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…

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…

Polar Equations

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…

Getting Ready

Today we continue to look at some previous posts that I hope will help you and your students throughout the year. We begin with some posts on graphing calculator use and then a few general things in three posts on beginning the year, followed by some mathematics I hope students know before they start studying…

Amortization

This is an example of how sequences and series are used in “real life.”  It could be used in a calculus class or an advanced math class. When you borrow money to buy a house or a car you are making a kind of loan called a mortgage. Paying off the loan is called amortizing…

Extremes without Calculus

There was an interesting question last week on the AP Calculus Community Bulletin Board. A teacher was working with polynomial functions in her pre-calculus class and the class had learned how to find the roots, and how the roots and their multiplicities affected the graph. Her question was whether there is a way to determine…