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…

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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…

A Lesson on Sequences

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…

Then there is this – Existence Theorems

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…

AP Calculus Prerequisites

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…