From the AMC FAQ http://www.maa.org/math-competitions/about-amc/faq :

Quote
Q. AMC 10/12 #1. What score do you have to get on the AMC 8 to be invited to take the AMC 10?
A. There is no invitation from the AMC 8 to the AMC 10 or AMC 12, Rather, with the AMC 8 Reports we send an AMC 10/12 information brochure, and an AMC 10/12 registration form to the Contest Manager of ALL schools which participate in the AMC 8. No school or student needs a special invitation, nor is any minimum score required. The AMC 10 and AMC 12 are both open competitions. Specifically, in the AMC 8 report which is sent to ALL participating schools is the following message:

"An AMC 10/AMC 12 Invitation Brochure has been included in this mailing... Any of your students may participate in the AMC 10/12. High scoring AMC 8 students should find the AMC 10 interesting and instructive."

The AMC 10 is significantly more difficult than the AMC 8. Teachers should evaluate the maturity of a specific student before suggesting participation. See FAQ AMC10/12 #9 as it would apply to young students.