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Re: HSC 2014 4U Marathon - Advanced Level H is the orthocenter of triangle ABC. Use AH as diameter to draw a circle which meets circle ABC at F. Prove that FH bisects BC

Re: HSC 2014 4U Marathon - Advanced Level Ah careless me. Sorry about that

Re: HSC 2014 4U Marathon haha alright

Re: HSC 2014 4U Marathon also, do not use a calculator under no cricumstances

Re: HSC 2014 4U Marathon Here's a nice Q (well in the syllabus carrot and Sean lol) ABC is a triangle with AB = 360, BC = 240 and AC = 180. The internal and external bisectors of CAB meet BC and BC produced at P and q respectively. Find the radius of the circle which passess through A, P and Q.

Re: HSC 2014 4U Marathon part i, ii are pretty self explanatory. for part iii) just expand (z - 1/z)^5 using binomial which will give pretty much give the required result. for the second part of part iii), just replace sin 3theta with 3 sin theta - 4sin^3 theta and rearrange to get sin5...

Re: HSC 2014 4U Marathon - Advanced Level These problems belong in another thread, which is just called the 4u marathon. anyways, a^3 + b^3 can be factoed to (a+b)(a^2-ab + b^2) =2 But from AM GM, a^2 + b^2 > 2ab > ab (for a,b>0). Hence the second factor is positive. Thus (a+b) multiplied...

Re: HSC 2014 4U Marathon - Advanced Level Sorry I mustve misunderstood then. Wait doesnt the strwjght vertical line refer to coprimality???

Re: HSC 2014 4U Marathon - Advanced Level On the last page you never provrd that if a is relatively prime to b then 2^a -1 is relatively prime to 2^b -1. All u did was prove that if a divides b then 2^a-1 divides 2^b-1.

Re: HSC 2014 4U Marathon p(n) = an^4 + bn^3+ .......+ e = 0 -e = an^4 + bn^3 + .....+dn = n(an^3+bn^2+.......d) Since factor in brackets is integer, -e/n must be integral hence n divides -e and hence also divides e

Re: HSC 2014 4U Marathon Which was why I was confused and asked if what you wrote was a typo

Re: HSC 2014 4U Marathon - Advanced Level Prove that (2^p)-1 is coprime to (2^q)-1 if p and q are distinct primes. Use HSC methods

Re: HSC 2015 4U Marathon Yes, but what's the point of doing it Realise's way? like in the end he still has to find the real value. I don't think there's anything wrong with my solution? (in the post after the question)

Re: HSC 2015 4U Marathon wasn't z on the numerator?

Re: HSC 2014 4U Marathon You change r to mod z. Then factor z out of denominator which cancels with the top. Then u get 1/ 2rcos theta EDIT: did u type the question wrongly or did Realisenothing read it wrong?

Re: HSC 2014 4U Marathon - Advanced Level Can anyone do the Q?

Re: HSC 2014 4U Marathon - Advanced Level firstly, i don't think you know what if and only if means. secondly, I think you're making wrong assumptions, for example opposite triangles in cyclic quads aren't necessarily similar. in other words, you've only proven it only one way. For...

Re: HSC 2014 4U Marathon - Advanced Level Prove that the tangents are opposite vertices of a cyclic quadrilateral intersect on the secant through the other two verticies IF AND ONLY IF the two products of opposite sides of the cyclic quadrilateral are equal (so prove both ways)

How was the paper? And if someone can upload the paper it would be nice

Yes, i do know, and just want to clarify that I never said that it was simple, nor that it was in the syllabus. All I said was that it can be done