My son's middle school gives the AMC 8 to all 6th graders and above and then let the top 20 scorers take the AMC 10 when it is given in February.
The math teacher gets the AMC 8 scores back to the kids pretty quickly but as I posted earlier, the kids get their actual test booklet back a few days after they take the test. All of the kids circle their answers on the test booklet and then go to AoPS forums and the unofficial answers are usually posted within a week or so. This way they have a pretty good idea of their score rather quickly, unless they misbubbled...
The local public schools where we live do not offer the AMC 8, 10 or 12. I do not think many of the math teachers are even aware of this series of tests and the purpose.
