I comment below on common problems with the Final Exam
solutions:

1: some people simply said things like "v = cz is only good 
fow low redshifts" - while this is true, it doesn't help the
"student" understand why you can have z's larger than 1.

2: most people did ok on this one

3: most people had forgotten almost everything about how 
kinematics within our own galaxy led to rotation curves (you
could either have said a little bit about kinematics of
local stars - i.e. Oort constants - or about using HI and
the tangent method. Very few people actually labeled the 
graphs fully, i.e. including not only what quantities the
x,y axis represent, but also the units and some numerical values.

4: most people did ok on this one (although many forgot about
irregular galaxies).

5: people here tended to misinterpret viable. Viable means that
the candidate is still a possible solution for the DM problem.
As such, the fact that WIMPS are difficult to detect because they
don't interact much with normal matter does not make them "not viable".
Actually, that's what contributes to them still being viable (since
no experiment can yet exclude them). Most people also forgot that
the constraints on the baryon density (from big bang nucleosynthesis)
makes baryonic candidates not viable for solving the entire dark
matter shortfall.

6: most people did ok on this one, although there was a lot
of confusion between special and general relativity. Special deals
with velocities, the constant speed of light, and the repurcussions
of the constant speed of light (it does not deal at all with accelerations
- aka forces - and so does not deal directly with black holes). General
deals with gravity, spacetime, etc.

7: this was the question people did worst on. The key was to remember
that "velocities" as plotted come from both the cosmological expansion
and any peculiar motions the galaxies may have. The "S" distortion
is due to large peculiar motions. Galaxies closer to us appear to 
be moving faster away from us and galaxies farther from us appear to 
moving slower (aka toward us relative to the overall expansion). 
This is caused by the presence of a large mass into which the
galaxies are falling (therefore things on our side of this mass
are moving faster than the Hubble flow and things on the far side
are moving slower than the Hubble flow). Part b gave you a hint to 
consider masses (by asking you to calculate the mass). In part B
then you could use GM/r = v^2 is you used the differential r (i.e.
not the distance from us to the sources but the distance over which
the distortion exists) and the v (not the obseved v, but that relative
to the mean of the distortion), to estimate M.

8: most people did ok on this one. (most problems just had to do
with not converting to radians before using the small angle formula)

9: some people were intimidated by this question, but in fact 
most people at least set up how they would have gone about it if
they could remember any numbers. Of course, there are many ways to 
get to the required numbers (for example, you might remember the 
mass of the galaxy, you might remember the distance from the Sun
to the Galactic Center and the velocity with which the Sun moves (from
which you can calculate the mass), you might remember the number 
of stars in the galaxy (and then multiply by 1 solar mass to get a
rough estimate), you might remember the luminosity of the galaxy
and then convert to mass, .....). The main point of this question 
was to get you to think about different ways to get the numbers 
you needed.


I realize that questions 7 and 9 where a bit tricky, but if you had
known everything else and completely missed these two questions - you
would have gotten the third highest grade on the final!