Algebra and Trigonometry

Algebra and Trigonometry - Michael Sullivan - 9780321998590 - Mathematics Statistics - Precalculus/Precollege Maths (115)
Series
Pearson
Author
Michael Sullivan  
Publisher
Pearson
Cover
Softcover
Edition
10
Language
English
Total pages
1176
Pub.-date
December 2014
ISBN13
9780321998590
ISBN
0321998596
Related Titles



Description

For courses in Algebra and Trigonometry.

 

Prepare. Practice. Review.

Mike Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Tenth Edition has evolved to meet today’s course needs.

 

With this new edition, Mike Sullivan has developed MyMathLab features to help better prepare students and get them thinking more visually and conceptually. Features like Getting Ready exercises, Video Assessment exercises Enhanced Graphing Functionality and Skills for Success modules benefit student learning. Also, by implementing the New! Guided Lecture notes that focus students on the important concepts and help structure studying, students will have the most effective tools to succeed.

 

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

 

Features

About the Book

 

Preparing for Class

  • Just-in-time review begins every section to prepare students for the topics ahead.
    • Preparing for This Section lists previously learned concepts that will be useful in the section ahead. Page references are included for easy review.
    • Now Work "Are You Prepared?" problems support the Preparing for This Section feature, allowing students to check that they are ready to proceed to the section ahead or if they need to turn back for further review. These problems appear at the start of each exercise set.
  • Section-level guidance in each section helps students master the material and develop their problem-solving skills.
    • Showcase Examples provide how-to instruction by offering a guided, step-by-step approach to solving a problem. Students can immediately see how each of the steps in a problem is employed. The two-column format describes the steps on the left and displays the algebra, complete with annotations, on the right.
    • Model It examples are now highlighted, making it easy to identify which examples help students learn to build a mathematical model from verbal descriptions or from data. Model It exercises are also included so that instructors can assign these for homework or practice.
    • "Now Work" Problems follow most examples, and point to a related exercise for immediate reinforcement of the skill or concept.
    • Step-by-Step, Annotated Examples contain detailed intermediate steps with additional annotations to help students see specific nuances.
    • Calculus icons appear next to information essential for the study of calculus. When the icon appears next to a definition, the notation used is consistent with that used in calculus.
    • In Words provide alternative descriptions of select definitions and theorems, translating math into plain English.
    • Warnings point out common mistakes and help students avoid them.

 

Practicing Skills

  • NEW! Guided Lecture Notes help students take thorough, organized, and understandable notes as they watch the Author in Action videos. They ask students to complete definitions, procedures, and examples based on the content of the videos and text.
  • Assess Your Understanding appears at the end of every section and contains a variety of problems for students to master the skills they need.
    • "Are You Prepared?" Problems appear at the start of every exercise set and help students determine exactly what they need to review and where to review it. This feature is referenced from the Preparing for This Section feature. Answers appear at the end of the section.
    • Concepts and Vocabulary questions are fill-in the-blank and true/false items that assess students’ understanding of key definitions and concepts. These have been written to serve as reading quizzes and are now assignable in MyMathLab® and MathXL®.
    • Skill Building problems provide straightforward practice, are organized by difficulty, and are correlated to section examples.
    • Graphical problems use graphs in a variety of ways, supplementing analytical understanding with graphical understanding.
    • Now Work problems, marked by a yellow icon in the exercise set, correspond to a related example within the section. If students get stuck while doing their homework, they can look for the closest Now Work problem and refer back to the related example.
    • Mixed Practice problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together.
    • Applications and Extensions allow students to apply their skills to real-world problems and to extend concepts learned in the section. These exercises have been updated and many new problems have been added involving sourced information and data sets to bring relevance and timeliness to these exercises. Model It exercises and examples are now highlighted, making it easy to identify which exercises ask students to build a mathematical model from verbal descriptions or from data.
    • Explaining Concepts: Discussion and Writing problems are marked by red numbers. These support class discussion, verbalization of mathematical ideas, and writing and research projects.
  • Exercise sets have been updated and expanded to integrate new question types that give instructors more flexibility and help students build their conceptual understanding.
    • NEW! Retain Your Knowledge exercises help students recall previously learned skills. These problems are considered “final exam material” that students can use to maintain their skills.
    • Mixed Practice problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together.
    • Concepts and Vocabulary exercises have been written to serve as reading quizzes and are now assignable in MyMathLab® and MathXL®.
    • Model It exercises and examples are now highlighted, making it easy to identify which exercises ask students to build a mathematical model from verbal descriptions or from data.
    • Applications and Extensions have been updated and many new problems have been added involving sourced information and data sets to bring relevance and timeliness to these exercises.

