The OTIS Mock AIME
Satisfactory. Keep cooking.
The OTIS Mock AIME is an annual 3-hour exam consisting of 15 problems whose answers are integers between $0$ and $999$. As the name suggests, it is yet another unofficial paper intended to emulate the American Invitational Mathematics Exam.
Starting from 2025, we offer two versions of the test, which are different:
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The OTIS Mock AIME I is going to be tough. It will definitely be harder than the actual AIME, by perhaps 2 to 4 problems. But more tangibly, it will also have significant artistic license.1 Problems will freely assume IMO-style background throughout the test, and intentionally stretch the boundary of what constitutes an “AIME problem”.
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The OTIS Mock AIME II is meant to be more practically useful. It will adhere more closely to the difficulty and style of past official AIME’s. There will inevitably still be some more IMO-flavored problems, but they’ll appear later in the ordering.
The defining characteristic of the OTIS Mock AIME is that all the problems are composed by students from the OTIS program. That is, Evan runs this annual exam as a way to give his students a chance to try their hand at problem composition.
Current edition#
The OTIS Mock AIME 2025 has concluded. You can download the problems below:
See you next year!
Past exams#
Here is an AoPS collection for all past threads.
Format#
Like the AIME, there are 15 problems to solve in 3 continuous hours and all answers are integers ranging from 000 to 999, inclusive.
Problem statements follow ARML 2014 conventions, so for example $\left\lfloor x \right\rfloor$ is the floor of $x$. You may refer to these conventions during the exam.
For scored submissions, no aids other than writing utensils and erasers, scratch paper, graph paper, ruler, compass, protractor are permitted. In particular, books, notes, calculators, cell phones, computers, abacuses, ChatGPT, magic crystal balls, etc., are all prohibited.
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I think of what the AIME could be, a vision of the one I see… ↩