Since Betazoids are telepathic, it would seem they would have a prohibitive advantage in an academic setting. How did Starfleet Academy deal with Betazoids and other telepaths in trying to keep everyone on a level playing field?
Tests can be administered by computer. We see an example of this in Star Trek IV with the "memory test" that Spock takes. Since Betazeds can't scan computers, this would be an effective way of testing them as long as they weren't in the vicinity of other testees.
I would assume that any live test where a telepathic alien was involved would require them to operate on the honour system, simply asking them not to use their abilities to subvert the purpose of the test.
Capt. Picard: The first duty of every Starfleet officer is to the truth, whether it's scientific truth or historical truth or personal truth! It is the guiding principle on which Starfleet is based. And if you can't find it within yourself to stand up and tell the truth about what happened, you don't deserve to wear that uniform!
There's also the possibility that in addition to computerised testing, they would also use holodeck simulations like the Bridge Officer's test administered to Deanna Troi in TNG: Thine Own Self (Mrs Troi confirms in TNG: Manhunt that she can't read holograms).
In extreme cases, they might also use aliens who're resistant to telepathy. Ferengis and Cardassians are probably out, but Vulcan masters are known to have this skill so there are almost certainly others that can be used.