Exam 1 Grading method

[goodwine]

Grading for Exam 1 was as follows:

Problem 1:
1. For all parts of the problem, I gave +1 if some written attempt was made (just drawing the axes for part c didn't count). +2 or +3 were given beyond this if significant manipulative attempts were made and likewise -1 or -2 for algebraic or simple calculus errors off of the correct solution.

1a. Many got this correct. +5 for the full solution. I gave +3 for recognizing that dV/dt @ t=infinity =0. .

1b. No one got full credit on this one, but some got very close. I gave +3 for recognizing it was nonlinear. Attempting an exact solution yielded +7 with -/+3 points for algebra and calculus errors or significant progress towards the solution. Recognizing that it was separable and integrating was worth +12 points. Trying a constant coefficient solution for homogeneous equations got little more than the +1 participation point.

1c. A good number of those who attempted this got it correct. I gave +5 for a decaying solution, an additional +3 for recognizing the shift in Vterm and +2 for some attempt at showing a different decay. I didn't penalize for drawing on two separate charts or for sparse labeling unless the difference between the two graphs wasn't clear.

Problem 2:
a. 15pts {Correct equation (1); Eigenvalues (5); x_h (2); x_p (2); 3 conditions of \Delta (2); Correct result of x (5)}
b. 10pts (Magnitude, frequency, maximal value; if wrong x, minus 5)
c. 5pts (Magnitude, frequency, maximal value; if wrong x, 0pt)

Problem 3:
3 points each and one free point.

1 point for just matching and 2 points for the justification.
Some people had a justification but no matching, and if it was valid it was worth 1 or 2 points depending on how valid.
Some people didn't match the curves (the just said graph in row 2, col 2, but didn't say solid curve). This was generally one point off if there was evidence that they could have distinguished them but just didn't read the problem correctly.