Exam 1 Data and Grading Methodology

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Grading:

• Problem 1:
  • 10 points for correct general solution. 3 points each for correct methodology for homogeneous and particular solutions. 2 points each for correct math to get answer.
  • 3 points each for parts (a)-(c). For full credit, answer must be supported by the mathematics.
  • 1 free point!
• Problem 2:
  • 10 points for correct solution. Implicit form was ok. 6-7 points for correct method, 3-4 points for right answer.
  • 10 points for graphs, 2-3 points each depending on qualitative accuracy.
• Problem 3:
  • 5 points each for each equation.
  • 3 points for actually using a correct method. 1-2 points for just stating or barely starting.
  • 2 points for right math.
• Problem 4:
  • 8 points each for correct homogeneous and particular solutions. 5 points for method, 3 for math.
  • 4 points for putting them together in general solution.
• Problem 5:
  • 10 points for right method
  • 5 points for right solution
  • 5 points for right graphs

In general there is "double jeopardy" where mistakes early in a problem will result in loss of points later as well; however, it is generally minimal. A computational error early will result in a one point loss at certain milestones in the solution process, e.g., right homogeneous solution but then another point off in general solution. A major qualification to this is that sometimes an early computational error transforms the problem into something completely different, in which case point loss will be greater. An example would be an undetermined coefficients problem where the assumed form of the particular solution is a homogeneous solution also, which must be recognized and action taken. A computational mistake could end up avoiding this complication and while all the work after that point may be correct given the mistake it is much easier and misses the point of the problem.

Data:

1. Average = 74
2. Standard deviation = 15.8
3. Max = 100
4. Min = 32