How to Best Prepare for the AP Calc AB Exam in a Week

First of all, don’t even think about cramming, period. Just don’t. If you’re trying to prepare for the AP Calc AB exam in a week, strategy matters more than stuffing formulas into your head at 2 a.m.

You don’t want to end up like this kid here:

Since it’s inception, it has remained one of the most popular AP exams, with over 1 million test takers every year. Yet, it also stands as one of the most notorious, with a measly 21% of students obtaining a score of 5 in 2024, comparable only to that of exams like AP Physics, AP Chemistry, and even APUSH, for that matter.

Just in 2022 alone, over 1.2 million people took this exam. Many high school students take this exam because it fulfills the first-year math requirement at many colleges.

Now, what is the right way to prepare, you may ask? Well, in this guide, I will detail the 3 essential things you should do to best prepare for the AP Calc AB exam.

Note: This article is not going to guarantee you a 5 on the exam. I will detail the things you SHOULD do, but it’s up to you to follow through.

Read to the end to get a free AP Calc AB study guide!

**All images taken from AP Classroom.

Know your AP Calc AB Theorems!

If you’re going to prepare for the AP Calc AB exam in a week, you NEED to know all the essential theorems. I’ve listed the major ones down below.

Obviously, you don’t have to know every theorem known to man, but you must have a strong grasp of the important ones. Additionally, you need to know not only the definition of these theorems, but also recognize and learn to apply them.

Why, you may ask? Some MCQ questions will require you to use such theorems. However, you might not realize that you need to use it if you don’t read the question carefully enough.

Example

In this question, we are asked to find the time t at which the instantaneous velocity is equal to the average velocity. 

First, we need to determine the velocity function, which you can find by taking the derivative of p(t).

Then, you find the average velocity of the function, which is just the slope of p(t).

To find that one time t  that will make the two values equal each other, we have to use the Mean Value Theorem. 

As you can see, the problem is a bit tricky as it doesn’t explicitly state the theorem verbatim. However, we do know that p(t), is differentiable on the interval, which implies continuity. 

Furthermore, since the velocity function is the derivative of the position function, it is essentially our “slope,” and the average and slope of a function should be EQUAL to each other.

Thus, by MVT, we know that there is a “c” (time t in the context of this question) in the interval 1t16, such that the instantaneous velocity is equal to the average velocity.

Study as Broadly as Possible in AP Calc AB

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This strategy is especially useful when you’re trying to prepare for the AP Calc AB exam in a week — you won’t have time to dive deep into everything, so you need a wide-angle view.

Now, I know this may seem counterintuitive at the beginning. You may be asking, “Why shouldn’t I study a topic in-depth?” “Shouldn’t you master a concept before moving on?” Yes, and yes. But let me explain.

You don’t actually need a very high score to get a 5 on the AP Calc AB exam. To get a 5, you only need around a 67%, which is a D+.

What does that mean for you? Well, it means that it’s in your favor to try to cover as many bases as possible. In other words, STUDY EVERYTHING. 

Go over key topics in every section, while grasping the general concept, to try to get as much information before test day. 

Example

You don’t want to only focus on one section, as many questions on the AP Calc AB exam, especially the FRQ, will test a wide range of topics.

In part (a), we are asked to find f(0) and f(5). This can be found using the Fundamental Theorem of Calculus, which requires integration.

However, in part (b), it asks for the points of inflection on the original function, which is completely unrelated to integration overall. You need to use the graph to identify these POIs.

Furthermore, in part (c), we can see that we need to use the derivative graph to define a new function that they give us, which, once again, isn’t related to local extrema.

Then, in part (d), it completely detaches from the original problem. You don’t need the graph or the original function anymore. Instead, you use the new function you defined in part (c) to algebraically calculate the absolute minimum. This, once again, is not related to integration and involves differentiation instead.

As you can see, the test’s contents are quite unpredictable, and CollegeBoard has complete freedom to alter what each part asks for.

Because Calculus in general is so intertwined, many concepts can be connected to each other, even if the main question isn’t related to such topic.

From these examples, I think it’s pretty clear that CollegeBoard can throw anything at you. Therefore, it’s in your favor to study as broadly as possible, covering all the essential concepts.

FRQ, FRQ, FRQ for AP Calc AB!

Arguably, the most important factor when you prepare for the AP Calc AB exam. You NEED to nail the FRQs. How? One word: Practice.

Time management in key in the FRQ, so make sure you get that practice in so you don’t take too much time.

With AP Calc AB being one of the few AP exams that is weighed equally, the FRQ is worth 50% of your score. It’s a lot more significant than the MCQ, simply because it’s a lot harder and you can get a LOT of partial credit.

AP Calc AB tests conceptual understanding. It’s as simple as that. Know why you’re taking the derivative. Know why you’re integrating.

Just knowing how you can apply these basic concepts can already get you 30-40% of the maximum points possible.

Don’t believe me? See this example here.

Example

In the example here, we can see that you can already get ⅔ just from setting up the equation. If you understand the theorem, you’ve already completed 66% of the question. This circles back to the fact that you NEED to know your theorems, since you need the Fundamental Theorem of Calculus to solve this question.

Not just in this part, but for every part that requires calculations, you don’t need to get the actual value correct to get points.

In fact, you get fewer points if you jump straight to the final answer with minimal work. The scoring guideline is designed in a way where you get points for every step you show. Thus, the less work you show, the fewer points you’ll get.

Since the final answer is only one step in the grand scheme of things, it’s more important that you show your set-up as well as your calculations in between to maximize your score.

In part (c) of Q3, we can see that you already get 1 point for knowing the 2nd Fundamental Theorem of Calculus!

Just writing that relation down gets you 33% immediately. You don’t even need an answer yet.

Then, finding the absolute max will get you the next point.

If you’re able to find the absolute max correctly, then you’ll get the point for justification.

However, even if you write an incorrect justification, you will still be awarded the point for the correct absolute maximum as long as you wrote it down.

Example #2

Even better, like I said before, many FRQs are split into parts. Frequently, there will be one part that is essentially free points.

In this question, we can see that in part (a), all they are asking us to do is integrate. Since this is a graphing calculator question, we just need to integrate from each function’s respective bounds, and add their initial conditions, punching the numbers into a calculator.

It really is that simple. You must get these questions right because they are very straightforward. Also, these types of questions normally don’t give a lot of partial credit because they don’t involve many steps.

In this case, we only get 1 point for getting the correct answer for BOTH functions. So, if you integrate even 1 function incorrectly, you lose that point.

Similarly, you get 1 point for setting up BOTH integrals correctly. Once again, if you set up one wrong, you won’t get that point.

You can think of it like high-risk, high-reward. You are risking the amount of partial credit you get if you miscalculate, but you have the opportunity to get the maximum amount of points if you get them correct.

Conclusion

As you can see, preparing for the AP Calc AB exam doesn’t mean grinding 10 hours a day on one obscure topic. It means being strategic — knowing your theorems, understanding the why behind every integral and derivative, and covering as much ground as possible before test day.

If you’ve made it this far, you already care more than most students — now it’s time to follow through. Practice those FRQs. Review the concepts, not just the formulas. Download the free study guide below and map out the rest of your review schedule.

Here’s your challenge:

What’s one Calc topic that always trips you up — and what are you going to do about it today?

Drop your answer in the comments!

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