First, the distribution of scores. No one got 7 or 8 out of 8, and someone got counted twice since there were 104 exams but we have 105 scores.
The average was 2.7 and the median 3.
The grading was a bit harsh because if the numerical answer wasn't exactly right, it was checked wrong. Since this is for me for other purposes, that will be sorted out later. In particular, I'll have 3 levels for the arithmetic problems, 0 = clueless, 1 = knows how to do it but goofed, 2 = got it right. Depending on what people did, I might have another category: people who didn't know how to do it but got it right anyway.
score 8 0
score 7 0
score 6 11
score 5 16
score 4 12
score 3 30
score 2 19
score 1 16
score 0 1
Notice the dip at 4. I won't be analyzing these until after the course is over, but I would not be surprised if these scores fairly accurately predict your grade in the course. That's one of the things I'm curious about.
It is clear that the score 5 and 6 group is distinct from the score 2 and 3 group. These are problems that all of you should be able to work, so you should think about that. I was more than a little surprised that there were no 7s or 8s.
For anyone who wants to try their hand at the exam before they see the solutions, here it is.
The solutions. I mentioned that the last problem, # 8, was not on a college admissions test in China, but on a high school admissions test. My mistake. In my solutions, I used calculus, which was cheating, so here is a "simple" algebra solution.