How important are AMC scores in the college admissions process? Is the time investment spent preparing worth the importance given to it by colleges, or would that time be better spent elsewhere?
I’m primarily asking about top tier colleges (HYPSM), but insight about others would be helpful as well. Does qualifying for the AIME merely serve as a tie breaker, or is it a significant consideration?
I’m asking strictly from a college admissions perspective; not interest and what one likes to do.
I don’t think that AIME really means anything. USAMO qualification counts for more of course. Anecdotally, people in the competition math world will often say that 20-40% of USAMO qualifiers are accepted to one or more HYP, while upwards of 80% are accepted to MIT, Caltech and similar. Try hard on the AIME the week after next!
I don’t agree that qualifying to take AIME seems nothing. There is a list on CC that ranks different extra-curricular accomplishments (and other high school accomplishments) from 1 to 10. Qualifying to take AIME is a 5 on that list, compared to `majority of state-level awards’, which are a 4. Qualifying to take USAMO is a 7, probably only below top 1-3 finishes in national competitions. National Merit Semi-Finalist is a 3, and National Merit Commended is a 1.
Obviously, this is nothing official and not something all (or any) admissions officers are going to follow. But, one data point, which does suggest that AIME qualification is a rather significant accomplishment.
Interesting, @osuprof, about AIME qualification. I am close to the competition math world, and those USAMO anecdotes about elite college acceptance “feel” right to me. Most USAMO qualifiers will have qualified AIME by 13 or 14 years old (a surprising number qualify by 10 or 11!), so I was just extrapolating a bit from the limited boost USAMO qualification seems to confer, especially in light of just how hard it truly is to qualify USAMO (roughly 300 kids out of approx. 400,000 who participate in the AMS series).
USAMO winners of course are a different story - there are only 12 each year (with great overlap over high school years) - but anecdotally even some of them have been turned down at HYP. I do hope you and cc (on that linked thread) are right that AIME counts for something because my DC14 is taking it next week 
Best of luck to the OP!
The often cited EC scale list on CC can be quite misleading IMO because it doesn’t take into account the fact that at schools like HYPSM the admission is holistic and by cohort. If the OP belongs to demographic groups that are over-represented in AIME/USAMOs these awards would not serve the purpose of making applicant stand out among similar profile candidates at HYPSM. If you do a quick math: HYPSM admit about 7000 into their freshmen class, my guess is that 1200 of 7000 would be unhooked Asian kids; among those, 600 would be boys and roughly 400 would be STEM boys of which 200 are math profile. If seventy percent of 5000 AIME invitees are Asian boys then we are looking at over 3000 similar profile candidates for 200 spots with math being the main spike among that cohort. For the same reason USAMO, a far more difficult feat, probably only 150 new kids every year, is not going to be enough of a guarantee for acceptance either. There are plenty of heartbreaking stories on CC even for a three time USAMO guy:
http://talk.qa.collegeconfidential.com/college-admissions/1876770-what-did-i-do-wrong-p1.html
As hard as AIME is—and I know this because my 13 yr old son is in it too—it is unlikely to be a significant accomplishment in the context of elite college admission. What makes more challenging at HYPSM admissions is that most AOs are of humanity background, who probably don’t quite know the talent and dedication it requires for AIME/USAMO and similar STEM awards.
Fair enough - I agree that there will be many Asian (mostly Chinese/Korean origin) kids with STEM interest applying to HYPSM with AIME under the belt and won’t stand out without USAMO or something else. It might help a white girl to have qualified for AIME.
Again, it is probably like any other accomplishment ranked 4 or 5 on that list – by itself it is not going to make you stand out. I am sure a white male pre-law applicant to Harvard won’t get a significant boost from a state-level award in Debate either, since that it is a common EC for pre-law students. A national award might help though.