What Topics are on the AP Calculus BC Exam?

 
Generally speaking, the AP Calculus BC exam is more comprehensive, but not necessarily more difficult, than the AB exam. Let’s take a look at what topics you may expect to find on the BC exam.

The AP Calculus BC Exam

The material on the BC exam is the equivalent of about two semesters of calculus at the college level. The topics come from four main areas:

1. Limits
2. Derivatives
3. Integrals
4. Sequences and Series

However, these broad categories are interrelated. Any given problem on the test might require techniques from multiple areas.

Scores and Credits

Many colleges and universities award up to two semesters of calculus credit for a high score on the BC exam. If you earn at least a 4 on the exam, you could be eligible to receive about 8 credits of calculus — that’s Calculus I and II — before even setting foot on campus! In addition, some schools offer credit in lower level courses such as Precalculus if you earn at least a 3 on the test. However, schools differ in their AP policies, so check with each school that you are applying to.

List of Topics on the AP Calculus BC Exam

Mathematics builds upon itself, and calculus is no different. Because of this, think of the AP Calculus BC exam as the AB exam but with the following topics thrown in as well.

Derivatives

• Derivatives of vector-valued functions, parametric functions, and functions expressed in polar coordinates.
• Analysis of polar graphs using derivatives.
• Velocity, speed, and acceleration for vector-valued or parametric functions.
• Euler’s method.

Integrals

• Improper integrals.
• Integration by parts and the method of partial fractions.
• Displacement, distance, and position of a particle moving according to a vector-valued or parametric function.
• Areas bounded by polar curves.
• Length of a parametric curve.
• Logistic growth model.

Sequences and Series

• Covergence and divergence.
• Common series such as the p-series, geometric series, and harmonic series.
• Absolute versus conditional convergence.
• Taylor polynomials and approximation.
• Lagrange error bound.
• Taylor series and power series.
• Radius and interval of convergence.

Summary

Basically, the AP Calculus BC Exam covers the same topics as the AB exam plus vector, parametric and polar functions, sequences, and series. In addition, the BC test includes more advanced techniques for finding derivatives and integrals as well as further applications of calculus not found on the AB exam.

For more information, check out What’s the Difference between that AP Calculus AB and BC tests?

More detailed descriptions of the topics covered on both the AB and BC test can be found here.