Calculus 1 -- Fall 2017

Results for Exam 1

The class did an excellent job on exam 1.

The histogram below shows all of the scores (rounded to the nearest whole number, with scores ending in .5 rounded up)  for the first exam. It shows, for example, that one student earned the top score of 97, and that five students (almost a third of the class) scored at or above 95.    Almost all of the students are on track to earn a course grade of B- or better at this point.  You can find your individual score posted on Blackboard.  Contact me if you need assistance accessing that. PLEASE review the score posted for you on blackboard and confirm that it is the same as what appears on your exam paper. If they are not the same, let me know.  Also, double check that your total for the exam has been added up correctly.  I am very careful totalling and recording scores, but errors sometimes occur.

exam 1 histogram

If you are dissatisfied with your performance on the exam, please make an appointment to see me.  I may be able to suggest ways to make your preparations more effective for the remaining exams.  And I am open to any suggestions about how I can make the course more supportive of your efforts.

Grading Comments. 

  1. In general, partial credit was awarded so that an A answer would receive at least 90% of the points, a B answer at least 80%, and so on.  For any question on which you received less than 70% of the credit, I am signaling an unsatisfactory response.  With less than 60% of the credit I am signalling a "failing" response.

  2. Multiple Choice.  These items were marked treating each option for each problem as a true/false item.  One mark of x was deducted for each item incorrectly circled, or incorrectly left uncircled.  Each x corresponds to a deduction of .75 on the score.  At the beginning of problem 1, the total number of x marks and the total score for probs 1-5 is shown. 

    Although you can tell for each problem how many x's were marked, I deliberately did NOT indicate which items were correct or incorrect.  In working on exam solutions, I want students to have something to think about on these items.

  3. In many cases students did not follow the directions in the problem statement.  For example, problem 6 calls for exact answers, and for an indication of the rules being used.  Most students did not meet one or both of these requirements.  On problem 7, items asked about specific marked points, but several students responded to one or more items by listing intervals.  I did not deduct much for such lapses on this exam, if I thought the answer demonstrated understanding of the concept being tested, but don't count on that for future exams.  To maximize your score, read the directions carefully, and follow the instructions.

  4. While grading the exams, I realized that problem 7g  involves a subtlety that we did not cover in class.  Although the graph is clearly concave up at point B that does not necessarily imply that the second derivative is positive.  It is certainly the case that the second derivative must be greater than or equal to 0, if it exists at all.  But from the given information, you cannot tell whether the second derivative is positive, zero, or undefined.  This can be seen in examples of the form y = |x|r where r is close to 2.  For r < 2 the second derivative does not exist at x = 0; for r = 2 the second derivative is 2 (so > 0) at x = 0; and for r > 2 the second derivative is zero at x = 0.  But all three of these functions have a smooth u shaped graph with its bottom point at x = 0.  You can verify these comments by graphing them on desmos, say with r = 1.8 or 2 or 2.2.  Use the equations f (x) = |x|2.2y = f '(x), and y = f ''(x) to see graphs of the function and the first two derivatives, for example.

    The fact is, I was sloppy in my thinking when I wrote the exam, and assumed (as almost all the students assumed) that the concavity at point B implies a positive second derivative.  Full credit was given for that answer, because it is an easy error to make.  But having discovered my error, I wanted to share it with the class.  It helps remind us that calculus involves subtleties, and that we have to pay close attention to the details of the theorems and other conclusions stated in the text.