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…
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…
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…
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…
Given equations that define a region in the plane students are asked to find its area and the volume of the solid formed when the region is revolved around a line or used as a base of a solid with regular cross-sections. This standard application of the integral has appeared every year since 1969 on…
“A particle (or car, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation or the acceleration equation of something that is moving, along with an initial condition. The questions ask for information about motion of the particle: its direction, when it changes direction, its maximum position…
