Exam 1 grading

[goodwine]

Exam 1: average=76, standard deviation=15.

Here is a histogram of the grades as of October 11, 2006.

• 

Here is a plot of how many homeworks were skipped versus grade on exam 1.

• 

Here is how I graded the problems for exam 1:

Problem 1:

1. If the answer was left with a plus/minus (a function satisfying the differential equation was part of the answer, and one of them satisfied the initial condition): 20 points.
2. If the answer was only in terms of plus sqrt(t) (the function satisfied the differential equation but not the initial condition): 18 points
3. An aswer like sqrt(t) + C, which usually came about by not taking the square root correctly (neither a function satisfying the differential equation nor satisfying the initial condition was provided): 15 points
4. Early computational error giving an incorrect answer: 12 points.

Problem 2:

1. Point allocation: homogeneous solution = 5 points, particular solution = 10 points, plot = 5 points, explain = 5 points.
2. algebra error in undetermined coefficients = -2 points (and then -1 for the incorrect plot)
3. plot the whole solution, not the steady state one: -5 points
4. plot sin instead of cos: -4 pints
5. Yes instead of no: -5 points.

Problem 3:

1. Ignoring the constant term in inhomogeneous term: -7 points
2. wrong assumption for undetermined coefficients: -10 points
3. putting an omega inside particular solution (and leaving it there): -7 points
4. tried incorrectly to use graphs, but still ignored the constatant term: -10
   points
5. messed up substituting into a standard form: -8 points
6. algebra errors: -2 points

Problem 4:

1. no constants in general solution: -1 point
2. using constants in incorrect manner: -2 points
3. part e) including a t exp(t) term instead of exp(-t): -2 points
4. parts g) and h) algebra errors: -1 point
5. parts g) and h) no t sin(t) term from particular solution: -2 points
6. part i) 1 point each for each correct term.