Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (2024)

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (1)Look InsideCalculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (2)

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ThirdEdition| ©2020Michael Sullivan; Kathleen Miranda

Specifically designed to support the needs of AP® students and teachers as well as align with the current College Board AP® Calculus Course and Exam Description (CED), Sullivan and Miranda’s Calculus for the AP® Course, third edition, offers a student-friendly and focused narrative

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Trusted authors and integrated student support for success in AP® Calculus.

Specifically designed to support the needs of AP® students and teachers as well as align with the current College Board AP® Calculus Course and Exam Description (CED), Sullivan and Miranda’s Calculus for the AP® Course, third edition, offers a student-friendly and focused narrative with distinctive features that provide integrated support.

This edition has been carefully developed to ensure that it adheres to the unit structure and coverage as set forth in the 2019 CED. Further, it aligns with the College Board’s overarching structure, meaning every Big Idea, Mathematical Practice, and Student Skill. This edition also aligns with the revised pedagogy of Enduring Understanding, Learning Objective, and Essential Knowledge statement that flow from the three revised Big Ideas.

Written to be read and understood by students as they learn calculus and prepare for either the AP® Calculus AB or AP® Calculus BC Exam – the Sullivan Miranda program offers abundant practice, AP® Specific content, distinctive features, and built-in support. The third edition comes complete with our SaplingPlus online-homework platform and a full set of updated teacher resources.

Features

AP® Exam Prep within Your Text

  • AP® Exam Tips throughout the text in the minor column
  • At Section level: AP® Practice Problems cover content that may appear on the AB or BC version of the exam
  • At Chapter level: AP® Review Problems include multiple choice and model FRQs for exam practice all year 
  • At Chapter level: AP Cumulative Review Problem sets encourage retention of content through cross-chapter review.
  • Two AP® Practice Exams
    • 1 full-length Calculus AB practice test, after chapter 8
    • 1 full- length Calculus BC practice test, after chapter 10

Review and Reinforce on all Levels

  • Abundant practice is provided through a well-scaffolded set of exercises at the section, chapter, and cross-chapter cumulative levels. 
  • The end of each section features exercise sets that focus on: 
    • Concepts and Vocabulary
    • Skill Building
    • Applications and Extensions
    • Challenge Problems
    • AP® Practice Problems 
  • All chapters end with general and AP® Review problems 
    • Things to Know
    • Objectives Table
    • Chapter Review Exercise set (covering all chapter concepts)
    • AP® Review Problems that include multiple-choice and FRQ questions (cover chapter concepts)  

Created to meet your students' needs

  • Written at an accessible level so that students can handle the concepts and the worked examples.
  • The textbook offers economical, focused description with integrated support written to be read and understood by students as they learn calculus and prepare for the AP® Exam 
  • Sullivan and Miranda’s distinctive NOW WORK example feature promotes good habits by directing students from a worked example in main text to a problem in the section exercise set that mirrors the example, providing immediate practice and reinforcement. Since we recognize that many students begin with exercises and seek help only as needed, we have crafted this backward/forward navigation system that effectively directs student from exercise to example and vice versa.
  • Includes numerous examples with worked solutions to serve as models for your students. Examples are calibrated in difficulty throughout sections to help students attain higher skill levels in dealing with complexity.
  • Selected worked examples are supported by short video clips that provide step-by-step support that give a worked example that mirrors the in-text example (CalcClips).
  • All AP® Review Problems are accompanied by short video clips that provide step-by-step support through the AP® problem.
  • All AP® Cumulative Review Problems are accompanied by short video clips that provide step-by-step support through the AP® problem.

Mind the Margins

Additional help for students is provided by taking advantage of the minor column to place eye-catching, helpful features: 

  • AP® EXAM TIPs: Contains explanations and suggestions to help students prepare for the AP® exam.
  • NEED TO REVIEW: Pinpoints cross-references to prior topics that students have to know to master new content.
  • RECALL: Provides a quick refresher of important information, which is used in examples, theorems, definitions, and descriptions.
  • NOTE: Provides supporting details to content on that page to help further explain topics.
  • CAUTION: Warns students about misconceptions and pitfalls. 
  • ORIGINS: Gives background and biographical information about key figures and discoveries as calculus developed.
  • IN WORDS: On-the-spot help in translating definitions, formulas, theorems, proofs, and corollaries into clear, plain language to support students when and where they need it.

