AP® Calculus BC Equation and Formula Sheet

The AP® Calculus BC is a challenging course to ace. If you spend a year learning the concepts of calculus, chances are you’ve forgotten a formula or two. You may even have missed a class day and didn’t have a chance to learn that day’s material as effectively. That’s where the AP Calculus BC formula sheet comes in.

What is the AP Calculus BC Formula Sheet?

The AP Calculus BC formula sheet that we provide below is exactly what it sounds like: a list of all the important formulas and theorems you need to know for the exam. It is meant to be a study aid to help you memorize key AP Calculus BC equations and to save you time on the exam.

The AP Calculus BC formula sheet, however, is not a substitute for learning the concepts of the course. You may be tempted to think you can just memorize a few formulas and you’ll be good to go for the exam. However, it’s more important to have a strong understanding of the concepts behind them. If you need help learning the AP Calculus BC curriculum or planning out your study approach, check out our AP Calculus BC Study Guide.

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Graph with semicircular cross sections
Graphing the area of a polar curve
A type of function

List of Formulas

There are a lot of formulas and theorems that you are expected to memorize for the AP Calculus BC exam, and seeing them all in one place may seem overwhelming at first. By the end of the course, you will get familiar with many of them, so isolate the ones you’re struggling to remember and incorporate them into your study plan. That will shrink the list down to the 5–10 formulas that you need more practice with.

Without further ado, let’s have a look at the formulas and theorems you need to know for the AP Calculus BC exam. For your ease of use, we have grouped the list of formulas into five bite-sized sections:

  • Section 1: Limits
  • Section 2: Derivatives
  • Section 3: Integrals and Differential Equations
  • Section 4: Polar Coordinates, Parametric,Equations, and Vector-Valued Functions
  • Section 5: Infinite Series

You can download a list of AP Calculus BC Formulas according to the sections mentioned above by clicking on the download link below.

Is there a reference sheet for AP Calculus BC?

No, the AP Calculus BC exam does not have a reference sheet. The College Board® expects each student to understand all of the concepts covered within the AP Calc BC curriculum, and the formulas extend directly from them. If you are familiar with the math behind these concepts, you should know and be able to recall (or even derive if necessary) the formulas on the exam.

Formulas outside the scope of calculus, like area and volume formulas for particular geometric shapes, are often provided in the stems of questions where they are needed.

How can I possibly memorize all the formulas?

The most effective way to memorize formulas is to use them a lot. If you’re struggling to remember one or two particular formulas, check out UWorld’s AP Calculus BC Practice Exam and practice lots of problems that require you to use them. For example, if you find it difficult to remember the difference between volume using the disk and washer methods, work on a bunch of problems in 8.7–8.13 of the UWorld’s AP Calculus BC QBank.

Another effective tool is flashcards, especially if there are more than a handful of formulas you find difficult to remember. Build a deck of flashcards with formulas and quiz yourself regularly. Pay close attention to the smallest details of each formula as well.

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Examples of estimated areas uses Riemann’s sum

Read more about the
AP Calculus BC

Whether you want to get a headstart before taking the course this summer or if you waited until two weeks before the exam to prepare, here are the essential tips and tricks no matter your timeframe.

Stay exam-ready with our free mock tests and thousands of exam-like questions. Created by former AP teachers and experts, all accompanied by our gold standard explanations.

Want to get a better sense of the AP Calculus BC course and exam? We’ve compiled some frequently asked questions and helpful information about AP Calculus BC.
The College Board’s Course and Exam Description is a lengthy document, so we’ve summarized the most important course information you need to know.
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