Hi guys,
These days, standard approach to Flash embedding is to go for Flash as the first option, which covers more than 90% of OS', and have an HTML fall-back, which can be HTML5 in the case of audio, video or animation.
Another option, although you'll have to subject yourselves to iTunes' opaque and somewhat capricious approval process, is to provide an iOS app for your quizzes. Actionscript 3.0 can easily cross-compile into native iOS desktop apps and this feature is well supported, in fact, the best selling iOS app at the moment is developed in Flash and cross-compiled: http://www.leebrimelow.com/?p=3000
The AJAX option looks like a good one too, since at least 30% of users' browsers don't support HTML5. (In other words, by going with HTML5 too soon, you'd be accommodating less than 2% of users at the expense of 30%) Good ol' XHTML4 + JS + CSS will work in almost all cases and if you need multimedia, just use Flash with an HTML5 fallback only for those elements.
I hope this helps!