AP Calculus AB is designed to be taught over the course of one academic school year or two semesters. The aim of the course is to teach students the basics of integral and differential calculus, which are the primary topics of the AP Calculus AB exam. Calculus AB prepares students for college-level work in mathematics and the sciences.
Calculus BC, like AB, is taught over the course of one academic year and shares the primary aim of preparing students for college-level math and science. Calculus BC teaches students the fundamentals of differential and integral calculus, as well as parametric equations, polar coordinate calculus and Taylor series. The extra material is included in both the BC coursework and on the AP exam for Calculus BC.
The major difference between the courses is that Calculus BC includes a number of topics not included in the AB curriculum. The students in a Calculus BC course are expected to learn all the material from the AB course, plus the extra material, in the same amount of time as the AB course is allotted. At some schools passing the Calculus AB exam yields less college credit than passing the Calculus BC test does. The credit awarded will depend on the school and the math requirements for the student's proposed major.
The primary subject matter for the two courses is for the most part the same. Although the BC class does cover extra material not covered in AB, all the basics of calculus are covered in both courses. Also, with the exception of the addition of extra topics in the BC exam, the AP test for the two courses is relatively similar.