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# The Ultimate Maths Competition Thread

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1. (Original post by gasfxekl)
okay
some other useful stuff is angle bisector theorem and angles subtended on the same arc but im sure you know that already
okay try this one
in a quadrilateral ABCD where BC//AD the diagonals intersect in P. the circumcircles of ABP and CPD intersect AD in S and T respectively. Let the midpoint of ST be . Show that MB=MC.
Can I take ptolemys theorem without proof?
2. (Original post by 11234)
Can I take ptolemys theorem without proof?
where?
3. (Original post by gasfxekl)
where?
Like generally in olympiad questions? Im quite unsure on what theorems we can take without proof
4. (Original post by 11234)
Like generally in olympiad questions? Im quite unsure on what theorems we can take without proof
i have no clue youd have to check the relevant websites. i think you can tho
5. (Original post by gasfxekl)
i have no clue youd have to check the relevant websites. i think you can tho
Ok thanks I'll have a look at your question
6. (Original post by Maths465Man)
Well I've got GCSE ICT tomorrow and AS and A2 Maths as well.
(Original post by Maths465Man)
No I'm in Year 10
Dafuk
7. (Original post by gasfxekl)
okay
some other useful stuff is angle bisector theorem and angles subtended on the same arc but im sure you know that already
okay try this one
in a quadrilateral ABCD where BC//AD the diagonals intersect in P. the circumcircles of ABP and CPD intersect AD in S and T respectively. Let the midpoint of ST be . Show that MB=MC.
Ive got a proof but it depends on the circumcircles having the same radii and I'm assuming you cant have them different otherwise BC would be parallel to AD? Am I on the right lines and how would I conclude my proof
8. (Original post by 11234)
Ive got a proof but it depends on the circumcircles having the same radii and I'm assuming you cant have them different otherwise BC would be parallel to AD? Am I on the right lines and how would I conclude my proof
as far as i know you dont need the radii to be the same... what were your ideas?
9. (Original post by gasfxekl)
as far as i know you dont need the radii to be the same... what were your ideas?
I'll have a second look after S2 on wednesday...
10. Can anyone help with bmo1 1993 q3
11. Roughly how well would a year 11 student need to do on BMO1 to get into the Hungary camp and BMO2 for trinity? Renzhi10122 physicsmaths
12. (Original post by ben167)
Roughly how well would a year 11 student need to do on BMO1 to get into the Hungary camp and BMO2 for trinity? Renzhi10122 physicsmaths
Erm like 40+ in BMO1 i would think and 10+ in BMO2. There werre like 5 kids in yr 10/11 q who were notnon theleaderbord this year
13. (Original post by physicsmaths)
Erm like 40+ in BMO1 i would think and 10+ in BMO2. There werre like 5 kids in yr 10/11 q who were notnon theleaderbord this year
Thank you
14. (Original post by ben167)
Thank you
That was for this years papers. It will change alot as each pper sometimes scores vary by alot.'
15. (Original post by physicsmaths)
That was for this years papers. It will change alot as each pper sometimes scores vary by alot.'
I would really like to get into these camps next year ; however on past papers I have only been getting around 25-30 points so clearly I am a long way off. How did you prepare, and how exactly does modular arithmetic work (i.e.Q1 in this years' BMO1 paper)? Thanks
16. (Original post by ben167)
I would really like to get into these camps next year ; however on past papers I have only been getting around 25-30 points so clearly I am a long way off. How did you prepare, and how exactly does modular arithmetic work (i.e.Q1 in this years' BMO1 paper)? Thanks
Just practice tbh! Modular arith is just looking at remainders upon division. You don't need mod for Q1 explicitly iirc. As i remember the sol not havibg it.
Tbh it was harder then usual as a Q1.
17. (Original post by physicsmaths)
Just practice tbh! Modular arith is just looking at remainders upon division. You don't need mod for Q1 explicitly iirc. As i remember the sol not havibg it.
Tbh it was harder then usual as a Q1.
Sorry to bother you ; I am just really interested. If you don't mind me asking, what was the trinity camp like and have you gone before this year? @renzhi10122 @physicsmaths
18. Could anyone help with functional equations...finding them really challenging
19. (Original post by 11234)
Could anyone help with functional equations...finding them really challenging
I will write something up about them later when I am free .

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20. (Original post by 11234)
Could anyone help with functional equations...finding them really challenging
give an example? you must always plug in easy values like x,0, x,-x etc. then another principle is to make things cancel- for example if u have xf(y)+y somewhere try subbing x=a/f(y) so that u get a+y, etc.
if you have a symmetric expression switch around x and y.
Note that f(f(x))=x or 6x or whatever implies injectivity! try to get injectivity as it is often very useful.

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