Mathematics

For undergraduate courses in Precalculus where the instructor would like to introduce functions early (in Chapter One) and takes a right triangle approach to trigonometry.

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 students apply what they have 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.

 

 • Now Work "Are You Prepared?" Problems

— Special problems that support the Preparing for This Section feature.

 

• Learning Objectives

— Each section begins with a list of objectives. Objective numbers appear in the margin where the objective is covered.

 

 Most sections contain. . .

• Calculus Icon

— These appear next to information essential for the study of calculus.

 

• "Now Work" Problems

— These follow most examples, and direct students to a related exercise.

 

• Cautions

— These point out common mistakes and help students avoid them.

 

• Seeing the Concept & Explorations

— These optional features suggest graphing utility activities.

 

• In Words

— These provide alternative descriptions of select definitions and theorems, translating math into plain English.

 

• Step-by-Step, Annotated Examples

— Examples contain detailed intermediate steps. Many include additional annotations.

 

 PRACTICE

 

"Assess Your Understanding"sections (end-of-section exercises) contain a variety of problems. . .

• "Are You Prepared?" Problems

— These assess students’ retention of prerequisite material. Answers are given at the end of the section exercises. This feature is related to the Preparing for This Section feature.

 

• Concepts and Vocabulary

— These Fill-in the-Blank and True/False items assess students’ understanding of key definitions and concepts.

  

• Skill Development

— Correlated to section examples, these problems provide straightforward practice, organized by difficulty.

 

 • Graphical

— These problems utilize graphs in a variety of ways, supplementing students’ analytical understanding with graphical understanding.

 

• Now Work Problems

— Many examples refer students 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

— Application problems ("word problems") follow basic skill development problems.

 

• Graphing Calculator

— These optional problems require the use of a graphing utility, and are marked by a special icon.

 

• "DWR" — Discussion, Writing, and Research problems.

— These are marked by a special icon and red numbers. They support class discussion, verbalization of mathematical ideas, and writing and research projects.

 

 REVIEW

 

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.

 

• "You Should be Able To. . ."

— Contains a complete list of objectives by section, with corresponding practice exercises.

 

• Review Exercises

— These provide comprehensive review and practice of key skills, matched to the Learning Objectives for each section. These problems combine exercises from all sections, giving students a comprehensive review in one place.

 

• Practice Test

— The Review Exercises contain blue-numbered problems. Together, these blue-numbered problems constitute a Chapter Practice Test.

 

• Chapter Projects

— The Chapter Project applies what students have learned in the chapter opening article. Additional projects are available on a website. 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.

 

 

 

FOUNDATIONS: A PRELUDE TO FUNCTIONS

F.1 The Distance and Midpoint Formulas

F.2 Graphs of Equations; Intercepts; Symmetry

F.3 Lines

F.4 Circles

 

Chapter 1 Functions and Their Graphs

1.1 Functions

1.2 The Graph of a Function

1.3 Properties of Functions

1.4 Library of Functions; Piecewise-defined Functions

1.5 Graphing Techniques: Transformations

1.6 Mathematical Models: Constructing Functions

Chapter Review

Chapter Test

Chapter Projects

 

Chapter 2 Linear and Quadratic Functions

2.1 Properties of Linear Functions

2.2 Building Linear Functions from Data; Direct Variation

2.3 Quadratic Functions and Their Real Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Quadratic Models; Building Quadratic Functions From Data

2.7 Complex Zeros of a Quadratic Function

2.8 Equations and Inequalities Involving the Absolute Value Function

Chapter Review

Chapter Test

Chapter Projects

      Cumulative Review

 

Chapter 3       Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 Properties of Rational Functions

3.3 The Graph of a Rational Function; Inverse and Joint Variation

3.4 Polynomial and Rational Inequalities

3.5 The Real Zeros of a Polynomial Function

3.6 Complex Zeros: Fundamental Theorem of Algebra

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 4       Exponential and Logarithmic Functions

4.1 Composite Functions

4.2 One-to-One Functions; Inverse Functions

4.3 Exponential Functions

4.4 Logarithmic Functions

4.5 Properties of Logarithms

4.6 Logarithmic and Exponential Equations

4.7 Compound Interest

4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay

4.9 Building Exponential, Logarithmic, and Logistic Functions from Data

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

 

Chapter 5       Trigonometric Functions

5.1 Angles and Their Measure

5.2 Right Triangle Trigonometry

5.3 Computing the Values of Trigonometric Functions of Acute Angles

5.4 Trigonometric Functions of General Angles

5.5 Unit Circle Approach: Properties of the Trigonometric Functions

5.6 Graphs of the Sine and Cosine Functions

5.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

5.8 Phase Shift; Building Sinusoidal Functions from Data

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

 

Chapter 6       Analytic Trigonometry

6.1 The Inverse Sine, Cosine, and Tangent Functions

6.2 The Inverse Trigonometric Functions (continued)

6.3 Trigonometric Identities

6.4 Sum and Difference Formulas

6.5 Double-Angle and Half-Angle Formulas

6.6 Product-to-Sum and Sum-to-Product Formulas

6.7 Trigonometric Equations (I)

6.8 Trigonometric Equations (II)

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 7       Applications of Trigonometric Functions

