Histogram of the student score distribution

The full grading rubric for quiz 2

Perfect score = 10. Extra credit = 2.

Part 1a (8 points) : vb = v1 ( 1 - v1 / (3 v_infty))

   100 %: practically perfect
    80 %: numerical coefficient error, but the form is good
    75 %: answer is good, but not in the perturbation form
    70 %: perturbation form with incorrect numerical coefficient and
          overall sign error
    70 %: got vb^2, correctly, but did not give vb
    70 %: answer has numerical error and also is not in the perturbation
          form
    60 %: the perturbation correction term has incorrect powers
    60 %: answer is very wrong due to a sign error in the steps, and is not
          in the perturbation form
    60 %: the answer is not finalized, while an approximately correct
          answer is there
    40 %: incorrect dimension, incorrect result
     0 %: answer missing, or completely incorrect

Part 1b.1 (2 points) : h2/h1 = 1 - 4 sqrt{2} alpha / 3, where alpha = k
                       sqrt{h1/g}

   100 %: practically perfect
    90 %: got correct expression, but the perturbation form is cluttered
          with unallowed, and complicating, higher order terms
    85 %: got a nearly correct perturbation expression, but there are
          numerical errors
    80 %: got (nearly) correct expression, but did not turn it into the
          final correct perturbation form, linear in k
    60 %: v2 = vb was used, very incorrectly
    60 %: got a perturbation expression, which is very incorrect
    60 %: got a dimensionally incorrect result
    60 %: answer is not approximately equal to 1
    25 %: correct starting formula, but no or little development from it
     0 %: answer missing, or completely incorrect

Part 1b.2 (2 points) : k = (3 / (4 sqrt(2))) * sqrt (g/h1) * (1 - h2/h1)

   100 %: practically perfect
    90 %: got correct expression, but cluttered with unallowed, and
          complicating, higher order terms
    80 %: got a dimensionally correct result, which is small (correctly),
          but contains numerical errors
    80 %: got a dimensionally correct result, which is small, but did not
          express it as a function of h1, h2
    70 %: the final answer is large, instead of being small
    70 %: got an implicit formula, which is dimensionally correct and could
          have given an almost correct answer if higher order terms were
          ignored
    70 %: dimensionally correct answer, but too small (e.g., second order
          or higher)
    70 %: got a dimensionally correct result, but the form was not
          simplified using perturbation and intermediate steps have error
    70 %: got a dimensionally correct result, but not small (not prop. to
          (1 - h2/h1)) and has numerical errors
    70 %: got a small result, correctly, which is however dimensionally
          incorrect
    60 %: got the final result, but dimensionally incorrect and not small
          (not prop. to (1 - h2/h1))
    50 %: got the final result, dimensionally incorrect, not small, and
          t-dependent
    50 %: got an implicit equation, dimensionally incorrect
    25 %: correct starting formula, but no or little development from it
     0 %: answer missing, or completely incorrect