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Title overview

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.

MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

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 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.

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.

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 th

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.

MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

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.

  • 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

1. Graphs

1.1 The Distance and Midpoint Formulas

1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

1.3 Lines

1.4 Circles

 

2. Functions and Their Graphs

2.1 Functions

2.2 The Graph of a Function

2.3 Properties of Functions

2.4 Library of Functions; Piecewise-defined Functions

2.5 Graphing Techniques: Transformations

2.6 Mathematical Models: Building Functions

 

3. Linear and Quadratic Functions

3.1 Properties of Linear Functions and Linear Models

3.2 Building Linear Models from Data

3.3 Quadratic Functions and Their Properties

3.4 Build Quadratic Models from Verbal Descriptions and from Data

3.5 Inequalities Involving Quadratic Functions

 

4. Polynomial and Rational Functions

4.1 Polynomial Functions and Models

4.2 Properties of Rational Functions

4.3 The Graph of a Rational Function

4.4 Polynomial and Rational Inequalities

4.5 The Real Zeros of a Polynomial Function

4.6 Complex Zeros; Fundamental Theorem of Algebra

 

5. Exponential and Logarithmic Functions

5.1 Composite Functions

5.2 One-to-One Functions; Inverse Functions

5.3 Exponential Functions

5.4 Logarithmic Functions

5.5 Properties of Logarithms

5.6 Logarithmic and Exponential Equations

5.7 Financial Models

5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

5.9 Building Exponential, Logarithmic, and Logistic Models from Data

 

6. Trigonometric Functions

6.1 Angles and Their Measure

6.2 Trigonometric Functions: Unit Circle Approach

6.3 Properties of the Trigonometric Functions

6.4 Graphs of the Sine and Cosine Functions

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

6.6 Phase Shift; Sinusoidal Curve Fitting

 

7. Analytic Trigonometry

7.1 The Inverse Sine, Cosine, and Tangent Functions

7.2 The Inverse Trigonometric Functions (Continued)

7.3 Trigonometric Equations

7.4 Trigonometric Identities

7.5 Sum and Difference Formulas

7.6 Double-angle and Half-angle Formulas

7.7 Product-to-Sum and Sum-to-Product Formulas

 

8. Applications of Trigonometric Functions

8.1 Right Triangle Trigonometry; Applications

8.2 The Law of Sines

8.3 The Law of Cosines

8.4 Area of a Triangle

8.5 Simple Harmonic Motion; Damped Motion; Combining Waves

 

9. Polar Coordinates; Vectors

9.1 Polar Coordinates

9.2 Polar Equations and Graphs

9.3 The Complex Plane; DeMoivre’s Theorem

9.4 Vectors

9.5 The Dot Product

9.6 Vectors in Space

9.7 The Cross Product

 

10. Analytic Geometry

10.1 Conics

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

10.5 Rotation of Axes; General Form of a Conic

10.6 Polar Equations of Conics

10.7 Plane Curves and Parametric Equations

 

11. Systems of Equations and Inequalities

11.1 Systems of Linear Equations: Substitution and Elimination

11.2 Systems of Linear Equations: Matrices

11.3 Systems of Linear Equations: Determinants

11.4 Matrix Algebra

11.5 Partial Fraction Decomposition

11.6 Systems of Nonlinear Equations

11.7 Systems of Inequalities

11.8 Linear Programming

 

12. Sequences; Induction; the Binomial Theorem

12.1 Sequences

12.2 Arithmetic Sequences

12.3 Geometric Sequences; Geometric Series

12.4 Mathematical Induction

12.5 The Binomial Theorem

 

13. Counting and Probability

13.1 Counting

13.2 Permutations and Combinations

13.3 Probab

Author bios

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.

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