I think many users were receiving 500 errors yesterday for about 45 minutes.
If you are using New Quizzes you may me able to capture this information by navigating to the "moderate" tab from the quiz building screen (1). Once there, and if the students started the quiz before the outage, you might see (not completely sure) what looks like the quiz is still "in progress" (4). To see what questions have been attempted, and at what time they were attempted, you may view details under "log" (5). I've provided a screen shot (below) of what I think you are after (6).
I'm sorry about this frustrating situation. I hope this helped. Please let me know if you have any further questions, comments, or concerns. The community is always happy to help. Others here may have a better idea than this to assist you:-)
All the very best,