Date: Oct 23, 2012 10:32 AM
Author: Dave L. Renfro
Subject: Re: MIT Math Diagnostic for Physics Placement
Dave L. Renfro wrote (in part):
>> Problem B2: Instead of saying "Find all possible values of x which
>> solve the equation x^4 - 13x^2 + 36 = 0", I would be less vague and
>> explicitly ask for all complex solutions.
Robert Hansen wrote (in part):
> Doesn't that factor to (x^2 - 9)(x^2 - 4)? -> x = +/-3, +/-2
Using "complex solutions" gives test takers making certain
kinds of errors more rope to hang themselves with, although
personally I consider something like x = +/- 3i, +/- 2i to
be better than something like x = +/-9, +/-4, which in turn
is better than something like x = +/-13, +/-36. Ideally, I'd
want to see their work, but in the absence of that, for a
total of 5 points for this problem, I might give 3 points
for x = +/- 3i, +/- 2i and 1-2 points for x = +/-9, +/-4.
Note that even x = +/-9, +/-4 suggests they correctly factored
and they recognized there will be two pairs of solutions.
Dave L. Renfro