Hi guys, I just came across this thread and had to reply even though it is an old one.
In particular I would like to address a couple of assertions made throughout the thread regarding Hot for Teacher and 1. That Alex over-dubbed this part and 2. That Alex never played the intro live.
Both these assertions are factually incorrect, he did not over-dub the intro and he certainly has played it live in the past.
The following YouTube link is a live recording from the 1984 tour that should put the debate to rest. Listen to the start and the ending where he expands on it at the end of the song.