7.1 Applications Involving Right Triangles

7.2 Law of Sines

7.3 Law of Cosines

7.4 Area of a Triangle

7.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 8       Polar Coordinates; Vectors

8.1 Polar Coordinates

8.2 Polar Equations and Graphs

8.3 The Complex Plane; DeMoivre’s Theorem

8.4 Vectors

8.5 The Dot Product

8.6 Vectors in Space

8.7 The Cross Product

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

 

Chapter 9       Analytic Geometry

9.1 Conics

9.2 The Parabola

9.3 The Ellipse

9.4 The Hyperbola

9.5 Rotation of Axes; General Form of a Conic

9.6 Polar Equations of Conics

9.7 Plane Curves and Parametric Equations

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 10       Systems of Equations and Inequalities

10.1 Systems of Linear Equations: Substitution and Elimination

10.2 Systems of Linear Equations: Matrices

10.3 Systems of Linear Equations: Determinants

10.4 Matrix Algebra

10.5 Partial Fraction Decomposition

10.6 Systems of Nonlinear Equations

10.7 Systems of Inequalities

10.8 Linear Programming

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 11       Sequences; Induction; The Binomial Theorem

11.1 Sequences

11.2 Arithmetic Sequences

11.3 Geometric Sequences; Geometric Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

 

Chapter 12       Counting and Probability

12.1 Sets and Counting

12.2 Permutations and Combinations

12.3 Probability

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

 

Chapter 13  A Preview of Calculus: The Limit, Derivative, and Integral of a Function

13.1 Finding Limits Using Tables and Graphs

13.2 Algebra Techniques for Finding Limits

13.3 One-sided Limits; Continuous Functions

13.4 The Tangent Problem; The Derivative

13.5 The Area Problem; The Integral

Chapter Review

Chapter Test

Chapter Project

 

Appendix A Review

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Polynomials

A.4 Factoring Polynomials

A.5 Synthetic Division

A.6 Rational Expressions

A.7 nth Roots; Rational Exponents

A.8 Solving Equations Algebraically

A.9 Interval Notation; Solving Inequalities

A.10 Problem Solving: Applications of Linear Equations

A.11 Complex Numbers

 

Appendix B Graphing Utilities

B.1 The Viewing Rectangle

B.2 Graphing Equations in Two Variables

B.3 Locating Intercepts and Checking for Symmetry

B.4 Solving Equations Using a Graphing Utility

B.5 Square Screens

B.6 Graphing Inequalities in Two Variables

B.7 Solving Systems of Linear Equations

B.8 Graphing a Polar Equation

B.9 Graphing Parametric Equations

 

Answers

Index

Precalculus Mathematics  (Mathematics)

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 30 years. He is a native of Chicago’s South Side and currently resides in Oaklawn.  Mike has four children.  The two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project.  Mike III co-authored the Sullivan Graphing with Data Analysis series as well as this series.  Dan, the youngest, sells for Prentice Hall as a generalist.

 

Mike has authored or co-authored over ten books.  He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oaklawn, where Mike enjoys gardening.  Mike first signed this series with Deleen Publishing (Acquired by Macmillan) in 1985.

 

Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

 

Why We Wrote the Book:

 

Work on this series began with a unique perspective.  Teaching at a large urban institution and a smaller two-year college has allowed us to see firsthand the challenges associated with teaching students with diverse backgrounds in an urban setting.  Successful textbooks must be accessible to students.  As lead author of this series, one of the most important things I bring to the project is my experience as author of a successful calculus text.  Mike and I are both aware that students must be prepared in a Precalculus course for subsequent mathematics courses.  We also realize that many College Algebra students will not be going on to take upper level math courses.  In this series we resolved the seeming dilemma without sacrificing accessibility.

 

The books in this series are designed to be mathematically comprehensive and to provide substantial mathematical preparation for subsequent courses.  At the same time, great effort has been expended to motivate the material and to make it accessible to even poorly prepared students.

My MathLab, 3/E
Mathematics
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0132210967 | ISBN-13: 9780132210966
URL:  http://www.mymathlab.com

Availability: Now! | Student Access Type: Access Code Required
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Instructor's Edition for Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, 3/E
Sullivan, Sullivan & III
©2007 | Prentice Hall | Cloth; 1248 pp | Instock
ISBN-10: 0132280663 | ISBN-13: 9780132280662

Chapter Projects - Right
Sullivan
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0136139434 | ISBN-13: 9780136139430
  View Downloadable Files

Instructor's Solutions Manual, 3/E
Bodden & Gallaher
©2007 | Prentice Hall | Paper; 1412 pp | Instock
ISBN-10: 0132210681 | ISBN-13: 9780132210683
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Mini Lecture Notes
Neal
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0136150969 | ISBN-13: 9780136150961
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My MathLab, 3/E
Mathematics
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0132210967 | ISBN-13: 9780132210966
URL:  http://www.mymathlab.com

