Ok, I know of myself and at least one other that are interested in this. I balked at first with all the information in the first few posts. I was worried about rigidity more than anything. 

I do have some questions though. 

In the letter sample from the Headmaster to the character in question, it only mentioned 'gifted'. He never said mutants. If mutants and mutant types are being persecuted (and the one I have in mind was, by his own family even) ... How likely do you think it's going to be that this kid (who's got a genius level intelligence, a side effect of his powers) will divulge them to a 'Prestigious' academy? A new age of education is one thing, but with the fear and prejudice against mutant-kind in the world, I think it unlikely that this would be openly mentioned in a formal application. Something that could be subpena'd by a court, or collected as intelligence by a military force. 

The original version of this character (and the current version) would worry that this wasn't a disguised 'roundup' attempt. So, according to the verbiage of the acceptance letter, what would prompt him/her to divulge that they have any powers at all?

This particular character would also wonder why he/she got the application in the first place. They don't see themselves as special, or unique (outside of their abilities which they keep hidden as much as possible). They don't see themselves as 'gifted' and would look at the application as suspect. This might well come through in the application. He might not apply certain verbiage which would render his app in a more positive light. Or he could even possibly fill it out in a sloppy or lazy way. This could be looked at as though he feels that it's not serious, not a challenge, and/or that it's fake. Or that his chances of getting in are minimal. (Considering he or she didn't complete high school, and dropped out.) And as he considers himself average (even though he's actually far from it), I'm sure this would show in his application (even if it were to be misleading, unless someone took a very close look, or perhaps used a psychic ability such as Psychometry on it)

This world view may also be a side effect of Depression. (A side thought)

And depending on which version (if they were on the run, homeless, etc) they'd wonder how they'd been found, and/or noticed.