Scaled average: 80% [2 s.f.]
Scaled standard deviation: 14%
Letter grade distribution:-
Raw average score: 66%
Raw standard deviation: 16%
Raw averages for parts of questions:-
Students generally did well on calculation-focused questions, Q3 on Christoffels/Riemanns and Q4 on the Newtonian limit. They did less well on Q2, which involved straightforward application of familiar rules of tensor calculus to a new situation: upstairs components of the EM field strength tensor. Performance on Q1, which involved explaining concepts, was the worst of all. Perhaps this was because some students did not rehearse answering any conceptual questions in the practice midterm, and/or did not regularly attend lectures where I often provide more conceptual depth or detail than in lecture notes.
Several students commented after the exam that the einbein question was rather unfair. The average raw score on Q1a reflected this. Although I was only expecting broad brushstroke answers (
it handles massless particles and, by recruiting a Lagrange multiplier, produces both the equation of motion and the mass shell constraint), in retrospect I can see how this question could have felt overly intimidating. So I scaled up scores for Q1a (worth 3 marks) separately, using the equation Scaled = Raw/3 + 2 marks. This resulted in a revised raw average of 72.2% for Q1a, which raised the overall Q1 average to 55.3%.
The overall revised median score, computed using the above Q1a scaling correction, was still lower than I wanted. This occurred partly because the class underperformed on the conceptual questions, and partly because the exam was a bit too long. So I added a +10% offset to everyone's revised raw percentage grade, except in two cases where the result would have exceeded 100%.