Comments:

2-66 = 30 pts
2-68 = 20 (10 and 10)
2-73 = 30 (10 and 10 and 10)
extra = 20

Average of 86.3, 21 assignments submitted, the low was 55 and there were a
handful of 100's. Generally I was impressed.

2-66 just about everybody set up the correct system of linear equations, but
some people soved it incorrectly (a ten point deduction). I considered the
gradient to be one whole thing, so if one component was wrong, the whole thing
was wrong. Honestly, I personally don't care if you show your calculations, as
long as you show the set up, because solving a system of 2 linear equations is
a middle school thing which I assume you can do. I expect exact answers and not
decimal approximations, however. It is easy to check your solution with a
calculator so there is really no reason why the answer should be wrong.

2-68 was tough to grade because it was so vague, so I tried to give students the
benefit of the doubt when possible. I expected to see hyperbolae centered
around both axes. Although a few other level sets existed, I just wanted the
general case becasue the problem did not specify. I expected to see gradients
pointing in the correct direction, perpendicular to the curves, in multiple
quadrents. I really don't care about calculations; I pretty much disregarded
any written work. I just want the sketch to indicate the students understand
the behavior of the function and its gradient. Many students drew the gradient
vectors in the wrong direction, for which I took away points because this can
easily be checked by simply calculating the gradient of the function.

2-73 gave people the most trouble. Most people understood the "if" and the
uniqueness, but the "only if" part tripped some people up. Some people tried it
using a different definition of affine from the one given, but I took points
off because this defeats the purpose of the problem. I was impressed to see
some people show that the gradient of F(ax+y-ay)= the gradient of F(x) and thus
the gradient is constant.

I was disappointed that nobody used my method, which is to begin by proving as a
lemma that any affine function intersecting the origin is linear. You can then
use show that F0(x) is affine, and therefore linear. Just in case anybody
cares...

On the extra I gave no partial credit, but that is a moot point because I
believe everybody got full credit anyway.