The AMC 10 is significantly more difficult than the AMC 8. There is no minimum score required to take the AMC 10.

I have general guidelines for recommending the AMC 10 for students in 8th grade and below. I consider the student's score on the AMC 8 and their attitude toward difficult problems.

In general, I recommend the AMC 10 for students in 8th grade with a score of 18 or above, 7th graders with a score of 20 or above, and students in 6th grade and below with a score of 22 and above.

I typically see three types of students in our extra curricular math program: students who are aggressive in their approach to hard problems and motivated by the challenge of a problem they can't solve, laid back students who don't really care whether they can solve a problem or not, and perfectionist students who are very frustrated when they can't solve a problem quickly or face a large number of problems they can't solve.

If the first type of student is close to the guideline score and really wants to take the AMC 10, they can. I recommend laid back students who meet or exceed the guideline score take the AMC 10. I only encourage perfectionist students who exceed the guideline scores to take it before 9th grade.

This is how I make my recommendations, but, ultimately, parents decide whether or not their children will participate.

I second Bostonian's recommendation of AoPS for AMC 10 preparation. You can find a downloadable pdf with live links on our math enrichment program website:

https://sites.google.com/site/polandbulldogmath/poland-seminary-high-school-math-club