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Re: HSC 2013 4U Marathon This is right. The whole point of the question is to get a telescoping sum... those come up in the HSC a lot (not really).

I think polynomials should be studied in extension 1 and complex numbers should remain. I'm not a uni student btw.

Re: HSC 2013 4U Marathon Yeah, I meant \sum_{k=0}^{n}k\times k! Your answer is wrong.

I like your ideas very much, very similar to mine. I think there is way too much applied maths in HSC maths. This may make it more interesting and 'useful' but I think applied maths belongs to university as it is basically divided into engineering, physics, actuary, stats, computing, etc. which...

Re: HSC 2013 4U Marathon Hint: expand and try to get a telescoping sum.

Re: MX2 Integration Marathon I will skip the IBP step: \int \sqrt{\frac{1}{a-x}}\sqrt{\frac{1}{x-a}}dx=\int \frac{1}{\sqrt{-(x-a)^{2}}}dx $Let$ u=x-a, du=dx \therefore -i\int \frac{1}{u}du=-ilogu=-ilog(x-a)+c \therefore \int \arcsin(\frac{x}{x-a})=x \arcsin(\frac{x}{x-a})+-ilog(x-a)+c

Re: MX2 Integration Marathon Make the substitution 2 theta = theta

Re: HSC 2013 4U Marathon Can also be done by expanding cos(nx+x) but your method is nice too. ============================== $What does$ \sum_{k=0}^{n}k\times k! $converge to?$

Re: HSC 2013 4U Marathon $Prove that$ \frac{ \sin x}{ \cos x}+\frac{\sin2x}{\cos^{2}x}+\frac{\sin3x}{\cos^{3}x}+\cdots+\frac{\sin nx}{\cos^{n}x}=\cot x-\frac{\cos(n+1)x}{\sin x \cos^{n}x} Do not use induction.

Re: HSC 2013 4U Marathon Nice work.

Re: MX2 Integration Marathon This is the integration test taken by applicants to MIT undergrad courses. Have a go at it and post you solutions. http://web.mit.edu/abhinavk/www/integrationbee/qual2012.pdf

But why should Australia take them? If we keep taking these people Australia will keep getting worse and worse. We are not a charity.

I agree.

Re: HSC 2013 4U Marathon $For any positive real numbers$ a,b,c $show that the following inequality holds$ \left ( \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \right )\geq \left ( \frac{c+a}{c+b}+\frac{a+b}{a+c}+\frac{b+c}{b+a} \right )

Hey, can you please do this: http://community.boredofstudies.org/showthread.php?t=304033 Curious to know your results :)

Re: MX2 Integration Marathon

Would neg.

Re: HSC 2013 2U Marathon $Solve \cos(x)=\cos(3x)

You can check your answers here: http://www.wolframalpha.com/

Re: HSC 2013 2U Marathon \int \sin(3x)dx I haven't done 2U so I don't know how difficult the questions are supposed to be. This is an easy one.