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The Ultimate Maths Competition Thread

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Reply 120
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11234
8
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 MM. Show that MB=MC.


Can I take ptolemys theorem without proof?
Original post by 11234
Can I take ptolemys theorem without proof?

where?
Reply 122
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11234
8
Original post by gasfxekl
where?


Like generally in olympiad questions? Im quite unsure on what theorems we can take without proof
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
Reply 124
Avatar for 11234
11234
8
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
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 :indiff:
Reply 126
Avatar for 11234
11234
8
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 MM. 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
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?
Reply 128
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11234
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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...
Reply 129
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11234
8
Can anyone help with bmo1 1993 q3
Reply 130
Avatar for ben167
ben167
4
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
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
Reply 132
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ben167
4
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
Original post by ben167
Thank you


That was for this years papers. It will change alot as each pper sometimes scores vary by alot.'
Reply 134
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ben167
4
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
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.
Reply 136
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ben167
4
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
(edited 7 years ago)
Reply 137
Avatar for 11234
11234
8
Could anyone help with functional equations...finding them really challenging :frown:
Original post by 11234
Could anyone help with functional equations...finding them really challenging :frown:


I will write something up about them later when I am free :smile:.


Posted from TSR Mobile
Original post by 11234
Could anyone help with functional equations...finding them really challenging :frown:


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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