Precalculus

Series
Pearson
Author
Michael Sullivan / Michael Sullivan  
Publisher
Pearson
Cover
Softcover
Edition
3
Language
English
Total pages
1152
Pub.-date
January 2014
ISBN13
9780321931054
ISBN
032193105X
Related Titles



Description

Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, Third Edition focuses on the fundamentals: preparation for class, practice with homework, and reviewing of key concepts. With the Concepts Through Functions series, the Sullivans expose students to functions in the first chapter and maintain a continuous theme of functions throughout the text. This approach ensures students master basic skills and develop the conceptual understanding they need for the course, ultimately preparing students for future math courses as well.master basic skills and develop the conceptual understanding they need for the course, ultimately preparing students for future math courses as well.


This program will provide a better teaching and learning experience–for you and your students. Here’s how:

  • Improve Results: MyMathLab® delivers proven results in helping students succeed and provides engaging experiences that personalize learning.
  • Help students prepare for class with just-in-time review for topics ahead.
  • Reinforce key concepts with practicing skills exercises that allow students to practice immediately after learning a new skill.
  • Review for exams and quizzes with comprehensive practice problems matched to learning objectives for each section.

 


Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. MyMathLab is not a self-paced technology and should only be purchased when required by an instructor. If you would like to purchase both the physical text and MyMathLab, search for:

032192598X / 9780321925985 Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry Plus NEW MyMathLab with eText -- Access Card Package

Package consists of

0321431308 / 9780321431301 MyMathLab -- Glue-in Access Card

0321654064 / 9780321654069 MyMathLab Inside Star Sticker

032193105X / 9780321931054 Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry 

Features

Improve Results with MyMathLab®: MyMathLab delivers proven results in helping students succeed and provides engaging experiences that personalize learning.

  • NEW! Ready-to-Go MyMathLab courses are pre-built MyMathLab courses that make the start-up time building your course quick and easy.  These courses include author-created assignments, Cumulative Review Tests, and more.
  • NEW! Getting Ready skill review quizzes are assignable throughout the course, testing students on prerequisite knowledge. Each student receives a personalized homework assignment to refresh forgotten concepts based on quiz results.
  • NEW! Retain Your Knowledge exercises:  These new exercises support ongoing review at the course level and help students maintain essential skills.  These new exercises are assignable in MyMathLab
  • NEW! The Adaptive Study Plan makes studying more efficient and effective for every student.  Performance and activity are assessed continually in real time. Data and analytics are used to provide personalized content-- reinforcing concepts that target each student's strengths and weaknesses. 
  • NEW! Video Assessment exercises are available with key Author in Action videos to check student’s conceptual understanding of important math concepts.
  • NEW! Skills for Success Modules support students toward continued success in college. This module provides tutorials and guidance on topics such as transitioning to college, online learning, time management and more. Additionally, there is content to help students with professional skills such as resume development and interview preparation.
  • NEW! Graphing Functionality allows students to graph 3-point cubic, 4-point quadratic and transformation graphs within MyMathLab exercises.

 

Preparing for Class

  • All sections begin with just-in-time review 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.
  • Within each section, students get guidance along the way to help them master the material and develop their problem-solving skills.
    • "Now Work" Problems follow most examples, and direct students 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.
    • Cautions boxes point out common mistakes and help students avoid them.

 

Practicing Skills

  • NEW! Retain Your Knowledge problems in the exercise set are based on the article "To Retain New Learning, Do the Math" published in the Edurati Review in which author Kevin Washburn suggests that "the more students are required to recall new content or skills, the better their memory will be.” It is frustrating when students cannot recall skills learned earlier in the course. To alleviate this recall problem, we have created "Retain Your Knowledge problems. These new exercises are assignable in MyMathLab.
  • 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 Development problems provide straightforward practice, are organized by difficulty, and are correlated to section examples.
    • Graphical problems use graphs in a variety of ways, supplementing students’ analytical understanding with graphical understanding.
    • Now Work problems–many examples refer to a related problem in the exercise set, which are marked by a yellow pencil icon. 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.
    • DWRDiscussion, Writing, and Research problems– are marked by a special icon and red numbers. They support class discussion, verbalization of mathematical ideas, and writing and research projects.

 

Reviewing for Exams and Quizzes

  • NEW! Guided Lecture Notes give students a note-taking guide that assist in taking thorough, organized, and understandable notes as they watch the Author in Action videos. The Notes ask students to complete definitions, procedures, and examples based on the content of the videos and book. By directing students into essential material, students can focus and retain the most important concepts. These notes help increase the success of your students in any course structure.
  • Chapter Reviews at the end of each chapter offer a variety of convenient tools for students’ 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.
    • Practice Tests–the Review Exercises contain blue-numbered problems, which can be combined to constitute a Practice Test for the chapter.
    • Chapter Tests contain about 15—20 problems that can help students prepare for in-class exams. For additional help, students 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.

 

New to this Edition

Updates to the MyMathLab® Course

  • Ready-to-Go MyMathLab courses are pre-built MyMathLab courses that make the start-up time building your course quick and easy.  These include author-designated assignments, and more.
  • 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.
  • Retain Your Knowledge exercises:  These new exercises support ongoing review at the course level and help students maintain essential skills.  These new exercises are assignable in MyMathLab.
  • Adaptive Study Plan makes studying more efficient and effective for every student.  Performance and activity are assessed continually in real time. Data and analytics are used to provide personalized content-- reinforcing concepts that target each student's strengths and weaknesses.
  • Video Assessment exercises are available with key Author in Action videos to check student’s conceptual understanding of important math concepts.
  • Skills for Success Modules support students toward continued success in college. This module provides tutorials and guidance on topics such as transitioning to college, online learning, time management and more. Additionally, there is content to help students develop professional skills such as resume development and interview preparation.
  • Graphing Functionality allows students to graph 3-point cubic, 4-point quadratic and transformation graphs within MyMathLab exercises.

 

Reviewing for Exams and Quizzes

  • Guided Lecture Notes give students a note-taking guide that assist in taking thorough, organized, and understandable notes as they watch the Author in Action videos. The Notes ask students to complete definitions, procedures, and examples based on the content of the videos and book. By directing students into essential material, students can focus and retain the most important concepts. These notes help increase the success of your students in any course structure.

 

Table of Contents

Foundations: A Prelude to Functions

F.1 The Distance and Midpoint Formulas

F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

F.3 Lines

F.4 Circles

 

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

1.7 Building Mathematical Models Using Variation

Chapter Review

Chapter Test

Chapter Projects

 

2. Linear and Quadratic Functions

2.1 Properties of Linear Functions and Linear Models

2.2 Building Linear Models from Data

2.3 Quadratic Functions and Their Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Building Quadratic Models from Verbal Descriptions and 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

 

3. Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 The Real Zeros of a Polynomial Function

3.3 Complex Zeros; Fundamental Theorem of Algebra

3.4 Properties of Rational Functions

3.5 The Graph of a Rational Function

3.6 Polynomial and Rational Inequalities

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

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 Projects

Cumulative Review

 

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 Any Angle

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; Sinusoidal Curve Fitting

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

6. Analytic Trigonometry

6.1 The Inverse Sine, Cosine, and Tangent Functions

6.2 The Inverse Trigonometric Functions (Continued)

6.3 Trigonometric Equations

6.4 Trigonometric Identities

6.5 Sum and Difference Formulas

6.6 Double-angle and Half-angle Formulas

6.7 Product-to-Sum and Sum-to-Product Formulas

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

7. Applications of Trigonometric Functions

7.1 Right Triangle Trigonometry; Applications Involving Right Triangles

7.2 The Law of Sines

7.3 The 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

 

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

 

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

 

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

 

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

 

12. Counting and Probability

12.1 Counting

12.2 Permutations and Combinations

12.3 Probability

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

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

A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

A.10 Interval Notation; Solving Inequalities

A.11 Complex Numbers

 

Appendix B. Graphing Utilities

B.1 The Viewing Rectangle

B.2 Using a Graphing Utility to Graph Equations

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

B.4 Using a Graphing Utility to Solve Equations

B.5 Square Screens

B.6 Using a Graphing Utility to Graph Inequalities

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

B.8 Using a Graphing Utility to Graph a Polar Equation

B.9 Using a Graphing Utility to Graph Parametric Equations

 

Answers

Index

 

 

Author

Mike Sullivan is Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. 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. His son, Mike Sullivan, III, co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where Mike enjoys gardening.

 

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.