# How to Study for the AP Calculus AB Exam

With AP tests coming up this spring, many students are concerned about how best to prepare for exam day. Whether or not you are currently taking a calculus class at school, it is important to familiarize yourself with the specifics of the AP test: what content is covered, how it is formatted, and what approaches can help optimize your score. This guide will provide you with everything you need to know to go into test day with confidence.

With AP tests coming up this spring, many students are concerned about how best to prepare for exam day. Whether or not you are currently taking a calculus class at school, it is important to familiarize yourself with the specifics of the AP test: what content is covered, how it is formatted, and what approaches can help optimize your score. This guide will provide you with everything you need to know to go into test day with confidence.

## What Is on the AP Calculus AB Exam

The most important part of the test is the content itself. According to College Board, ideas covered on the test can be divided (with overlap) into 8 main units:

- Limits and Continuity (10-12% of the test score)
- Differentiation: Definition and Fundamental Properties (10-12% of the test score)
- Differentiation: Composite, Implicit, and Inverse Functions (9-13% of the test score)
- Contextual Applications of Differentiation (10-15% of test score)
- Analytical Applications of Differentiation (15-18% of test score)
- Integration and Accumulation of Change (17-20% of test score)
- Differential Equations (6-12% of test score)
- Applications of Integration (10-15% of test score)

The best way to make sure you have mastered this content is to do practice problems in each of these areas. You can find questions from previous AP exams on the College Board website.

Another very important part of understanding the test itself is understanding the language used in the questions. Understanding this language will help you know exactly what kinds of answers the test-makers are looking for. We highly recommend reviewing the “Task Verbs Used in Free-Response Questions” page of this guide written by the College Board (page 227).

### When Is the AP Calculus AB Exam in 2022?

The 2022 AP Calc BC test is on Monday, May 9, at 8 am. Make sure you know where you will be taking the exam.

### How Long Is the AP Calculus AB Exam?

The test is 3 hours and 15 minutes, with one break between the two major sections.

### How Many Questions Are on the AP Calculus AB Exam?

There are 45 multiple choice and 6 free response questions on the exam, each of which is divided into calculator and no-calculator portions.

### How Is the AP Calculus AB Exam Formatted?

The test is made up of two major sections: multiple choice and free response.

Section I (multiple choice) has a 60-minute no-calculator portion with 30 questions and a 45-minute calculator-required portion with 15 questions.

Section II (free response) has a 30-minute calculator-required portion with 2 questions and a 60-minute no-calculator portion with 4 questions.

Notice that most of the test (2 hours out of total 3 hours and fifteen minutes) will be without a calculator, so make sure you’re comfortable doing basic calculations by hand!

### How Is the AP Calculus AB Exam Scored?

Each section (multiple choice and free response) are worth 50% of your overall score, at 54 points for each section. The multiple choice questions are each worth 1.2 points, while the free response questions are each worth 9 points, with the potential to achieve partial credit for sub-parts of a problem.

The exact formula for converting your raw score to a traditional AP score between 1 and 5 can vary year to year, but if you’re aiming for a 5, you should try to get at least 70 points.

Remember: The multiple choice has no penalty for incorrect responses, so you should answer every question, even if you’re just guessing.

### Is it Hard to Get a 5 on the AP Calculus AB Exam?

In 2020, AP Calculus AB was the 7th most popular AP exam to take, with about 19% of the test-takers getting a 5. These statistics look pretty favorable (by comparison, the most popular AP test, English Language, only saw 10% of test-takers receiving a 5).

That being said, it’s likely that the group of test-takers reflects a self-selecting group of students who have been relatively successful in math during high school. The test certainly isn’t easy, but with the right practice and preparation, it’s very possible to do well.

Additionally, most prestigious schools recommend or even require high-school level calculus, so taking the AP Calculus AB exam could be a great step towards attending your dream school.

### AP Calculus AB vs. BC: What’s the Difference?

Roughly speaking, the Calculus AB exam covers one semester’s worth of introductory college level math, whereas the Calculus BC exam covers two semesters. All topics in the eight units of AP Calculus AB are covered on the Calculus BC exam.

The Calculus BC exam covers two additional units (“Parametric equations, polar coordinates, and vector-valued functions” and “Infinite sequences and series”), and also covers additional topics in each of the 8 units already covered on the AB exam. This includes, for example, additional techniques of integration such as integration by parts, arc length and distance traveled along a curve, and Euler’s method and logistic models.

## What Should I Memorize for the AP Calculus AB Exam?

Unlike some other standardized tests, there’s no formula sheet on the AP Calculus exams, so you’ll need to know important formulas. A good rule of thumb is that any formula, theorem, or equation that you use regularly (either in class or while doing practice problems) is probably something you’ll want to have memorized.

Here are some (non-exhaustive, but very important) examples:

- The derivatives of trig functions, logarithmic, and exponential functions
- The definition of a derivative
- The power rule, product rule, and quotient rule for derivatives
- The chain rule
- The integrals of common functions such as trig expressions, 1/x, etc.
- The Fundamental Theorem of Calculus
- The first and second derivative tests
- The Intermediate Value Theorem, Mean Value Theorem, and Extreme Value Theorem
- Riemann sums
- Using integrals to find the average rate of change on an interval

## AP Calculus AB Exam Tips

**Show your work… all your work.**Remember: the people scoring your exam want to see what you know. Showing your work demonstrates to the scorers that you understand how to solve the problem, and can help you get partial credit for correct steps even if your final answer is incorrect. On the flipside, you’re not likely to get any credit for answers that you give without any demonstrated steps.**Don’t give up on a free-response question if you can’t answer the first part.**Free-response questions are often split up into sub-parts (a,b,c,...), which each ask for an intermediary answer. These sub-questions are scored independently of each other, so you should always attempt every part. Even if the answers to subsequent parts of a question are dependent on one another, you will get credit so long as the answers are related in the right way. So, if your answer to part a is wrong, your answer to part b will be marked as correct, as long as it is found correctly, given your wrong answer to part a. If you don’t know how to find the answer to part a, you can always choose an arbitrary value or variable as a stand-in for the answer to a. Just make sure you’re explicit about doing so when you are showing your work.**Double check what the question is asking for.**Many students sadly lose points by, during their calculations, losing track of what the original question was asking for. For example, if a question asks for the sum of the coordinates of the target point, you won’t get full credit if you merely give the coordinates themselves.**Do not round partial answers.**As previously stated, sub-parts of the free-response questions may be dependent on previous sub-parts. Often, students are tempted to round their answers along the way, but this can create small errors that amplify as you move forward in the problem, ultimately leading to incorrect responses. Make sure to save precise answers in your calculator so you can use them in their unrounded forms in further calculations.**Know how to use your calculator.**Fifteen multiple choice and two free-response questions require the use of a graphing calculator. That’s a large portion of your overall score! You want to be as comfortable as possible using your calculator in order to use your time efficiently and effectively.

We hope that was helpful! Of course, it never hurts to ask for help either. Ivy Tutors Network is more than happy to match you with one of brilliant and caring tutors to help you prepare for the AP Calculus exam. Our top-tier STEM tutors, many of whom hold PhDs and other advanced degrees, are excited to pass on what they know. They can help unpack difficult concepts and provide you with the best study strategies for excelling in AP Calculus (AB or BC), and earning a 5 on the exam!