AP Calculus Exam Free Response Strategies

Section II of the AP Calculus exam is worth 50% of your grade. The section consists of two parts, just like the multiple-choice section. Part A contains two free-response questions for which you are allowed (and in fact, will most likely need) to use your graphing calculator. Part B contains four free-response questions for which you may not use your calculator.

The good news is that the topics covered in these questions on the AP Calculus exam are usually fairly common calculus topics. You won’t see trick questions asking about an obscure subject. However, the fact that a topic is well known doesn’t mean the problem will be simple or easy. All free-response questions are divided into parts—that is, they are stuffed with smaller questions. You won’t usually get one broad question like, “Is a Riemann sum ever really happy?” Instead, you’ll get an initial setup followed by questions labeled (a), (b), (c), and so on.



Expect to write at least one paragraph (or provide multistep equations) for each lettered part of a free-response question on the AP Calculus exam, and to clearly label the part you are answering (e.g., [a] or [part a]). Use proper notation and always include units where applicable. Don’t try to fill up every inch of the space provided. If you only use half the space, but have a complete solution, that’s fine. The test makers provide extra space for students who write big or for corrections. You don’t want to add extra information (that may contain a mistake) if you already have the correct answer written on the page.

For the free-response questions, you receive points for responding properly to each subquestion prompt. The more points you score, the better off you are on that question. Going into the details about how points are scored would make your head spin, but in general, the AP Calculus exam readers have a rubric that works as a blueprint for a good answer. Every subsection of a question has one to four key ideas attached to it. If you write about one of those ideas, you earn yourself a point. Readers always use the same rubric for a question and all questions are evaluated using a rubric. Any reader who reads your exam should, in theory, award you the same number of points on a given question. Readers check and cross-check each other to ensure that each answer is evaluated in the same way.

There’s a limit to how many points you can earn on a single subquestion and there are other complex rules guiding the grading of the AP Calculus exam, but it boils down to this: Writing smart things about each question will earn you points on that question.

If you get a question on a subject you don’t know well, things might look grim for that problem. Still, take heart. Quite often, you’ll be able to earn at least some points on every question because there will be some subquestion or segment in each question that you know. Remember, the goal is not perfection. If you can ace four of the questions and slug your way to partial credit on the other two, you will put yourself in position to get a good score on the entire section. That’s the Big Picture, so don’t lose sight of it just because you don’t know the answer to every subquestion of every question.

Finally, because you are allowed to use a calculator on Part A of Section II of the AP Calculus Exam, you should expect to use it. There’s no point in permitting a calculator for part of the exam if you aren’t going to actually need it. This isn’t 100% certain, of course, because nothing on an unknown test ever is, but it is a good guess. As a general rule, you can expect to have to:

• Find the zeros of a complicated function (for example, to determine where a particle is at rest)
• Evaluate a messy derivative at a specified value (for example, to find an instantaneous rate of change)
• Calculate a definite integral (for example, to find the volume of a solid of revolution)