Guide to the AP® Calculus AB and BC Exams

Why take AP^® Calculus AB/BC?

When faced with the choice of whether or not to take AP^® Calculus AB/BC, the benefits often outweigh the costs for most students.

Many colleges require students to fulfill a mathematics course before they can graduate. However, if you take the AP^® Calculus AB/BC Exam and attain a high score while you are in high school, you may be able to qualify for credit toward that requirement and not have to take another math exam in college.

A more recent argument for taking AP^® Exams, is that more colleges are going test-optional. This means that SAT^® and ACT^® scores are potentially holding less weight when it comes to college applications, and a good AP^® score could help tip the scale in your favor when it comes to college admissions.

Besides creating the opportunity to earn college credit for the work you do, AP^® Calculus courses also develop problem-solving and critical-thinking skills, challenge you academically, and prepare you for college-level mathematics courses. Preparing for and taking the AP^® Calculus Exams provide excellent practice for college-level exams you may take in the future.

How to sign up for the AP^® Calculus AB/BC Exam

To register for the AP^® Calculus Exam, you need to contact your school’s AP^® Coordinator, who can help facilitate your courses and exams.

Bear in mind, you’ll likely need to complete requirements to be eligible to enroll in an AP^® course. In order to register for the AP^® Calculus Exam, you have to join your class section online, using College Board’s My AP^® portal. Some schools will automatically register you for the exam if you’re enrolled in an AP^® Calculus class, but others won’t, and you will have to register online through the portal. If you are unsure whether or not you are registered for the AP^® Calculus Exam, check wIth your AP^® Coordinator.

There is also a deadline for exam registration, so make sure you register through your AP^® Coordinator by then to avoid paying any late fees. The deadline to register for exams is in the fall, but specific deadlines may vary by school—be sure to check with your teacher or AP^® Coordinator.

How much does the AP^® Exam cost?

Each AP^® Exam costs a total of $96—if you’re in the mainland United States and its territories and commonwealths, Canada, or a U.S. Department of Defense Dependents School.

If you’re outside of those areas, the AP^® Exam will cost $126 per exam.

College Board has a financial aid program that offers a $34 fee reduction in the exam. Read more about exam fees here.

You cannot use the My AP^® portal to pay fees—they will be collected by your AP^® Coordinator.

When you take into account the cost of a college course versus the cost of the exam, though, you’ll see that the AP^® Exam is actually a bargain. With a passing score, you may be able to earn college credit and save hundreds or even thousands of dollars.

When can I take the AP^® Calculus AB/BC Exam?

Both the AP^® Calculus AB and BC Exam date in 2022 is Monday, May 9th. You can find more information about dates, specific times, and late-testing schedules for the 2022 AP^® Calculus AB/BC Exam in our 2022 AP^® Exam Dates article.

What’s on the AP^® Calculus AB/BC Exam?

The AP^® Calculus AB/BC curriculum covers three “big ideas” that serve as a foundation of the course.

BIG IDEA 1: CHANGE. Using derivatives to describe rates of change of one variable with respect to another or using definite integrals to describe the net change in one variable over an interval of another allows students to understand change in a variety of contexts. It is critical that students grasp the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus—a central idea in AP^® Calculus.

BIG IDEA 2: LIMITS. Beginning with a discrete model and then considering the consequences of a limiting case allows us to model real-world behavior and to discover and understand important ideas, definitions, formulas, and theorems in calculus: for example, continuity, differentiation, integration, and series (BC only).

BIG IDEA 3: ANALYSIS OF FUNCTIONS. Calculus allows us to analyze the behaviors of functions by relating limits to differentiation, integration, and infinite series and relating each of these concepts to the others.

The course content is organized by units (eight units in AP^® Calculus AB and ten units in AP^® Calculus BC).

Unit 1: Limits and Continuity.

Calculus AB Exam Weighting: 10-12%

Calculus BC Exam Weighting: 4-7%

Limits introduce the subtle distinction between evaluating a function at a point and considering what value the function is approaching, if anything, as x approaches a point.

Unit 2: Differentiation: Definition and Fundamental Properties.

Calculus AB Exam Weighting: 10-12%

Calculus BC Exam Weighting: 4-7%

Derivatives allow us to determine instantaneous rates of change by applying limits to average rates of change over increasingly small intervals.

