Math 135:52--54 Fall 2001


  1. This section is not currently selected to use WeBWorK.
  2. The first midterm exam was held on Friday, October 12. There are Observations made during grading.
  3. The second midterm exam was held on Friday, November 16 in the regular lecture room. As with the first exam, the exam was in two parts: a short part to be done without calculators, and a longer part in which calculators may be used.
  4. The final exam was held at the Math Group time Monday, Dec. 17, 4 - 7 PM in FS-AUD.
  5. The exam was graded on Tuesday, December 18 and grades submitted electronically on Wednesday, December 19. There is evidence that grades were available through the usual University channels by the end of the week. There were guidelines that aimed for uniform grading for all sections of the course, so the distribution of grades on the final exam was reflected in the grades for the course.
  6. The grade distribution was set by the department based on the distribution of final exam grades for the whole course. If you have any questions about the grading of the exam, you are encouraged to review the graded exam. The exams for this lecture section will be on file in the lecturer's office, Room 438 in Hill Center on Busch Campus for one year.

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Exams and grades.

A total of all graded work (midterms, graded homework and quizzes, and final exam) will be used to produce a ranking of the class, so that I will know who has the (for example) twentyninth best score in the class. To arrive at the letter grades for the course, letter grades will be assigned on the common final exam and the number of scores with each grade on the exam in each lecture section will equal (up to a small adjustment) the number of that letter grade that will be assigned in that lecture section. Any projection of grades on midterm exams is based on a guess about both the quality of the work relative to the historical standards of the course and the distribution of grades in the course.

For the first exam, there were two parts: part A dealt with the use of differentiation formulas from memory, with no formula sheet or calculator available; part B gave a survey of all topics met so far in the course, allowing both formula sheet and calculator to aid in solving the problems. A scatter plot, with a trend line, is included to show the relation between these two parts of the score. There are also two tables giving information about grades on the exam. In the table of problem averages, scaling means that the raw score has been multiplied by 10 over the maximum score allowed for the problem to allow easy comparison between problems by treating them as if each problem was scored on a basis of 10 points. The other table shows clusters of grades with an estimated equivalence to letter grades. The scores shown were actually attained, so there are usually gaps between the clusters. In some case, grades are combined to avoid giving the impression that a single point on the exam makes a difference between different letter grades. These grades are only projections, but a grade lower than expected indicates a need for more effective preparation for the exams.

scatter plot of grades
Exam 1
Prob. # Scaled Avg.
A1 9.20
A2 9.04
A3 7.05
B1 7.88
B2 5.22
B3 7.97
B4 9.03
B5 5.97
B6 5.56
B7 4.60
Grade Range Count
A 91-95 10
B and B+ 80-89 20
C+ 76-78 9
C 65-73 13
D 42-59 17
F 23-37 9

The averages on the two parts of the exam were 17.01 out of 20 on Part A and 51.53 out of 80 on Part B for a combined average of 68.54.

scatter plot of grades
Exam 2
Prob. # Scaled Avg.
A1 2.08
A2 7.63
A3 6.85
A4 7.39
A5 6.67
B1 7.92
B2 5.39
B3 6.94
B4 5.52
B5 7.79
B6 4.47
B7 6.08
Grade Range Count
A 85-99 9
B+ 74-82 10
B 71-72 6
C+ 64-68 11
C 49-62 21
D 40-47 11
F 20-38 7

The scatter plot compares the scores on the two midterm exams.

The averages on the two parts of the exam were 15.31 out of 25 on part A and 46.2 out of 75 on part B for a combined average of 61.51.

When exams were returned on November 21, there were some comments that one point was lost on problem A5 if results were not expressed as a single decimal number. However, no such requirement was announced and the presentation of similar problems at the review session did not include such a step. Since this is a widespread problem with grading, it will be assumed that all grades of 4 on this problem had this cause and they will be raised to 5 in the course records with an individual review. However, the original grades will continue to be used in the tables and graphs on this page.

scatter plot of grades Some more scatter plots were prepared to show the relation between different components of the grade: (1) Homework versus quizzes; (2) recitation work versus midterm exams; (3) recitation work versus final exam; (4)midterm exams versus final exam. All show that all components of the grade are well correlated, that is, doing well in one suggests that you will do well in all. We like to believe that this means that all parts of the grade measure the effort you put into mastering the subject, and that regular work is the best preparation for exams. Although the weighting of these parts seems to make little difference in determining class rank, one formula needed to be chosen. Class rank was determined using 50 points for homework, 50 points for quizzes, 100 points for each midterm and 200 points for the final. Course coordination policy required that course grades be distributed in the same way as final exam grades, with slight adjustments allowed to avoid splitting clusters of grades. This led to this section having a concentration of grades of B although the whole course had a more even distribution of grades (except that the grade of D is used rarely in mathematics courses).
scatter plot of grades In addition to grade distribution, a table of scaled averages for each problem is available. Version A had the white cover; version B had the green cover; version C had the blue cover; and versin D had the yellow cover.
Final Exam
Prob. # Scaled Avg.
A1, B10, C7, D14, 5.77
A2, B11, C8, D15 6.53
A3, B12, C9, D16 6.92
A4, B13, C10, D17 6.95
A5, B14, C11, D18 7.66
A6, B15, C12, D19 6.30
A7, B16, C13, D1 6.03
A8, B17, C14, D2 8.38
A9, B18, C15, D3 5.89
A10, B19, C16, D4 6.95
A11, B1, C17, D5 6.83
A12, B2, C18, D6 6.21
A13, B3, C19, D7 5.76
A14, B4, C1, D8 8.16
A15, B5, C2, D9 6.47
A16, B6, C3, D10 2.27
A17, B7, C4, D11 4.62
A18, B8, C5, D12 7.04
A19, B9, C6, D13 6.92
EC 0.88
Grade Range Count
A 175-200 7
B+ 160-174 11
B 140-159 21
C+ 125-139 4
C 100-124 8
D 90-99 2
F 0-89 18
No Exam 11

scatter plot of grades scatter plot of grades

Copies of slides shown in lecture.

They are in two formats: the viewing format has two slides per page, and the printing format has four slides per page. Some typographical errors may remain in these files. Since the material is typeset, it would be necessary to recreate them from the source to make these corrections, but the tools for doing this or on my home computer, so there may be some delay in making corrections. The survey of handwritten slides was produced only for viewing.

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Last updated: December 21, 2001