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AP Calculus AB is a college-level course offered by the College Board to high school students who are interested in studying biology at an advanced level. It was opted by 135,458 students in 2023 as it is one of the preferred AP courses.
The subject was given a difficulty rating of 5.5 out of 10 by class alumnae on a Reddit survey. AP Calculus AB is known for its challenging curriculum and rigorous exams. The course covers a broad range of topics in calculus, including derivatives, integrals, and the fundamental theorem of calculus.
Course Contents
Based on the Understanding by Design® (Wiggins and McTighe) model, this course framework provides a clear and detailed description of the course requirements necessary for student success. The framework specifies what students must know, be able to do, and understand, with a focus on big ideas that encompass core principles, theories, and processes of the discipline. The framework also encourages instruction that prepares students for advanced coursework in mathematics or other fields engaged in modeling change (e.g., pure sciences, engineering, or economics) and for creating useful, reasonable solutions to problems encountered in an ever-changing world.
The AP Calculus AB framework is organized into eight commonly taught units of study that provide one possible sequence for the course. As always, you have the flexibility to organize the course content as you like.
| Unit | Details | Exam Weighting (Multiple-Choice) |
|---|---|---|
| Unit 1: Limits and Continuity | You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions. | 10%–12% |
| Unit 2: Differentiation: Definition and Fundamental Properties | You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills. | 10%–12% |
| Unit 3: Differentiation: Composite, Implicit, and Inverse Functions | You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives. | 9%–13% |
| Unit 4: Contextual Applications of Differentiation | You’ll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine the limits of certain indeterminate forms. | 10%–15% |
| Unit 5: Analytical Applications of Differentiation | After exploring relationships among the graphs of a function and its derivatives, you’ll learn to apply calculus to solve optimization problems. | 15%–18% |
| Unit 6: Integration and Accumulation of Change | You’ll learn to apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. You’ll apply properties of integrals and practice useful integration techniques. | 17%–20% |
| Unit 7: Differential Equations | You’ll learn how to solve certain differential equations and apply that knowledge to deepen your understanding of exponential growth and decay. | 6%–12% |
| Unit 8: Applications of Integration | You’ll make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions. | 10%–15% |
AP Calculus AB Resources
Mar 27, 2025
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