# Precalculus: Graphical, Numerical, and Algebraic AP® Edition 11th Edition

Precalculus: Graphical, Numerical, and Algebraic AP Edition, published by Pearson, is the first Precalculus textbook written specifically to align with the AP Precalculus framework. This program prepares students for the AP® Precalculus exam with a focus on modeling, functions, use of technology, and multiple representations. A balanced approach to problem-solving offers a powerful toolkit for mathematical thinking.

• Full alignment with the AP Framework
• Increased integration of Technology and Modeling
• Focus on functions
• Emphasis on student collaboration and communication
• Improved diversity, equity, and inclusion
• Pacing guides and Teacher support for the AP classroom

## AP® Precalculus Curriculum with Digital Resources

An AP Precalculus program built on time-tested foundations that caters to today’s students and today’s AP Exam.

### AP Exam Alignment

The authors worked with the College Board® to make sure this edition thoroughly follows the new curriculum and exam descriptions.

### The Rule of Four – A Balanced Approach

Students are urged to solve math problems with an algebraic, numerical, graphical, or verbal method. By using another method, they can support or confirm their solutions.

### Focus on Functions

The full vocabulary of functions is introduced in Chapter 1. Students encounter the concepts of domain and range, change in tandem, increasing and decreasing concavity, points of inflection, and more.

### Technological Integration

While use of technology has been a cornerstone of this curriculum for decades, the authors have marked certain problems to be solved without a calculator to help students prepare for the AP® Exam.

## AP® Precalculus Teaching Solutions

• New Features
• New Teacher’s Edition Features
• New Technology Features
• Text Features
• Exercise Sets
• AP® Test Preparation
AP® Test preparation is a regular part of the coursework. Quick Quizzes appear every 2-3 sections and include multiple-choice and free-response questions.
• Prep Quizzes
End-of-Chapter AP® Test Prep Quizzes call upon all the skills learned to that point in the textbook.
• Chapter Challenges
Chapter Challenges appear in Chapters 1-7. These multi-part investigative activities are introduced on the opening page and build part-by-part throughout the chapter.
• Group Activities
Group Activities appear right before the exercise sets in Chapters 1-7. They support collaborative learning among your students.
• Function Spotlight
The Function Spotlight feature provides all key information about a given function in a single location, including new concepts such as concavity that are called for in the AP Precalculus Guidelines.
• Post-It Notes
The Table of Contents contains “Post-It Notes” in the margin to explain key aspects of the revised contents.
• Pacing Guides
Separate AP® Precalculus Pacing Guides are available for teachers and schools focusing on Units 1-3 or Units 1-4.
• Concept Outline
The Concept Outline for AP® Precalculus shows which sections concept which AP® Learning Objectives and AP® Essential Knowledge.
• GeoGebra
GeoGebra activities are sprinkled throughout the text. These provide students with a chance to interactively manipulate mathematical objects and discover key ideas and relationships. We include a QR code and a short URL for each GeoGebra activity to make it easy for students to access the content.
• Online Data Sets
Online data sets are included for larger data arrays in the text. Teachers and students can access these data sets in *.xls format, which they can then paste into their spreadsheet software.
• Calculator Screenshots
Graphing calculator screens have been added to the TI-84 Plus Color Edition.
• Chapter Overviews
Chapter Overviews give students a sense of what they are going to learn. They provide a roadmap of the chapter and indicate how topics are connected under one big idea. Math is interconnected, rather than modular, so skills build off themselves continually throughout the course. As time goes on, students better understand more complicated processes and relationships.
• What You’ll Learn… and Why
The “What You’ll Learn… and Why” feature presents the big ideas in each section and explains their purpose.
• Group Activity
A Group Activity is provided immediately before each exercise set. These activities give students a way to develop their communication and collaborative skills and help you assess their program as problem solvers.
• Explorations
Explorations appear throughout the text and provide students with the perfect opportunity to become active learners and to discover mathematics on their own. Some are based on technology, while others guide students through mathematical ideas and connections. All of them help hone critical-thinking and problem-solving skills.
• Pencil and Paper Problems
Some exercise numbers are underlined in red. This means they should be solved without a calculator, and students are urged to use pencil and paper first. Afterwards, they can support their answers graphically or numerically.
• Quick Review Exercises
Quick Review exercises at the beginning of each section’s exercises help students review skills needed in the exercise set. Often there is a reference to where students can go for a refresher earlier in the book or in the Appendix.
• Writing to Learn Exercises
Writing to Learn exercises give students opportunities to communicate their thinking and demonstrate their understanding of important ideas.
• Extending the Ideas Exercises
Extending the Ideas exercises go beyond what is presented in the section. These exercises are challenging extensions of the material in the text.

