A recent thread on the AP Calculus Community bulletin boards concerned polar equations. One teacher observed that her students do not have a very solid understanding of polar graphs when they get to calculus. I expect this is a common problem. While ideally the polar coordinate system should be a major topic in pre-calculus course,…
Many, perhaps all, of you, are looking at a vastly different teaching situation in the Fall. A teacher wrote to me recently asking if I could describe how he could give several versions of a test on the same material to his online classes and scale them so as to be fair everyone even though…
Why “scaling” is necessary No teacher can make two tests on the same topics equal in difficulty. No two teachers, even if they collaborate, can make two tests on the same topic equal in difficulty. No two teachers in different schools, districts, or states can make two tests on the same subject equal in difficulty.…
I got to thinking about grading the other day after seeing a question on Facebook. We’ll get to that question in a minute, but first I want to try to outline a grading scheme I used towards the end of my teaching career. It is based on how free-response question on AP Calculus exams are…
Some thoughts on pacing and planning your year’s work for AP Calculus AB or BC. The ideas are my own and are only suggestions for you to consider. Almost all textbooks provide an AP pacing guide among their ancillary material. You can consult the guide for your book for specific suggestions for the number of days…
Unit 10 concerns sequences and series. These are BC only topics (CED – 2019 p. 177 – 197). These topics account for about 17 – 18% of questions on the BC exam. Topics 10.1 – 10.2 Timing The suggested time for Unit 9 is about 17 – 18 BC classes of 40 – 50-minutes, this…
Unit 9 includes all the topics listed in the title. These are BC only topics (CED – 2019 p. 163 – 176). These topics account for about 11 – 12% of questions on the BC exam. Comments on Prerequisites: In BC Calculus the work with parametric, vector, and polar equations is somewhat limited. I always…
Unit 7 is an introduction to the initial ideas and easy techniques related to differential equations . (CED – 2019 p. 129 – 142 ). These topics account for about 6 – 12% of questions on the AB exam and 6 – 9% of the BC questions. Topics 7.1 – 7.9 Topic 7.1 Modeling Situations…
I haven’t missed Unit 7! This unit seems to fit more logically after the opening unit on integration (Unit 6). The Course and Exam Description (CED) places Unit 7 Differential Equations before Unit 8 probably because the previous unit ended with techniques of antidifferentiation. My guess is that many teachers will teach Unit 8: Applications…
Unit 6 develops the ideas behind integration, the Fundamental Theorem of Calculus, and Accumulation. (CED – 2019 p. 109 – 128 ). These topics account for about 17 – 20% of questions on the AB exam and 17 – 20% of the BC questions. Topics 6.1 – 6.4 Working up to the FTC Topic 6.1…
Today’s Blog is an exploration that will lead up to the Mean Value Theorem (MVT) and, I hope, help your students better understand the MVT and why it is true. While you may do this by hand, using a graphing calculator will make things way easier. This is good calculator practice and can be done…
Unit 5 covers the application of derivatives to the analysis of functions and graphs. Reasoning and justification of results are also important themes in this unit. (CED – 2019 p. 92 – 107). These topics account for about 15 – 18% of questions on the AB exam and 8 – 11% of the BC questions.…
