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How to Pass the AP® Calculus Exam

Updated: Feb 7

A study plan and tips on how to pass the AP® Calculus exam, from a former teacher and current AP Calculus tutor.

It was my first year teaching AP® Calculus. My classes finished the curriculum at the end of March and I was excited to have a month to review for the AP® exam. But then I opened my storage cabinet of resources.

If you sat through an AP® Calculus class this year, you likely accumulated hundreds of pages of notes, activities, and assessments. You may have multiple notebooks covering the immense curriculum.

Where do you start in preparing for the upcoming AP® exam? Should you get a study manual? Should you review topic by topic or just take practice tests? Should you even take the AP Calculus exam?

My eyes grew wide as the doors of the storage cabinet opened. I wondered how the previous Calculus teacher even maneuver the dozens of books, flashcards, and boxes into the cabinet. For several minutes, I stared into the storage closet. Not only were there dozens of workbooks and textbooks, there were multiple versions and publishers of each. Where to begin?

How to pass AP Calculus Exam
Okay, it wasn’t this many books but this is how I felt (Photo by Carles Rabada)

When I finally overcame the paralysis of overwhelm, I grabbed several resources and spread them across a large table. I started skimming through the resources to identify which ones were most useful.

I could only imagine how confused a student would be trying to identify the best approach to studying for the AP® Calculus exam!

In this article, I’ll take the guess work out of studying for the exam. I’ll provide a sample study plan and tips to help you pass the AP® Calculus exam.

Study Plan for AP® Calculus Exam

When I was teaching, Peterson’s Master AP® Calculus book was available as a free PDF. You can still find it online with a Google search but many websites took it down, for copyright reasons I imagine. Teaching in a Title I school, I didn’t expect my students to buy a review book, so we used Peterson’s book. If you’re interested in buying a review book, see my suggestions for the best AP® Calculus review book.

There are two different approaches to preparing for the AP® Calculus exam: some students should review topic by topic and others should just practice Calculus problems.

Which is best for you? That depends on how you performed on chapter tests throughout the year.

If you earned an A on every test and feel you have a solid understanding of the Calculus curriculum, I would suggest jumping in to practice problems. Master Math Mentor has great resources to help you pass the AP® Calculus exam; I suggest starting with his Diving into Calculus problem sets.

If you don’t feel confident in every topic, I would suggest going back and reviewing topic by topic. Review books are set up in this manner, starting with limits and progressing through derivatives and integrals (and series if you’re in BC). Or, to save money, you can use your textbook!

Regardless if you’re going to review with book or just solving problems, outlined below is a sample study plan for the month before the exam. This ensures you cover the entire AP Calculus curriculum.

Week 1: Take a practice test and score yourself. See where you stand on your understanding of Calculus and how much time you can expect for each section. If you notice you missed several questions on Riemann sums, for example, go back and review that topic first.

Review Limits (including definition of derivative and L’Hopital) and Derivative Rules (power, product, quotient, chain, trigonometry, inverse trigonometry, logarithms, exponential functions, implicit differentiation, equation of tangent line).

Week 2: Applications of Derivatives (minimums/maximums, points of inflection, linearization, Intermediate, Extreme, and Mean Value Theorems). Notes: optimization and related rates are minimally assessed on the AP® exam so don’t get bogged down with those difficult, time-consuming problems!

Complete all 6 Free Response questions from last year.

Week 3: Integration (Riemann sums, basic antiderivatives, Fundamental Theorem of Calculus, u-substitution, trig, parts and partial fractions for BC). Review these steps to determine which integration technique to use.

Complete all 6 Free Response questions from two years ago.

Week 4: Applications of Integrals (average value, area, volume, differential equations, particle motion). Series for BC.

Take another practice test.

Be sure to check your solutions to the free response questions so you know how they’re graded.

Tips on studying for the AP® Calculus Exam:

Before you dive into your study plan, consider the tips below. These tips are even more important if you don’t have a full month to study for the exam.

