Cranberrys 4 point answer is exactly it!!
My son went to a small middle school where there was heavy participation in math counts and heavy participated in just about every contest local and national they could find. The whole middle school took the AMC8 in class. Everyone trying out for MathCounts took the AMC 10A. The top kids also to the 10B. In hopes to qualify for AIME. After every contest the kids would break up in groups and compare solutions.
He is now a freshman at a very big high school where there is very little interest in math also.
Last weekend I drove him 2 hours to a University that hosted a High School Math competition. He was the only one from his school to participate. The school said they did participate in this contest but apparently they don’t so we signed up the school ourselves and he went. It was good for his soul to run into all the other kids and coaches he had been participating in contest with for the last few years.
I am not going to count on the high school to proctor the AMC 10 and 12 and have made other arrangements to take it at another location.
You can look at the statistics, including % that get each question correct, at AMC's statistics site. The first 5 questions are typically answered by 60-70% of students. Questions 21-25, about 20% on the AMC8, 2-10% on the 10 and 12.
A big reason there are lower percentage of answers on the last 5 questions on the 10 and 12 vs 8 other than being harder question. There is a strategy to follow when taking the 10 and 12. There is no penalty for guessing on the 8. On the 10 and 12 you get 1.5 points for leaving the question blank. 6 points for a correct answer and 0 for incorrect answer. Some kids will leave them blank. Cut off scores for AIME was 112.5 for the 10A and 96 for the 12A.
Approximately the top 2.5% of the AMC 10 and the top 5% of the AMC 12 qualify to take the AIME. This seems to be the prize for the kids who have worked hard.
