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…

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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…

Tuesday and Beyond

So, Tuesday is the day. My usual suggestion for Monday is to get the kids both relaxed and psyched. They know it by now; not much more you can pour into their heads. So, not last minute advice or hints. Good Luck and best wishes. Looking ahead – May: the new Course and Exam Description for…

AP Exam Review Posts

Here are the links to the various review post for this year. Tuesday February 27 – AP Exam Review Friday, March 2 – Resources for reviewing Tuesday March 6 – Type 1 questions – Rate and accumulation questions Friday March 9 – Type 2 questions – Linear motion problems Tuesday March 13 – Type 3…

Type 9: Polar Equation Questions

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 with calculus ideas related to polar curves. Students have not been asked to know the names of the various curves (rose curves, limaçons, etc.). The graphs are usually…