Engage your students

  • Chapter Projects are introduced at the opening of each chapter and are revisited at the end of the chapter to help relate calculus to everyday life, which provides students with a chance to apply the math that they learned throughout the chapter.
  • Additional, "just-in-time," help is offered through a suite of videos that accompany selected worked examples (CalcClip), AP Review Problems (at the end of chapters), and the AP Cumulative Review Problem sets. In these videos, experienced AP teachers walk students step-by-step through key examples, AP review, and major concepts.  

New to This Edition

The third edition of Sullivan and Miranda’s Calculus for the AP® Course mirrors the unit structure set out in College Board’s 2019 Course and Exam Description (CED).

  • Chapters are reordered to align with the new unit structure.
  • AP® Cumulative Review Problem sets included for Chapters 2-10.
  • Chapter 7 includes differential equations, which are included to show that the authors’ coverage aligns with the new unit structure and personalized progress checks.
  • Streamlined coverage of certain topics that receive less attention in the 2019 CED.
  • Aligned terminology that accords better with The College Board’s usage.
  • Additional topics that receive more coverage in the 2019 CED.

Basic coverage of polar coordinates and vectors are located in Appendix A for an additional resource for BC students.

A strong SaplingPlus e-book and Online Homework offering built for this edition with approximately 2000+ questions (many of which are algorithmically created, essentially making thousands more). Along with these, SaplingPlus will also include the following in-book questions with targeted feedback:

  • All of the end-of-section, end-of-chapter, and AP® Practice problems.
  • All of the problems in the "suggested assignments" grid in Teacher’s Edition.
  • All of the NOW WORK problems.

A fully updated teacher resources suite to match the 3rd edition:

  • New Teacher’s Edition, Teacher Resources Flashdrive, and Examview Flashdrive.
  • Welcoming expert AP® Calculus educator and AP® Exam Reader Joshua Newton to the team as a co-author to the Teacher’s Edition, Joining fellow AP® Exam Reader and veteran AP® Calculus and mathematics teacher, Brent Ferguson.

The teacher resources will now include Desmos activities to give teachers the opportunity to use Desmos in the classroom that goes beyond problem setup and solution.

"WOW! This is BY FAR the BEST calculus book I have seen in my 20+ years of teaching."
- Kent Thele (John Paul II High School)

"Calculus for the AP® Course does a phenomenal job of not only preparing students for the AP® exam, but also showing each student the connections between the calculus classroom, the workplace, and the world."
- Textbook & Academic Authors Association (TAA) Judge.

"If I had any issues I was able to get in touch with someone that was easily accessible. That is the #1 thing about working [with BFW]. It really paid off that [our district] switched over [to Calculus for the AP® Course, 3e]."
-AP® Calculus Teacher, Pennsylvania

"This is a phenomenal textbook that is really lined up with the AP® exam...I'm really happy and my students are excited to use this textbook. In the past, our old textbook wasn't as exciting."
-AP® Calculus Teacher, Pennsylvania

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (5)Look InsideCalculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (6)

