This a re-post and update of the first in a series of posts from last year. It contains links to posts on this blog about the topics of limits and continuity for your reference in planning. Other updated post on the 2019 CED will come throughout the year, hopefully, a few weeks before you get…
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…
In one of my math classes – it may have been calculus – many decades ago, we started by determining what kind of functions we were going to study. A good part of the answer was continuous functions. Looking closely, you will find that almost all the theorems in beginning calculus require that the function…
Summertime and the living is easy, or so they sing. The school year is over, quite a year as it turned out. Looking ahead I do not plan on a lot of posts for the blog. I am going to do a little more reorganization to make things easier to find. In August I will…
While calculus teachers are concerned with the new format of this year’s AP Calculus exams, there is other testing that is important now: tests for disease. Today’s post is not about calculus; mathematically, it is about conditional probability. In the big picture, it is about tests for disease and their accuracy. . No test for…
Here is the latest information on the 2020 AP Calculus Exams as of April 3, 2020. Updated 4/29/2020 Update: A message from the AP Program 4/28/2020 Subject: How to Prepare Your Students for the 2020 AP Exams Dear Colleagues, Additional information is now available to help guide you and your students through the exam day experience.…
For updated information for the special 2020 exams click here. AP Questions Type 10: Sequences and Series (BC Only) The last BC question on the exams usually concerns sequences and series. The question may ask students to write a Taylor or Maclaurin series and to answer questions about it and its interval of convergence, or…
AP Questions Type 9: Polar Equations (BC Only) 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 only with calculus ideas related to polar curves. Students have not been asked to know the names of the various…
AP Questions Type 8: Parametric and Vector Equations (BC Only) The parametric/vector equation questions only concern motion in a plane. Other topics, such as dot product and cross product, are not tested. 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…
