Shaun Ault

3-Month AP Calculus Exam Study Guide

The AP Calculus exam (AB or BC) is not your typical high school exam. It requires substantial preparation. In this article, I’ll present some tips for prepping for the exam and suggest a 3-month AP Calculus exam study plan.

Making a 3-Month AP Calculus Exam Study Plan -Magoosh

The AP Calculus Exam

The AP Calculus AB or BC test has two main sections, taking a total of 3 hours and 15 minutes to complete. Fortunately, there is always a short break between the two sections.

There are two types of problem on the exam.

Section I consists of 45 multiple choice questions. You will have an hour and 45 minutes to complete them.

Multiple choice bubble sheet

Be sure to fill in your answer choices completely on the multiple choice section.

Section II has only 6 free response questions in an hour and a half. However, each free response question has 3 to 4 parts each. Most importantly, you must show all steps of your work.

Both sections are divided into a Part A and Part B. One part requires a graphing calculator while the other does not permit one to be used at all. It’s a good idea to familiarize yourself with the features of a good graphing calculator well in advance of the test.

Preparing for the Exam

Effective studying consists of a number of different tasks spread out over the whole year.

  • Learning the concepts (classwork)
  • Drilling basic skills (homework)
  • Doing practice tests
  • Reviewing weak spots

Learning the Concepts

This is what your course work is all about. As you read through the textbook and listen to lectures in class each day, you are learning what calculus is all about. Pay attention to all of the examples. Try to understand every theorem and property.

This takes time, but it’s essential to building a firm foundation.

 Students in a math class at Match

Pay attention in AP Calculus class! Credit Shiho Fukada for The New York Times

Drilling Basic Skills

If you have ever felt that you have too much homework to do, you are not alone. However, all that homework provides you with enough practice to hone your skills.

The more homework you do, the easier the material will become!

Homer Simpson reading a book and looking worried

So much homework!

Doing Practice Tests

Once you have learned the fundamentals and practiced your skills on homework, it’s time to get your feet wet by taking practice exams. In fact, your teacher has probably been giving you actual AP questions as part of their in-class quizzes and tests.

But as early as February, you should start taking entire practice tests on your own.

I recommend doing as many practice tests as you can get your hands on. Most AP Calculus prep books have at least 3 tests included, so my advice is to get two books from different publishers.

There are also practice problems from past tests available on the AP Students page at CollegeBoard.

Reviewing Weak Spots

As you work on each practice exam, take note of every problem that gives you trouble. You can either mark the problem number in the test booklet, or jot it down in a journal.

In fact, think of each practice exam as a diagnostic tool to discover your weak areas.

During the rest of the week, review each incorrect problem as well as any problems that you may have gotten correct due to a lucky guess but that you didn’t fully grasp.

If a certain topic consistently causes you headaches, then you must go back to your class notes and textbook to review that concept. Make notes like, “I just don’t get velocity!” or “What do they mean by the term vector field?” Then find those topics in your book and study them thoroughly.

The Content of the Exams

It’s important to know what concepts will be tested on the AP Calculus Exams. The AB test covers three Big Ideas:

  1. Limits
  2. Differential Calculus
  3. Integral Calculus

For a detailed list of topics see What Topics are on the AP Calculus AB Exam?

The AP Calculus BC exam covers one additional Big Idea, Sequences and Series, as well as more advanced topics within the other three Big Ideas:

  1. Limits (including L’Hospital’s Rule)
  2. Differential Calculus (including vector, parametric, and polar derivatives)
  3. Integral Calculus (including vector, parametric, and polar integrals)
  4. Sequences and Series

More information about the BC topics can be found here: What Topics are on the AP Calculus BC Exam?

3-Month AP Calculus Exam Schedule

Because the Calculus AB and BC tests usually occur in the second week of May, you should start prepping in February. The following 14-week schedule is based on the 2017 test dates.

Note, the suggested review topics depend on whether you plan to take the AB or the BC test.

WeekPractice TestAB ReviewBC Review
Week 1 (2/5 - 2/11)Practice Test 1Review testReview test
Week 2 (2/12 - 2/18)Interpreting graphs / asymptotesLimits, Continuity, asymptotes, etc.
Week 3 (2/19 - 2/25)Limits and continuityDerivative rules
Week 4 (2/26 - 3/4)Practice Test 2Review testReview test
Week 5 (3/5 - 3/11)Derivative rulesApplications of derivatives
Week 6 (3/12 - 3/18)Velocity and Acceleration / Analysis of graphs using derivativesAntidifferentiation rules
Week 7 (3/19 - 3/25)Practice Test 3Review testReview test
Week 8 (3/26 - 4/1)Related rates / OptimizationApplications of integrals
Week 9 (4/2 - 4/8)Antidifferentiation rulesVector, parametric, and polar functions
Week 10 (4/9 - 4/15)Practice Test 4Review testReview test
Week 11 (4/16 - 4/22)Applications of integralsSequences and Series
Week 12 (4/23 - 4/29)Practice Test 5Review testReview test
Week 13 (4/30-5/6)All topicsAll topics
Week 14 (5/7-5/9)AP Calculus Exam Day!

General Tips

According to this schedule, you will take a practice exam every two or three weeks. Then use the rest of that week to review missed problems.

On weeks in which you have no practice test, review challenging topics from the suggested category. Feel free to adjust the review topics as needed.

Final Thoughts

The main idea is that you must prepare for your AP Calculus exam far in advance of the actual test. Cramming the night before will do no good.

This post outlines a 3-month AP Calculus study plan that should give you plenty of time to work on your skills before the test.

Good luck on the exam!!!

AP Calculus exam? Challenge accepted!

About 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!


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