I spent some of Burrito Girl's birthday* and then much of this morning writing solutions to the 2013 AP physics B exam. (Scroll down to find them, or do a control-F on my name. Chris Becke beat me to posting solutions by a few hours; don't be shy about using his solutions.) You can access my solutions at the link, but it's through "pretty good physics secure." You must have an account with PGP.
* Burriro Girl is my wife and sidekick. My work yesterday was interrupted with a directive that physics time had ended, and Burrito Time had arrived.
Teachers can get an account with PGP by following the instructions at the PGP-secure homepage. Students should ask their teacher to sign up. PGP-secure is a wonderful resource, one that teachers will often use throughout the year. It's worth signing up.
My comments: The first question is similar to a famous old Hewitt question, in which he asks about the water level of a lake when a freighter full with iron cannonballs throws its merchandise overboard. Excellent question. Questions 2-5 and 7 are straightforward and interesting. You can add the experiment described in #3 to your repertoire of laboratory exercises.
I'll note that question 5, the thermodynamics question, uses language in anticipation of AP physics 2. No longer will the exam say "heat added to a gas." Instead, you'll see phrases like "energy transferred into the gas by heating."
Question 6 is difficult but excellent. A student really has to know about magnetic fields and forces in order to handle this one. The last part, about the emf induced in a straight wire, is something I've never before seen on AP physics B; usually we discussed emf induced in a loop of wire. But it's straightforward enough to use BLv to get the emf. The side of the wire with higher electric potential can be determined by applying the right-hand-rule for magnetic force to the positive charges in the wire.
Please holler at me in the comments if you find a mistake, which you surely will. I guarantee I got a 5, but not that I got 100%.