Create a simple quiz
You can always try the Quiz module. I have some experience with it and it mighty suffice for your needs.

Or you can always create your own form with the well-documented FormAPI. You can define your own validation- and submithandlers. Very, véry cool features.
What you can do is create a custom block, and fill it up with your own form. 

Depending on your experience level (and time), you can one of above options...
Good luck!