This is the second IOQM Mock test from MOMC Season 3! The problems for this test are taken from HMMT Feb 2024 and BMT 2012. As always, all credit and authorship of the problems belong to their respective sources.
The MOMC application will be available soon in a separate blog post. So stay tuned for that! Also, please remember to fill out this very short form about the mock test! You can find its results here. The results of the previous mock test form have been added to that blog now.
Before discussing the mock test, I want to talk about a few things. I've been frequently asked about providing solutions for the mock tests, and I would like to clarify that the sources mentioned in the first paragraph of each blog do have the solutions. I prefer not to post the solutions along with the answer key because a) it encourages you to explore new resources, and b) I don't own the problems, so directing you to their official sources is the right thing to do.
This might be a bit out of place for my blog, but I want to emphasise the importance of checking your work at the end of your mock test. I am convinced that the only reason capable aspirants fail is due to silly errors. Many MOMC members solve 45-50 marks worth of problems but score only about 30. While 30 is probably enough to clear IOQM, there is no guarantee you will perform at least as well on the actual exam day. I wouldn't have cleared IOQM had I not carefully checked my work. So I insist you to follow this advice as an unspoken rule.
Regarding the mock's difficulty, I asked for feedback on Donut 1 and learned that it was slightly easier compared to last year's IOQM. So, this mock is a bit harder. All the 2-markers are non-routine, and all the 3 and 5-marker problems require considerable effort to solve. Most terrifying of all, the mock is filled to the brim with geometry. Nevertheless, the mock features a diverse set of problems with interesting elements. Problem 9 is an IOQM classic, featuring all three main stars of geometry: altitude, angle bisector, and median. Similarly, I hope that solving the 5-marker geometry problems will help you appreciate the beauty of HMMT Feb Geo!
Meanwhile, Problems 10 and 15, while still combinatorics, provide a break from counting. Problem 14, on the other hand, is a classic error-prone cube counting problem. Problem 29 is one of those Olympiad-like combinatorial problems where proving the answer correct is much harder than reaching it. Regarding number theory, Problem 19 features the Euler totient function. While it's usually not considered part of the IOQM syllabus, MTAI likes to throw surprises, so it's not a bad idea to include it in the mock. An IOQM mock is incomplete without lengthy bash problems. Thankfully, P11 and P25 deliver just that!
These are the CODS difficulty ratings for the 5 marks problems:
| P21 | P22 | P23 | P24 | P25 | P26 | P27 | P28 | P29 | P30 |
|---|---|---|---|---|---|---|---|---|---|
| 3 | 3 | 4 | 1 | 2 | 3 | 3 | 4 | 5 | 4 |
Before closing the post, I want to thank each one of you for the incredible response to this year's first MOMC IOQM mock exam! Your enthusiasm is truly motivating. I am thrilled that you all are enjoying them. Looking forward to continuing this journey together, I'll catch you in the next one!