Are you familiar with the Mean Value Theorem? Can you calculate derivatives? The AP^{®}Calculus AB exam tests topics and skills discussed in your AP Calculus AB course. If you score high enough on the exam, your AP Calculus score could earn you college credit!
Check out our AP Calculus AB Guide for the essential information you need for the exam:
- Exam Overview
- AP Calculus AB vs AP Calculus BC
- Sections and Question Types
- Scoring
- How to Prepare
What’s on the AP Calculus AB Exam?
The College Board is very detailed in what they require your AP teacher to cover in his or her AP Calculus AB course. You should be familiar with the following topics:
- Limits and Continuity—Defining limits, estimating limits from graphs and tables, determining limits using algebraic properties and manipulation, applying the Squeeze Theorem, Determining types of discontinuities, understanding asympototes, and the applying IntermediateValue Theorem
- Differentiation: Definition and Basic Rules—Defining average and instantaneous rates of change, defining the derivative of a function, estimating derivatives at a point, connecting differentiability and continuity, applying the Power Rule, the Product Rule, and the Quotient Rule, and determining derivatives of constants, sums, differences, and constant multiples, trigonometric functions, e^{x}, and ln x
- Differentiation: Composite, Implicit, and Inverse Functions—Applying the Chain Rule, using implicit differentiation, differentiating inverse functions, and calculating higher order derivatives
- Contextual Applications of Differentiation—Interpreting derivatives in context, using rates of change in motion and other context, applying related rates, approximating using linearization, and applying L’Hospital’s Rule
- Analytical Applications of Differentiation—Understanding the Mean Value Theorem, using the Extreme Value Theorem, finding global and local extrema, applying the First Derivative Test and Second Derivative Test, finding intervals of increase and decrease, understanding concavity, sketching graphs, solving optimization problems, and using implicit relations
- Integration and Accumulation of Change—Finding accumulations of change, Reimann sums, and definite integrals, understanding the Fundamental Theorem of Calculus, interpreting accumulation functions, finding anti-derivatives and indefinite integrals, and integrating using substitutions, long division, and completing the square
- Differential Equations—Modeling situations with differential equations, verifying solutions for differential equations, sketching slope fields, and using separation of variables
- Applications of Integration—Finding the average value of a function, connecting position, velocity, and acceleration using integrals, applying accumulation functions, finding area between curves of functions, and finding volumes from cross-sections and revolutions
Read More: Review for the exam with our AP Calculus AB Cram Course
AP Calculus AB vs. BC
AP Calculus is divided into two classes: AB and BC. The College Board says Calculus AB is the equivalent of a semester of college calculus and BC is the equivalent of a year of college calculus. In truth, AB calculus covers closer to three quarters of a year of college calculus. The main difference between the two is that BC Calculus tests some more theoretical aspects of calculus, and it covers a few additional topics.Check out ourline of AP guidesfor a comprehensive content review.
AP Calculus AB Sections and Question Types
The AP Calculus AB exam is three hours long and has two sections: a multiple-choice section and and free-response section. Each exam section has a Part A and a Part B.
Section | Timing | Number of Questions | % of Exam Score |
Section 1 | Part A: 60 minutes Part B: 45 minutes | Part A:
Part B:
| 50% |
Section 2 | Part A: 30 minutes Part B: 60 minutes | Part A:
Part B:
| 50% |
Multiple-Choice
The multiple-choice questions on the AP Calculus AB exam cover a variety of calculus topic and are discrete, as opposed to appearing in question sets, and will have a similar format that is followed by five answer choices. At times, it may seem that there could be more than one possible correct answer. Answers resulting from common mistakes are often included in the five answer choices to trap you.
Free Response Questions
The FRQ section of the AP Calculus AB exam consists of six questions that require you to write out the solutions and steps by which you solved it. Partial credit is given for various steps in the solution of each problem. You’ll usually be required to sketch a graph in one of the questions.
AP Calculus AB Scores
AP scores are reported from 1 to 5. Colleges are generally looking for a 4 or 5 on the AP Calculus AB exam, but some may grant credit for a 3. Learn more about college AP credit policies. Each test is curved so scores vary from year to year. Here’s how AP Calculus AB students scored on the May 2022 test:
Score | Meaning | Percentage of Test Takers |
5 | Extremely qualified | 20.4% |
4 | Well qualified | 16.1% |
3 | Qualified | 19.1% |
2 | Possibly qualified | 22.6% |
1 | No recommendation | 21.7% |
Source: College Board
How can I prepare?
AP classes are great, but for many students they’re not enough! For a thorough review of AP Calculus AB content and strategy, pick the AP prep option that works best for your goals and learning style.
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- AP Exams