AP Calculus AB Overview
There are 2 calculus courses offered as part of the advanced placement program: Calculus AB and Calculus BC. AP Calculus AB is equivalent to a first semester College Calculus course, while AP Calculus BC is equivalent to both first and second semester college calculus. AP Calculus BC is an extension to AB, so much of the information in this list is applicable to the College BC course as well. As such, many of the entries below are applicable to our list of the Best AP Calculus BC Books for 2020-2021 as well. Prerequisites for AP Calculus AB include the full 4 years of high school mathematics courses.
We’ll cover the course, exams, and our picks for the best AP Calculus AB books, Flashcards, and Review Guides for test year 2021 below, but if you just can’t wait, here’s our short list:
A full Course Description for AP Calculus AB is available from collegeboard.org.
The AP Calculus AB course is comprised of material covering 3 main concepts, each with their own set of learning objectives and essential knowledge:
- The concept of a limit can be used to describe the behavior of a function.
- Students learn to express and interpret limits symbolically.
- Continuity is a key property of a function that can be expressed using limits.
- A functions derivative can be used to understand the behavior of a function.
- The derivative of a function has many interpretations and applications.
- The Mean Value Theorem connects the behavior of a differentiable function over an interval to a derivative at a point on that interval.
Integrals and the Fundamental Theorem of Calculus
- Antidifferentiation is the inverse process of differentiation.
- The definite integral of a function over an interval can be calculated using a variety of strategies.
- The Fundamental Theorem of Calculus connects differentiation and integration.
- The definite integral of a function has many interpretations and applications.
The structure and organization of the AP Calculus AB course is variable and depends on instructor preference. In general, the curriculum is taught in the order listed above, with key concepts from earlier units feeding into the later ones. In each unit, a healthy mix of instruction, interactive questioning, and practical application through problem solving should be expected.
Students taking the AP Calculus AB Exam are responsible for demonstrating knowledge of each of the above mentioned learning objectives through multiple choice and free response problem solving.
The AP Calculus AB exam requires extensive use of a graphing calculator, and students are required to provide their own (see the collegeboard calculator policy).
The AP Calculus AB test is comprised of 2 sections each with 2 parts. Each of the 2 sections make up 50% of the overall score.
The Multiple Choice section:
- 1 hour and 45 minutes long and consists of 45 multiple choice questions.
- It accounts for 50% of the overall exam score.
- Part A is 30 questions, 60 minutes long, and a graphing calculator is not permitted.
- Part B is 15 questions, 45 minutes long, and a graphing calculator is required.
The Free Response section:
- 1 hour and 30 minutes long and contains 6 questions.
- It accounts for 50% of the overall exam score.
- Part A is 2 questions, 30 minutes long, and a graphing calculator is required.
- Part B is 3 questions, 60 minutes long, and a graphing calculator is not permitted.
Though topics in algebra, geometry, pre-calculus, etc are not explicitly assessed, some concepts from them will be incorporated in order to successfully and accurately answer the calculus questions posed.
In the free response section, students are expected to show their work in order to receive credit.
Students taking the AP Calculus BC exam are given a secondary score on the AB portion of the test (approximately 60%), which allows colleges to evaluate their understanding of concepts from the AB portion of the test independently.
For exam dates, refer to The College Board AP Calendar.
Best AP Calculus AB Books
AP Calculus AB has several strong contenders for the best textbooks and review guides which we’ve ranked for you above. Continue on for detailed information on each one!
Cracking the AP Calculus AB Exam
Pros: Numerous practice tests and extensive content reviews.
Cons: Answer key explanations are sparse in some cases.
Best For: Study guide and review throughout the year.
Our Rating: 5 / 5
Once again Princeton Review places at the top of our list of Best AP Calculus AB review guides. Both Calculus AB and BC students will find a wealth of valuable content from this book. Key features include:
- 6 full length practice tests.
- Access to online study plans, key terms, and more.
- Up to date information on current year tests.
- Practice drills at the end of each chapter.
- Handy reference guide of key formulas.
Once again, with its low price tag and useful content, Cracking the AP Calculus AB Exam is ranked as our best overall value. With a significant amount of online resources and guides to help tailor your study plan to your unique needs, you can’t go wrong with this book.
5 Steps To A 5: AP Calculus AB
Pros: Massive set of online content, practice tests, etc.
Cons: Some people may find the online resources unintuitive in some cases.
Best For: Supplemental learning material throughout the year, and last minute review leading up to the exam.
Our Rating: 4.5 / 5
5 Steps To a 5: AP Calculus AB is a valuable resource for exam preparation and as a study aide throughout the year. It contains a ton of useful information, practice tests, and online material. Full list of key features:
- 2 full length practice tests included and 2 more available online.
