Is it reasonable for a professor to ask students to stay 30-45 minutes past scheduled class time every week?
I guess I'm going to be the contrary opinion here. I don't think your professor's request is reasonable at all. Class time is scheduled the way it is so that people can plan the rest of their lives around the schedule. In this case, nobody but you seems to have anything from 12:50 on, but that shouldn't encourage the prof to monopolize that time. 

Some may think your extracurricular activity is trivial or that you should skip it, but that math club could easily have been another class or your job. The professor is in a position of power, and he should respect his position by not trying to compel you to work outside the system because it's convenient to him. Several of your peers may actually appreciate that you're the lone hold out even if they won't ever admit it. 

I would have no problem with the prof offering extra sessions where no required material was covered. This could be extra practice working example problems or a Q&amp;A session to clear up anything confusing from class. That being said, I think professors should be held to teaching the required stuff in the allotted time.