In this article
AP Calculus BC 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 136,000 students in 2023 as it is one of the preferred AP courses.
The exam’s difficulty rating stands at 5.5 out of 10 by class alumnae on a Reddit survey. AP Calculus BC is known for its challenging curriculum and rigorous exams. The course covers a broad range of topics such as integration techniques, infinite series, and parametric equations.
Course Contents
The AP Calculus BC framework included in the course and exam description outlines distinct skills, called Mathematical Practices, that students should practice throughout the year—skills that will help them learn to think and act like mathematicians.
| Unit | Details | Exam Weighting (Multiple-Choice Section) |
|---|---|---|
| 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. | 4%–7% |
| 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. | 4%–7% |
| 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. | 4%–7% |
| 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. | 6%–9% |
| 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. | 8%–11% |
| 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 and logistic models. | 6%–9% |
| 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 lengths of curves, areas of regions, or volumes of solids defined using functions. | 6%–9% |
| Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions | You’ll solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration. You’ll also deepen your understanding of straight-line motion to solve problems involving curves. | 11%–12% |
| Unit 10: Infinite Sequences and Series | You’ll explore convergence and divergence behaviors of infinite series and learn how to represent familiar functions as infinite series. You’ll also learn how to determine the largest possible error associated with certain approximations involving series. | 17%–18% |
AP Calculus BC Resources
Mar 10, 2025
Was this helpful?
