<p>JHS, keep in mind that the whole AMC/AIME/USAMO/MOP process is to pick a team that will represent the US in IMO. So, I know a bunch of kids who barely qualified for AIME last year (Since the cutoff was very low- 88.5), but they felt they would not perform well on the AIME and rather than risk and get a score of 0, they just left it as “I qualified for AIME.” So, that might be a possible answer to why not all the kids who qualify take the AIME. </p>
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Comparing numbers is completely useless in this case. You can’t compare difficulty of tests based on how many kids perform well in each one. Remember, at least in my school, the kids that generally take the AMC are at least in an honors Math class or enrolled in an AP math class, so the students taking the exam are quite familiar with math and have shown some sort of adeptness in the area of mathematics. </p>
<p>So, maybe I’m missing something here, but would you like to enlighten me why getting an 800 on SAT Math 1 would be more respectable than scoring in the top 5% or scoring above a 100 on the American Mathematics Competition? There are many many people who have done extremely well on SAT Math 1 (750+) who would do poorly on AMC let alone qualify for AIME. However, the majority of the students who qualify to take the AIME would perform extremely well (and many already have) (750+) on the SAT Math 1. </p>
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<p>Keep in mind that number includes underclassmen (and middle schoolers and elementary students). They can qualify through either the AMC 12 or AMC 10, but, for the AMC 10, the levels are definitely higher-you need to score in the top 2.5% to qualify for AIME.</p>
<p>Lastly, you can “prepare” for the SAT Math section, and it has definitely been proven that it is beatable. However, for the AMC, while you can prepare somewhat, you can never completely plan to do well on it. The type of math they test are just different with SAT Math being a breeze for students who can qualify for AIME but not necessarily the other way around.</p>
<p>EDIT: And no, this is not me complaining about how I couldn’t get an 800 on SAT Math 1…</p>