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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.
Read an Excerpt
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
FourColor Format: Color is used pedagogically in the following ways:
Reability: One of the most important features of text is its readability. The book is very readable, even for those with weak reading skills. Short, clear senses 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 makeconnections. That is, we introduce a concept, then later 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.
Preview and Perspective: This feature at the beginning of each chapter explains to the students why they are studying the material and 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.
Students Solution Manual, Videotape, and Software Icons: At the beginning of each section, Student's Solution Manual, videotape, and tutorial software icons are displayed. These icons tell the student where material in the section can be found in the Student's Solution Manual, on the videotapes, and in the tutorial software, saving your students time when they want to review this material. Small videotape icons are also placed next to exercises that are worked out on the videotapes.
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 symbols.
Problem Solving: Polya's fivestep problemsolving procedure is discussed in Section 2.2. 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.
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.
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.
Using Your Calculator: The Using Your Calculator boxes, placed at appropriate intervals in the text, are written to reinforce the algebraic topics presented in the section and to give the student pertinent information on using the 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 Instrument 83 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. Many exercise sets contain graphing calculator exercises for instructors who wish to assign them.
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 a symbol.
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.
Problem Solving Exercises: These exercises have been added to help students become better thinkers and problem solvers. Many of these exercises are applied in nature.
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 will reinforce topics that were previously covered and help students retain the earlier material, while they are learning new material. For the students' benefit the Cumulative Review Exercises are keyed to the section where the material is covered.
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 which includes a glossary and important chapter facts.
Review Exercises: At the end of each chapter are review exercises that cover all types of exercises presented the chapter. The review exercises are keyed to the sections where the material was first introduced.
Practice Tests: The comprehensive endofchapter practice test will enable the students to see how well they are prepared for the actual class test. The Test Item File includes several forms of each chapter test that are similar to the student's practice test. Multiple choice tests are also included in the Test Item File.
Cumulative Review Test: These tests, which appear at the end of each chapter, 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.
Answers: The odd answers are provided for the exercise sets. All answers are provided for the Using Your Graphing Calculator Exercises, Cumulative Review Exercises, the Review Exercises, Practice Tests, and the Cumulative Practice Test. 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:
Contents
This book covers both intermediate algebra material and material from college algebra. The material from some of the later chapters, especially Chapters 10 through 12, is often covered in college algebra.
Here are some content features of this book.
Table of Contents
Note: Each chapter concludes with Chapter Summary, Chapter Review Exercises, and Chapter Practice Test and after Chapter 1, Cumulative Review Test.
Preface
To the Student
CHAPTER 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
MidChapter Test: Sections 1.1—1.4
1.5 Exponents
1.6 Scientific Notation
CHAPTER 2: Equations and Inequalities
2.1 Solving Linear Equations
2.2 Problem Solving and Using Formulas
2.3 Applications of Algebra
MidChapter Test: Sections 2.1—2.3
2.4 Additional Application Problems
2.5 Solving Linear Inequalities
2.6 Solving Equations and Inequalities Containing Absolute Values
CHAPTER 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
MidChapter Test: Sections 3.1—3.4
3.5 The PointSlope Form of a Linear Equation
3.6 The Algebra of Functions
3.7 Graphing Linear Inequalities
CHAPTER 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
MidChapter Test: Sections 4.1—4.3
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
CHAPTER 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
MidChapter Test: Sections 5.1—5.4
5.5 Factoring Trinomials
5.6 Special Factoring Formulas
5.7 A General Review of Factoring
5.8 Polynomial Equations
CHAPTER 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
MidChapter Test: Sections 6.1—6.4
6.5 Rational Equations: Applications and Problem Solving
6.6 Variation
CHAPTER 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
MidChapter Test: Sections 7.1—7.4
7.5 Dividing Radicals
