First of nine. One of the things many successful AP Calculus teachers do is to use past AP exam questions throughout the year. Individual multiple-choice exam questions are used as the topics they test are taught; free-response questions are adapted and expanded. There are several ways to do this: Assign parts of a free-response (FR)…
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…
I hope you have all either completed your year or are close to it. Take some time to relax. I am working on a series of nine summer post which will be begin on Tuesdays starting June 22. Each will look at one of the nine 2021 free-response questions. I will not be presenting their…
Or is it more like a month? Either way the time has come; all that work is about to finish. Hope you can look back on a good year of teaching, even though it was very different. Good Luck to your students.
For years, there have been various lists of the most common mistakes on the AP Calculus exams. This one was originally drawn up by the late Ben Cornelius. Larry Peterson added some comments and posted it to the AP Calculus Community bulletin board a few days ago. Both Ben and Larry are long time AP…
A Little Calculus is an app for iPad and iPhones. While I don’t usually do product reviews, I think this one is so good that I am making an exception. There are many good websites that illustrate calculus concepts. Many of them, however, do not allow teachers to enter their own examples; they must use…
A few days ago, a reader asked if you could find the location of horizontal asymptotes from the derivative of a function. The answer, alas, is no. You can determine that a function has a horizontal asymptote from its derivative, but not where it is. This is because a function and its many possible vertical…
About this time of year, I have been posting notes on reviewing and on the ten types of problems that usually appear on the AP Calculus Exams AB and BC. Since the types do not change, I am posting all the links below. They are only slightly revised from last year. You can also find…
Looking at the graphs of polar curves can be quite fascinating. Doing “calculus” kinds of things is different, yet the same as in Cartesian coordinates. A discussion on the AP Calculus Community here got me thinking about extreme values of polar functions. The terms maximum and minimum here refers to the value of r(θ) which…
