How To Study For The AP® Calculus AB Exam
The AP® Calculus AB exam tends to be one of the more challenging AP® exams, with about 58% of students achieving a score of 3 or above in 2023. That's good for the sixthlowest mark of all the AP course offerings that year. However, the right preparation and resources can make the test substantially more manageable. Whether you’re aiming for a 3 to get some college credit or a 5 to stand out in your college applications, UWorld has you covered! This AP Calculus AB study plan gives you all the essential knowledge and preparation tips you need to crush the exam and attain your target score.
How To Prepare Effectively for the AP Calculus AB Exam
In this guide, we will help you with every stage of the process. From the moment you sign up for an AP Calculus AB course to exam day, you can take the following steps to prepare and improve your chances of getting the score you want.
How to prepare for an AP Calculus AB class
It's spring, and you've signed up to take an AP Calculus AB class next year. What now? Here are some things you can do before the school year starts to hit the ground running:
 Get a head start by preparing over the summer before school starts in the fall.
 Review College Board®'s AP Calculus AB course and exam description.
 If possible, talk to your AP Calculus AB teacher about the class expectations. You might also want to discuss the course rigor with your guidance counselor.
 Brush up on algebra and precalculus concepts. Specifically, focus on functions and graphs, rational functions, limits, trigonometry, and the unit circle, factoring polynomials, completing the square, exponent, and logarithm rules, and working with e and natural logarithms.
 Review formulas from geometry, such as the areas of circles, triangles, rectangles, and trapezoids. Volume and surface area of common 3D shapes like cubes, spheres, cylinders, and cones also show up occasionally, but the College Board will often provide formulas in a question stem when applicable.
 Study Unit 1 concepts and practice UWorld AP Calculus AB questions on limits. Paul’s online math notes are an excellent, free resource for getting started with calculus and reviewing some precalculus topics. Khan Academy is another free resource if your learning style is geared more toward watching videos than reading.
 Identify the ideal learning strategy for you: how do you best absorb information? Reading? Reading while taking notes? Watching videos? Practicing problems? A combination of these? The summer is a great time to figure this out.
How to pass the AP Calculus AB class
Most of the concepts in AB Calculus stem from two things: the derivative and the integral. Knowing how to differentiate and integrate various kinds of functions is key to doing well in AP Calculus. Practice with UWorld questions in Topics 2.5  2.10 and 3.1  3.2 for derivatives and Unit 6 for integrals. Try Units 4 and 8 to apply the derivative and integral to context for more advanced practice with these concepts.
Below are some AP Calculus AB study tips for passing your exam:
 Keep working on your homework, even if it feels tough at first—that's how you get better. If you make mistakes, it's a great chance to go back and see how to do it right next time.
 Make flashcards for basic derivative and integral rules and review them regularly until you have them down.
 Try getting some extra practice with UWorld MCQs. Focus on working through derivatives and integrals, particularly chain rule and usubstitution. Ensure you've got these basics solid before moving on to other topics.
 Practice FRQs using the ones the College Board provides from past years’ tests. Analyze the scoring guidelines to understand what the College Board expects. If you have access to AP Classroom, it is also a good source of FRQs.
 Take a moment to brush up on the early units; by the end of the year, the material from the beginning might be somewhat rusty.
How to do well on the AP Calculus AB exam
If you're aiming for a top score and really want to nail the basics, focus a lot on word problems and different contexts. Concentrate on Units 4, 5, 7, and 8. It's also a good idea to practice Free Response Questions (FRQs) using past exams from the College Board. They often use similar types of questions, so spotting patterns can really help.
For instance, every test since 2012 (except possibly for 2020, as those FRQs haven’t been released) has included an FRQ that features a table of data and asks questions about approximating derivatives with average rates of change or estimating integrals using Riemann sums, all within a specific context. Get comfortable with these kinds of questions to boost your confidence for the exam.
Here are AP Calculus AB study tips for improving your score from a 3 to a 4:
Start Early
Regular Practice
Focus on FRQs
Start Early
Regular Practice
Focus on FRQs
How to score a 5 on the AP Calculus AB exam
Want to score a 5 on the AP Calculus AB exam? Here's a comforting fact: you don't need to ace it to earn that top score. You don’t even need to hit 90%—the usual Agrade mark in most US schools. In fact, you generally need just under twothirds of the total points available to score a 5. Remember, everyone makes mistakes, especially in a challenging exam like this, and that’s perfectly fine.
According to the College Board, 22.4% of 273,987 testtakers scored a 5 on the 2023 AP Calculus AB exam.
Aiming for perfection isn't the goal; focus on achieving what you know best. If you're stuck, try to rule out wrong answers and make an educated guess instead of spending too much time on it.
It's crucial to know where to focus your study time. Create a systematic AP Calculus AB study plan that allocates enough time for practicing core concepts. For instance, the derivative of inverse functions usually appears in just one multiplechoice question per test and isn't typically featured in the freeresponse section. If this formula trips you up, review it with a few UWorld questions, and maybe make a flashcard to test yourself now and then. But remember, spending time on more important concepts is more beneficial.
Study strategy for scoring a 5 on the AP Calculus AB exam:
Start Early
Practice Regularly
Work on Free Response Questions (FRQs)
Understand the Scoring
Start Early
Practice Regularly
Work on Free Response Questions (FRQs)
Understand the Scoring
What units are most difficult to learn or require focus due to complexity?
According to the College Board, the 2023 AP Calculus AB testtakers 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 7.67.7 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 (8.78.12). 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 crosssectional 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 (4.44.5), 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 usubstitution 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 selfstudy for the AP Calculus AB exam
If you plan to selfstudy 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 baselevel 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 (singlevariable) 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 indepth 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:

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

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.

