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re: HSC Chemistry Marathon Archive Correct, nice work.

re: HSC Chemistry Marathon Archive Nice trick question, after normal calculation you would arrive at pH9, but HCl is acidic and hence we can never go above a 7 pH (assuming standard conditions). Therefore the pH is extremely close to 7.

Re: HSC 2013 4U Marathon Well my working out was 1+x^2+...+x^{n-1}= \frac{1-x^n}{1-x} Differentiate: 1+2x+3x^2+...+(n-1)x^{n-2}=\frac{-nx^{n-1}+(n-1)x^n+1}{(1-x)^2} Sub in x=1/4, then make n approach infinity, here we do assume that \lim_{n \to \infty} n \cdot k^{-n} = 0 \ \ \ \ \ k>1...

re: HSC Chemistry Marathon Archive $You have 100mL of acidic solution of pH 1. 900mL of water is added, what is the new pH?

Re: HSC 2013 4U Marathon This is correct, I am wondering what you mean by summing each individually, I was aiming at a geometric series differentiation approach

Re: HSC 2013 4U Marathon :(, I will have a go at it later: As for another question: $Find the limiting sum$ \\ \\ \sum_{n=1}^{\infty} n \left(\frac{1}{4}\right) ^n

Re: HSC 2013 4U Marathon This problem only arises with choosing an even number of fruit, we will disregard the the situation with 6 fruits as you have mentioned as it will be reflected in 12 fruits and hence cancels out the arrangements anyway (but I get there is a problem). However the...

Re: HSC 2013 4U Marathon Let us establish the fact that if we pick an odd number of fruits, we cannot retain proportionality. Hence we keep all the odd numbered fruits arrangements (odd numbers above 6, I will get to this later) Now, for even number of fruits picked, for example say we pick 3...

Re: HSC 2013 4U Marathon Is my reasoning correct? I need to get better at perms and combs :(

Re: HSC 2013 4U Marathon The figurate numbers give the triangular numbers, sum of tri numbers (tetra), sum of that, and so on: The cool thing is that they can all be expressed in the form of a binomial co-efficient: http://en.wikipedia.org/wiki/Figurate_number I had another look at it, the...

Re: HSC 2013 4U Marathon For the first one I got 425

2U - Consumer Arithmetic 3U - (I love the 3U course so its hard for me to choose), but I will say 'Harder Inequalities' (they aren't even hard) 4U - (Can't comment yet, but I am guessing it will be Volumes or Conics) Perms and Combs is actually one of my favourite even though I am horrible at...

Re: HSC 2013 4U Marathon Correct - Nice work. I am working on a Complex Numbers question at the moment, should be good.

Re: HSC 2013 4U Marathon Correct, but those are the easy marks :s For part iii, use the result in part ii.

Re: HSC 2013 4U Marathon Your first value is wrong -> which has made the whole sequence wrong.

Re: HSC 2013 4U Marathon You can find all roots without finding a and b by considering conjugate root theorem and product of roots: 4=(1+i)(1-i) \alpha \ \ \ \ \rightarrow \alpha=2 And then considering sum of roots 2 at a time and sum of roots we can then find a and b. You are correct.

Re: HSC 2013 4U Marathon $Question Pell - 15 marks $Define the Pell numbers by the recursive relation$ P_n=\begin{cases} 0 \ \ \ \ \ $if$ \ \ n = 0 \\ 1 \ \ \ \ \ $if$ \ \ n = 1 \\ 2P_{n-1}+P_{n-2} \ \ \ \ \ n \geq 2 \end{cases} $i) Find the first 5 Pell numbers$ \ \ \ \ \ \fbox{1}...

re: HSC Chemistry Marathon Archive It would still fall under mole calculations wouldn't it? It tests ability to interpret the question and change from mass to moles. It doesn't really matter anyway.

re: HSC Chemistry Marathon Archive I guess :(

re: HSC Chemistry Marathon Archive But that isn't fun at all, talking about pH6 neutral water is fun. I would hate this thread to turn into a rote fest where people just spit out their rote learnt answers... to generic questions. (but then again I didn't make this thread so...)