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For 2U and 3U, you only need to do the past HSC and commercial papers (don't bother at all with school papers unless its early in the year). Then it comes down to efficiency, speed and accuracy during the exam. In 2U you need to have great enough speed for you to properly complete the paper...

Re: HSC 2013 3U Marathon Thread Hmm what makes you think Pythagoras Theorem will hold?

Re: HSC 2013 4U Marathon This was a good one (even though I said I won't post more series questions) $\sum_{k=1}^{n} \tan^{-1} \left (\frac{1}{1+k(k+1)} \right )

Re: HSC 2013 3U Marathon Thread I believe you this time :3 ====================== $In the above diagram, PQ is tangent to the circle with centre O$ $By considering what happens as P approaches Q, prove that the the radius of a circle to its tangent is always perpendicular$

I'm pretty sure Omed is just a troll, really.

Re: HSC 2013 3U Marathon Thread \sum_{n=1}^{\infty} \frac{n-1}{n!}

Re: HSC 2013 4U Marathon \int \tan (x) \tan(2x) \tan(3x) \ dx (provide proof)

siddy <3

If you don't get the ATAR you need, you have to spend more time in Uni to get to your desired course. The longer you stay in Uni, the more money you pay, hence the higher ATAR you have, if you are aiming for a high cut-off course will save you money in the long run.

Re: HSC 2013 4U Marathon That is the method I had in mind, nice work. This is the last series question I will post in a while, I want to ask more different questions. It is one that I'm trying to solve now but I haven't cracked it yet. $Prove that$ \tan \theta + \tan \left (\theta +...

Re: HSC 2013 4U Marathon Nice work guys, $Simplify$ \sin \theta \sin(2\theta) + \sin (2\theta)\sin(3\theta) + \dots + \sin(n\theta) \sin((n+1)\theta)

Re: HSC 2013 4U Marathon $Find 1+3x+6x^2+10x^3+ \dots

Re: HSC 2013 3U Marathon Thread $Find$ 1+ \frac{4}{5} + \frac{7}{5^2} + \frac{10}{5^3} + \dots + \frac{3n-2}{5^{n-1}}

Re: HSC 2013 4U Marathon i) First let x=cos theta, substitute it into the expression they ask to prove. We get: Prove: \cos n\theta = 2\cos \theta \cos(n-1) \theta - \cos(n-2)\theta With simple algebra and compound angle formula we arrive that LHS = RHS, also see that C_1(cos...

Re: HSC 2013 3U Marathon Thread Yeah as you can see, it isn't necessarily hard, just a nice little result. Very nice. (the only reason why I ask for a possible combinatorial proof is because I want someone to show me one)

Yeah sure I can try to help.

Re: HSC 2013 3U Marathon Thread $Take a number line interval from 0 to 1$ $Remove the middle third of this interval, i.e. remove the interval from 1/3 to 2/3$ $We are left with 2 intervals. Remove the middle third of each of these intervals$ $We create 4 more intervals, remove the middle...

re: HSC Physics Marathon Archive I'm pretty sure it is, isn't it? If we define work properly, let point A be on the equator and point B be the point 600km away: W_{AB} = \int_{A}^{B} F \ dx Where F is force, and x is the distance. By Newton's Law of Universal Gravitation: F=...

Re: HSC 2013 4U Marathon They're pretty cool aren't they?

Re: HSC 2013 3U Marathon Thread $Prove using Binomial Theorem or Combinatorics or otherwise$ \binom{k}{k} + \binom{k+1}{k} + \binom{k+2}{k} + \dots + \binom{n}{k} = \binom{n+1}{k+1} EDIT: Have I already posted this question? I have a feeling I already have.