It has come to my attention that there’s a typo in the key for the final for Fall 2012. In the very last problem, the answer key refers to the verb have but it should be referring to the verb be (since there is actually no have in that sentence).

Relevant also to that problem is the assumption that adverbs can adjoin not just to TP and to vP but also to the phrases headed by auxiliary verbs (PerfP, ProgP, PassP). As an example, Pat will quietly be solving the problem. That sentence doesn’t sound fantastic to me, but it doesn’t sound ungrammatical.