First Examination Results
Solutions with commentary:
All problems on the exam were related to problems in the suggested exercises. I think everybody should have been able to get at least 17 points on this exam:
- 3 points on Problem 1, because I practically did it in class;
- 4 points on Problem 2, because it is a standard example of the Chinese Remainder Theorem, with a routine solution;
- 3 points on Problem 3, because I did it in class;
- 3 points on Problem 4(a), because it is a standard application of the Euclidean algorithm;
- 4 points on Problem 5, because it is a standard instance of modular arithmetic, if not Fermat's Little Theorem.
The median score on this exam was 17. (That is, as many scored this or more, as scored this or less.)
Column A: ID number, modulo 100,000
Column B: score (out of 30)
A B 26089 25 25974 23 26055 23 79674 23 79773 23 73802 22 26501 22 73323 21 73679 21 26329 21 73005 21 77474 20 73943 20 25719 20 25750 20 25990 20 26063 20 27212 19 27303 19 73133 19 73588 19 76961 19 25933 19 26097 19 26352 19 26386 19 25859 18 26014 18 79559 18 79583 18 73315 17 25925 17 25966 17 26071 17 26436 17 29364 17 27048 16 73356 16 26238 16 20225 15 31313 15 26287 15 29786 15 73174 14 21171 14 73687 13 25883 13 26428 13 73349 12 73638 12 88909 12 26030 12 25768 10 26105 10 26212 10 26519 10 26394 9 40965 9 70669 7 67028 7 77466 5 33973 4 28140 --