7.6 Solving Radical Equations
7.7 Complex Numbers
CHAPTER 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
MidChapter Test: Sections 8.1—8.3
8.4 Writing Equations in Quadratic Form
8.5 Graphing Quadratic Functions
8.6 Quadratic and Other Inequalities in One Variable
CHAPTER 9: Exponential and Logarithmic Functions
9.1 Composite and Inverse Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithms
MidChapter Test: Sections 9.1—9.4
9.5 Common Logarithms
9.6 Exponential and Logarithmic Equations
9.7 Natural Exponential and Natural Logarithmic Functions
CHAPTER 10: Characteristics of Functions and Their Graphs
10.1 Continuous and Discontinuous Functions
10.2 Characteristics of Graphs of Polynomial Functions
MidChapter Test: Sections 10.1—10.2
10.3 Finding the Rational Zeros of a Polynomial Function
10.4 Finding the Real Zeros of a Polynomial Function
10.5 Characteristics of Graphs of Rational Functions
CHAPTER 11: Conic Sections
11.1 T he Parabola and the Circle
11.2 The Ellipse
MidChapter Test: Sections 11.1—11.2
11.3 The Hyperbola
11.4 Nonlinear Systems of Equations and Their Applications
11.5 Nonlinear Systems of Inequalities
CHAPTER 12: Sequences, Series, and Probability
12.1 Sequences and Series
12.2 Arithmetic Sequences and Series
12.3 Geometric Sequences and Series
MidChapter Test: Sections 12.1—12.3
12.4 Mathematical Induction
12.5 The Binomial Theorem
12.6 The Counting Principle, Permutations, and Combinations
12.7 Probability
APPENDIX Geometric Formulas
Answers
Graphing Answer Section *found only in the Annotated Instructor's Edition
Applications Index
Index
Photo Credits
Preface
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
FourColor Format: Color is used pedagogically in the following ways:
Reability: One of the most important features of text is its readability. The book is very readable, even for those with weak reading skills. Short, clear senses 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 makeconnections. That is, we introduce a concept, then later 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.
Preview and Perspective: This feature at the beginning of each chapter explains to the students why they are studying the material and 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.
Students Solution Manual, Videotape, and Software Icons: At the beginning of each section, Student's Solution Manual, videotape, and tutorial software icons are displayed. These icons tell the student where material in the section can be found in the Student's Solution Manual, on the videotapes, and in the tutorial software, saving your students time when they want to review this material. Small videotape icons are also placed next to exercises that are worked out on the videotapes.
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 symbols.
Problem Solving: Polya's fivestep problemsolving procedure is discussed in Section 2.2. 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.
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.
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.
Using Your Calculator: The Using Your Calculator boxes, placed at appropriate intervals in the text, are written to reinforce the algebraic topics presented in the section and to give the student pertinent information on using the 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 Instrument 83 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. Many exercise sets contain graphing calculator exercises for instructors who wish to assign them.
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 a symbol.
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.
Problem Solving Exercises: These exercises have been added to help students become better thinkers and problem solvers. Many of these exercises are applied in nature.
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 will reinforce topics that were previously covered and help students retain the earlier material, while they are learning new material. For the students' benefit the Cumulative Review Exercises are keyed to the section where the material is covered.
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 which includes a glossary and important chapter facts.
Review Exercises: At the end of each chapter are review exercises that cover all types of exercises presented the chapter. The review exercises are keyed to the sections where the material was first introduced.
Practice Tests: The comprehensive endofchapter practice test will enable the students to see how well they are prepared for the actual class test. The Test Item File includes several forms of each chapter test that are similar to the student's practice test. Multiple choice tests are also included in the Test Item File.
Cumulative Review Test: These tests, which appear at the end of each chapter, 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.
Answers: The odd answers are provided for the exercise sets. All answers are provided for the Using Your Graphing Calculator Exercises, Cumulative Review Exercises, the Review Exercises, Practice Tests, and the Cumulative Practice Test. 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:
Contents
This book covers both intermediate algebra material and material from college algebra. The material from some of the later chapters, especially Chapters 10 through 12, is often covered in college algebra.
Here are some content features of this book.