This is the third IOQM Mock test from MOMC Season 3! The problems for this test are taken from CMIMC 2016 and PUMaC 2011. All credit and authorship of the problems belong to their respective sources.
Before discussing the mock, I want to reiterate that MOMC Applications are still open! In fact, they will remain open until RMO takes place. However, applying early is highly advantageous as we admit participants on a rolling basis. You can find the application here. Also, please remember to fill out this very short form about the mock test! You can find its results here.
The mock presents some intriguing problems. It features all the main components of Algebra: Polynomials (P21), Algebraic Manipulation (P1, P22), Inequalities (P5, P22), Summation (P14, P23), and the Greatest Integer Function (P23)! I love Problem 14 because it reminds me of PRMO 2018 P16. It used to be one of my favourites during my preparation. In number theory, I couldn't resist including bashy problems. So I just had to include P17 there. On a brighter note, the 5-marker number theory problems are more Olympiad-esque yet still elementary. In geometry, we have a few construction problems (where you have to cleverly add a point) like P11 and P28.
This mock is actually a reboot of one of Season 1's mocks "JL3" (July 3). In Season 1, the mocks used to be extremely trivial. Problems like P1 used to come as 5-markers! We used to believe that they were too challenging and that the IOQM would "of course be a bit easier". Good ol' days!
These are the CODS difficulty ratings for the 5-mark problems:
| P21 | P22 | P23 | P24 | P25 | P26 | P27 | P28 | P29 | P30 |
|---|---|---|---|---|---|---|---|---|---|
| 4 | 2 | 4 | 3 | 2 | 3 | 3 | 2 | 5 | 3 |