Olympiad
Resources
Firstly I would like to recommend a couple of books that are superb in helping you improve at olympiad type problems.
A Mathematical
Olympiad Primer by
Geoff Smith (available
from UKMT)
The
Mathematical Olympiad Handbook by
A. Gardner (available
here)
Initially these problems can seem impossible, but with perseverance you CAN improve at them. I did dreadfully in the BMO1 when I took it at school but I can now do the majority of questions they throw at you. (Alas I still find BMO2 impossible. I would wager that you could give me the rest of my life to solve question one from the 2010 paper and I would still not be able to do it!) Everyone gets stuck at some point or other on a problem; for example
Isaac Newton (despite being the greatest mind in history and solving the problems of gravitation and motion in the greatest work of science ever) couldn't turn base metals to gold. [Probably ought to forgive him for this failure(!)]
Albert Einstein (despite coming up with the mind-bending ideas of special and general relativity and also being one of the fathers of quantum mechanics) never found a unified field theory.
Paul Dirac (despite doing more than anyone else to construct a mature theory of quantum mechanics and introducing the idea of the 'principle of least action' into quantum mechanics) could not find a way to eliminate the 'infinities' from his theories.
Grisha Perelman (despite solving the Poincare Conjecture, one of the toughest problems in maths with a $1 million dollar prize and also gaining a perfect score for the USSR in the International Maths Olympiad) got stuck on a problem involving Alexandrov Spaces.
It can be argued that you only learn anything from the times you make mistakes or can't solve things.
Secondly you can find the British Maths Olympiad here with all the past papers, but without answers unfortunately. The UKMT provides a very cheap booklet with BMO problems and solutions from previous years.