I would do a search for "quiz" on
www.hotscripts.com. I'm sure there's a BUNCH of solutions, many of which are open source and/or freeware that would do exactly what you want.
But as TwoD mentioned, if you have a PHP -enabled server, chances are you have the ability to setup a database (MySQL) along with it. A lot of script authors will usually offer an installation service as well to get you up and running for a small fee.