<p>You won’t need “esoteric” math knowledge to score well. You can get 100+ (i.e. qualify for AIME) without knowing anything beyond what you learn in the classroom. Scoring extremely well (140-150 range) probably requires knowing some techniques that are along the same lines as what you learn in classroom, but can be brought to bear on more complex and tricky problems. (Examples of techniques I’d put in this category include theorems about the medians of a triangle; modular arithmetic, Viete’s Theorem, etc.) Plenty of people from my school took AMC12 without any competition training and put up respectable scores, in many cases qualifying for AIME.</p>
<p>The difficulty of the A and B exams is as equal as the committee can make them. I know the process for AIME-I and -II is that they write an “AIME heads” and “AIME tails” and then when they’re done, flip a coin to determine which is the AIME-I. I’m guessing a similar process is used for the 12A and 12B.</p>