Preparing for the JEE, and specifically JEE Advanced, exposed me to some foreign mathematics problems. Usually, these problem sets were from university-level mathematics competitions for first- and second-year undergraduate students, competitions organized by universities for high school students, or simply problems from other entrance examinations.
I have omitted Mathematical Olympiads and their respective national-level equivalents.
A 10+2 level student with a background in the JEE or any equivalent entrance exam, who also has a decent amount of additional interest in the subject, can tackle a fair number of problems from here.
Are they really useful for the JEE?
The ones oriented towards high school students kind of are (except the IMO, obviously). The difficulty of these varies from very easy to very hard. Obviously, the primary aim of solving these is not to get a boost in the JEE; one can refer to my resources list for that.
The list
- The Southern California Math Competition (USC)
- Berkeley Math Tournament
- TAMU High School Math Competition (Only the ‘DE’ and ‘EF’ exams)
- UT Austin Bennett
- CMI BSc Entrance Test
- Princeton PUMaC
- ISI (B Stat and B Math)
- The Oxford MAT
- Stanford Math Tournament
- Imperial-Cambridge Mathematics Competition
- Cambridge STEP
- Harvard-MIT HMMT
- Virginia Tech VTRMC
Bonus: Difficult territory
Though I confess my capability to solve the problems from here are very limited, I must still remain inclusive…
The severe deficiency of East Asian content here can only be cured once entire papers (mostly entrance papers) from Taiwan, China, South Korea, Japan, etc. are officially translated and released to the public. Until then, one must make do with the occasional odd question that appears in a YouTube video or pops up on the Mathematics Stack Exchange.
If I missed anything else, it is simply because I am not aware of it OR I have missed it (in which case I would update the list later).
Happy solving.