Teaching Limits So That Students Will Understand Limits
The PowerPoint slides from my presentation at the Advanced Placement Annual Conference July 19, 2008 in Seattle, Washington. There are also two Winplot files that illustrate the meaning of the delta-epsilon definition of limit: A linear function and a quadratic.
The talk is based on my book Understand Limits.
AP* Calculus Free-response Type Questions
A guide to the AP Calculus free-response questions. Includes tables indexing each type by year and question numbers. Updated for the 2008 Operational and Form B exams.
Explorations for teachers to guide you in the analysis of the free-response "type" questions on the AP* Calculus exams. Each includes an annotated guide to specific questions from 1998 - present. These are explorations for teachers
Power Series
The slides and the handout from a presentation given in February 2004, at the College Board Math Specialty Conference. These were requested by the participants at a recent BC Calculus one-day workshop.
SLOPE FIELDS An online presentation archived at AP Central on Slope Fields. Scroll down the page, it is near the bottom. Also there is a brief presentation on using Winplot with slope fields and a handout as well. (The other online presentations here are also good.) Winplot video for slope fields
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 flash cards 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.
Article
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.
Article
GOING UP by Lin McMullin. A discussion of increasing and decreasing functions and the common misunderstandings about them. This article 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].
Article
IMPROPER INTEGRALS AND PROPER AREAS by Lin McMullin A students question about improper integrals and the range of the Arctangent function.
Article
AP CALCULUS CURRICULUM SURVEY (2004) A survey of 169 college and university calculus programs with point by point comparison to the AP Calculus course description.
Article
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.
Article
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.
Article
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.
Article
ADAPTING AP MATHEMATICS QUESTIONS AS A PRE- AP STATEGY 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.
Book
TEACHING AP CALCULUS by Lin McMullin. A guide and resource book for AP calculus teachers. Second Edition.
Chapters on preparing to teach the courses, the topics and hints on teaching them, the exam, and activities. This is
based on what I cover in my one-week summer institutes.
Questions of the Month
From AP Central.
1. Learning from Mistakes - Cylindrical Shells (May 2003) The solution has disappeared from AP Central. Click here for the solution.
* 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
Lin McMullin
Educational Consultant
Handouts from various AP* Calculus workshops and institutes
& Articles that may be of interest to calculus teachers.
