This blog post describes a lesson that investigates some ideas about sequences that are not stressed in the AP Calculus curriculum. The lesson could be an introduction to sequences. I think the lesson would work in an Algebra I course and is certainly suitable for a pre-calculus course. The investigation is of irrational numbers and…
In March, I attending a training session given by the College Board on the new 2019 AP Calculus Course and Exam Description (2019 CED). I was impressed by the copious other materials the College Board had prepared for the roll-out that will be available at summer institutes. Among these was the Mathematical Practices. The MPACs…
The new 2019 AP Calculus AB and BC Course and Exam Description is now available. New and experienced AP Calculus teachers should download a copy and read it carefully. (A paper copy with binder can be ordered here – it’s FREE.) The main sections of the book are here with notes on each. Part 1: General…
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…
Existence Theorems An existence theorem is a theorem that says, if the hypotheses are met, that something, usually a number, must exist. For example, the Mean Value Theorem is an existence theorem: If a function f is defined on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists…
College Board Prerequisites Whenever I led a calculus workshop or APSI, I always spent a little time discussing the prerequisites for AP Calculus. Unfortunately, in some schools AP Calculus is a course for only the talented and little time is spent aligning the mathematics program and courses from 7th grade on so that more students…
The new Course and Exam Description for AP Calculus AB & BC (CED 2019) effective for the coming school year has been published and is available electronically at the course homepages. The direct link is https://apcentral.collegeboard.org/pdf/ap-calculus-ab-bc-course-and-exam-description-0.pdf?course=ap-calculus-ab This document is for both AB and BC courses. There will be no change in the exam style and…
So, Tuesday is the day. My usual suggestion for Monday is to get the kids both relaxed and psyched. They know it by now; not much more you can pour into their heads. So, not last minute advice or hints. Good Luck and best wishes. Looking ahead – May: the new Course and Exam Description for…
Here are the links to the various review post for this year. Tuesday February 27 – AP Exam Review Friday, March 2 – Resources for reviewing Tuesday March 6 – Type 1 questions – Rate and accumulation questions Friday March 9 – Type 2 questions – Linear motion problems Tuesday March 13 – Type 3…
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…
