In conjunction with the on-line gateway testing, we are developing a tutorial system to help with the development of the skills that are being tested. In particular, for the math 115 derivative gateway, we have a prototype system that is connected to the on-line practice tests (or, if you're not in a section using the on-line gateway, this practice test). This page explains how to use this tutorial.
To enter the tutorial system, take a practice test (as noted above). When you're done, for any problem you get wrong, you will see a comment similar to that shown in the figure below.
In this example there is only one rule being used (the chain rule). When there are multiple parts to the derivative (e.g., when the problem is the derivative of a sum) there will be more than one link, the first to explain the whole problem and each one after that to explain the subsequent terms in the derivative. These links take you into the tutorial system.
Once you've entered the tutorial system, you'll be going through a series of explanation pages linked to additional practice problems. A sample page (obtained by clicking the link shown in the figure above) is shown in the figure below.
This tells you what rule is being used for the expression, and why,
and then works out the derivative. At the bottom of the page are a
series of navigation links to allow you to move around the system, as
shown in the figure to the right (not all of the links shown will
appear on all pages). These are:
If you have any questions about the tutorial system, encounter errors when using it, or have suggestions for its improvement, please e-mail Gavin LaRose (glarose@umich.edu). Thanks!