Problem #1 |
Problem #2 |
Problem #3 |
Problem #4 |
Problem #5 |
Problem #6 |
Problem #7 |
Problem #8 |
Problem #9 |
Total | |
---|---|---|---|---|---|---|---|---|---|---|

Max grade | 12 | 10 | 10 | 12 | 12 | 12 | 12 | 12 | 8 | 99 |

Min grade | 2 | 0 | 0 | 0 | 6 | 0 | 2 | 4 | 0 | 31 |

Mean grade | 9.75 | 5.94 | 5.81 | 7.88 | 10.63 | 7.56 | 10.31 | 10.13 | 5.88 | 73.88 |

Median grade | 11 | 7 | 8 | 9.5 | 12 | 6.5 | 12 | 11 | 8 | 74 |

Numerical grades will be retained for use in computing the final letter grade in the course. Here are approximate letter grade assignments for this exam:

Letter equivalent | A | B+ | B | C+ | C | D | F |
---|---|---|---|---|---|---|---|

Range | [85,100] | [80,84] | [70,79] | [65,69] | [60,64] | [55,59] | [0,54] |

Problem #1 |
Problem #2 |
Problem #3 |
Problem #4 |
Problem #5 |
Problem #6 |
Problem #7 |
Total | |
---|---|---|---|---|---|---|---|---|

Max grade | 15 | 14 | 12 | 16 | 12 | 15 | 16 | 98 |

Min grade | 8 | 10 | 4 | 5 | 4 | 3 | 4 | 51 |

Mean grade | 13.13 | 13.33 | 11.33 | 10.07 | 10 | 10.53 | 14.87 | 83.34 |

Median grade | 14 | 14 | 12 | 8 | 11 | 12 | 16 | 85 |

Numerical grades will be retained for use in computing the final letter grade in the course. Here are approximate letter grade assignments for this exam:

Letter equivalent | A | B+ | B | C+ | C | D | F |
---|---|---|---|---|---|---|---|

Range | [85,100] | [80,84] | [70,79] | [65,69] | [60,64] | [55,59] | [0,54] |

I misstated the point values of problems 1 and 2. I wanted #1 to be worth 15 points and #2 to be worth 14 points. That's a 1 point shift, and that's how I graded the exam.

The Lagrange multiplier problem was difficult to grade. Credit is
difficult to give when logic is not *clearly* shown. I gave 4
points for the setup (the multiplier equations and the constraint
equation). This problem
has many "candidates" for where extreme values can be found. One
collection (the points (+/-1,0,0)) come from setting lambda=0. This
was worth 1 point. The collection (0,0,+/-1) was worth 2 points. The
four candidates with z=0 (where the minimum occurs) was worth 3
points, and the candidates gotten by solving a quadratic (in either x
or the multiplier -- I saw both) were worth another 3 points. I then
gave 2 points for the *correct* answers (which had to be the
values of the function!). Finally, I gave 1 point to the perhaps
subjective evaluation of the logical clarity of the
presentation. Perhaps I should have weighted that more heavily, but
then I'd have to worry about partial credit. A few students did the
problem in a non-routine fashion, and I tried to score their work
consistently with what I described above.

The other non-routine problem was #6, involving Green's Theorem. Here
I also found difficulty in understanding some solutions. There was
sufficient time to *explain* what was written, I believe. Some
students might have lost points because I could not understand their
assertions. I wanted to see explicit mention of how Green's Theorem
was used, including description and evaluation of the "bottom"
integral. I wanted to read some reason that the integrand in the
double integral simplifies greatly.

Problem #1 |
Problem #2 |
Problem #3 |
Problem #4 |
Problem #5 |
Problem #6 |
Problem #7 |
Problem #8 |
Problem #9 |
Problem #10 |
Problem #11 |
Total | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Max grade | 20 | 18 | 18 | 20 | 20 | 16 | 20 | 16 | 16 | 16 | 20 | 198 |

Min grade | 11 | 9 | 0 | 5 | 4 | 7 | 14 | 2 | 0 | 0 | 14 | 100 |

Mean grade | 18.33 | 15.27 | 15.6 | 11.9 | 16.13 | 12.33 | 17.67 | 15 | 7.2 | 10.87 | 19.13 | 159.3 |

Median grade | 20 | 17 | 18 | 10 | 19 | 12 | 20 | 16 | 8 | 12 | 20 | 163 |

Numerical grades will be retained for use in computing the final letter grade in the course. Here are approximate letter grade assignments for this exam:

Letter equivalent | A | B+ | B | C+ | C | D | F |
---|---|---|---|---|---|---|---|

Range | [170,200] | [160,169] | [140,159] | [130,139] | [120,129] | [110,119] | [0,109] |

The problem which was most difficult to grade was #4. I expected this,
because the question had no hints, and, since it used no "calculus"
yet also asked for a creative solution, it generated a very wide
variety of responses. The cosine called for, by the way, is indeed
1/3. I don't know the angle in terms of "standard" angles. I've been
told that methane's molecule (CH_{4}) is a regular
tetrahedron. You may know that there are exactly
**five** regular polyhedra with all faces congruent: these are
called the **Platonic solids**.

The problem whose results surprised me the most was #9, about the chain rule. The chain rule is an important and difficult result in in several variable calculus, and a question about it probably should have been expected on the final. I thought the question I asked was not as difficult as others on the same topic which students in this class were already asked. I found the poor scores on this problem disappointing.

Of course the curvature problem was also non-routine, but most
students did o.k. on it. I tried to apply an unbiased grading scheme,
which is somewhat difficult in such qualitative problems. In #12, the
weird double integral, I wanted some reason that the
sin(x^{3}) term would disapper, and I penalized people a tiny
bit who didn't give a reason or gave a wrong one.

**
Maintained by
greenfie@math.rutgers.edu and last modified 5/16/2003.
**