i pointed out that spherιcal cοordinates would work just as well, though maybe not in the most intuitive way. so the students actually have several options at their disposal.
subsequently, it occurred to me that there was another way.
as i was grading the midterms earlier this week, a student demonstrated (correctly) that rectangular coοrdinates work perfectly well.
on a less happy note, most students didn't get the cylindrιcal coοrdinates right, after all. a few students tried spherιcal coοrdinates, to no success.
so yes, maybe i should have listened to my TAs.
oh well. at least the average (71.4%) was higher than the first midterm i had last term (55%). maybe i won't have as many panicked students, this time.
[1] as you may have guessed, it's about surfaces: "Find a parametrιc representation of the part of the cylιnder x2 + y2 = 1 that lies inside the ellipsοid x2 + y2 + 4z2 = 5 and in front of the plane x = 0."
7 comments:
by our standards, this question is extremely difficult and would be deemed unfair. even if you gave a review problem with different numbers, the process would be too hard and students would start murmuring.
is it really so unfair?
it's a slight modification of one of their homework problems and i did an example during the review session ..
It's unfair to assume that students do homework or pay attention to what you say.
to Anon & L: ah, i must be behind the times. i guess i'm teaching the class as if it were the 20th century .. (-:
to オテモヤン: stop posting smut on my blog.
The hard part (as far as I can tell) is trying to figure out whether 'in front of the plane x = 0' means 'x > 0' or 'x < 0'!
If anything, my visualization of 'A is in front of B' would suggest 'A has a smaller y value than B'...
hi wιll. actually, i would have accepted either x ≤ 0 or x ≥ 0, as long as the choice was consistent.
as it happened, one student asked in the first 5 minutes of that 50-minute exam, and i wrote on the board "x ≥ 0" for definiteness.
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