Rate & Accumulation (Type 1)

For updated information for the special 2020 exams click here. The Free-response Questions There are ten general categories of AP Calculus free-response questions. As I’ve done in part years, I will consider each individually over the next few weeks posting on Tuesdays and Fridays. These will be updates of last year’s posts. A list of all…

Reviewing Resources 2020

For updated information for the special 2020 exams click here. This is a list of links to some resources for reviewing. The 2019 AP Calculus AB and BC Course and Exam Description (CED) The 10 units in this document list which topics may be tested on the exams. The rule of thumb is that is…

AP Exam Review 2020

For updated information for the special 2020 exams click here. It will soon be time to start reviewing for the AP Calculus Exams. So, it’s time to start planning your review. For the next weeks through the beginning of April I will be posting notes for reviewing. There are not new; versions have been posted…

Some Notes

I didn’t come across anything calculusy to write about this week, so here are a few other items you might be interested in. Two Explorations Two explorations previously posted on topics that come up this time of year. Differential Equations. An exploration in Differential Equations is a summary/review exploration in which students will work with…

A Curiosity

Thoughts on the power series for  , which I found curious. Last week someone asked me a question about the Maclaurin series for  .  Finding the Maclaurin series is straightforward:   Substituting for x gives   We can find the radius and interval of convergence by using the Ratio test: This indicates that Maclaurin series…

What’s the “Best” Error Bound?

A know a lot of people like mathematics because there is only one answer, everything is exact. Alas, that’s not really the case. Numbers written as non-terminating decimals are not “exact;” they must be rounded or truncated somewhere. Even things like  and 5/17 may look “exact,” but if you ever had to measure something to…

Good Question 17

A common question in (older?) textbooks is to give students a function or relation and have them graph it without technology (because in the old days technology was not available). Students had to find all the appropriate information without hints or further direction: they were supposed to know what to do and do it. AP…