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions.

Calculus AB Exam Weighting: 9-13%

Calculus BC Exam Weighting: 4-7%

In this unit, you will learn how to differentiate composite functions using the chain rule and apply that understanding to determine derivatives of implicit and inverse functions.

Unit 4: Contextual Applications of Differentiation.

Calculus AB Exam Weighting: 10-15%

Calculus BC Exam Weighting: 6-9%

In this unit, you will apply average and instantaneous rates of change in problems involving motion. In addition, you will identify differentiation as a common underlying structure on which to build understanding of change in a variety of contexts.

Unit 5: Analytical Applications of Differentiation.

Calculus AB Exam Weighting: 15-18%

Calculus BC Exam Weighting: 8-11%

In this unit, you will learn to present justifications for conclusions about the behavior of functions over certain intervals or the locations of extreme values or points of inflection.

Unit 6: Integration and Accumulation of Change.

Calculus AB Exam Weighting: 17-20%

Calculus BC Exam Weighting: 17-20%

This unit establishes the relationship between differentiation and integration using the Fundamental Theorem of Calculus.

Unit 7: Differential Equations.

Calculus AB Exam Weighting: 6-12%

Calculus BC Exam Weighting: 6-9%

In this unit, you will learn to set up and solve separable differential equations, approximate solutions graphically using slope fields, and approximate solutions numerically (BC ONLY) using Euler’s method.

Unit 8: Applications of Integration.

Calculus AB Exam Weighting: 10-15%

Calculus BC Exam Weighting: 6-9%

In this unit, students will learn how to find the average value of a function, model particle motion and net change, and determine areas, volumes, and lengths (BC ONLY) defined by the graphs of functions.

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions.

Calculus BC Exam Weighting: 11-12%

In this unit, you will build on your understanding of straight-line motion to solve problems in which particles are moving along curves in the plane. You will use parametric equations and vector-valued functions to model planar motion and apply calculus to solve motion problems.

Unit 10: Sequences and Series.

Calculus BC Exam Weighting: 17-18%

In this unit, you will learn that a sum of infinitely many terms may converge to a finite value. You will explore graphs, tables, and symbolic expressions for series that converge and diverge and for Taylor polynomials.

What is the test format for the AP^® Calculus AB/BC Exam?

The AP^® Calculus AB/BC exam consists of two sections: one multiple-choice section and one free-response section. Within each of these sections, there is a calculator-active part and a calculator-inactive part.

Section 1: Multiple-Choice Questions

45 Questions | 1 Hour 45 minutes | 50% of Exam Score

• Part A: 30 questions; 60 minutes (calculator not permitted).
• Part B: 15 questions; 45 minutes (graphing calculator required).
• Questions include algebraic, exponential, logarithmic, trigonometric, and general types of functions.
• Questions include analytical, graphical, tabular, and verbal types of representations.

Section 2: Free-Response Questions

6 Questions | 1 Hour 30 Minutes | 50% of Exam Score

• Part A: 2 questions; 30 minutes (graphing calculator required).
• Part B: 4 questions; 60 minutes (calculator not permitted).
• Questions include various types of functions and function representations and a roughly equal mix of procedural and conceptual tasks.
• Questions include at least 2 questions that incorporate a real-world context or scenario into the question.

The questions typically do not vary much from year to year, so practicing past AP^® Calculus AB/BC exam questions is a great way to prepare for the exam.

How is the AP^® Calculus AB/BC Exam scored?

Both sections of the AP^® Calculus AB/BC exam are weighted equally. This is achieved by multiplying the number of correct responses in the multiple-choice section by 1.2000 and adding that to the number of points earned in the free-response section.

• Section 1: Multiple-Choice Questions. The number of correct responses in the multiple-choice section is multiplied by 1.2000, for a maximum possible score of 54 points.
• Section 2: Free-Response Questions. Each of the six free-response questions is scored out of 9 points, for a maximum possible score of 54 points.
• The composite score consists of the total score from Sections 1 and 2.

Although it varies slightly from year to year, students need to achieve a minimum combined score of about 45 points in order to earn a passing grade on the exam.

