What’s the Format of the AP Calculus AB Exam?
The AP Calculus AB exam is three 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
Here is an overview of the format of the AP Calculus AB multiple-choice section:
- 45 questions total
- One hour 45 minutes total
- Worth 50% of your total score
- Part
A
- 30 questions
- 60 minutes
- No calculator allowed
- Part
B
- 15 questions
- 45 minutes
- Calculator required
Note that 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
Here is a rundown of the format of the AP Calculus AB free-response section:
- Six questions total
- One hour 30 minutes total
- Worth 50% of your total score
- Part
A
- Two questions
- 30 minutes
- Calculator required
- Part
B
- Four questions
- 60 minutes
- No calculator allowed
This can all look a little complicated, but basically, the AP Calculus AB exam consists of four parts. The first two are multiple choice, and the last two are free response.
You are required to use a calculator for the middle two parts (one each for multiple choice and free response), but you may not use a calculator for the first and last parts of the exam.
What Topics Does the AP Calculus AB Exam Cover?
Content on the Calculus AB exam can be divided into three main topic areas, referred to by the College Board as Big Ideas. Within these three Big Ideas are more specific topics called Enduring Understandings (often abbreviated as “EU”). Each Enduring Understanding contains both Learning Objectives and Essential Knowledge that the student should have learned by the time of the exam.
As I mentioned, there have been some 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, and this will affect instructors of the course more than it will you. The only significant change to the content of the AP Calculus AB exam is that L’Hospital’s Rule will now be included on it—and students will be expected to understand and apply it.
I’ve listed each of the Big Ideas and their Learning Objectives below, since these are the most relevant for students looking for what the exam covers.
For the sake of length and clarity, I left out the Enduring Understandings and Essential Knowledge. If you’d like to see these, as well as more detailed information on the content covered by the exam, check out the official AP Calculus AB Course Description. Still, 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 that students are expected to know how to do for the exam.
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 derivative
- 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
How Is the AP Calculus AB Exam Scored?
As mentioned, 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 1 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 9 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 AP Calculus AB 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.
However, in 2008, the process for converting raw AP scores to scaled scores involved multiplying the number of multiple-choice questions you answered correctly by 1.2272, and then adding that number to the points you received on the free-response section. This value is 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 and score distributions for test takers from the 2018 Calculus AB exam:
Composite Score Range | AP Score | % of Students Who Got Score |
0-26 | 1 | 20.0% |
27-38 | 2 | 22.4% |
39-51 | 3 | 21.0% |
52-67 | 4 | 17.3% |
68-108 | 5 | 19.4% |
Source: The College Board