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Re: MX2 Integration Marathon I don't think that is correct

Re: HSC 2013 4U Marathon The answer should be \frac{\pi^2}{2}

Yeah I'll make sure to come this year (only the 4U paper though). I hope you haven't decreased the difficulty by a lot though =(

Re: MX2 Integration Marathon \int \frac{x+2}{(x^2+3x+3) \sqrt{x+1}} \ dx

Re: HSC 2013 4U Marathon $Show$ \sum_{k=1}^{\infty} \frac{6^k}{(3^{k+1} - 2^{k+1})(3^{k} - 2^k)} = 2

When this happens its done in a way that there is a lot of handholding involved (HSC 2010 Q8 for example), making it lose a lot of difficulty.

Re: MX2 Integration Marathon Ah yes of course, that a little silly of me

Re: HSC 2013 4U Marathon This is a good inequality: $Prove for real$ \ \ \{ a_k \} \ \ $and$ \ \ \{b_k \} \sum_{k=1}^{n} \sqrt{a_k^2+ b_k^2} \geq \sqrt{ \left(\sum_{k=1}^n a_k \right)^2 + \left(\sum_{k=1}^n b_k \right )^2}

Re: MX2 Integration Marathon Yep (but a=0 is also a solution :P)

Re: MX2 Integration Marathon $Find$ \ \ a \ \ $such that$ \int_0^{a} x^n \ln x = 0

Re: HSC 2013 4U Marathon Oh I see, my answer was way off. Pretty amazing how that strategy increases probability by a lot though.... ===== $A regular polygon of unit length with points$ \ \ X_1, X_2, X_3, \dots , X_n $Let$ \ \ d_k = X_n X_k $Evaluate$ \lim_{n \to \infty}...

I'll answer this to the best of my knowledge Principal square root or positive square root is as its name suggests the positive number which when squared gets that new number. When you do complex numbers, there will be a question saying: 'Find the square roots of 5+2i', there is no concept...

Re: HSC 2013 4U Marathon Ah well, can you post the solution soon if no one gets it? ===== $Consider the sequence$ a_0 = x a_{k+1} = \sin (a_k) \ \ \ $for$ \ \ k \geq 0 $Show that$ |a_{n+1}| < |a_n| \ \ \ $for non-negative integer$ \ \ n

Animal Farm - George Orwell is a nice short one, I wouldn't call it 'realistic' fiction, but the metaphors are incredibly obvious so you can link it to real life anyway A more 'realistic' one would be, 1984 - George Orwell, very thought provoking in my opinion Lord of the Flies - William...

Probability (everything in it)

Re: HSC 2013 4U Marathon $Let$ \ n \ $be an even positive integer$ $Let$ \ p(x) \ $be an$ \ n$-degree polynomial such that$ p(k) = p(-k) \ \ $for$ \ \ k=1,2,3,\dots,n $Prove that there is a polynomial$ \ \ q(x) \ \ $such that$ \ \ p(x) = q(x^2)

Re: HSC 2013 4U Marathon Here is my attempt for (iii) First, lets generalize this for (2n) unlucky HSC students. Consider the sequences: a_1, a_2, \dots, a_n b_1, b_2, \dots , b_n Now, instead of having the student 'k' picking a box, it will be student a_n Now, the first sequence...

Yes because extremist muslims have never killed other Muslims before

Mathematics is not about learning each type of question and then using your knowledge on what to do for each one, maybe this is more common in 2U maths. But 4U maths, especially at HSC level (probably not at school level due to quality), they will largely have different types of questions here...

Re: HSC 2013 4U Marathon Could you clarify what is meant by (iv), what does it mean to make a triangle of 'equal area' what is it equal to?