 

Reviewing for Exams and Quizzes

  • Chapter Reviews at the end of each chapter offer a variety of convenient tools for reference and review.
    • "You Should be Able To…” is a list of every objective by section, with corresponding practice exercises. Doing the recommended exercises allows students to master the key concepts. If they get something wrong, they can easily review the examples and exposition and try again.
    • Review Exercises 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 comprehensive review in one place.
    • Chapter Tests contain about 15—20 problems that can help students prepare for in-class exams. For additional help, they can watch an instructor work out full solutions on the Chapter Test Prep Video on YouTube, on DVD, or in MyMathLab.
    • Cumulative Review problem sets appear at the end of every chapter after Chapter 1. They combine problems from previous chapters, providing an ongoing cumulative review.
    • NEW! Internet-based Chapter Projects, with assignable exercises in MyMathLab, allow students the opportunity to experience mathematics firsthand in an active learning environment. By exploring and considering a variety of carefully guided “what-if” scenarios, they will develop a better understanding of the concepts presented in the section. Students will learn by doing and have fun in the process.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, Mike Sullivan has developed MyMathLab features that help better prepare students and get them thinking more visually and conceptually.

  • MyMathLab is closely integrated with the text and offers a variety of question types, for a robust online experience that mirrors the author’s approach.
  • MyMathLab with Integrated Review is a new course option for College Algebra that includes additional review resources (skill check quizzes, personalized homework, review worksheets, and videos) at the beginning of chapters.
  • NEW! Video Assessment is tied to key Author in Action videos, created by Michael Sullivan III,which walk students through exercises typically requested by students for more explanation or tutoring. Instructors can assign these videos and check for students’ conceptual understanding.
  • NEW! Getting Ready: skill review quizzes are assignable throughout the course, testing students on prerequisite knowledge. From these quizzes, each student receives a personalized homework assignment to refresh forgotten concepts.
  • NEW! Adaptive Study Plan: Pearson now offers adaptive learning functionality that continuously analyzes student work and points them toward resources that will maximize their potential for understanding and success.
  • NEW! Skills for Success Module: these modules help students develop the good habits needed in the transition to college and then to professional life.
  • NEW! Enhanced Graphing Functionality: new functionality within the graphing utility allows graphing of 3-point quadratic functions, 4-point cubic graphs, and transformations in exercises.
  • Internet-based Chapter Projects, with assignable exercises in MyMathLab, allow students to experience mathematics first hand in an active learning environment. By exploring and considering a variety of carefully guided “what-if” scenarios, they will develop a better understanding of the concepts presented in the section. Students will learn by doing and have fun in the process.
  • Author Solves It MathXL Videos show Mike Sullivan III working by section through MathXL exercises typically requested by students for more explanation or tutoring. These videos are a result of Sullivan’s experiences in teaching online.

 

 

New to this Edition

New and updated features

  • Guided Lecture Notes help students take thorough, organized, and understandable notes as they watch the Author in Action videos. They ask students to complete definitions, procedures, and examples based on the content of the videos and text.
  • Retain Your Knowledge exercises help students recall previously learned skills. These problems are considered “final exam material” that students can use to maintain their skills.
  • Internet-based Chapter Projects, with assignable exercises in MyMathLab, allow students the opportunity to experience mathematics firsthand in an active learning environment. By exploring and considering a variety of carefully guided “what-if” scenarios, they will develop a better understanding of the concepts presented in the section. Students will learn by doing and have fun in the process.

Personalize learning with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, Mike Sullivan has developed MyMathLab features that help better prepare students and get them thinking more visually and conceptually.

  • Video Assessment is tied to key Author in Action videos, created by Michael Sullivan III,which walk students through exercises typically requested by students for more explanation or tutoring. Instructors can assign these videos and check for students’ conceptual understanding.
  • Getting Ready: skill review quizzes are assignable throughout the course, testing students on prerequisite knowledge. From these quizzes, each student receives a personalized homework assignment to refresh forgotten concepts.
  • Adaptive Study Plan: Pearson now offers adaptive learning functionality that continuously analyzes student work and points them toward resources that will maximize their potential for understanding and success.
  • Skills for Success Module: these modules help students develop the good habits needed in the transition to college and then to professional life.
  • Enhanced Graphing Functionality: new functionality within the graphing utility allows graphing of 3-point quadratic functions, 4-point cubic graphs, and transformations in exercises.

