Yes, there are Olympiads for Maths, Physics, Chemistry and
Biology.
I was personally a national representative for Physics Olympiad,
so I can comment on this. The information is for JC only.
Basically, schools will choose JC1 students to represent the
school for the Singapore Physics Olympiad. The selection can be
based on recommendations, your class physics results, maths
results, a selection test, and/or a combination of the above.
After you finish the Singapore Physics Olympiad, which is
conducted by NUS, NUS will select students based on scores. The top
few will be selected to go for a short stint of training at NUS.
From there, there will be another selection test to select students
to represent Singapore.
There is Asian Physics Olympiad (8 representatives) and
International Physics Olympiad (5 representatives).
As far as I know, the same goes for Maths, Chemistry and
Biology. I'm unsure if there is a Asian competition for these.
