``` Here is how to fiddle the number on the back of your Test 1 paper to get the number I have recorded for you as grade on Test 1 in my grades file: Let x be the number on the back of your test paper. Then y, below, is the number I have recorded for you in my grades file (round to the nearest tenth of a mark): If x ≤ 21, y = 3 + (11/9)(x - 3). If 21 ≤ x, y = 25 + (8/9)(x - 21). Thus, for instance, if the number on the back is 24.3, then the second line above applies, so the fiddled mark is 25 + (8/9)(24.3 - 21) = 8(33) 4(11) 14 25 + ----- = 25 + ----- = 27 + -- , 9(10) 3(5) 15 which, to the nearest tenth, is 27.9. If x is 18 then, since that is less than 21, the first line applies, and y is 3 + (11/9)15 = 3 + 55/3 = 21 + 1/3, which rounds to 21.3. I am fiddling the marks upward mainly because I think I could have done a better job teaching than I have in the course. I also think you folks could have done a better job learning (which keeps me from raising the marks TOO much), but ... what I have or have not done concerns me more than what you have or have not done. The average raw (=unfiddled) score out of 50 was 23.8. 8 people got raw scores of 40 or more. Three of those were over 44. 11 people got raw scores below 10 out of 50. The average of those 11 scores was about 7 out of 50. ```