My choices for the Good Question series are somewhat eclectic. Some are chosen because they are good, some because they are bad, some because I learned something from them, some because they can be extended, and some because they can illustrate some point of mathematics. This question and the next, Good Question 16, are in…
Best wishes to everyone tomorrow. Hope your students do well!
The annual AP Calculus Panel Discussion at the NCTM Annual meeting was held on Saturday April 28, 2018. The principal speaker was Stephen Davis, the chief reader for calculus. Stephen has made his slides available for anyone who is interested. The slides are here http://www.ncaapmt.org/archive/crTalks/nctm-apr2018-notes.pdf . The items highlighted in blue are the ones Stephen discussed in…
The AP Calculus AB and BC exams are scheduled for Tuesday May 15, 2018 at 08:00 local time. That’s about 5 weeks away. I’ve posted all my review notes, finishing well ahead of time so, if you find something useful in them, you’ll have time to incorporate it into your review. I hope you find them…
A quick note on speed. The idea of differentiating speed to determine where it is increasing or decreasing is perfectly reasonable. . Then, Since the denominator is positive, and speed is increasing when and have the same sign, and and speed is decreasing when they have different signs. As a practical matter, this is the…
The last BC question on the exams usually concerns sequences and series. The question usually asks students to write a Taylor or Maclaurin series and to answer questions about it and its interval of convergence, or about a related series found by differentiating or integrating. The topics may appear in other free-response questions and in…
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…
The parametric/vector equation questions only concern motion in a plane. In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement…
Any topic in the Course and Exam Description may be the subject of a free-response or multiple-choice question. There are topics that are not asked often enough to be classified as a type of their own. The two topics listed here have been the subject of full free-response questions or major parts of them. Other…
Differential equations are tested every year. The actual solving of the differential equation is usually the main part of the problem, but it is accompanied by a related question such as a slope field or a tangent line approximation. BC students may also be asked to approximate using Euler’s Method. Large parts of the BC…
Tables may be used to test a variety of ideas in calculus including analysis of functions, accumulation, theory and theorems, and position-velocity-acceleration, among others. Numbers and working with numbers is part of the Rule of Four and table problems are one way this is tested. This question often includes an equation in a latter part of the…
Given equations that define a region in the plane students are asked to find its area, the volume of the solid formed when the region is revolved around a line, and/or the region is used as a base of a solid with regular cross-sections. This standard application of the integral has appeared every year since…
