4 The SlopeIntercept Form of a Linear Equation
3.5 The PointSlope Form of a Linear Equation
3.6 The Algebra of Functions
3.7 Graphing Linear Inequalities
4. Systems of Equations and Inequalities
4.1 Solving Systems of Linear Equations in Two Variables
4.2 Solving Systems of Linear Equations in Three Variables
4.3 Systems of Linear Equations: Applications and Problem Solving
4.4 Solving Systems of Equations Using Matrices
4.5 Solving Systems of Equations Using Determinants and Cramer’s Rule
4.6 Solving Systems of Linear Inequalities
5. Polynomials and Polynomial Functions
5.1 Addition and Subtraction of Polynomials
5.2 Multiplication of Polynomials
5.3 Division of Polynomials and Synthetic Division
5.4 Factoring a Monomial from a Polynomial and Factoring by Grouping
5.5 Factoring Trinomials
5.6 Special Factoring Formulas
5.7 A General Review of Factoring
5.8 Polynomial Equations
6. Rational Expressions and Equations
6.1 The Domains of Rational Functions and Multiplication and Division of Rational Expressions
6.2 Addition and Subtraction of Rational Expressions
6.3 Complex Fractions
6.4 Solving Rational Equations
6.5 Rational Equations: Applications and Problem Solving
6.6 Variation
7. Roots, Radicals, and Complex Numbers
7.1 Roots and Radicals
7.2 Rational Exponents
7.3 Simplifying Radicals
7.4 Adding, Subtracting, and Multiplying Radicals
7.5 Dividing Radicals
7.6 Solving Radical Equations
7.7 Complex Numbers
8. Quadratic Functions
8.1 Solving Quadratic Equations by Completing the Square
8.2 Solving Quadratic Equations by the Quadratic Formula
8.3 Quadratic Equations: Applications and Problem Solving
8.4 Writing Equations in Quadratic Form
8.5 Graphing Quadratic Functions
8.6 Quadratic and Other Inequalities in One Variable
9. Exponential and Logarithmic Functions
9.1 Composite and Inverse Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithms
9.5 Common Logarithms
9.6 Exponential and Logarithmic Equations
9.7 Natural Exponential and Natural Logarithmic Functions
10. Conic Sections
10.1 The Parabola and the Circle
10.2 The Ellipse
10.3 The Hyperbola
10.4 Nonlinear Systems of Equations and Their Applications
11. Sequences, Series, and the Binomial Theorem
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
11.4 The Binomial Theorem
Preface
This book was written for college students who have successfully completed a first course in elementary algebra. My primary goal was to write a book that students can read, understand, and enjoy. To achieve this goal I have used short sentences, clear explanations, and many detailed, workedout examples. I have tried to make the book relevant to college students by using practical applications of algebra throughout the text.
Features of the Text
FullColor Format. Color is used pedagogically in the following ways:
Readability. One of the most important features of the text is its readability. The book is very readable, even for those with weak reading skills. Short, clear sentences are used and more easily recognized, and easytounderstand language is used whenever possible.
Accuracy. Accuracy in a mathematics text is essential. To ensure accuracy in this book, mathematicians from around the country have read the pages carefully for typographical errors and have checked all the answers.
Connections. Many of our students do not thoroughly grasp new concepts the first time they are presented. In this text, we encourage students to make connections. That is, we introduce a concept, thenlater in the text briefly reintroduce it and build upon it. Often an important concept is used in many sections of the text. Students are reminded where the material was seen before, or where it will be used again. This also serves to emphasize the importance of the concept. Important concepts are also reinforced throughout the text in the Cumulative Review Exercises and Cumulative Review Tests.
Chapter Opening Application. Each chapter begins with a reallife application related to the material covered in the chapter. By the time students complete the chapter, they should have the knowledge to work the problem.
A Look Ahead. This feature at the beginning of each chapter gives students a preview of the chapter. This feature also indicates where this material will be used again in other chapters of the book. This material helps students see the connections between various topics in the book and the connection to realworld situations.
The Use of Icons. At the beginning of each chapter and of each section, a variety of icons are illustrated. These icons are provided to tell students where they may be able to get extra help if needed. There are icons for the Student's Solution Manual; the Student's Study Guide; CDs and videotapes; Math Pro 4/5 Software; the Prentice Hall Tutor Center; and the Angel Website. Each of these items will be discussed shortly.
Keyed Section Objectives. Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portions of the sections with red numbers such as 1.
Problem Solving. George Polya's fivestep problemsolving procedure is discussed in Section 1.2. Throughout the book problem solving and Polya's problemsolving procedure are emphasized.
Practical Applications. Practical applications of algebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problemsolving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applications motivates students.
Detailed; WorkedOut Examples. A wealth of examples have been worked out in a stepbystep, detailed manner. Important steps are highlighted in color, and no steps are omitted until after the student has seen a sufficient number of similar examples.
Now Try Exercise. In each section, students are asked to work exercises that parallel the examples given in the text. These Now Try Exercises make the students active, rather than passive, learners and they reinforce the concepts as students work the exercises. Through these exercises students have the opportunity to immediately apply what they have learned. Now Try Exercises are indicated in green type, such as 35, in the exercise sets.
Study Skills Section. Many students taking this course have poor study skills in mathematics. Section 1.1, the first section of this text, discusses the study skills needed to be successful in mathematics. This section should be very beneficial for your students and should help them to achieve success in mathematics.
Helpful Hints. The Helpful Hint boxes offer useful suggestions for problem solving and other varied topics. They are set off in a special manner so that students will be sure to read them.
