Test 2 results

The results for this test were eerily like those for the first midterm. The median is a bit higher because some people who should not have been in the course have departed, so fewer scores lower than 50 were recorded.
Preliminary results for the first test: the median score was 78. The grade distribution was as follows:

90-100: 50
80-89: 45
70-79: 43
60-69: 36
50-59: 23
Below 50: 24

If you have any questions about grading on this test, they must be submitted by Friday 10 November. You may give the test paper to your TA who will forward it for regrading to the TA who graded that particular question.

(Pre-test information)

The second test will cover the material in Chapter 9 and sections 1,2 and 3 of Chapter 10. Approximately 60% of the test will involve basic setup and calculation of various integrals relating to area, arc length and surface area of surfaces of revolution with polar and parametric equations, lines tangent to graphs of polar and parametric equations, and also basic limits of sequences. The remaining 40% may contain more advanced calculation or a derivation.

Basic Calculations

Basic calculations represent a minimal level of calculational competency. For integrals relating to area, arc length and surface area of surfaces of revolution with polar and parametric equations this means the ability to set up the integral correctly, especially determining the limits of integration. This usually requires the ability to draw a sketch which shows the relationship among the curves involved. I expect you to be able to sketch quickly the graphs of the standard limacons (especially cardioids), circles, cycloids, lemniscates and "roses" which we have discussed as well as the standard Archimedean and exponential spirals. While I might or might not ask questions specifically on graphing, you should understand that the ability to graph these objects may well be necessary to set up the questions which I do ask. Practice with the VANDER polar graphing module if you need the exercise. Derivations you might be expected to know include the derivation of the formula for arc length in polar coordinates from the parametric version. You can expect to see questions asking you to set up integrals for arc length in both polar and parametric settings, and area of surface of revolution of a parametrically presnted curve. Also, Area inside and between polar curves will be on the test. You will have to evaluate at least one of these integrals. A list of trigonometric formulas will be provided; PDF or PostScript