Calculus

These links are from my old website. Some of the material may be outdated, but most is still of interest.

AP* Calculus Free-response Type Questions (1998 – 2014)

A guide to the AP Calculus free-response questions. Includes tables indexing each type by year and question numbers. Updated to include the 2014 Exams.

The Writing Questions on the AP Calculus Exams 

Full Handout and PowerPoint Slides (.pptx)

The Ubiquitous Particle Motion Problem 

My presentation at the 2013 NCTM Annual Meeting, April 19,2013 in Denver Colorado

Full Handout  Answers to Velocity Game
PowerPoint Slides

Accumulation and Functions Defined by Integrals

My presentation at the 2011 NCTM Annual meeting, April 15, 2011 in Indianapolis, Indiana and for the webinar for Calculus for AP* by Rogawski and Cannon, December 5, 2102

Handout
PowerPoint Slides

Here’s the Graph of the Derivative … Tell me about the Function

Presentation from NCTM Annual Meeting, April 2012, Philadelphia, PA.and webinar for Calculus for AP* by Rogawski and Cannon, February 15, 2012
Main Handout
PowerPoint Slides (.pptx)

Thoughts on the AP Free-response questions and Pacing :

A Discussion of the 2011 AP Calculus free-response questions and where the concepts tested appear and, more importantly, do not appear in textbooks. Implications for pacing. The ideas here apply to all AP Calculus exams.

Some thought on Pacing for AP Calculus based in part on the discussion above.

Teaching Limits So That Students Will Understand Limits

My presentation at the National Conference of Teachers of Mathematics Annual Conference April 22, 2010 in San Diego, California. The talk is based on my book Understand Limits (c) 2007 People Education ISBN 978-1-4138-1943-4 (out of print)

PowerPoint slides (.pptx)

Power Series

A presentation given in February 2004, at the College Board Math Specialty Conference.

Power Series Slides (.pdf)

Power Series Handout

Slope Fields 

Handout from an online presentation given at AP Central.

AB Calculus Summer Institute Questions

Questions used and discussed in class in my 2007 AB and BC Calculus one-week summer institutes.

Painting a Sphere

A variation on related rates leads to an accumulation problem. Click here for this article from my book Teaching AP Calculus

Flash Cards

Two sets of flashcards for practice with calculus concepts by Dixie Ross and Scott Pass. Set 1 and Set 2

Applets

A great set of applets by Thomas S. Downey that illustrate over six dozen of the main ideas of calculus. Each applet has detailed instructions. No special software is required. Click here.

Calculus the Musical

No kidding. Songs about Calculus. Click here.

Newsletter

NCAAPMT Newsletter: Two issues per year. The summer issue contains detailed information on each of
the free-response questions (Calculus, Statistics and Computer Science): how the points were divided, how students
did, common mistakes, and much more.

Various Articles 

THE AP CLACULUS EXAM: HOW NOT ONLY TO SURVIVE, BUT TO PREVAIL by Lin McMullin Advice for your students (and you) on how to prepare and review for the AP* Calculus Exams.

GOING UP by Lin McMullin. A discussion of increasing and decreasing functions and the common misunderstandings about them. This article (link missing) by Louis A. Talman shows that if f is a function given continuous on a closed interval [a, b] and increasing in the open interval (a, b), then f must be increasing on the closed interval [a, b].

IMPROPER INTEGRALS AND PROPER AREAS by Lin McMullin A student’s question about improper integrals and the range of the Arctangent function.

Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States A report by the American Mathematical Society (2000). See especially Chapter 5 on technology use Calculus I and II courses.

THE CHANGING FACE OF CALCULUS by David M Bressoud Part 1: First Semester Calculus as a high school course and Part II: First- and Second – Semester Calculus as College Courses.

ASSESSING TRUE ACADEMIC SUCCESS: THE NEXT FRONTIER OF REFORM by Dan Kennedy. An
excellent article not only relevant to Calculus but to all mathematics courses.

ADAPTING AP MATHEMATICS QUESTIONS AS A PRE- AP STRATEGY by Dixie Ross. One thing you can
do to prepare your students, starting before Algebra 1 and continuing through their precalculus course is to adapt AP free-response questions to the skills students are presently learning. This article explains so of the techniques you can use and links to actual examples.

Taylor Gibson’s simulation of the “Most Triangles are Obtuse” activity.Warning: This is a Java applet and may not run in a Chrome browser; try Internet Explorer or Firefox.

Questions of the Month

Questions I wrote for AP Central

1. Learning from Mistakes – Cylindrical Shells (May 2003) The solution has disappeared from AP Central. Click here for the solution.

2. Neighborhoods of Infinity (June 2003)

3. Calculus with Compass and Straight Edge? (July 2003)

4. My Favorite Function (August 2003)

5. Is There Anything Remaining from the Remainder Theorem? (September 2003)

6. What’s Normal for a Quadratic? (October 2003)

7. Fun Investigations with a CAS – Third Degree Polynomials Part I (November 2003)

8. Fun Investigations with a CAS – Third Degree Polynomials Part II (December 2003)

* AP and Advanced Placement Program are registered trademarks of The College Board, which was not involved in the production of and does not endorse any of the material here except those actually linked to AP Central

 

 

 

 

 

 

 

 

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