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<p>It’s maybe two or three times more selective than 800 math SAT (or equivalent ACT), in number of US graduates per year who possess the credential. In 2010, the USA had at most 7000 AIME qualifiers in grades 11-12. That’s 8144 qualifiers minus the unknown number of grade 10-and-below US students who qualified through AMC12 and the large number of international qualifiers. Based on the hundreds of high AIME scores from Canada, China, Korea, and Singapore it is safe to assume that there were over 1000 foreign qualifiers.</p>
<p>The number of AIME qualifiers was lower in the past, maybe half the 2010 numbers for most of the past decade, hence more meaningful relative to the SAT. </p>
<p>In test content, AIME qualification is much less of a time trial and is less error-sensitive than 800 on the math SAT (I). Relatively few qualifiers answer all questions without guessing, and there aren’t so many qualifiers close to the cutoff that an extra point gained or lost is decisive. The score distribution has a longer tail than on the SAT. Consequently, AIME qualification is a more stable and informative measurement of ability than 800 on the SAT, which might be equivalent to a high 770 to a low 850+ (if the latter score range existed). Between that and the more advanced content it’s fair to say that anyone in the know would give AIME as such considerably more weight than a high SAT score.</p>
<p>However, qualifying <em>for the first time</em> in 12th grade, and without scoring a few points on the AIME itself, puts one in the bottom half of this doubly- or triply-selective pool, like getting an 820 instead of an 860 on the hypothetical supraSAT scale.</p>