Calculus for the AP® Course

ThirdEdition| ©2020

Michael Sullivan; Kathleen Miranda

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Calculus for the AP® Course

Third Edition| 2020

Michael Sullivan; Kathleen Miranda

Table of Contents

About the Authors
Acknowledgments

What Is Calculus?
Student’s Guide to This Book

Chapter P Preparing for Calculus

UNIT 1 Limits and Continuity

Chapter 1 Limits and Continuity

UNIT 2 Differentiation: Definition and Fundamental Properties

Chapter 2 The Derivative and Its Properties

UNIT 3 Differentiation: Composite, Implicit, and Inverse Functions

Chapter 3 The Derivative of Composite, Implicit, and Inverse Functions

UNIT 4 Contextual Applications of Differentiation

Chapter 4 Applications of the Derivative, Part 1

UNIT 5 Analytical Applications of Differentiation

Chapter 5 Applications of the Derivative, Part 2

UNIT 6 Integration and Accumulation of Change

Chapter 6: Part 1 The Integral

Chapter 6: Part 2 Techniques of Integration

UNIT 7 Differential Equations

Chapter 7: Differential Equations

UNIT 8 Applications of Integration

Chapter 8: Applications of the Integral

AP® Practice Exam: Calculus AB

UNIT 9 Parametric Equations; Polar Coordinates; and Vector-Valued Functions

Chapter 9: Parametric Equations; Polar Coordinates; Vector Functions

UNIT 10 Infinite Sequences and Series

Chapter 10: Infinite Series

AP® Practice Exam: Calculus BC

Appendix A Precalculus Used in Calculus

Appendix B Theorems and Proofs

Appendix C Using Calculators on the AP® Calculus Exam

Answers

End Sheets

Table of Derivatives

Table of Integrals

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Calculus for the AP® Course

Third Edition| 2020

Michael Sullivan; Kathleen Miranda

Find Your Rep

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (11)

Michael Sullivan

Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Before retiring, Mike taught at Chicago State for 35 years, where he honed an approach to teaching and writing that forms the foundation for his textbooks. Mike has been writing for more than 35 years and currently has 15 books in print. His books have been awarded both Texty and McGuffey awards from the Textbook and Academic Authors Association (TAA). In 2007, he received the TAA Lifetime Achievement Award. 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.

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (12)

Kathleen Miranda

Kathleen Miranda, Ed.D from St. John’s University, is an Emeritus Associate Professor of the State University of New York (SUNY), where she taught for 25 years. Kathleen is a recipient of the prestigious New York State Chancellor’s Award for Excellence in Teaching, and she particularly enjoys teaching mathematics to underprepared and fearful students. Kathleen served as director of Curriculum and Assessment Development at Old Westbury. In addition to her extensive classroom experience, Kathleen has worked as accuracy reviewer and solutions author on several mathematics textbooks, including Michael Sullivan’s Brief Calculus and Finite Mathematics. Kathleen’s goal is to help students unlock the complexities of calculus and appreciate its many applications.

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Calculus for the AP® Course

ThirdEdition| 2020

Michael Sullivan; Kathleen Miranda

Find Your Rep

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Chapter 2 AP Skill Builders

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Chapter 2 Alternate Examples

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (17)

Chapter 2 Bell Ringers

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (18)

Chapter 2 Calc Clips

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (19)

Chapter 2 Correlation Guide

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (20)

Chapter 2 Desmos Activities

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (21)

Chapter 2 Flashcards

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (22)

Chapter 2 Prepared Tests

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (23)

Chapter 2 Projects and Solutions

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (24)

Chapter 2 Student Solutions Manual (coming soon)

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (25)

Chapter 2 Teacher's Solutions Manual

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (26)

Chapter 2 Videos Overview

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (27)

Chapter 2 Web Resources

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (28)

Chapter 2 Worksheets

ExamView Assessment Suite for Calculus for the AP® Course

Michael Sullivan; Kathleen Miranda | ThirdEdition | ©2020 | ISBN:9781319248789

With more than 2000 questions (many of which are algorithmic) written by our extended team of AP® Calculus and content expert this testbank provides t...

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Teacher's Edition for Calculus for the AP® Course

Michael Sullivan; Kathleen Miranda | ThirdEdition | ©2021 | ISBN:9781319248185

This one-of-kind Teacher’s Edition, built specifically for the 3rd edition of Sullivan and Miranda, provides an in-depth correlation as well as AB and...

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Teacher's Resource Flash Drive for Calculus for the AP® Course

Michael Sullivan; Kathleen Miranda | ThirdEdition | ©2020 | ISBN:9781319248796

This invaluable resource includes the essential teacher resources that go along with Sullivan/Miranda 3rd edition program, including: Calc Clip videos...

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Calculus for the AP® Course

Third Edition| 2020

Michael Sullivan; Kathleen Miranda

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Calculus for the AP® Course

Third Edition| 2020

Michael Sullivan; Kathleen Miranda

Videos

Introduction to SaplingPlus

This video explains the value of Bedford, Freeman & Worth's SaplingPlus platform for teachers and students.

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning (2024)

FAQs

Calculus for the AP® Course, Third Edition (9781319244316) | Macmillan Learning? ›

This common question has no easy answer. To achieve a 5 on the AP® Calculus AB exam you will need a combination of tenacity, commitment to learning the material, and a dedicated study plan.

