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 these topics using the tools of algebra, calculus, and technology to fully investigate a function and to find all its foibles.

    • Finding the general solution of the differential equation by separating the variables
    • Checking the solution by substitution
    • Using a graphing utility to explore the solutions for all values of the constant of integration, C
    • Finding the solutions’ horizontal and vertical asymptotes
    • Finding several particular solutions
    • Finding the domains of the particular solutions
    • Finding the extreme value of all solutions in terms of C
    • Finding the second derivative (implicit differentiation)
    • Considering concavity
    • Investigating a special case or two


A Lesson on Sequences was originally posted last July. The lesson explores sequences and the Completeness Axiom. Parts of it could work for an Algebra 1 class studying Irrational numbers and all of it could be used as an introductory lesson on sequences in calculus.

If you use either or both of these, I’d like to hear about how they went. Please use to Comment button at the end of any post to share your experiences.

AP Calculus Panel Discussion

The AP Calculus panel discussion at the NCTM Annual Meeting in Chicago will take place on April 2, 2020 from 3:00 to 5:30 pm CST in room #E253d of the McCormick Place – Lakeside Center.

The speakers will include:

Julie Clarke, chief reader.

Stephanie Ogden, director, AP Calculus for the College Board.

Mary Wiltjer, Long time AP Calculus teacher and (fairly) new reader.

Lin McMullin, AP Calculus Community moderator and your host.

The main topic will be the scoring of the 2019 AP Calculus exams. There will be time for your questions for the panel. There will be a raffle. The event is sponsored by Bedford, Freeman and Worth publisher of AP Calculus textbooks, and D & S Marketing Systems, Inc. publishers of review books for AP subjects.

Hope you can make it.

Posts on reviewing for the AP Calculus Exams

I have revised and updated the series of posts on reviewing for the exams that I post each year. This series of 12 posts will appear on Tuesdays and Fridays starting February 25, 2020, ending in the beginning of April. These include the 10 “type” questions that appear on the free-response sections with suggestions on what and how to review them. You’re not behind schedule: most classes begin reviewing in April. These are posted before then, so you’ll have time to use them for planning ahead of time.

Tuesday February 25, 2020 – AP Exam Review
Friday, February 28, 2020 – Resources for reviewing
Tuesday March 3, 2020: Rate and accumulation questions (Type 1)
Friday March 6, 2020: Linear motion problems (Type 2)
Tuesday March 10, 2020: Graph analysis problems (Type 3)
Friday March 13, 2020: Area and volume problems (Type 4)
Tuesday March 17, 2020: Table and Riemann sum questions (Type 5)
Friday March 20, 2020: Differential equation questions (Type 6)
Tuesday March 24, 2020: Other questions (Type 7)
Friday March 27, 2020: Parametric and vector questions (Type 8) BC topic
Tuesday March 31, 2020: Polar equations questions (Type 9) BC Topic
Friday April 3, 2020: Sequences and Series questions (Type 10) BC Topic

Quanta Magazine

Quanta Magazine is an online magazine that has articles on Physics. Mathematics, Biology, and Computer Science. The articles are interesting and timely. There are always a few articles on mathematics and many on the other subjects include mathematics.

They also publish a podcast.  A new puzzle appears bi-monthly.

You may subscribe to a weekly e-mail with links to current articles. (While all I need is another e-mail, getting this one reminds me to read the magazine so I don’t forget this great resource.)

You and your students may find Quanta interesting.









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