AP Calculus BC 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 AB course as well. As such, our list of the Best AP Calculus BC Books for 2020 contains some of the entries below. Prerequisites for AP Calculus BC include the full 4 years of high school mathematics courses.
We’ll cover the course, exams, and our picks for the best AP Calculus BC books, Flashcards, and Review Guides for test year 2020 below, but if you just can’t wait, here’s our short list:
A full Course Description for AP Calculus BC is available from collegeboard.org.
The AP Calculus BC course is comprised of all of the material covering the 3 main concepts included in Calculus AB, plus the concept of Series, added for BC. Each of the main concepts has their own set of learning objectives and essential knowledge:
Limits [Included in AB]
- 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.
Derivatives [Included in AB]
- 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 [Included in AB]
- 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 sum of an infinite number of real numbers may converge.
- A function can be represented by an associated power series over the interval of convergence.
As with AP Calculus AB, the structure and organization of the AP Calculus BC 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 BC 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 BC exam requires extensive use of a graphing calculator, and students are required to provide their own (see the collegeboard calculator policy).
The AP Calculus BC 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.
In the AP Calculus BC exam, you are given a secondary score on the AB portion of the test (which makes up about 60% of the exam material). This lets colleges evaluate your understanding of concepts from the AB portion of the test independently from the BC portion.
For exam dates, refer to The College Board AP Calendar.
Best AP Calculus BC Books
AP Calculus BC 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 BC Exam
Pros: Full length practice tests (3) with access to online resources.
Cons: Some explanations lack clarity.
Best For: Supplementing course textbooks throughout the year or lead up to the exam..
Our Rating: 5 / 5
Princeton Review produces high quality review guides for most Advanced Placement exams, and Calculus BC is no exception. Consider this guide as a supplement for required course materials, or as a stand alone study aid leading up to the exam date. Key features include:
- 3 practice tests (full length) with detailed explanations.
- Step by step walkthroughs of key formulas and sample questions
- Questions drawn from up to date information on the current year (2020) tests.
- End of chapter practice drills with tips and tricks for exam preparation.
- List of essential tactics to help you focus your limited study time.
The Princeton Review’s Cracking the AP Calculus BC Exam is our pick for best overall value again this year. It comes packaged with a ton of valuable online and offline content, and will help you do your absolute best on the exam. A score of 5 is within your reach!
AP Calculus AB & BC Crash Course
Pros: Narrow focus is perfect for last minute or accelerated review.
Cons: Some practice questions lack clarity or accuracy.
Best For: Last minute review leading up to the exam.
Our Rating: 4.5 / 5
AP Calculus AB & BC Crash Course is just that, an accelerated crash course in Calculus. The guide consists of extensive practice tests with full answer keys, as well as exam tips and tricks. Full list of key features:
- 2 Full length practice tests online.
- Just the information necessary for the test, without all the fluff.
- Expert test taking strategies covering both the multiple choice and free response sections.
- Content and course layout focused entirely on the exam.
While this isn’t the most well rounded guide, it’s narrow focus on test content and strategies can be extremely useful as a list minute review leading up to the test. If you’re looking for a resource to complement your required course textbooks throughout the year, consider one of the other books on this list. However, for the right audience, this book can’t be beat!
5 Steps to A 5: AP Calculus BC
Pros: 3 practice tests and a free study planner app.
Cons: Some small errors on answer / explanation keys.
Best For: Supplemental review throughout the course.
Our Rating: 4.5 / 5
5 Steps To A 5: AP Calculus BC by William Ma, is another fine entry in the list of top AP Calculus BC guidebooks. In addition to 3 full length practice tests, it has a great overview of the exam format, and an appendix of common formulas and theorems.
- Three full length practice exams with thorough answer explanations.
- Complete overview of the exam format.
- Appendix of common formulas found on the exam.
- Free study planner app.
The 5 Steps To A 5 series of review guides are typically high up on the list of best exam review materials, and this is no exception. Between the printed material and the huge amount of online resources, this book is an all around great deal. The study planning app in particular is great for helping you focus your limited review time.
Barron’s AP Calculus
Pros: Multiple practice tests and online resources.
Cons: Some people find the practice questions to be overly difficult (but you may see this as a plus).
Best For: Use in addition to required course textbook year long and leading up to the exam.
Our Rating: 4 / 5
The Barron’s AP Calculus review guide is suitable for students studying for either the AB or BC version of the exam. As with the other books on this list, the guide is jam packed with both printed materials and access to online content. The full list of features includes:
- 4 full length Calculus AB + 4 Calculus BC practice tests.
- Graphing calculator review with tips for the exam.
- Detailed review covering topics for both AB and BC exams.
Barron’s AP Calculus review is another solid guidebook if you’re looking to compliment other works on this list or your course textbook. They do a good job of presenting the material, and provide a ton of useful practice exams to help you assess your readiness for the real thing.
AP Calculus BC Lecture Notes
Pros: Well organized and easy to follow review notes covering all of the material.
Cons: No quiz or practice tests included, no online resources.
Best For: Supplementing other review materials.
Our Rating: 4 / 5
As with the AP Calculus AB recommendation, this entry is different from the other books 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 BC curriculum topics and exam.
- List of formulas and theorems required for the test.
- Concise and accurate explanations of all example problems.
Even though this book lacks some of the extra benefits of the other guidebooks, we strongly recommend it as a supplement to your required textbooks. The information is presented in an easy to follow fashion that helps it all click for some students and serves as reinforcement for others. Again, if you’re in crunch mode leading up to the exam you might be better off with one of the other recommendations.
Best AP Calculus BC Flashcards
In addition to the excellent books mentioned above, AP Calculus BC students will see significant benefits in prepping for the exam using flashcards. Our top picks for Best AP Calculus BC Flashcards are outlined below.
Barron’s AP Calculus Flash Cards
Pros: In depth questions and explanations covering all major exam topics.
Cons: No digital format option.
Our Rating: 4 / 5
Barron’s AP Calculus BC 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 listed above, 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 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.
Whether a particular book is right for your unique circumstances depends on a variety of factors we’ve tried to account for. To recap our recommendations:
|Top Overall Recommendation||Cracking the AP Calculus BC Exam|
|Top Pick For Course Supplement||Cracking the AP Calculus BC Exam|
|Top Pick For Last Minute Prep||AP Calculus AB & BC Crash Course|
|Top Pick For Flashcards||Barron’s AP Calculus Flash Cards|
Our top overall pick and recommendation for students interested in supplementing their assigned course material is Cracking the AP Calculus BC Exam, from Princeton Review. It’s a comprehensive books crammed with extra goodies, and does a great job illustrating concepts.
AP Calculus AB & BC crash course is the best overall pick for students who are short on time before the exam. It does a good job of covering just the material and concepts that are most critical to the exam, so you can make the most of your study time.
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 BC resources available. Good luck, and study hard!