How To Study For The AP® Calculus AB Exam

What units are most difficult to learn or require focus due to complexity?

According to the College Board, the 2023 AP Calculus AB test-takers struggled with Unit 5 the most on MCQs. Slope fields tend to be an area where students struggle, but they don't show up very often on the test. Focus more attention on separating variables and solving differential equations, where algebra, exponent, and logarithm rules will be valuable. Brush up on previous years' math concepts. 

Also, pay close attention to the constant of integration, as it may simplify in unexpected ways. Practice is the key here. Try all of UWorld's questions in 7.6-7.7 to see several examples of how these questions may appear.

One concept that UWorld's AP Calculus team identified that gives AB students a lot of trouble is volume in Unit 8 at the end of the course (8.7-8.12). Know the formulas for the disk and washer methods for volumes of revolution and when to apply each. Also, strive to understand how to find cross-sectional volume; area formulas for semicircles and other shapes are also important here.

Generally, word problems and contextual questions tend to be difficult for many AP Calculus AB students. Specifically, related rates questions in Unit 4 give students a lot of trouble (4.4-4.5), and they consistently appear on the exam as both MCQs and FRQs. The key to these questions is organizing information. Pay close attention to the specific quantity the question asks and what information it provides (formulas, values of quantities or derivatives/rates, etc.). Scrutinize whether a quantity is “increasing” or “decreasing," as this determines whether the derivative is positive or negative, respectively. This is also where many geometric area and volume formulas come in handy.

Many AP Calculus AB students make a lot of small mechanical errors that add up throughout the exam. Practice is the key to avoiding these mistakes. Complete UWorld AP Calculus AB practice questions, and note any common mistakes you make. Review your notes and the explanations for those questions, and then practice more UWorld questions on those topics, keeping a careful eye out for your typical pitfalls. The College Board knows a lot of common errors students make and structures their answer choices accordingly (and so do we!), so just because the answer you arrived at happens to be an answer choice doesn’t mean it’s correct.

One common source of such errors is u-substitution in Unit 6. This advanced integration technique has many steps and parts to consider, each of which could be the source of a minor mistake. To avoid such mistakes, recall that differentiation and integration are inverse operations. If you have time, check your answer by differentiating the result of your integration and making sure it matches the integrand you started with. If it doesn't, you may have made a mistake along the way.

How to self-study for the AP Calculus AB exam

If you plan to self-study for the AP Calculus AB exam without taking an AP course, you may have a few more obstacles and challenges ahead. However, it is definitely doable. The biggest challenge will be not having a teacher introduce concepts and help you improve. So, your first step is to find what learning style works best for you:

• Do you learn best from watching videos or visual presentations?

  Khan Academy is a great place to start. Their videos introduce the concepts at a great pace, and they provide good base-level questions for building your skills. Another popular set of videos is Professor Leonard on YouTube. He breaks down concepts well and is passionate about learning. However, his videos are lengthy, so you might need to break them up and spend multiple days on each one.

• Do you learn best from reading a textbook and taking notes?

  A good free resource is Paul's Online Math Notes. As a college professor's notes on calculus, they aren’t specifically geared toward AP, but they are nonetheless a good starting point. If your budget permits, buy AP Calculus AB study material from Amazon or a secondhand bookstore. Any (single-variable) calculus textbook will work but try to find one specifically for AP Calculus so you know it’s written for high school students and follows the flow of the AP coursework. Otherwise, follow along with the AP Calculus AB Course and Exam Description to ensure that each topic is necessary for the exam.

• Do you learn best from practice problems?

  Subscribe to a question bank. Our UWorld AP Calculus AB QBank is specifically geared towards helping you learn from mistakes with in-depth explanations. Take similar questions as ones you’ve previously made mistakes to show your improvement in preparation for the AP Calculus AB exam. If you’ve purchased a textbook, you can practice problems inside or practice some problems in Paul’s Online Math Notes.

Most students learn from a combination of these approaches, so try different things and see what works best for you. Our recommendation would be to incorporate all of them. Here's a general flow you can use to facilitate your learning process:

1. Watch a video on a topic (Khan, Leonard, or other) and take notes.

   1. If you use Khan Academy, the videos are short enough to watch two or three in one session. They are also very well organized for proper pacing.
   2. If you use Professor Leonard, the videos are lengthy, so segment them into multiple viewing sessions. He stitches together multiple lectures into one video, so maybe watch until it cuts to the next lecture (his clothes will be different).

2. If the topic still isn't clear, rewatch parts or the full video or watch a similar video from another source. Sometimes, hearing or seeing a concept presented in multiple ways can help clear up confusion.

3. Read a text explanation of the topic (textbook, Paul’s, or other), and add it to your notes.

4. Work practice problems on the topic (UWorld, Khan, textbook, Paul’s, or other).

   1. If you use Khan Academy for videos, take their progress checks and quizzes along the way to help cement the ideas. They are generally not AP-level questions but are great when first learning a topic.
   2. If you use UWorld, read through our explanations, especially on questions you answer incorrectly. We also include hyperlinks to general explanations of concepts or alternate/more detailed solutions, so we encourage you to explore those as well.

5. Review your notes at the end of your study session.

   This flow may or may not work for you. Experiment and figure out what elements to incorporate into your study plan. The next section provides tips on creating a study plan that’s right for you.