Some people say you can train your body so that you’ll be rested by short 20–30 minute naps. Some even take it to the extreme and have had success with 6 of these naps spaced throughout the day being the only sleep they get. If done consistently it is supposed to be sustainable. (check out polyphasic sleep sometime after your test)...
I tried several sleep schedules and the only one (other than a standard 6–8 hours at one time) that I could stick with was simply breaking that period into two 2–3 hour naps.
More to your question though, the only time I would really feel “rested” when trying the 30 minute naps spaced throughout the day was if I was truly completely exhausted. The theory I heard goes that you fall more quickly into REM sleep in these situations, but as nikipedia said, there don’t seem to be a lot of definitive answers.
Although I didn’t test this specifically with memorization, I would guess the rested feeling would probably help with learning new material or the actual test more than simple memorization.
Good luck on the test, I’m sure you’ll do great.