Also, if you submit a portfolio and application that piques their interest, as I suspect this would, Davidson would offer some ideas (maybe even aid? though I say that with no actual knowledge) for testing or other missing information.
I'm pretty sure they do not offer aid for testing. Aid is available once kids are accepted into the program, but not beforehand for testing.
I'm also in the "Give it a try" camp. The worst they'll say is no, and then all you're out is time. You're not even out the time if you get your child tested and he hits the scores--the application stands and you just add the scores to it.
What have you got to lose?