## Empower Your Math Students with the MyMathLab® Platform from Pearson

MyMathLab for School® from Pearson empowers students through personalized instruction and resources available anywhere they can find an internet connection.

### NEW! AP Precalculus Test Prep Workbook

This student-friendly workbook is available in print and is also available electronically within MyMathLab® for School. It contains unit-by-unit practice and two full sample exams. The workbook provides comprehensive solutions with helpful learning tips so students can learn from their mistakes. It was written by four veteran teachers with extensive AP development experience.

## Correlation for AP®

Our solutions for AP® are designed to support and correlate the College Board's Course and Exam Descriptions for each corresponding course.

## More About Precalculus: Graphical, Numerical, Algebraic

Chapter 1: Prerequisites for Calculus

• 1.1 Linear Functions
• 1.2 Functions and Graphs
• 1.3 Exponential Functions
• 1.4 Parametric Equations
• 1.5 Inverse Functions and Logarithms
• 1.6 Trigonometric Functions

Chapter 2: Limits and Continuity

• 2.1 Rates of Change and Limits
• 2.2 Limits Involving Infinity
• 2.3 Continuity
• 2.4 Rates of Change, Tangent Lines, and Sensitivity

Chapter 3: Derivatives

• 3.1 Derivative of a Function
• 3.2 Differentiability
• 3.3 Rules for Differentiation
• 3.4 Velocity and Other Rates of Change
• 3.5 Derivatives of Trigonometric Functions

Chapter 4: More Derivatives

• 4.1 Chain Rule
• 4.2 Implicit Differentiation
• 4.3 Derivatives of Inverse Trigonometric Functions
• 4.4 Derivatives of Exponential and Logarithmic Functions

Chapter 5: Applications of Derivatives

• 5.1 Extreme Values of Functions
• 5.2 Mean Value Theorem
• 5.3 Connecting ƒ_ and ƒ _ with the Graph of ƒ
• 5.4 Modeling and Optimization
• 5.5 Linearization, Sensitivity, and Differentials
• 5.6 Related Rates

Chapter 6: The Definite Integral

• 6.1 Estimating with Finite Sums
• 6.2 Definite Integrals
• 6.3 Definite Integrals and Antiderivatives
• 6.4 Fundamental Theorem of Calculus
• 6.5 Trapezoidal Rule

Chapter 7: Differential Equations and Mathematical Modeling

• 7.1 Slope Fields and Euler’s Method
• 7.2 Antidifferentiation by Substitution
• 7.3 Antidifferentiation by Parts
• 7.4 Exponential Growth and Decay
• 7.5 Logistic Growth

Chapter 8: Applications of Definite Integrals

• 8.1 Accumulation and Net Change
• 8.2 Areas in the Plane
• 8.3 Volumes
• 8.4 Lengths of Curves
• 8.5 Applications from Science and Statistics

Chapter 9: Sequences, L’Hospital’s Rule, and Improper Integrals

• 9.1 Sequences
• 9.2 L ’Hospital’s Rule
• 9.3 Relative Rates of Growth
• 9.4 Improper Integrals

Chapter 10: Infinite Series

• 10.1 Power Series
• 10.2 Taylor Series
• 10.3 Taylor’s Theorem
• 10.5 Testing Convergence at Endpoints

Chapter 11: Parametric, Vector, and Polar Functions

• 11.1 Parametric Functions
• 11.2 Vectors in the Plane
• 11.3 Polar Functions

Appendices

• A1 Formulas from Precalculus Mathematics
• A2 A Formal Definition of Limit
• A3 A Proof of the Chain Rule
• A4 Hyperbolic Functions
• A5 A Very Brief Table of Integrals

Glossary

Applications Index

Subject Index

• Gregory D. Foley Author Bio

Greg Foley received B.A. and M.A. degrees in mathematics and a Ph.D. in mathematics education from The University of Texas at Austin. He is the Robert L. Morton Professor of Mathematics Education at Ohio University. Greg has taught elementary arithmetic through graduate-level mathematics, as well as undergraduate and graduate-level mathematics education classes. He has held full-time faculty positions at North Harris County College, Austin Community College, The Ohio State University, Sam Houston State University, and Appalachian State University, and served as Director of the Liberal Arts and Science Academy and as Senior Scientist for Secondary School Mathematics Improvement for the Austin Independent School District in Austin, Texas.

