R = -0.322, S = -0.3 (blue) and S = +0.3 (green) and their derivatives (orange and   xxx  15 Revolutions

Roulettes and Art – 1

For the last few post we have been exploring roulettes using the roulette generator (RG) for either Winplot or Geometer’s Sketchpad. These files use the equations      The derivative is given by the equations Notice that the derivative is also a form of roulette. To generate various roulettes by changing the values of R…

“Easier” Exams

There were two questions posted recently on the AP Calculus Community bulletin board. One teacher was concerned that his students took two different forms of the Calculus exam and the means were not the same. He felt that one group has an easier time than the other. The other writer noted that on his (physics)…

Epicycloid with velocity vectors

Roulettes and Calculus

Roulettes – 5: Calculus Considerations. In the first post of this series Roulette Generators (RG) are explained. Here are the files for Winplot or Geometer’s Sketchpad. Use them to quickly see the graphs of these curves by adjusting one or two parameters. While writing this series of posts I was intrigued by the cusps that appear in some of the curves.…

Your AP IPR

The AP Instructional Planning Report, IPR, is available today from your audit website, the same place you found your students’ scores. While we all like to see how or students performed individually on the AP exams, the IPR may be of more use to you. It will help you learn where the strengths and weaknesses…