I have been selected for a national Chemistry Olympiad in my country and I received an honorable mention for it. Should I mention it in the honors section? Or should I only mention medals I've won in other olympiads?
This is great, congratulations! If you have the space I would suggest putting the honorable mention in the honors section. I would also suggest prioritizing state/national-level awards in this section over regional/local high school awards -- if they are unique and harder to accomplish as a high schooler. Not all awards that you list have to be placements (i.e. first/second/third place), honorable mentions at a high level are still substantial awards.
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You should mention that for sure!! That’s pretty amazing to represent a country! Congrats! (I attempted the National Chemistry Olympiad [ASC it’s called here] but failed; it’s much tougher to represent the U.S.)