1. Practice! Do as many AP® level questions as possible, starting as soon as possible. They ask the same type of questions each year. Practicing early will build your confidence in knowing what the question is asking and being able to solve it. See the 7 best resources to study for AP Calculus tests.

2. Study what you don’t know. I know it builds your confidence to get the right answer, but you’ll make bigger gains in minimizing weaknesses instead of sharpening strengths.

3. Make notecards for derivative rules including the power rule, product rule, quotient rules, trig derivatives, inverse trig derivatives, exponential derivatives (and do them backwards to practice your antiderivatives)

4. Know your justifications. Make sure your justifications are Calculus based (including a derivative)! See some examples in the table below:

And read more about first and second derivative test justifications.

Tips for the Free Response portion of the AP® Calculus Exam:

1. Clearly answer the question asked. Include a justification or units if it asks. Make sure to use f, f', g, g'', etc. instead of "the function," "the graph," or "it."

2. Write everything in the box provided. Anything in the margins will not be scored.

3. No need to write an essay or even full sentences. Again, just answer the question.

And don’t waste time explaining how to do a problem or adding units if it's not asked. It won’t earn you any points.

4. The computations are generally straightforward. If you’re caught up solving a complicated equation, pause for a moment to see if you can come up with a different way to solve the problem.

5. Write down your set up for calculator questions. For example, in the 2018 Free Response #2b shown below, you earn 2 points for the set up and only 1 point for the answer.

6. If you do something incorrectly, cross it out or erase it. If you have two separate answers or two ways to solve the problem, the grader will average those points earned.

7. Don’t simplify numerical answers like e + 1/5 - sin(0). It wastes time and if you simplify incorrectly, you won’t earn credit.

8. Round to 3 decimal places. I know it’s specific but don’t lose points when you have the correct answer. Fun fact: if you don't feel confident in rounding, just write the first 3 decimal places or even 4! The reader will only look at the first 3 decimals places for accuracy. You will lose a point if you write less than 3 decimal places.

9. You’re allowed to go back to the first two Calculator questions even after the first 30 minutes has passed; you just won’t have a calculator. You can still set up integrals to earn points!

10. Understand what the questions is asking. College Board explains what different verbs are asking the student to do.

Tips on how to pass the AP® Calculus Exam:

Once you’ve reviewed the curriculum, review these tips the night before you take the exam.

1. Eliminate answers on the multiple choice. Given the answer choices below, could you make an educated guess without even knowing the question?

Choice (A) looks completely different than the others so you could eliminate that. Then look at the coefficients. Choice (D) has whole numbers but the other three choices have fractions so I would eliminate that. Then both (A) and (B) have 1/3 as the last coefficient without knowing the question, I would guess (B).

2. All questions boil down to being about a limit, derivative, or integral (or series in BC). If you’re stuck, ask yourself which topic is being assessed.

3. Relax! You don’t need a perfect to pass. Scoring changes from year to year but in the released 2008 scoring guide, about 36%-47% correct will earn a 3, 48%-62% will earn a 4, and 63% or above will earn a 5!

4. Find the problems you know how to do and solve them first. You won’t likely have the time to get to every problem (and that’s okay because remember you don’t need a perfect score). Go back through a second round for the more difficult problems.

5. Get your graphing calculator ready. Double check it’s in radian mode and that you have spare batteries.

Use Your Time Wisely

Don’t spend hours staring at all your Calculus resources spread out across your table like I did. Create a study plan and stick to it. Just like with any sport or hobby, the only way to get better at something is to practice. Practicing Calculus is the best way to pass the AP® exam. And I believe you can do it.

If you're looking for individual help, consider hiring an AP Calculus tutor or joining me in Calculus Crew. Calculus Crew is an online Calculus community where students meet with a veteran AP Calculus teacher twice a week for group sessions. The sessions focus on challenging test questions and incorporate previous AP exam questions to help you prepare for the AP exam. Best of luck!

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