NCTM Calculus Panel Notes

This past week I attended the NCTM Annual Meeting in San Antonio, Texas. For many years now, the sessions included a panel discussion on AP Calculus. This year Stephen Davis, chief reader for AP Calculus, was the principal speaker. I would like to share a few of his comments and insights some of which may…

Polar Curves (Type 9 for BC only)

Ideally, as with parametric and vector functions, polar curves should be introduced and covered thoroughly in a pre-calculus course. Questions on the BC exams have been concerned with calculus ideas related to polar curves. Students have not been asked to know the names of the various curves (rose, curves, limaçons, etc.). The graphs are usually…

Other Topics (Type 7)

Any topic in the Course and Exam Description may be the subject of a free-response question. The two topics listed here have been the subject of full free-response questions or major parts of them. Implicitly defined relations and implicit differentiation These questions may ask students to find the first or second derivative of an implicitly…

Table & Riemann Sum Questions (Type 5)

Tables may be used to test a variety of ideas in calculus including analysis of functions, accumulation, position-velocity-acceleration, theory and theorems among others. Numbers and working with numbers is part of the Rule of Four and table problems are one way this is tested.  What students should be able to do: Find the average rate…