What percent is a 3 on AP Calc test? ›

AP Calculus AB Exam: What You Need to Know
Exam ScoreNumber of StudentsPercentage of Students
455,75420.9%
355,92321.0%
264,11124.1%
138,63714.5%
1 more row

How easy is it to get a 5 on AP Calc? ›

This common question has no easy answer. To achieve a 5 on the AP® Calculus AB exam you will need a combination of tenacity, commitment to learning the material, and a dedicated study plan.

Is it hard to get a 3 on AP Calc? ›

Generally speaking a score of 3 on the AP Calculus AB exam is somewhere between (around) 41 to 53 out of the possible 108 points…so roughly 38% to 49% correct. There are 45 multiple choice problems worth 54 points and 6 free response questions worth 54 points…

Which AP calculus is the hardest? ›

Finally, AP Calculus BC is the toughest AP math exam, if not one of the hardest AP exams period. AP Calculus AB is also challenging, but covers less material and moves more slowly.

What is a 60% on an AP test? ›

Yes, a 60 is a passing rate in AP classes. The average passing rate in AP is 60-70%.

What is a 70% on an AP test? ›

Usually, a 70 to 75 percent out of 100 translates to a 5. However, there are some exams that are exceptions to this rule of thumb. The AP Grades that are reported to students, high schools, colleges, and universities in July are on AP's five-point scale: 5: Extremely well qualified.

What is the hardest AP to get a 5 on? ›

Top 10 Hardest AP Classes by Exam Pass Rate
AP Class/ExamPass Rate (3+)Perfect Score (5)
1. Physics 151.6%8.8%
2. Environmental Science53.4%11.9%
3. Chemistry56.1%10.6%
4. U.S. Government and Politics57.5%15.5%
6 more rows

What is the passing rate for AP Calculus? ›

The passing rate for AP® Calculus AB is higher than average at around 58.4%. This is helpful to know if you are planning to use your AP® Calculus AB exam score for college credit. Assuming you have an aptitude for math, you would have over a 50% chance of passing with a score of 3 or better.

Which AP Calc is easier? ›

AP Calculus AB Topics

Just because AP Calculus AB is the easier of the two courses, doesn't mean students should expect to breeze through this class.

What is the average grade for AP Calc? ›

Average AP Score by Test
Exam NameAverage Score
Calculus AB2.77
Latin2.76
German Language and Culture (Standard Group)2.75
Macroeconomics2.74
40 more rows
Dec 18, 2021

What's the easiest AP class? ›

Top 10 Easiest AP Classes by Exam Pass Rate
  • Physics C: Mechanics. 84.3% 41.6%
  • Calculus BC. 81.6% 44.6%
  • Spanish Literature. 75.1% 17.6%
  • Physics C: Electricity and Magnetism. 74.4% 40.4%
  • Physics 2. 73.3% 14.0%
  • Computer Science Principles. 71.6% 10.9%
  • Psychology. 71.3% 22.4%
  • Computer Science A. 70.4% 25.6%

Is AP Calculus hard to pass? ›

How Difficult Are AP Calculus AB and BC – As Rated By Class Alumnae. APs Calculus AB / BC are considered moderate difficulty, with class alumnae rating them 5.5/10 for overall difficulty, making them the joint 12th-most-difficult out of the 28 large AP classes surveyed.

What score is a 3 on the AP test? ›

AP Score Scale Table
AP Exam ScoreRecommendationCollege Course Grade Equivalent
5Extremely well qualifiedA+ or A
4Very well qualifiedA-, B+, or B
3QualifiedB-, C+, or C
2Possibly qualified----
1 more row

What is a 3 equivalent to on an AP test? ›

AP Exam scores of 3 are equivalent to grades of B-, C+, and C in college. The multiple-choice section is scored by computer. The free-response section (essays and open-ended questions) is scored at the annual AP Reading held during the first two weeks in June.

What score is a 3 on AP Chem? ›

What is a 3 score on AP Chemistry? According to the College Board's AP score distributions, 24.5% of students earned a 3 on the AP Chemistry exam. In order to achieve a 3 on the 2022 exam, you'll have needed to correctly answer 42% of the questions.

Is a 3 on the AP Calculus BC exam good? ›

What is a good AP® Calculus BC score? Receiving a 3, 4, or 5 is generally accepted as scoring well on an AP® exam.

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