 

 

Table of Contents

Preface to the Instructor

List of Applications

Photo Credits

To the Student

 

R. Review

R.1 Real Numbers

R.2 Algebra Essentials

R.3 Geometry Essentials

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Synthetic Division

R.7 Rational Expressions

R.8 nth Roots; Rational Exponents

 

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 Jobs Applications

   Chapter Review

   Chapter Test

   Chapter Projects

 

2. Graphs

2.1 The Distance and Midpoint Formulas

2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

2.3 Lines

2.4 Circles

2.5 Variation

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

3. Functions and Their Graphs

3.1 Functions

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 Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

4. Linear and Quadratic Functions

4.1 Properties of Linear Functions and Linear Models

4.2 Building Linear Models from Data

4.3 Quadratic Functions and Their Properties

4.4 Build Quadratic Models from Verbal Description and From Data

4.5 Inequalities Involving Quadratic Functions

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

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 Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

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 Financial Models

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 Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

7. Trigonometric Functions

7.1 Angles and Their Measure

7.2 Right Triangle Trigonometry

7.3 Computing the Values of Trigonometric Functions of Acute Angles

7.4 Trigonometric Functions of Any Angle

7.5 Unit Circle Approach: Properties of the Trigonometric Functions

7.6 Graphs of the Sine and Cosine Functions

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

7.8 Phase Shift; Sinusoidal Curve Fitting

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

8. Analytic Trigonometry

8.1 The Inverse Sine, Cosine, and Tangent Functions

8.2 The Inverse Trigonometric Functions (continued)

8.3 Trigonometric Equations

8.4 Trigonometric Identities

8.5 Sum and Difference Formulas

8.6 Double-angle and Half-angle Formulas

8.7 Product-to-Sum and Sum-to-Product Formulas

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

9. Applications of Trigonometric Functions

9.1 Applications Involving Right Triangles

9.2 Law of Sines

9.3 Law of Cosines

9.4 Area of a Triangle

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

10. Polar Coordinates; Vectors

10.1 Polar Coordinates

10.2 Polar Equations and Graphs

10.3 The Complex Plane; DeMoivre’s Theorem

10.4 Vectors

10.5 The Dot Product

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

11. Analytic Geometry

11.1 Conics

11.2 The Parabola

11.3 The Ellipse

11.4 The Hyperbola

11.5 Rotation of Axes; General Form of a Conic

11.6 Polar Equations of Conics

11.7 Plane Curves and Parametric Equations

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

12. Systems of Equations and Inequalities

12.1 Systems of Linear Equations: Substitution and Elimination

12.2 Systems of Linear Equations: Matrices

12.3 Systems of Linear Equations: Determinants

12.4 Matrix Algebra

12.5 Partial Fraction Decomposition

12.6 Systems of Nonlinear Equations

12.7 Systems of Inequalities

12.8 Linear Programming

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

13. Sequences; Induction; the Binomial Theorem

13.1 Sequences

13.2 Arithmetic Sequences

13.3 Geometric Sequences; Geometric Series

13.4 Mathematical Induction

13.5 The Binomial Theorem

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

14. Counting and Probability

14.1 Counting

14.2 Permutations and Combinations

14.3 Probability

   Chapter Review

   Chapter Test

   Cumulative Review

   Chapter Projects

 

Appendix: Graphing Utilities

1. The Viewing Rectangle

2. Using a Graphing Utility to Graph Equations

3. Using a Graphing Utility to Locate Intercepts and Check for Symmetry

4. Using a Graphing Utility to Solve Equations

5. Square Screens

6. Using a Graphing Utility to Graph Inequalities

7. Using a Graphing Utility to Solve Systems of Linear Equations

8. Using a Graphing Utility to Graph a Polar Equation

9. Using a Graphing Utility to Graph Parametric Equations

 

Answers

Index

Author

Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before recently retiring. He is a native of Chicago’s South Side and divides his time between a home in Oak Lawn IL and a condo in Naples FL.

 

Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America.

 

Mike has been writing textbooks for more than 35 years and currently has 15 books in print, twelve with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.

 

Mike has four children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his coauthor on two precalculus series; Dan works in publishing; and Colleen teaches middle-school and secondary school mathematics. Twelve grandchildren round out the family.