Algebra Review, 3rd Edition
Sullivan & Sullivan
The Eighth Edition of this dependable text retains its best features — accuracy, precision, depth, strong student support, and abundant exercises — while substantially updating content and pedagogy. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus.
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Prepare for Class
Every chapter begins with...
- Chapter Opening Article & Project
- Each chapter begins with a current article and ends with a related project. The Article poses a real problem. The Project lets you apply what you learned to solve that problem.
Every section begins with...
- Preparing for This Section
- Sections begin with a list of key concepts to review, with page numbers.
- Ever forget what you've learned? This feature highlights previously learned material to be used in this section. Review it, and you'll always be prepared for quizzes and tests.
- Now Work 'Are You Prepared?' Problems
- Special problems that support the Preparing for This Section feature.
- Not sure you need the Preparing for This Section review? Work the 'Are You Prepared?' Problems. If you get one wrong, you'll know exactly what you need to review and where to review it!
- Learning Objectives
- Each section begins with a list of objectives. Objective numbers appear in the margin where the objective is covered.
- These focus your studying by emphasizing what's most important and where to find it.
Most sections contain...
- Calculus Icon
- These appear next to information essential for the study of calculus.
- Pay attention — if you spend extra time now, you'll do better later!
- "Now Work" Problems
- These follow most examples, and direct you to a related exercise.
- We learn best by doing. You'll solidify your understanding of examples if you try a similar problem right away, before you forget what you've learned.
- Warnings are provided in the text. These point out common mistakes and help you avoid them.
- Seeing the Concept & Explorations
- These optional features suggest graphing utility activities.
- You will obtain a deeper and more intuitive understanding of theorems and definitions.
- In Words
- These provide alternative descriptions of select definitions and theorems.
- Does math ever look foreign to you? This feature translates math into plain English.
- Step-by-Step, Annotated Examples
- Examples contain detailed intermediate steps. Many include additional annotations.
- Work the examples on your own, uncovering the solution line-by-line as you go. Each line will verify your work, or stimulate your thinking. For additional help, consult the blue annotations.
"Assess Your Understanding"sections (end-of-section exercises) contain a variety of problems...
- 'Are You Prepared?' Problems
- These assess your retention of the prerequisite material you'll need. Answers are given at the end of the section exercises. This feature is related to the Preparing for This Section feature.
- Do you always remember what you've learned? Working these problems is the best way to find out. If you get one wrong, you'll know exactly what you need to review, and where to review it!
- Concepts and Vocabulary
- These Fill-in the-Blank and True/False items assess your understanding of key definitions and concepts.
- Learning math is more than memorization — it's about discovering connections. These problems help you understand the 'big ideas' before diving into skill building.
- Skill Development
- Correlated to section examples, these problems provide straightforward practice, organized by difficulty.
- It's important to dig in and develop your problem-solving skills. These problems provide you with ample practice to do so.
- These problems utilize graphs in a variety of ways. You will supplement your analytical understanding with graphical understanding.
- Now Work Problems
- Many examples refer you to a related homework problem. These related problems are marked by a yellow pencil. If you get stuck while working problems, look for the closest Now Work problem and refer back to the related example to see if it helps.
- Applications and Extensions
- Application problems ("word problems") follow basic skill development problems.
- Math is everywhere, and these problems demonstrate that. You'll learn to approach real problems, and how to break them down into manageable parts. These can be challenging, but are worth the effort.
- Graphing Calculator
- These optional problems require the use of a graphing utility, and are marked by a special icon.
- Your instructor will usually provide guidance on whether or not to do these problems. If so, these problems help to verify and visualize your analytical results.
- Discussion & Writing
- "Discussion, Writing, and Research" problems are marked by a special icon and red numbers. These support class discussion, verbalization of mathematical ideas, and writing and research projects.
- To verbalize an idea, or to describe it clearly in writing, shows real understanding. These problems nurture that understanding. They're challenging, but you'll get out what you put in.
Chapter Reviews at the end of each chapter contain...
- "Things to Know"
- A detailed list of important theorems, formulas, identities, definitions, and functions from the chapter.
- Study these ideas and you'll know the most important material in the book!
- "You Should be Able To..."
- Contains a complete list of objectives by section, with corresponding practice exercises.
- Do the recommended exercises and you'll have mastery over the key material. If you get something wrong, go review the suggested page numbers and try again.
- Review Exercises
- These provide comprehensive review and practice of key skills, matched to the Learning Objectives for each section. Practice makes perfect. These problems combine exercises from all sections, giving you a comprehensive in one place.
- NEW - Chapter Test
- About 15-20 problems that can be taken as a Chapter Test. Be sure to take the Chapter Test under test conditions – no notes! Be prepared. This will get you ready for your instructor’s test. If you get a problem wrong, watch the Chapter Test Prep Video found at the back of your book.
- Chapter Projects
- The Chapter Project applies what you've learned in the chapter the chapter opener article. Additional projects are available on a website. The Project gives you an opportunity to apply what you've learned in the chapter to solve the problem posed in the opening article. If your instructor allows, these make excellent opportunities to work in a group, which is often the best way of learning math.
- Cumulative Review
- These problem sets appear at the end of Chapters 2-13. They combine problems from previous chapters, providing an ongoing cumulative review. These are really important. They will ensure that you are not forgetting anything as you go. These will go a long way toward keeping you constantly primed for quizzes and tests.