The AP^® Exam’s scoring system is on a scale of one to five—with five being the best and one being the worst. The following table breaks down the score you could earn and what that would mean.

When it comes to AP^® Calculus AB/BC, you’ll want to aim for a score of 3 or higher. Most colleges will award you college credit if you score within that range.

It varies from college to college though. So, if you want to know the score that a specific college will accept in exchange for credit, you’ll need to check with the college’s registrar’s office to find out information about AP^® credit for the AP^® Calculus AB/BC Exam. Often, you can find this information on the school’s website. You can also check out the College Board’s search tool for AP^® credit policies.

NOTE: Colleges sometimes change their requirements for awarding college credit or offering placement out of required courses. So always check in with the college to make sure you have the most relevant and recent information.

Bottom line: You’re going to want to score as high as you possibly can. Sure your dream school only requires a 3—but you should always be aiming for the highest possible score regardless.

When you get that credit, you will effectively be walking into college with part of the requirements already completed. It means you could skip a mathematics requirement and take whatever class you wanted instead. Or, you could even save money on college tuition by spending less time getting credits. Either way, earning that college credit before you start college is a great way to set yourself up for the next four years. Read more about how AP^® exams helped Marco Learning’s tutors earn college credits.

What can I bring to the AP^® Calculus AB/BC Exam?

Below is a list of all the things you can bring with you into the exam room. Note: It’s possible that not all of the items will apply to you (e.g., the Student Accommodations Letter).

• Approved graphing calculator (i.e., TI-84+). Be sure to check College Board’s Calculator Policy prior to taking the exam to ensure your calculator is on the list of approved devices.
• Two No. 2 pencils with erasers. These will be used on the multiple-choice portion of the exam.
• Two black or dark blue ink pens. These may be used for the free-response questions. Be sure to bring black or dark blue ink pens only. Leave your gold glitter pens at home.
• A watch. This is a simple analog or digital watch with no internet access or alarms. Don’t even try to bring your smart watch in the room.
• The AP^® Student Pack. This is given to you just before you take your exam and contains a label that you need to place on your exam. Follow the labeling instructions carefully.
• Government- or school-issued ID. If you don’t attend the school where you’re taking the AP^® Calculus AB/BC Exam, you must also bring a government- or school-issued ID.
• College Board SSD Student Accommodation Letter. If you require accommodations beyond the regular exam, you’ll receive a letter that verifies this (e.g., you need a braille or large-type exam).

Remember, you won’t have to bring all these things—but it’s in your best interest to be as prepared as you can for the exam.

Take a look at our Test Day Checklist to make sure you are 100% prepared to take your AP^® Calculus AB/BC Exam when the time comes!

How do I study for AP^® Calculus AB/BC?

Here are the best study tips for AP^® Calculus AB/BC:

#1 Work through several practice exams. The types of questions asked (and the question format) has been consistent from year to year (even during remote learning). Practice working through old free-response and multiple-choice questions to prepare for the upcoming AP^® Calculus AB/BC Exam.

#2 Practice under realistic time constraints. For multiple-choice questions, you’ll be given an average of 2 minutes per question for calculator inactive problems, and an average of 3 minutes per question for calculator active problems. For free response questions, you’ll be given an average of 15 minutes per problem.

#3 Memorize all important formulas, theorems, and definitions. Traditionally, students are not able to use a formula sheet on the exam.

#4 Study concepts, not just problems. When you are solving practice problems, think about how you know to use a particular strategy and why it works. This will help you deepen your conceptual understanding.

#5 Read and annotate the problem. Key words such as “estimate” are easily overlooked when you’re knee deep into solving a problem. It’s a good idea to circle key words and information in the question prompt. After solving a problem, always reread the question to ensure you’ve answered it completely.

#6: Avoid common errors. If you are aware of commonly made errors, you’ll be more likely to avoid them. Always be sure to do the following:

• Check conditions before using theorems
• Consider endpoints when using intervals
• Don’t drop your limits prematurely
• Use proper notation
• Name your functions
• Recognize when to use chain rule
• Change your bounds during u-sub

Looking for more help on the AP Calculus AB/BC Exams? Check out Marco Learning Teacher, Michelle Krummel’s YouTube Channel for review videos.