Availability: Now! | Student Access Type: Access Code Required
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PowerPoint, 3/E
Haider
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0132369737 | ISBN-13: 9780132369732
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Test Item File Online, 3/E
Tamarack
©2007 | Prentice Hall | On-line Supplement; 500 pp | Instock
ISBN-10: 0131992155 | ISBN-13: 9780131992153
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TestGen 7.2 (download ony), 3/E
Tamarack
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 013236980X | ISBN-13: 9780132369800
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Algebra Review (stand alone), 2/E
Sullivan & Ledet
©2005 | Prentice Hall | Paper; 312 pp | Instock
ISBN-10: 0131480065 | ISBN-13: 9780131480063
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MathXL with CD (standalone), 3/E
Mathematics
©2007 | Prentice Hall | CD-ROM Only | Instock
ISBN-10: 0132210983 | ISBN-13: 9780132210980
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My MathLab, 3/E
Mathematics
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0132210967 | ISBN-13: 9780132210966
URL:  http://www.mymathlab.com

Availability: Now! | Student Access Type: Access Code Required
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Precalculus: Concepts Through Functions & S/Study Pack
SULLIVAN
©2007 | Prentice Hall | Kit/Package/ShrinkWrap | Instock
ISBN-10: 0132294818 | ISBN-13: 9780132294812
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Student Solutions Manual (STANDALONE) for Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry
Sullivan, Sullivan & III
©2007 | Prentice Hall | Paper; 848 pp | Instock
ISBN-10: 0321607864 | ISBN-13: 9780321607867
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Students Solutions Manual (Value Pack) for Precalculus: Concepts Through Funcitons, A Right Triangle Approach to Trigonometry
Bodden & Gallaher
©2007 | Prentice Hall | Paper; 848 pp | Instock
ISBN-10: 0131744089 | ISBN-13: 9780131744080

Addison-Wesley's Algebra Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Out of Stock
ISBN-10: 0321247086 | ISBN-13: 9780321247087

Addison-Wesley's Basic Math Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321247078 | ISBN-13: 9780321247070

Algebra Review Study Card, 2/E
D'Ippolito & Generazzo
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394739 | ISBN-13: 9780321394736
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Allied Health Study Card, 2/E
Forshier
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
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Concept Videos: Algebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Prentice Hall | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
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Finite Mathematics Study Card
Addison-Wesley
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321374398 | ISBN-13: 9780321374394
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Flash Review Series: Algebra
Becker
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321143094 | ISBN-13: 9780321143099
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Graphing Calculator Reference Card, 3/E
Ripley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394755 | ISBN-13: 9780321394750
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Prentice Hall | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
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Interwrite Personal Response System
EduCue, Addison-Wesley & Benjamin Cummings
©2004 | Prentice Hall | Electronic Supplement | Instock
ISBN-10: 0321267354 | ISBN-13: 9780321267351

Math for Allied Health Study/Reference Card
Forshier
©2006 | Prentice Hall | Study Card; 0 pp | Out of Stock
ISBN-10: 0321336542 | ISBN-13: 9780321336545

Mathematics Spanish Glossary, 2/E
Lara & Peeples
©2000 | Prentice Hall | Paper; 48 pp | Instock
ISBN-10: 0201728966 | ISBN-13: 9780201728965
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Prentice Hall | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
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Pearson TI Rebate Coupon $15, 2/E
Pearson
©2009 | Prentice Hall | Paper | Instock
ISBN-10: 0321566041 | ISBN-13: 9780321566041

Prealgebra Review Workbook
Wheel
©2006 | Prentice Hall | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
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Review of Algebra, A
Howard
©2002 | Prentice Hall | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
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Saleable Technology Bundle, 2/E
Pearson
©2009 | Prentice Hall | Multiple Media Package | Estimated Availability : 09/01/2008
ISBN-10: 0321561880 | ISBN-13: 9780321561886

Spanish Basic Math Study Card
Leonarte
©2007 | Prentice Hall | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
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Stand-alone Access Code Tutor Center
Addison-Wesley
©2008 | Prentice Hall | Access Code Card | Instock
ISBN-10: 0201721708 | ISBN-13: 9780201721706
URL:  http://www.aw-bc.com/tutorcenter
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My MathLab, 3/E
Mathematics
©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0132210967 | ISBN-13: 9780132210966
URL:  http://www.mymathlab.com

Availability: Now! | Student Access Type: Access Code Required
Request Content       Take a Tour

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• 
  Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, A La Carte + MyMathLab
  Sullivan, Sullivan & III
  ©2007 | Prentice Hall | Paper Package | Estimated Availability : 03/02/2006
  ISBN-10: 0321627830 | ISBN-13: 9780321627834
  

• 
  Precalculus: Concepts through Functions, A Right Triangle Approach to Trigonometry, A La Carte
  Sullivan, Sullivan & III
  ©2007 | Prentice Hall | Unbound (Saleable) | Instock
  ISBN-10: 0321627822 | ISBN-13: 9780321627827
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