Calculus AB and BC are advanced placement high school calculus courses that are taken after precalculus, and span the course of a year. Often, students taking calculus AB or BC gain college credit for their efforts. Although calculus AB and calculus BC are both advanced placement courses and share the same prerequisites, there are differences between the courses that students should be aware of before deciding on which course to enroll.
Students may choose to take an advanced placement calculus course to prepare for a test that allows them to earn college credit while still in high school. Upon the completion of an advanced placement test, students can gain college credit for one or two terms of college calculus. The student may individually set his goal for how much college credit he thinks he is capable of obtaining. This is an important goal, because the course a student chooses will prepare her for the corresponding advanced placement test. Passing the calculus AB advanced placement exam yields less college credit than passing the BC exam.
Teachers of advanced placement calculus courses often give students advice as to which of the advanced placement courses most suit them. Teachers may use a student's past grades as an indicator of that student's ability to perform well in an advanced placement class. Upon observing a student's grades in precalculus and algebra, a calculus teacher may suggest that the student avoid the more intensive BC course in favor of the AB course. Previous experience with advanced-level or honors courses may also qualify a student for the BC advanced placement course. Some schools offer pre-advanced placement or honors precalculus courses that have the purpose of preparing students for advanced placement courses. Students taking such courses are more likely to qualify for the BC course.
The material covered in the two courses differ in the extent that the BC course includes additional content. Calculus AB contains topics relating to differentiation and integration, including limits, derivative rules, implicit differentiation, function optimization and the fundamental theorem of calculus. In addition to the content included in the AB course, Taylor series, polar coordinate calculus, integration by parts and parametric equations appear in calculus BC course content and on the calculus BC advanced placement exam.
While the two advanced placement calculus courses both span one year of high school, the calculus BC course will require more of the student. This is because the BC course contains more content yet does not offer students more class time to study these topics. In other words, teachers of the calculus BC course must teach at a faster rate. Often, this is accompanied with extra homework and more frequent exams for the students.