2019 CED – Unit 2: Differentiation: Definition and Fundamental Properties.

Unit 2 contains topics rates of change, difference quotients, and the definition of the derivative (CED – 2019 p. 51 – 66). These topics account for about 10 – 12% of questions on the AB exam and 4 – 7% of the BC questions. Topics 2.1 – 2.4: Introducing and Defining the Derivative  Topic 2.1:…

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Did He, or Didn’t He?

Since it’s soon time to start derivatives, today we look at one way people found maximums and minimums before calculus was invented. Pierre de Fermat (1607 – 1655) was a French lawyer. His hobby, so to speak, was mathematics. He is considered one of the people who built the foundations of calculus. Along with Descartes,…

Limit of Composite Functions

Recently, a number of questions about the limit of composite functions have been discussed on the AP Calculus Community bulletin board and also on the AP Calc TEACHERS – AB/BC Facebook page. The theorem that we would like to apply in these cases is this: If f is continuous at b and , then .…

Infinite Musings

Students get confused about infinity, , because they think of it as a number, because used like a number. Even though they know there is no largest number, they think of infinity as the largest number. In studying limits, the starting point of calculus, infinite limits come up early on. We tell them . But…

Getting Started

As you get ready to start school, here are some thoughts on the first week in AP Calculus. I looked back recently at some of the “first week of school” advice I offered in the past. Here’s a quick (actually, a bit longer then I planned) summary with some new ideas. The last time I…

Optimization – Reflections

First, a new resource has been added to the resource page.  An index of all free-response questions from 1971 – 2018 listed by major topics. These were researched by by Kalpana Kanwar a teacher at Wisconsin Heights High School. Thank you Kalpana! They include precalculus topics that were tested on the exams before 1998. These…