I would like to recommend a couple of books that are superb in
helping you improve at olympiad type problems.
Olympiad Primer by
Geoff Smith (available
Mathematical Olympiad Handbook by
A. Gardner (available
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
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.
ought to forgive him for this failure(!)]
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.
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.
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.
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