So, soon time to start another year – both for you and for me. In my over 200 posts to this blog I’ve discussed a lot of calculus topics in hopes that it may help some of my readers teach or learn about calculus. The problem is that I’ve sort of run out of topics…
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…
A reader recently asked me to do a post answering some questions about differential equations: The 2016 AP Calculus course description now includes a new statement about domain restrictions for the solutions of differential equations. Specifically, EK 3.5A3 states “Solutions to differential equations may be subject to domain restrictions.” Could you write a blog…
Convergence tests for series appear on both sections of the BC Calculus exam. In the multiple-choice section, students may be asked to say if a sequence or series converges or which of several series converge. The Ratio test is used most often to determine the radius of convergence and the other tests to determine the…
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…
My friend Ted Gott has just prepared a new index to the AP Calculus exam free-response questions from 1998 to the present. Expanding on an earlier spread sheet by Mark Howell, Ted has referenced all the questions to the Learning Outcomes (LO) and Essential Knowledge (EK) statements of the new Course and Exam Description. AND…
I have always had the impression that the AP exam assumed that parametric equations and vectors were first studied and developed in a pre-calculus course. In fact, many schools do just that. It would be nice if students knew all about these topics when they started BC calculus. Because of time considerations, this very rich…
