We recently went to the Davidson Academy tour and they clearly stated that students should be functioning at a 9th grade level for it to be a possible good fit. According to what we were told their middle school students are working at a 9th + grade level and their high school students are working at a college level.
They don't expect 9-11 year olds to have the background of a high school student, but expect the student to function at that level. There were quite a few 8-11 year olds at the tour and there were a lot of questions regarding this issue.
Besides having the scores and working at this level it was clear that students that attend the Academy are eager learners, study hard, work hard, and get a good amount of work outside of school. It appears to be a rigorous program. We were extremely impressed. There were families with kids 9-11 that were working 4+ years above grade level and not all felt their child was ready for the program. Hope this helps. I highly recommend going on a tour.