We know that Wesley Crusher was worried about passing exams to get into StarFleet Academy (Does Starfleet accept cadets based on quotas?).
Since it's clear he was not worried about IQ/science tests, my next best theory (NOT backed up by canon yet) is that he was worried about tests that measure leadership abilities, decisiveness, behavior under pressure, and other such skills that distinguish an officer from an enlisted technician.
Was there any canon material which showed clearly the presence - or absence - of such leadership-related abilities in Wesley?