Greg has presented over 500 lectures, workshops, and institutes around the world and has directed or codirected more than 60 funded projects totaling over \$5 million. He has published over 50 book chapters and journal articles. At Ohio University, Greg has received Patton College awards for distinguished graduate teaching in 2013, mentoring in 2019, and outreach in 2020. In addition, he received the American Mathematical Association of Two-Year Colleges (AMATYC) Award for Mathematics Excellence in 1998, the Teachers Teaching with Technology T3 Leadership Award in 2013, and the Ohio Council of Teachers of Mathematics (OCTM) Kenneth Cummins Award for exemplary mathematics teaching at the university level in 2015 and Christofferson-Fawcett Award for lifetime contributions to mathematics education in 2022.

Greg coauthored Precalculus: A Graphing Approach; Precalculus: Functions and Graphs; and Advanced Quantitative Reasoning: Mathematics for the World Around Us.

• Daniel Kennedy Author Bio

Dan Kennedy received his undergraduate degree at the College of the Holy Cross in 1968 and went on to earn a master’s degree and Ph.D. in mathematics from the University of North Carolina at Chapel Hill. From 1973 until his retirement in 2019 he taught mathematics at the Baylor School in Chattanooga, Tennessee, where he held the Cartter Lupton Distinguished Professorship. Although retired from the classroom, he continues his involvement with Baylor as the “Voice of the Red Raiders” for announcing home games in basketball, football, and softball.

Dan became an Advanced Placement Calculus reader in 1978, which led to an increasing level of involvement with the AP program as workshop consultant, table leader, and exam leader. He joined the AP® Calculus Test Development Committee in 1986, then in 1990 became the first high school teacher in 35 years to chair that committee. Dan was named a Tandy Technology Scholar in 1992 and a Presidential Award winner in 1995. He has served on the executive committee of the Mathematical Sciences Education Board and on the Board of Governors of the Mathematical Association of America. His articles on mathematics and education reform have appeared in the Mathematics Teacher, the American Mathematical Monthly, and the College Mathematics Journal.

Dan coauthored Calculus: Graphical, Numerical, Algebraic.  He is also a series author of the Savvas enVision® A|G|A high school series (Algebra I, Geometry, and Algebra II).

• Rachael Gorsuch Author Bio

Rachael Gorsuch is currently teaching mathematics in grades 9–12 at Teays Valley High School in Ashville, Ohio. With more than 17 years of teaching experience in a rural public school, suburban independent school, and inner-city charter school, Rachael has a passion for helping students engage with mathematics through modeling and technology. She has taught grades 7–12, including precalculus, AP® Statistics, quantitative reasoning, algebra 2, geometry, algebra 1, physics, and middle school math. Rachael received her B.S. degree in mathematics from Muskingum University and her M.A.T. degree in STEM education from The Ohio State University.

Rachael has partnered with several researchers from universities on mathematics education research, particularly in the field of teaching mathematical modeling. She has steadily been presenting on mathematical modeling and technology at conferences and delivering workshops since 2012. Rachael was the 2019 recipient of the Ohio Council of Teachers of Mathematics’ Buck Martin Award for exemplary secondary mathematics teaching and recipient of Muskingum University’s Emerging Leader Award for Social Responsibility in 2018. She is a Teachers Teaching with Technology Regional Instructor.

Rachael coauthored Ohio’s Mathematical Modeling and Reasoning course for the Ohio Department of Education.

• Steve Phelps Author Bio

Steve Phelps—a long-time secondary teacher and K–12 instructional technology coach in southwest Ohio—is currently serving as a mathematics and computer science teacher as well as an instructional mathematics coach and instructional technology coach for Mariemont City Schools in Cincinnati, Ohio. He received his B.S. degree in secondary mathematics education and his M.A.T. degree from the University of Cincinnati. Steve has more than 30 years of classroom teaching experience in grades 7–12, teaching everything from pre-algebra through AP courses including Calculus, Statistics, Computer Science, and Computer Science Principles. He also has over 15 years of experience in teaching education and mathematics courses at the University of Cincinnati and at the University of Cincinnati’s Blue Ash College.

Steve has authored or co-authored over 20 journal articles and has delivered over 100 presentations and workshops, typically on the topic of the intelligent use of educational technology in mathematics. He was the 2016 recipient of the Ohio Council of Teachers of Mathematics’ Buck Martin Award for exemplary secondary mathematics teaching. Steve is a Teacher’s Teaching with Technology National Instructor, a Code.org facilitator, a Desmos Teaching Fellow, and a GeoGebra author.

Steve coauthored Advanced Quantitative Reasoning: Mathematics for the World Around Us.

PEARSON, MYLAB, MYMATHLAB, MATHXL, MASTERING, STATCRUNCH, REVEL and the Pearson Logo are trademarks owned and/or registered by Pearson plc and/or its affiliates. All other third party marks associated with these products are the property of their respective owners. Copyright in the works referenced herein is owned by Pearson Education, Inc. Pearson Education has control over the editorial content in these instructional materials.

AP® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, these products.