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The Expert's Guide to the AP Calculus AB Exam

Posted by Christine Sarikas | Oct 7, 2016 8:00:00 PM

Advanced Placement (AP)

 

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Are you taking the AP Calculus AB exam this spring and want to be well prepared on test day? The AP Calculus AB exam is generally held on Thursday morning of the first week of testing.

Before you sit down to take the final exam, it’s critical to know how the test is formatted, what topics it will cover, and how you’ll be scored. This guide will go over all of that information, as well as show you official sample problems and give you tips on the best way to prepare for AP Calculus AB. 

The exam has undergone recent updates that will first be implemented on the May 2017 exam, so this guide will also explain what changes have been made and how they affect your review. The AP Calculus AB exam can sometimes seem overwhelming, but this guide will break it down into clear and manageable information. Let’s get started!

 

What’s the Format of the AP Calculus AB Exam?

The AP Calculus AB exam is 3 hours and 15 minutes long and has two sections. Both of these sections are divided into two parts (based on whether or not a calculator is allowed). 

 

Multiple-Choice Section

  • 45 questions total
  • 1 hour 45 minutes total
  • Worth 50% of your total score
  • Part A:
    • 30 questions
    • 55 minutes long
    • No calculator allowed
  • Part B:
    • 15 questions
    • 50 minutes long
    • Calculator permitted

(The AP Calculus AB exam has had small changes made to its format. Previously, Part A of the multiple-choice section had 28 questions, and Part B had 17 questions.)

 

Free-Response Section

  • Six questions total
  • 1 hour 30 minutes total
  • Worth 50% of your total score
  • Part A:
    • Two questions
    • 30 minutes long
    • Calculator permitted
  • Part B:
    • Four questions
    • 60 minutes long
    • No calculator allowed

 

This can all look a little complicated, but basically, the exam contains four parts, the first two of which are multiple-choice and the last two are free-response. You’ll be allowed a calculator for the middle two parts (one each for multiple choice and free response), but you cannot use a calculator for the first and last parts of the exam.

 

What Does the AP Calculus AB Exam Cover?

The content that the Calculus AB exam covers is divided into three main topic areas, referred to by the College Board as Big Ideas. Within each Big Idea are more specific topics called Enduring Understandings (often abbreviated as “EU”). Each Enduring Understanding contains Learning Objectives and Essential Knowledge the student should have learned by the time of the exam.

As I mentioned in the introduction, there have been some recent updates to the AP Calculus AB exam. Fortunately, they’re relatively minor changes that mostly have to do with how the course framework is structured, most of which will affect instructors teaching the course more than you. The only really significant change to the content of the AP Calculus AB exam is that L’Hospital’s Rule will now be included, and students will be expected to understand and apply it.

I’ve listed each of the Big Ideas and their Learning Objectives, since these are most relevant for students looking for what the exam covers. For the sake of length and clarity, I’ve left out the Enduring Understandings and Essential Knowledge. If you’d like to see these, as well as more detailed information on the content the exam will cover, check out the Calculus AB Course Description, but also know that the information below will give you a solid look at what you’re expected to know for the exam.

Learning Objectives are listed below Big Ideas. These Learning Objectives are skills students are expected to know how to do for the exam.

 

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Big Idea 1: Limits

  • Express limits symbolically using correct notation.
  • Interpret limits expressed symbolically.
  • Estimate limits of functions.
  • Determine limits of functions.
  • Analyze functions for intervals of continuity or points of discontinuity.
  • Determine the applicability of important calculus theorems using continuity.

 

Big Idea 2: Derivatives

  • Identify the derivative of a function as the limit of a difference quotient.
  • Estimate derivatives.
  • Calculate derivatives.
  • Determine higher order derivatives.
  • Use derivatives to analyze properties of a function.
  • Recognize the connection between differentiability and continuity.
  • Interpret the meaning of a derivative within a problem.
  • Solve problems involving the slope of a tangent line.
  • Solve problems involving related rates, optimization, and rectilinear motion
  • Solve problems involving rates of change in applied contexts.
  • Verify solutions to differential equations.
  • Estimate solutions to differential equations.
  • Apply the Mean Value Theorem to describe the behavior of a function over an interval.

 

Big Idea 3: Integrals and the Fundamental Theorem of Calculus

  • Recognize antiderivatives of basic functions.
  • Interpret the definite integral as the limit of a Riemann sum.
  • Express the limit of a Riemann sum in integral notation.
  • Approximate a definite integral.
  • Calculate a definite integral using areas and properties of definite integrals.
  • Analyze functions defined by an integral.
  • Calculate antiderivatives.
  • Evaluate definite integrals.
  • Interpret the meaning of a definite integral within a problem.
  • Apply definite integrals to problems involving the average value of a function.
  • Apply definite integrals to problems involving motion.
  • Apply definite integrals to problems involving area and volume.
  • Use the definite integral to solve problems in various contexts.
  • Analyze differential equations to obtain general and specific solutions.
  • Interpret, create, and solve differential equations from problems in context.

 

AP Calculus AB Sample Questions

Looking at sample questions is one of the best ways to get a feel for what the AP Calculus AB exam will be like. Below are four sample questions, one from each part of the exam. Each of these questions was taken from the official AP Calculus AB Course Description which you can peruse for more complete answer explanations as well as additional sample problems.

