Tips to Conquering AP Calculus Free Response Questions

Both the AP Calculus AB and BC tests include a section of six free response (FR) questions. These questions differ in many ways from standard multiple choice problems. In this post, we’ll talk about a few tips to help you conquer the AP Calculus free response questions.

Tip #1: Don’t Panic (and Be Prepared)

I’m sure that you’ve seen free response questions before. By definition, any problem that does not provide a set of answer choices to select your response from is a free response question. That typically covers the majority of quizzes and tests in high school.

So there’s no need to panic, as long as you know your material.

Panic - photo by Nate Steiner (public domain)

Don’t panic!

Make sure that you’ve prepared for the AP Calculus exam well in advance.

For a good start on your exam prep, check out either of the following helpful articles, depending on which exam you plan to take.

Tip #2: Read Carefully

This should go without saying, but read every question very carefully.

Often mistakes arise when the student misreads or misinterprets a question. Make sure you know:

  1. What is the question asking? (Goal)
  2. What do I know from reading the question statement? (Givens)


Not sure if Math Problem is Easy or... AP Calculus Free Response Questions can be tricky

Read each problem carefully. AP Calculus Free Response Questions can be tricky.

Tip #3: Show Your Work

This is probably the most important tip for achieving a high score on the FR section.

The graders are not just looking for a final answer. Instead, you must show every step of your work in a logical progression toward the answer.

This means that if you have invented some wacky way to do an integral in your head for example, but you have no clue how to explain what you did on paper, then you won’t get a lot of points in the FR section.

SAT Math: Word Problems -Magoosh

What About Calculators?

Calculators are permitted on some problems in the FR section. But you must explain how you used the calculator functions (except for routine arithmetic).

For example, suppose there is a question asking you to find the area between two curves. You must first show the integral that properly computes this area.

Only then can you plug it into your calculator and find the answer. On your test paper, you would write down something like this:

“I used numerical integration on my calculator to evaluate the integral.”

Then jot down the answer, and now you’ll be sure to get full credit!


Here are those tips one more time.

  1. Don’t Panic (and Be Prepared)
  2. Read Carefully
  3. Show Your Work

For more information and tips for the Free Response section, check out
Understanding AP Calculus Free Response Questions.

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  • Shaun Ault

    Shaun earned his Ph. D. in mathematics from The Ohio State University in 2008 (Go Bucks!!). He received his BA in Mathematics with a minor in computer science from Oberlin College in 2002. In addition, Shaun earned a B. Mus. from the Oberlin Conservatory in the same year, with a major in music composition. Shaun still loves music -- almost as much as math! -- and he (thinks he) can play piano, guitar, and bass. Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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