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

Work practice problems on the topic (UWorld, Khan, textbook, Paul’s, or other).
 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 APlevel questions but are great when first learning a topic.
 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.

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.
AP Calculus AB Study Plan
It's the spring semester and it's crunch time! No matter how much time you have left, we've got some handy tips to help you get ready for the AP Calculus AB exam. Here’s a straightforward study plan you can follow:
Early Start
Review Strategy
Basic Concepts
Refine Your MCQ Skills
FRQ Practice
Flashcards
Essential Breaks
Early Start
 Begin in February to ensure ample time to cover all units.
Review Strategy
 Unit 1 – Limits: Spend 1 week.
 Units 25 – Derivatives: Allocate 2 weeks.
 Units 68 – Integrals: Dedicate 2 weeks.
Basic Concepts
 Refresh your understanding using your textbook or UWorld’s prep book.
Refine Your MCQ Skills
 Set aside two to three short sessions each week to review MCQstyle practice questions.
 Consistently revisit challenging concepts.
 Start timing your MCQs to match exam conditions: aim for 2 minutes per noncalculator question and 3 minutes per calculator question.
FRQ Practice
 Review past FRQs from the College Board to familiarize yourself with potential essay questions.
 Outline and practice writing responses at least twice a month.
 Time yourself to adapt to the exam pace.
Flashcards
 Create and review flashcards daily for key formulas and rules.
Essential Breaks
 Regularly schedule breaks to stay refreshed—plan a day off each week or take an afternoon off when necessary.
Initial Review
Practice Focus
Timeframe Breakdown
Final Week Preparation
Initial Review
 Start with a general review of course topics, unitbyunit at a quicker pace.
 Utilize resources such as textbooks, class notes, and course materials for concept refreshers.
Practice Focus
 Prioritize completing textbook practice problems and using the UWorld QBank two to three times per week for 2030 minutes per study session.
 With UWorld:
To save time, focus on explanations for missed questions reviewing the concepts that need the most improvement.
Timeframe Breakdown
 Limits and Derivatives (Units 1–5):
Allocate 2 weeks, approximately one unit every two days.  Integrals (Units 6–8):
Allocate 1 week, approximately one unit every two days.
Final Week Preparation
 Use any remaining time to review concepts from each unit which you missed previously to reinforce learning.
First Week: Review Growth Areas
Second Week: Focus on FRQs
First Week: Review Growth Areas
Kick off your study by tackling a few UWorld AP Calculus AB MCQs in each topic to spot the ones that are harder to you. Dive into the explanations for any questions you miss. If you’re still feeling shaky, throw in a video or review your notes on those tough topics. Then, circle back with more UWorld questions to see how much you’ve improved!
Second Week: Focus on FRQs
Spend most of your week diving into FRQs—they’re a great way to cover lots of topics at once and really efficient for review. Plus, they make you show your work, which helps you get a solid handle on the whole problemsolving process.
AP Calculus AB Review/Study Materials
Finally, here is a collection of AB Calculus AB study materials you can use to facilitate your exam prep. Most of these links are sprinkled throughout this guide, but we've listed them in one section for your convenience.
Question Banks and Practice Problems
 UWorld: APlevel MCQs with indepth explanations that help you learn from mistakes.
 College Board FRQs: FRQs from past exams that provide excellent practice for those sections.
Video Content
 Khan Academy: Great introductorylevel videos to learn concepts with skillbuilding questions.
 Professor Leonard: A set of college lecture videos where he breaks down the concepts and emphasizes the core ideas behind calculus.
Now that you know how to study for AP Calculus AB, it's time to begin your exam prep. Good luck, and happy studying!
References
 Student Score Distributions* AP Exams  May 2022. (2022). apcentral.collegeboard.org. Retrieved February 14, 2024, from https://apcentral.collegeboard.org/media/pdf/apscoredistributionsbysubject2022.pdf
 Student Score Distributions* AP Exams  May 2023. (2023). apcentral.collegeboard.org. Retrieved February 14, 2024, from https://apcentral.collegeboard.org/media/pdf/apscoredistributionsbysubject2023.pdf
 Packer. (2023, June 30). The 2023 AP Calculus AB scores. twitter.com. Retrieved February 14, 2024, from https://twitter.com/AP_Trevor/status/1674500852122255360?lang=en
 2021 AP Exam Administration Scoring Guidelines  AP Calculus AB. (2021). apcentral.collegeboard.org. Retrieved February 14, 2024, from https://apcentral.collegeboard.org/media/pdf/ap21sgcalculusab.pdf