BMO mark scheme?

worried about BMO...
Hmm...
how about bmo making?
can i use some principle such as Cauchy's Inequality or Chebyshev's inequality without proving it?

Reply 1

OCC++

i would'nt be too sure but i think as a general rule of thumb u can.

Reply 2

Simba

Winter

can i use some principle such as Cauchy's Inequality or Chebyshev's inequality without proving it?

Yes as long as you clearly state what you're doing. That said - the general rule of thumb in mathematics is that you shouldn't use a theorem unless you're at least familiar with the proof!

Reply 3

Kolya

Simba

Yes as long as you clearly state what you're doing.

Perhaps add the caveat that the theorem one quotes should not completely trivialize the problem?

Reply 4

Simba

Lusus Naturae

Perhaps add the caveat that the theorem one quotes should not completely trivialize the problem?

Hmm, I'm not sure where the boundary comes in olympiads (if indeed there is one). To be on the safe side I suppose if you do wish to use such a theorem you could prove it :smile:

Reply 5

wiio

I think there is an extent to which they might not appreciate you doing that, particularly if it were to provide any kind of advantageous short-cut to the answer. I'm pretty sure that the BMOs tend to ask only questions which can be answered using the more basic elements of the school curriculum, which will therefore be how they might expect you to get the answer - so I would only resort to using such theorems once you are sure you cannot find a way without.

Reply 6

DFranklin

Simba

Hmm, I'm not sure where the boundary comes in olympiads (if indeed there is one). To be on the safe side I suppose if you do wish to use such a theorem you could prove it :smile:

For the IMO, at any rate, I have a feeling that you can quote any published result without proof; I specifically seem to recall this causing problems when set questions do turn out to be trivialised by some obscure theorem or lemma. On the other hand, I also hear that if you do something like that, they will be very very strict on the marking, so if you making the slightest slip-up you might end up with no marks.

As a specific, I'm pretty sure people have said using Muirhead's inequality is frowned upon, and you are better off using AM-GM etc if possible.

Reply 7

evariste_3086

quoted from from the ukmt yearbook uk leader's diary 2006:
"the imo 2006 question 5 invovled reducing the problem to the known part (the case k<=2). The jury decided that doing this known problem was worth 3 marks, but merely quoting the result, chapter and verse, from the literature was worth 0. However, quoting known results has always been legitimate mathematics and introducing a special rule that on this occasion only, quotation is not allowed, was im my opinino unfair"

you could always finish off by saying by Muller's theorem result follow, if you are truly stuck :smile:

(at least ive not wasted money on these books now : still cant fathom out BMO!!)

Reply 8

Winter

I got 2002/3 paper and the official solution to a inequality question given is AM-GM. but what's the boundary. certainly i can't say " as xxxx said, so the inequality is correct" >.< i have been in england for only 4 months , duno what the "basic" theorem is. i don't want to prove it not for i cannot sometimes the proof is too complex to write......time is limited.....