New to This Edition
NEW TO THE EIGHTH EDITION
- Chapter Tests are now part of the end of chapter material. Students can watch the solutions being worked out on the Chapter Test Prep Video CD found at the back of the book. These along with the Cumulative Review found at the end of each chapter provide ample opportunity for students to prepare for tests and continually review earlier material.
- Exercise Sets at the end of each section have been classified according to purpose. Where appropriate, more problems to challenge the better student have been added.
- Applied problems have been updated and many new problems involving sourced information as well as data sets have been added to bring relevance and timeliness to these exercises.
- MyMathLab coverage: Every odd exercise is now coded!
- New Content
Section R.3, Geometry Essentials, now contains a discussion of congruent and similar triangles
The analysis of the graph of a polynomial function now includes the behavior of the graph near an x-intercept.
Examples and exercises that involve a more in-depth analysis of graphing exponential and logarithmic functions is provided.
Examples and exercises that involve graphing a wider variety of inverse trigonometric functions is provided.
- Chapter 4 Linear and Quadratic Functions New to this edition, this chapter gives more emphasis to Linear Functions than before, with more applications, and allows for a fuller discussion of the Quadratic Function, is properties, models involving it, and building such functions from data. A full section on quadratic inequalities is also provided.
ORGANIZATIONAL CHANGES IN THE EIGHTH EDITION
- Chapter R Polynomial division is now part of the discussion of polynomials, leaving synthetic division as a stand-alone (optional) section.
- Chapter 1 Parallel and perpendicular lines are now part of the section on Lines. The section on Lines now precedes the section on Circles.
- Chapter 2 Scatter diagrams; linear curve fitting has been removed and moved to the new chapter on Linear and Quadratic Functions.
Table of Contents
TABLE OF CONTENTS
Chapter R Review
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents
Chapter 1 Equations and Inequalities
1.1 Linear Equations
1.2 Quadratic Equations
1.3 Complex Numbers; Quadratic Equations in the Complex Number System
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
1.5 Solving Inequalities
1.6 Equations and Inequalities Involving Absolute Value
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
Chapter 3 Functions and Their Graphs
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewise-defined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions
Chapter 4 Linear and Quadratic Functions
4.1 Linear Functions and Their Properties
4.2 Building Linear Functions from Data
4.3 Quadratic Functions and Their Properties
4.4 Quadratic Models; Building Quadratic Functions from Data
4.5 Inequalities Involving QuadraticFunctions
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions and Models
5.2 Properties of Rational Functions
5.3 The Graph of a Rational Function
5.4 Polynomial and Rational Inequalities
5.5 The Real Zeros of a Polynomial Function
5.6 Complex Zeros: Fundamental Theorem of Algebra
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 One-to-One Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Compound Interest
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Functions from Data
Chapter 7 Analytic Geometry
7.2 The Parabola
7.3 The Ellipse
7.4 The Hyperbola
Chapter 8 Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination
8.2 Systems of Linear Equations: Matrices
8.3 Systems of Linear Equations: Determinants
8.4 Matrix Algebra
8.5 Partial Fraction Decomposition
8.6 Systems of Nonlinear Equations
8.7 Systems of Inequalities
8.8 Linear Programming
Chapter 9 Sequences; Induction; the Binomial Theorem
9.2 Arithmetic Sequences
9.3 Geometric Sequences; Geometric Series
9.4 Mathematical Induction
9.5 The Binomial Theorem
Chapter 10 Counting and Probability
10.1 Sets and Counting
10.2 Permutations and Combinations
Appendix Graphing Utilities
1 The Viewing Rectangle
2 Graphing Equations in Two Variables
3 Locating Intercepts and Checking for Symmetry
4 Solving Equations Using a Graphing Utility
5 Square Screens
6 Graphing Inequalities in Two Variables
7 Solving Systems of Linear Equations
8 Graphing a Polar Equation
9 Graphing Parametric Equations
Websites and online courses
Graphing Calculator Reference Card, 3rd Edition
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About the Author(s)
Mike Sullivan Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 35 years. He has been writing textbooks in mathematics for over 30 years. Mike has authored or co-authored over ten books. He is a native of Chicago’s South Side and currently resides in Oaklawn. He has four children: Kathleen, who teaches college mathematics, Mike III, who co-authors many titles as well as teaches college mathematics, Dan, who is a Prentice Hall sales representative, and Colleen, who teaches middle-school mathematics. Nine grandchildren round out the family.
Why I Wrote This Book:
As a professor of mathematics at an urban public university for over 35 years, I understand the varied needs of precalculus students who range from having little mathematical background and a fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others may decide to further their mathematical education. I have written this text for both groups. As the author of precalculus, engineering calculus, finite math and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses. However, as a father of four, I also understand the realities of college life. I have taken great pains to insure that this text contains solid, student-friendly examples and problems, as well as a clear writing style. I encourage you to share with me your experiences teaching from this text.
The eighth edition of this series builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of the previous edition that have proved successful remain, while many changes, some obvious, others subtle, have been made. A huge benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made from colleagues and students who have used the previous edition. I am sincerely grateful for this feedback and have tried to make changes that improve the flow and usability of this text.
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