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I THINK you can only get a maximum 10 bonus points from the Uni's I've heard offering this You better make sure you know before you give up quite yet :P (still 10 bonus points is huge)

bad luck :/ I don't think its just your school that has the bad trials, a lot of the selective schools are very similar in how bad their trials are imo

Re: HSC 2013 4U Marathon $An$ \ n \ $sided regular polygon is such that no side is vertical in gradient$ $Prove that if$ \ \ m_k \ \ $is the gradient of the$ \ k^{th} \ $ side of the polygon then$ m_1m_2 + m_2m_3 + m_3 m_4 + \dots + m_{n-1}m_n + m_n m_1 = -n

Re: HSC 2013 4U Marathon 1. It is clear through Demoivre's theorem: \cos x + \cos(2x) + \cos(3x) + \dots + \cos (nx) = \frac{\sin \left(n+\frac{1}{2})x}{\sin\frac{x}{2}} - \frac{1}{2} Substituting in x=\frac{2\pi m}{d} We get: f(m,d) = 0 \ \ $iff$ \ \frac{m}{d} \ $is not an integer$...

Same for me except I write small and it looks like I don't write as much as others D:

Re: HSC 2013 3U Marathon Thread Yep nice work.

Its a paper any school can do if they buy it off the CSSA company. The school is obliged to not release the paper until the security period is up and there are set examination dates for which the paper is given, for Paper 1 English that time is tomorrow. Each school marks their own papers to...

Re: HSC 2013 3U Marathon Thread $Consider the equation$ \ \ x^3+a = bx \ \ $for positive$ \ a, b $Show that$ $ There are 3 real solutions if$ \ \ a < \frac{2b}{3} \sqrt{\frac{b}{3}} $ There are 2 real solutions if $ \ \ a = \frac{2b}{3} \sqrt{\frac{b}{3}} $There is only 1 real solution...

If I can write a good story today I think I might go with that order as well

So is 1000 words the optimum amount for an Adv English essay? Also for AOS, what section do you start with? I know some people start with essay and move backwards.

You need to put all your code into tags: [ tex] \frac{10}{\pi!} [ / tex] (without the spaces) Just like when you press the black B to bold things, it automatically puts in [B ] and [/ B ] tags. Similarly just type in [ tex] [/ tex] (without the spaces)

Re: HSC 2013 4U Marathon I got 840 and I think i got a more logical answer now: My Solution

good luck!

Was it the 8 mark volumes one? :P

Re: HSC 2013 4U Marathon Ah ok thanks for the clarification

Re: HSC 2013 4U Marathon Ah yep that is true Apologies EDIT: What if I showed H_n - \ln (n) >H_{n+1} - \ln(n+1) And then made the argument that as n increases H_n - ln(n) keeps decreasing however it is bounded on the lower by 0, then it approaches some finite limit? We can show the above...

It is possible that the state rankers were lucky that the essay they made coincides precisely with the 2010 HSC question. It is good to know your text really well, and know the context and background well, then make the thesis on the day during reading time, then make your poitns based off of...

Re: HSC 2013 4U Marathon Ah sorry I thought you meant the e^k question for some reason. For that one, I aimed for students to first consider the upper rectangles of the graph y=1/x from x=1 to x=(n) H_n > \int_0^{n+1} \frac{dx}{x} H_n - \ln(n+1) > 0 H_n - \ln(n) > 0 Now the lower...

Re: HSC 2013 4U Marathon I expected students to do something similar to what Realise did. Does the existence of the limit need to be specified despite the upper bound that is independent of n? The limit should be able to be done simply using squeeze theorem Let the equal sides of the...

Re: HSC 2013 4U Marathon $Prove for some positive$ \ n \ $and real$ \ k e^{k\frac{n}{n+1}} < \left( 1+ \frac{k}{n} \right )^n < e^k $Hence evaluate the limit$ \lim_{n \to \infty} \left( 1+ \frac{k}{n} \right )^n