Algebra and Trigonometry Enhanced with Graphing Utilities

Series
Pearson
Author
Michael Sullivan / Michael Sullivan  
Publisher
Pearson
Cover
Softcover
Edition
7
Language
English
Total pages
1200
Pub.-date
January 2016
ISBN13
9780134119267
ISBN
0134119266
Related Titles


Textbook

Product Price CHF Available  
9780134119267
Algebra and Trigonometry Enhanced with Graphing Utilities
278.20 approx. 7-9 days

Free evaluation copy for lecturers


Description

For courses in algebra and trigonometry.


Prepare, Practice, Review

The 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 Enhanced with Graphing Utilities Series has evolved to meet today’s course needs by integrating the usage of graphing calculators, active-learning, and technology in new ways to help students be successful in their course, as well as in their future endeavors.

 

In the Seventh Edition, there are several new features that appear in both the text and MyMathLab. Retain Your Knowledge problems offer the type of “final exam material” that students can use to maintain their skills throughout each chapter.

 

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. NEW! Guided Lecture Notes help students take thorough, organized, and understandable notes during class or while 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.

 

Features

 About the Book

 

Preparing for Class

  • Just-in-time review begins all sections 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 the "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.
    • Prebuilt Quizzes for the Are You Prepared? questions are assignable in MyMathLab.
  • 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 provides alternative descriptions of select definitions and theorems, translating math into plain English.
    • Warnings point out common mistakes and help students avoid them.

 

Practicing Skills

  • Concept and Vocabulary exercises are now assignable in MyMathLab as reading quizzes.
  • Assess Your Understanding appears at the end of every section and contains a variety of problems for students to master the skills they need.
    • NEW! Retain Your Knowledge problems offer the type of “final exam material” that students can use to maintain their skills throughout each chapter.
    • "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 pencil 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.

 

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 combine exercises from all sections, giving students comprehensive review in one place.
    • Chapter Tests contain 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, 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.
    • Internet-based Chapter Projects reinforce mathematical concepts, encouraging students to actively learn through research on the internet and to problem-solve using critical thinking. These projects are assignable in MyMathLab. By exploring and considering a variety of carefully guided “what-if” scenarios, students develop a better understanding of the concepts presented in the section.

 

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.

  • NEW! Guided Lecture Notes help students take thorough, organized, and understandable notes during class or while 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.
    • NEW! Video assessment questions are tied to key Author in Action videos to check students’ conceptual understanding of important math concepts.
  • NEW! With Getting Ready content, students refresh prerequisite topics through assignable skill-review quizzes and personalized homework.
  • NEW! Guided Visualizations help students better understand the visual aspects of key concepts in figure format. The figures are included in MyMathLab as both a teaching and an assignable learning tool.
  • NEW! Retain Your Knowledge quizzes promote ongoing review at the course level and help students maintain essential skills.
  • NEW! Skills for Success Modules help students succeed in collegiate courses and prepare for future professions. Topics such as “Time Management,” “Stress Management,” and “Financial Literacy” are available for you to assign to your students.
  • NEW! Functionality within the graphing utility allows graphing of 3-point quadratic functions, 4-point cubic graphs, and transformations in exercises.
  • Prebuilt quizzes for the Are You Prepared? questions are assignable in MyMathLab.
  • UPDATED! Concept and Vocabulary exercises are now assignable in MyMathLab as reading quizzes. Question types have been expanded to include multiple choice, fill-in-the-blank, and true/false problems.
  • Author-Solves-It MathXL Videos show Mike Sullivan III working key MathXL exercises typically requested by students for more explanation or tutoring. These videos are a result of Sullivan’s experiences in teaching online courses.
  • Author-designated sample homework problems are available in MyMathLab for quick and easy assignment creation.

New to this Edition

New and updated features

  • Most illustrations now have captions to connect them to the explanations in the body of the text.
  • Calculator screenshots have been updated with the TI-84 Plus C, helping students visualize concepts clearly and make stronger connections between equations, data, and graphs in full color.

 

Content Updates

  • Section 3.1 The objective, Find the Difference Quotient of a Function, has been added.
  • Section 3.3 The description of where a function is increasing, decreasing, or constant is now expressed in terms of a closed interval, rather than an open interval.
  • Section 5.2 The objective, Use Descartes’ Rule of Signs, has been included.
  • Section 5.2 The theorem, Bounds on the Zeros of a Polynomial Function, is now based on the traditional method of using synthetic division.
  • Section 5.5 Content has been added, discussing the role of multiplicity of the zeros of the denominator of a rational function as it relates to the graph near a vertical asymptote.

 

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.

  • Guided Lecture Notes help students take thorough, organized, and understandable notes during class or while 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.
    • NEW! Video assessment questions are tied to key Author in Action videos to check students’ conceptual understanding of important math concepts.
  • With Getting Ready content, students refresh prerequisite topics through assignable skill-review quizzes and personalized homework.
  • Guided Visualizations help students better understand the visual aspects of key concepts in figure format. The figures are included in MyMathLab as both a teaching and an assignable learning tool.
  • Retain Your Knowledge quizzes promote ongoing review at the course level and help students maintain essential skills.
  • Skills for Success Modules help students succeed in collegiate courses and prepare for future professions. Topics such as “Time Management,” “Stress Management,” and “Financial Literacy” are available for you to assign to your students.
  • Functionality within the graphing utility allows graphing of 3-point quadratic functions, 4-point cubic graphs, and transformations in exercises.
  • UPDATED! Concept and Vocabulary exercises are now assignable in MyMathLab as reading quizzes. Question types have been expanded to include multiple choice, fill-in-the-blank, and true/false problems.

 

Table of Contents

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. Graphs, Equations, and Inequalities

1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations

1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations

1.3 Quadratic Equation

1.4 Complex Numbers; Quadratic Equations in the Complex Number System

1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations

1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

1.7 Solving Inequalities

Chapter Review

Chapter Test

Chapter Projects

 

2. Graphs

2.1 Intercepts: Syemmetry; Graphing Key Equations

2.2 Lines

2.3 Circles

2.4 Variation

Chapter Review

Chapter Test

Cumulative Review

Chapter Project

 

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 Descriptions 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 The Real Zeros of a Polynomial Function

5.3 Complex Zeros; Fundamental Theorem of Algebra

5.4 Properties of Rational Functions

5.5 The Graph of a Rational Function

5.6 Polynomial and Rational Inequalities

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 Models 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 The Law of Sines

9.3 The 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, De Moivre’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: Substitutions and Elimination

12.2 Systems of Linear Equations: Matrices

12.3 Systems of Linear Equations: Determinants

12.4 Matric 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 Induciton

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

 

Answers

Credits

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 Oak Lawn, Illinois, and Naples, Florida.

 

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, 12 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 co-author on two precalculus series; Dan works in publishing; and Colleen teaches middle school and secondary school mathematics. Twelve grandchildren round out the family.

 

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.