IOQM 2024 Donut Mock One

7 July 20243 minutesviews

This article contains spoilers for the mock test.

I recommend attempting the problems before proceeding to read the article. You can download the problems and the answer key using the buttons below.

This is the first IOQM Mock test from MOMC Season 3! I'm so excited to be back with a freshly baked batch of mock tests for y'all to savour and enjoy! The problems for this test are taken from ARML 2024, HMMT February 2015 and BmMT 2023. As always, all the credit and authorship of the problems belongs to their respective sources.

Just like last year, I want to collect the solve rates of each problem in the test. These will be public and will help you to accurately gauge the difficulty of the problems, crucial during post-mock analysis. So please consider filling in this very short form about the mock. The results can now be found here.

The mock features various interesting problems such as P21, 22 and 27. Most notably, the 23rd problem is absolute binomial hell. It requires sophisticated manipulation with popular identities followed by a challenging ν2\nu_2 analysis of the simplified expression. The test also features a significant amount of bash, namely: P16, 19, 24 and 25. The 11th problem is reminiscent of PRMO 2019 P26, a hit-and-trial maximisation problem. It's hard to judge whether we've really achieved the maximum or not.

These are the CODS difficulty ratings for the 5 mark problems:


You might notice from the ratings that the initial 5 markers are harder than the later ones. Problem selection is a huge part of IOQM and I want to make sure you are good at it. For instance, despite its looks, P27 is actually pretty simple. On the other hand, P22 and 23 are quite inviting, but they will likely prove challenging for most.

The subject distribution of the mock distinctly benefits number theory mains. The geometry weightage, in particular, is lower than usual. Scarily enough, the mock might feature an intentional bonus problem as well. A little quirk about this mock is that I changed the clean division between 2, 3 and 5 marker problems in the way they are laid out in the PDF. This is to match last year's IOQM paper's aesthetic a bit.

Before I wrap up this post, I'm excited to announce that applications for MOMC Season 3 will open next week! MOMC, short for Math Olympiad Mock Club, is the official discussion group for the blog's mock tests. I'm eager to welcome as many math enthusiasts as possible. If you love connecting with fellow mathletes and immersing yourself in test discussions, this club is the perfect place for you!

See you next week :)