Yeah, I hand it to them (the nats event supervisors, I checked it over before it went out, and I basically had no corrections), and the test is pretty good as a kind of "base line" for what you should know. There's of course much more to learn than is just on that test. Remember the heavy use of diagrams and understand as many as you can because they really are quite important in astronomy. Also, east made a nice catch...was wondering if they'd ever bring up the webinar. The AAVSO test actually wasn't as hard as they could make it (maybe saving that for the nats test

). One important thing in general with studying is being able to know what you don't know (need work on). Basics are also important. You could save up all the notes you want on exoplanet trivia "firsts", and that may come up, but you should definitely invest some time in understanding really where these different formulas come from and their associated concepts (if you've ever taken a physics class, and it was good, then you'd know to go beyond simply just using formulas). Not saying these are all your problems, but stuff to think about if you're trying to come up with what's wrong with you're studying.
Onto answering questions. They often tend to use some glossary from Introduction to Modern Astrophysics by Carroll and Ostlie as the reference of choice for getting luminosity or apparent magnitude for stars based on luminosity and spectral class. If you don't own a copy, then fret not as your answer is within error! You can submit a FAQ for this, but quite normally 10% error is good enough. In case you're wondering, 0.1 * 13.9 = 1.39, and 13.9 - 1.39 obviously puts you're answer within range

. The glossary they use may be online. Another hint as an alternative is that you can get it off an HR diagram if you're in a real pinch, but the tables are of course far more precise than guesstimating.
Part b is interesting. I already said:
"As a thinking exercise take the ratio of the flux in to flux out for the planet and you can try that for deriving the planetary equilibrium temperature (which will REALLY teach you where it comes from). This should also help you to get the answer just from that step alone.
If you want it even "more formulaic", here's another way to think about it. If you use the Stefan-Boltzmann law to find the luminosity of the planet and for the star, make the ratio for the star to the planet, and then plug it in for the planet. To get it to work, you need to plug in the equilibrium temperature (hah, here we have it again) of the planet."
since you (as I remember it) asked this questions before! Did you try that, and you don't understand it either way? If so I'll try to type up a derivation (I was going to, but I kept making it too long...on paper I do it faster, oh well).
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteo, Phys Sci Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Fresh Waters), Fermi Questions, GeoMaps, Grav Vehicle, Scrambler, Rocks, Astro
Grad: Writing Tests/Supervising (NY/MI)