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BMO2-28th January

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IMO compendium (1959-2004, there's one to 2009, but couldn't find it)
http://www.cs.elte.hu/~nagyzoli/compendium.pdf
the first bit may be useful...
Original post by Renzhi10122
IMO compendium (1959-2004, there's one to 2009, but couldn't find it)
http://www.cs.elte.hu/~nagyzoli/compendium.pdf
the first bit may be useful...


Very nice! Added!


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Alright lads plan of action

1. Bang out these awesome resources
2. Smash a 0 in the test

All me
Original post by StrangeBanana
Alright lads plan of action

1. Bang out these awesome resources
2. Smash a 0 in the test

All me

Quick mote to alot of people, alot of yhese resources are bmo2<=


Thanks a lot, have already begun on the number theory one.

They all seem to be great resources but I have heard rumours that recently they have stopped putting the standard type inequalities on the papers because Muirhead's Theorem just kills them. Has anyone else heard anything like this and is it true?
Original post by EmptyMathsBox
Thanks a lot, have already begun on the number theory one.

They all seem to be great resources but I have heard rumours that recently they have stopped putting the standard type inequalities on the papers because Muirhead's Theorem just kills them. Has anyone else heard anything like this and is it true?


That is kinda true, but they may still appear, especially asymmetric inequalities and those involving squares being more than 0

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Original post by EmptyMathsBox
Thanks a lot, have already begun on the number theory one.

They all seem to be great resources but I have heard rumours that recently they have stopped putting the standard type inequalities on the papers because Muirhead's Theorem just kills them. Has anyone else heard anything like this and is it true?


Yh they still might put them in there, or if one makes a problem tricial they could put a note and say (Muirhead cannot be used) although I doubt they would. Inequalities come up every 4-5 years anyway. I guess one is due tbh.
Original post by Renzhi10122
IMO compendium (1959-2004, there's one to 2009, but couldn't find it)
http://www.cs.elte.hu/~nagyzoli/compendium.pdf
the first bit may be useful...


Looking back to the 1960's and early 1970's it amazes me how easy the IMO used to be back then (I don't think it the level is much higher than difficult BMO1).
Original post by EmptyMathsBox
Looking back to the 1960's and early 1970's it amazes me how easy the IMO used to be back then (I don't think it the level is much higher than difficult BMO1).


Lol yep. First paper first question prove this is irreducible
21n+4/14n+3 or something.
But then there werent any rounds before tbh like BMO or national contests and it was a few countries.


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Original post by Renzhi10122
IMO compendium (1959-2004, there's one to 2009, but couldn't find it)
http://www.cs.elte.hu/~nagyzoli/compendium.pdf
the first bit may be useful...


2002/03 Question 2 can you check?
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ImageUploadedByStudent Room1452192171.254117.jpg



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Original post by physicsmaths
2002/03 Question 2 can you check?
Attachment not found

ImageUploadedByStudent Room1452192171.254117.jpg



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I can't read it...
Original post by Renzhi10122
I can't read it...


Which prt lol?
All of it? If so I can quickly rewrite it


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Original post by physicsmaths
Which prt lol?
All of it? If so I can quickly rewrite it


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Yup, please rewrite the whole thing lol.
Original post by physicsmaths
Which prt lol?
All of it? If so I can quickly rewrite it


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My solution.

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Original post by Renzhi10122
Yup, please rewrite the whole thing lol.


ImageUploadedByStudent Room1452194297.072675.jpg



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Ok, so on the most part, it's fine. Your proof for why one area was a quarter of the other was not needed, since it comes straight away from the fact that AB=4AD and also, the formula you quoted for phi was wrong. Areas should be in square brackets, eg [APD]. But yeah, correct on the whole.
Original post by Renzhi10122
Ok, so on the most part, it's fine. Your proof for why one area was a quarter of the other was not needed, since it comes straight away from the fact that AB=4AD and also, the formula you quoted for phi was wrong. Areas should be in square brackets, eg [APD]. But yeah, correct on the whole.


Oh yh forgot the sinheta.
Cheers yh I forgot about the square brackets thing.
So one would not have to consider the sintheta=0 and sin(theta-alpha)=0 cases? As I divide through by them
To get to my final two expressions.


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Original post by physicsmaths
Oh yh forgot the sinheta.
Cheers yh I forgot about the square brackets thing.
So one would not have to consider the sintheta=0 and sin(theta-alpha)=0 cases? As I divide through by them
To get to my final two expressions.


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Well, those cases are degenerate. I would recommend just using similar triangles tbh, it saves a lot of time and algebra. If you see a lot of terms cancel, that should probably suggest similar triangles to you. If you use similar triangles, you could also possibly gain some new information about angles from information about lengths.
Original post by Renzhi10122
Well, those cases are degenerate. I would recommend just using similar triangles tbh, it saves a lot of time and algebra. If you see a lot of terms cancel, that should probably suggest similar triangles to you. If you use similar triangles, you could also possibly gain some new information about angles from information about lengths.


Yh I seen they were similar but didnt use those ratios.
For some reason in my head it went
similar triangles->ratios of areas


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