- Cross-Platform bonus prep course with personalized study plans, interactive tests, flashcards, and more.
- TI-89 graphing calculator demos / guide for solving problems.
- AP Scoring guidelines for the free response questions.
Between its extensive coverage of the major course topics, and treasure trove of online goodies, 5 Steps to a 5: Calculus AB is something you should seriously consider adding to your test-prep arsenal. Whether studying for the AB or BC exam, you’ll find this material extremely useful.
AP Calculus AB Prep Plus
Pros: 3 full length practice tests and access to online resources.
Cons: Some practice test question explanations can be difficult to follow.
Best For: Practice problems and review throughout the year.
Our Rating: 4 / 5
AP Calculus AB Prep Plus from Kaplan, is a fantastic resource for Calculus AB students preparing for the exam. It comes bundled with several full length practice tests, a number of online resources, and tools for planning your study and tracking progress. Key features:
- Three full length practice exams with online scoring tool.
- Pre and post chapter quizzes.
- Over 400 practice questions with detailed explanations.
- Customizable study plans.
Kaplan has firmly established itself as a powerhouse in test-prep resources, and this book is no exception. Its focused review of the essential concepts will help you capitalize on your limited study time, and boost scores. Overall the review guide is highly recommended by teachers and students alike.
AP Calculus AB Lecture Notes
Pros: Broad scope and easy to understand review notes.
Cons: No quiz or practice test material included.
Best For: Supplementing other review materials.
Our Rating: 4 / 5
This entry is somewhat different from the rest of the entries in this list. Rather than a structured review guide with practice tests, it’s a set of lecture notes with examples and explanations. The book is well done and well reviewed, but we recommend it as a supplement to other prep materials rather than using it as your only resource. Features included in the book:
- Full slides and review of all Calculus AB curriculum topics and exam.
- List of formulas and theorems required for the test.
- Concise and accurate explanations of all example problems.
AP Calculus AB Lecture Notes by Rita Korsunsky is a useful and thorough resource for students preparing for the AP exam. Overall, it’s best used as a supplement to another more comprehensive resource, but it definitely has a strong place in the list of Best AP Calculus AB books.
Best AP Calculus AB Flashcards
In addition to the excellent books mentioned above, AP Calculus AB students will see significant benefits in prepping for the exam using flashcards. Our top picks for Best AP Calculus AB Flashcards are outlined below.
Barron’s AP Calculus Flash Cards
Pros: In depth questions and explanations covering all major exam topics.
Cons: Cards include AP Calculus BC material as well.
Our Rating: 4 / 5
Barron’s AP Calculus AB Flash Cards are a set of 300 physical flashcards covering Calculus AB and BC topics including formulas, functions, graphs, derivatives, and more. These flashcards pair well with the Barron’s AP Calculus book (covered in our list of best Calculus BC books), but will work with any of the other resources (or on their own as a supplement to your course textbook). Key features include:
- Over 300 cards covering AP Calculus AB and BC topics.
The Barron’s AP Calculus AB Flash Cards help ease the task of repetition memorization, and make your final preparation for the exam much easier. The cars are relatively in-depth rather than simple multiple choice, so they can take a while to work through, but this helps in the long run.
AP Calculus represents the culmination of over 4 years of secondary math courses, and any student completing it should feel a huge sense of accomplishment. It’s a tough course, and assigned course materials aren’t always enough to prepare you well for the exam.
We’ve rounded up our top picks of useful, high quality books and flashcards for AP Calculus students. Ultimately, which is right for you depends on your own unique circumstances. To recap our recommendations:
|Top Overall Recommendation||Cracking the AP Calculus AB Exam|
|Top Pick For Course Supplement||5 Steps To A 5: AP Calculus AB|
|Top Pick For Last Minute Prep||Cracking the AP Calculus AB Exam|
|Top Pick For Flashcards||Barron’s AP Calculus Flash Cards|
For students looking to add to their list of assigned textbooks and other materials throughout the AP Calculus course, we recommend 5 Steps To A 5: AP Calculus AB, due to the in-depth explanations, and access to significant content.
For students shorter on time, Cracking the AP Calculus AB Exam is a more focused book which helps you make the most out of the limited time available. This book is also our overall top pick, so consider it even if you are planning well ahead.
Finally, flashcards can be a huge aide for last minute review and memorization of formulas, etc. Our top pick in this area is the Barron’s AP Calculus Flash Cards set.
Whatever your circumstance, supplemental study and review materials are a key part of ensuring success on the exam. We’ve listed some of the best AP Calculus AB resources available. Good luck, and study hard!