Helpful Hints—Study Tips. This is a new feature. These Helpful HintStudy Tips boxes offer valuable information on items related to studying and learning the material.
Avoiding Common Errors. Errors that students often make are illustrated. The reasons why certain procedures are wrong are explained, and the correct procedure for working the problem is illustrated. These Avoiding Common Errors boxes will help prevent your students from making those errors we see so often.
Mathematics in Action. This new feature stresses the need for and the uses of mathematics in reallife situations. Examples of the use of mathematics in many professions, and how we use mathematics daily without ever giving it much thought, are given. This can be a motivational feature for your students and can give them a better appreciation of mathematics.
Using Your Calculator. The Using Your Calculator boxes, placed at appropriate locations in the text, are written to reinforce the algebraic topics presented in the section and to give the student pertinent information on using a scientific calculator to solve algebraic problems.
Using Your Graphing Calculator. Using Your Graphing Calculator boxes are placed at appropriate locations throughout the text. They reinforce the algebraic topics taught and sometimes offer alternate methods of working problems. This book is designed to give the instructor the option of using or not using a graphing calculator in their course. Many Using Your Graphing Calculator boxes contain graphing calculator exercises, whose answers appear in the answer section of the book. The illustrations shown in the Using Your Graphing Calculator boxes are from a Texas Instruments 83 Plus calculator. The Using Your Graphing Calculator boxes are written assuming that the student has no prior graphing calculator experience.
Exercise Sets
The exercise sets are broken into three main categories: Concept/Writing Exercises, Practice the Skills, and Problem Solving. Many exercise sets also contain Challenge Problems and/or Group Activities. Each exercise set is graded in difficulty. The early problems help develop the student's confidence, and then students are eased gradually into the more difficult problems. A sufficient number and variety of examples are given in each section for the student to successfully complete even the more difficult exercises. The number of exercises in each section is more than ample for student assignments and practice.
Concept/Writing Exercises. Most exercise sets include exercises that require students to write out the answers in words. These exercises improve students' understanding and comprehension of the material. Many of these exercises involve problem solving and conceptualization and help develop better reasoning and critical thinking skills. Writing exercises are indicated by the pencil symbol.
Problem Solving Exercises. These exercises help students become better thinkers and problem solvers. Many of these exercises involve reallife applications of algebra. It is important for students to be able to apply what they learn to reallife situations. Many problem solving exercises help with this.
Challenge Problems. These exercises, which are part of many exercise sets, provide a variety of problems. Many were written to stimulate student thinking. Others provide additional applications of algebra or present material from future sections of the book so that students can see and learn the material on their own before it is covered in class. Others are more challenging than those in the regular exercise set.
Cumulative Review Exercises. All exercise sets (after the first two) contain questions from previous sections in the chapter and from previous chapters. These cumulative review exercises reinforce topics that were previously covered and help students retain the earlier material, while they are learning the new material. For the students' benefit the Cumulative Review Exercises are keyed to the section where the material is covered using brackets, such as (3.4).
Video Icon Exercises. The exercises that are worked out in detail on the videotapes are marked with the video icon, iii. This will prove helpful to your students.
Group Activities. Many exercise sets have group activity exercises that lead to interesting group discussions. Many students learn well in a cooperative learning atmosphere, and these exercises will get students talking mathematics to one another.
Chapter Summary. At the end of each chapter is a chapter summary that includes a glossary and important chapter facts.
Chapter Review Exercises. At the end of each chapter are review exercises that cover all types of exercises presented in the chapter. The review exercises are keyed, using color numbers and brackets, to the sections where the material was first introduced.
Chapter Practice Tests . The comprehensive endofchapter practice test will enable the students to see how well they are prepared for the actual class test. The Instructor's Test Manual includes several forms of each chapter test that are similar to the student's practice test. Multiple choice tests are also included in the Instructor's Test Manual.
Cumulative Review Tests. These tests, which appear at the end of each chapter after the first, test the students' knowledge of material from the beginning of the book to the end of that chapter. Students can use these tests for review, as well as for preparation for the final exam. These exams, like the cumulative review exercises, will serve to reinforce topics taught earlier. The answers to the Cumulative Review Test questions directly follow the test so that students can quickly check their work. After each answer, the section and objective numbers where that material was covered are given using brackets, such as Sec. 4.2, Obj. 5.
Answers. The odd answers are provided for the exercise sets. All answers are provided for the Using Your Graphing Calculator Exercises, Cumulative Review Exercises, Review Exercises, Practice Tests, and the Cumulative Review Tests. Answers are not provided for the Group Activity exercises since we want students to reach agreement by themselves on the answers to these exercises.
National Standards
Recommendations of the Curriculum and Evaluation Standards for School Mathematics, prepared by the National Council of Teachers of Mathematics (NCTM), and Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus, prepared by the American Mathematical Association of Two Year Colleges (AMATYC), are incorporated into this edition.
Prerequisite
The prerequisite for this course is a working knowledge of elementary algebra. Although some elementary algebra topics are briefly reviewed in the text, students should have a basic understanding of elementary algebra before taking this course.
Modes of Instruction
The format and readability of this book lends itself to many different modes of instruction. The constant reinforcement of concepts will result in greater understanding and retention of the material by your students.
The features of the text and the large variety of supplements available make this text suitable for many types of instructional modes including:
Changes in the Sixth Edition
When I wrote the sixth edition, I considered many letters and reviews I got from students and faculty alike. I would like to thank all of you who made suggestions for improving the sixth edition. I would also like to thank the many instructors and students who wrote to inform me of how much they enjoyed, appreciated, and learned from the text.
Some of the changes made in the sixth edition of the text include: