Sullivan, Precalculus, 12th Edition
Michael Sullivan’s time-tested approach focuses students on the fundamental skills they need for the AP® precalculus course: preparing for class, practicing with homework, and reviewing the concepts. The 12th Edition, published by Pearson, continues to evolve to meet the needs of today’s students:
- New and revised graphing utility screen captures include more Desmos and TI-84 Plus images–they provide alternate ways of visualizing concepts and making connections between equations, data, and graphs in full color.
- Desmos simplifies finding points of interest such as local extrema, intercepts, and points of intersection with systems of equations.
- Need To Review? questions are a timely reference to the chapter, section and page where a student may need to refresh a particular skill needed for the material.
- Career Tips and Fun Facts help students connect the topic at hand to the world around them. Caution notes help students avoid common mistakes.
AP Precalculus Program for Middle and High Schoolers with Digital Integration
Precalculus features Sullivan’s proven cycle of continuous preparation and retention: prepare for class, practice with homework, and review concepts.
Revitalized with New Content
The 12th Edition adds many new and revised exercises and examples; adds new learning tips in margin notes; and updates all graphing utility content and images.
Features Integrated Review
Integrated Review is now included in all Sullivan 12th Edition MyMathLab® for School courses, including Precalculus.Integrated review can be used to help students who enter without a full understanding of prerequisite skills and concepts.
Essential Video Series
College Algebra Essential Video Series covers the essential topics a college algebra student needs to understand to be successful in this course. Videos can be assigned in a MyMathLab for School homework assignment to remind students of the crucial content before students begin on their exercises.
Mathematician Profiles
New, inspirational Contemporary Mathematicians highlights appear near the start of each chapter. This selection of diverse accomplished mathematicians and scientists explores “who is a mathematician? What are they working on, and what was their journey?”
AP Precalculus Program for Middle and High Schoolers with Digital Integration
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Robust Preparation Features and Examples
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Real Mathematician Profiles Inspire Learning
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New and Updated Practice Resources
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Comprehensive Review Resources
Robust Preparation Features and Examples
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Just-in-Time ReviewJust-in-time review begins all sections to prepare students for the topics ahead.
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Preparing for This SectionPreparing for This Section lists previously learned concepts that will be useful in the section ahead.
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Are You Prepared?"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.
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Showcase ExamplesShowcase Examples provide how-to instruction by offering a guided, step-by-step approach to problem-solving.
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Model ItModel It examples and exercises are now highlighted, making it easy to identify which exercises ask students to build a mathematical model from verbal descriptions or from data.
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Need to Review QuestionsNew Need to Review? Questions are placed at the point of need for students. They provide references and page numbers to the discussion of a previous topic used in the current presentation.
Real Mathematician Profiles Inspire Learning
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Contemporary MathematiciansNew, inspirational Contemporary Mathematicians highlights appear near the start of each chapter.
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Who is a Mathematician?These selections of diverse, accomplished mathematicians and scientists explore “who is a mathematician? What are they working on, and what was their journey?”
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Mindset MaterialNew Mindset material in MyMathLab® for School from Pearson encourages students to overcome major hurdles for math students by maintaining a positive attitude about learning, valuing their own ability to grow, and viewing mistakes as learning opportunities.
New and Updated Practice Resources
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Updated Guided Lecture NotesUpdated Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and text. By directing students into essential material, students can focus and retain the most important concepts.
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Guided VisualizationsNew Guided Visualizations, powered by GeoGebra and created by Michael Sullivan III, help students visualize concepts through directed exploration and purposeful manipulation. They are assignable in MyMathLab for School with assessment questions to check students’ conceptual understanding.
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Assess Your UnderstandingUpdated Assess Your Understanding appears at the end of every section and contains a variety of problems for students to master the skills they need. Updated and expanded exercise sets appear throughout.
Comprehensive Review Resources
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Review ExercisesReview 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.
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Cumulative ReviewCumulative Review problem sets appear at the end of every chapter after Chapter 1. They combine problems from previous chapters, providing an ongoing cumulative review.
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Chapter TestsChapter Tests contain between 15-20 problems that can help students prepare for in-class exams. Chapter Test Prep Videos are available for additional help.
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Chapter ProjectInternet-based Chapter Projects, with assignable exercises in MyMathLab for School, enable students to learn by doing and have fun in the process via guided “what-if” scenarios.
Online Platform for Your Precalculus Curriculum
MyMathLab® for School from Pearson is the world’s leading online tutorial and assessment program for teaching and learning mathematics, whether you’re looking for a 100% digital solution or digital support for a blended program. MyMathLab for School courses provide you with:
- Interactive practice with immediate feedback
- Flexible course designs to fit your course
- Comprehensive gradebook with enhanced reporting
- Complete eText, accessible anywhere with the Pearson eText app
Sullivan, Precalculus, 12th Edition Frequently Asked Questions
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What topics are included in the 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
- Chapter 1 Review, Test, and Projects
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
- Chapter 2 Review, Test, and Projects
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
- Chapter 3 Review, Test, and Projects
4) Polynomial and Rational Functions
- 4.1 Polynomial Functions
- 4.2 Graphing Polynomial Functions; Models
- 4.3 Properties of Rational Functions
- 4.4 The Graph of a Rational Function
- 4.5 Polynomial and Rational Inequalities
- 4.6 The Real Zeros of a Polynomial Function
- Chapter 4 Review, Test, and Projects
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
- Chapter 5 Review, Test, and Projects
6) Trigonometric Functions
- 6.1 Angles, Arc, Length, and Circular Motion
- 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
- Chapter 6 Review, Test, and Projects
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
- Chapter 7 Review, Test, and Projects
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
- Chapter 8 Review, Test, and Projects
9) Polar Coordinates; Vectors
- 9.1 Polar Coordinates
- 9.2 Polar Equations and Graphs
- 9.3 The Complex Plane; De Moivre's Theorem
- 9.4 Vectors
- 9.5 The Dot Product
- 9.6 Vectors in Space
- 9.7 The Cross Product
- Chapter 9 Review, Test, and Projects
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
- Chapter 10 Review, Test, and Projects
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
- Chapter 11 Review, Test, and Projects
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
- Chapter 12 Review, Test, and Projects
13) Counting and Probability
- 13.1 Counting
- 13.2 Permutations and Combinations
- 13.3 Probability
- Chapter 13 Review, Test, and Projects
14) A Preview of Calculus: The Limit, Derivative, and Integral of a Function
- 14.1 Finding Limits Using Tables and Graphs
- 14.2 Algebra Techniques for Finding Limits
- 14.3 One-sided Limits; Continuous Functions
- 14.4 The Tangent Problem; The Derivative
- 14.5 The Area Problem; The Integral
- Chapter 14 Review, Test, and Projects
Appendix A: Review
- A.1 Algebra Essentials
- A.2 Geometry Essentials
- A.3 Polynomials
- A.4 Synthetic Division
- A.5 Rational Expressions
- A.6 Solving Equations
- A.7 Complex Numbers; Quadratic Equations in the Complex Number System
- A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
- A.9 Interval Notation; Solving Inequalities
- A.10 nth Roots; Rational Exponents
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
Credits
Index
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About the Author: Michael Sullivan
After graduating from Saint Ignatius College Prep (Chicago), Michael Sullivan attended DePaul University as an undergraduate, completing a major in mathematics and a minor in physics in 3 years. He pursued his graduate studies at the Illinois Institute of Technology, receiving a master's degree in 1963 and a Doctor of Philosophy (PhD) in 1967, both in mathematics.
Mike had a teaching career of over 30 years at Chicago State University as a Professor of Mathematics, where he honed an approach to teaching and writing that forms the foundation for his textbooks. He has authored more than 120 textbooks in mathematics and currently has 15 books in print. His textbooks are used in high schools and universities across the United States and have been translated into a variety of foreign languages. His books have been awarded both the Texty and McGuffey awards from the Textbook and Academic Authors Association (TAA), and in 2007 he received the TAA Lifetime Achievement Award. In 2023, Mike was awarded the Saint Ignatius College Prep Alumni Award for Excellence, in recognition of his outstanding commitment to his profession and to the Saint Ignatius community.
Mike is a member of the American Mathematical Association of Two-Year Colleges, the American Mathematical Society, the Mathematical Association of America, and the Textbook and Academic Authors Association. He has 4 children, all of whom are involved with mathematics or publishing. His son, Michael Sullivan III, also teaches college mathematics and is his coauthor on 2 Pearson precalculus series. He divides his time between living in Naples, FL and Oak Lawn, IL. When not writing textbooks he enjoys tennis, travel and gardening.