 

Multiple Choice (No Calculator)

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This question tests your ability to calculate derivatives. You'll need to use the chain rule to differentiate composite functions. The correct answer to this problem is B.

 

Multiple Choice (Calculator Allowed)

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This question tests your ability to solve problems with rapid rates of change. You'll have to find the derivative in order to find the rate of change of the temperature of the water. The correct answer is B.

 

Free Response (Calculator Allowed)

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This question tests your knowledge of integrals. Parts A, B, and C are each worth three points.

 

Free Response (No Calculator)

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This question tests your knowledge of multiple topics, including  derivatives and integrals. You can receive up to one point for part A, two points for part B, and three points each for parts C and D.

 

How Is the AP Calculus AB Exam Scored?

As mentioned above, the multiple-choice section and the free-response section are each worth 50% of your total exam score. For the multiple-choice section, you earn one point for each question you answer correctly. No points are deducted for incorrect answers, so you should answer every question! You can earn up to 45 points for this section.

For the free-response section, each of the six questions is worth nine points, so you can earn up to 54 points. Different parts of each question can be worth a different amount of points (for example, on one question you may be able to earn up to 1 point for part A, 3 points for part B, 3 points for part C, and 2 points for part D).

After your points are added up for each of your sections, your score is converted to the standard AP scoring scale of 1-5. The exact formula for doing this can change slightly from year to year, but in 2008, the process for doing this involved multiplying the number of multiple-choice questions you answered correctly by 1.2272, then adding that number to the points you received on the free-response section. That value is then rounded to the nearest whole number and becomes your composite score. Each AP score (from 1-5) corresponds to a range of composite scores.

Below you can see the conversion chart as well as the score distributions for test takers from the 2016 Calculus AB exam.

 

Composite Score Range

AP Score

Percent of Students Who Received That Score

0-26

1

30.7%

27-38

2

9.7%

39-51

3

17.4%

52-67

4

17.3%

68-108

5

24.8%

 

 

3 Tips for Preparing for the AP Calculus AB Exam

Studying for the AP Calculus AB exam can be tough. Use these three tips to make your studying more effective and increase your chances of getting a great score.

 

Tip 1: Memorize Important Formulas

There are certain formulas for AP Calculus AB that you should have down cold. There is no formula sheet given on the AP exam, so you’ll have to have the formulas you’ll need already memorized. Many teachers give out formula sheets for students to memorize, and there’s also a variety of formula “cheat sheets” you can use to review before the exam. Google “AP Calculus AB formula sheet” to look at your options.

In general, any formula that you use regularly in class is a good one to memorize. Major formulas you should have memorized include those for limits, differentiation, and integration, as well as the fundamental theorems.

 

Tip 2: Know How to Use Your Calculator

You’re allowed to use your calculator for two of the four exam parts, and most of the questions in those two sections will be difficult, if not impossible, for you to solve without a graphing calculator. While it may seem obvious that you should know how to work your calculator, knowing exactly how and when to use its different functions can save you a lot of time on the exam and increase your chances of getting a correct answer.

According to the College Board, the four calculator capabilities that you’ll use the most during the exam and should easily be able to do with your calculator are:

  • Plot the graph of a function within an arbitrary viewing window
  • Find the zeros of functions (solve equations numerically)
  • Numerically calculate the derivative of a function
  • Numerically calculate the value of a definite integral

When you’re preparing for the exam, know how to do each of these (completing practice problems can help).

 

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Tip 3: Get Used to Showing All Your Work

For most free-response questions, the final answer to a problem is only worth 1-2 points out of a possible nine. This means that the majority of points are earned through intermediate steps of the problem, and if you don’t show how you reached those intermediate steps, you won’t get a high score on this section.

Even if you get an answer by using your calculator, you have to write the setup (such as the equation being solved or the derivative being evaluated) as well as the answer in order to get credit for the work. You may be used to not writing down certain work that seems particularly obvious on homework and class tests. However, even if your teacher doesn’t mind, AP graders will.

Remember, graders are more interested in how you reached your final answer than what that final answer is, so get yourself in the habit of showing each step of your work well before exam time.

 

Conclusion

The AP Calculus AB exam can seem intimidating if you don’t know what to expect. Knowing how the exam will be formatted and the types of questions it will ask can go a long way towards helping you feel more prepared and confident on test day.

The exam has two sections, multiple-choice and free-response, which are each further divided into two parts, based on whether or not you can use a calculator. Each of these sections is worth 50% of your total score.

The exam itself covers three main topics:

  • Limits
  • Derivatives
  • Integrals and the Fundamental Theorem of Calculus

In order to prepare for the exam in the best way, keep these three tips in mind during your review:

  • Memorize Important Formulas
  • Know How to Use Your Calculator
  • Get Used to Showing All Your Work

 

What's Next?

Now that you know what the AP Calculus AB exam covers, the next step is to practice! Read our guide to get links to every practice test available online.

Wondering how challenging other AP classes are? Learn what the easiest AP classes are and what the hardest AP classes are so that you know what to expect!

Not sure which other math classes you should take? Math is often the trickiest subject to choose classes for, but out guide will help you figure out exactly which math classes to take for each year of high school.

 

Want to improve your SAT score by 160 points or your ACT score by 4 points? We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

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Christine Sarikas
About the Author

Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.



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