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Re: MX2 2016 Integration Marathon Other method is to just rationalise the numerator straight away and then have a square root of quadratic in the denominator and a linear term in the numerator, which can easily be split up and integrated (bit tedious).

Yep thought so after posting, couldn't be bothered deleting the post though.

"Literally"? :p

Re: HSC 2016 4U Marathon - Advanced Level $Also, not sure about dan964's Q. If $f(nx)$ and $g(nx)$ are identical degree $n$ polynomials, they are equal for more than $n$ input values, so they are identical polynomials. Then if $f(x)^2 + g(x)^2=1$ (by this I assume he meant identically 1), we...

Maths Extension 1 is not necessary for Medicine in terms of content (i.e. there's not much maths in Medicine).

Re: HSC 2016 4U Marathon - Advanced Level I do remember some of these had solutions posted up (e.g. definitely remember simpleetal posting up his solution to his problem).

Re: HSC 2015 4U Marathon - Advanced Level My guess is this thread will get locked soon unfortunately, since the 2015 HSC is over. You might want to check out the corresponding 2016 HSC thread...

$Given: $z=f(x,y) = z = x^2 y+xy+xy^2+x^2+y^2+x^3+y$.$ $Compute partial derivatives:$ $$\frac{\partial f}{\partial x}(x,y)=2xy + y + y^2 + 2x + 3x^2 $$ $$\frac{\partial f}{\partial y}(x,y)= x^2 + x + 2xy +2y + 1 .$$ $Set both partials to 0 to obtain simultaneous equations:$...

I think he meant how to create a thread.

He said be did best in HSC Economics and Physics:

Well reading that document, we see that the "Course Score" is not simply the average of the school and examination marks. The average of the (standardised) examination mark and (standardised moderated) school mark is actually termed the "Combined Mark". (As that document says, they standardise...

Does WA's version of BOSTES have any information about how moderation is done? For NSW HSC, BOSTES has information about this on their website.

I don't know how the WACE system works, but if the important "School mark" is not 90 (i.e. is 76.2 or something), why are they showing the 90 as your school mark on the certificate? It's like how in the HSC, they show you your relevant mark for the school mark (called Assessment Mark in HSC)...

Yeah it's nothing like HSC 4U Mechanics. One way to put it is that people like Einstein would probably have failed it (ironic, as there's parts of the course about Einstein. Just not enough about his physics. Haha.).

'Doozy' in what way haha? As in easy, or hard? (Could be either since according to Google, 'doozy' means 'something outstanding or unique of its kind.').

HSC Physics Module 1 (Space) is mainly just subbing numbers into formulas for the quantitative questions. There's some rote learning too, but not as much as the later HSC Physics Modules. Meanwhile, HSC Chemistry Module 1 (Production of Materials) is almost entirely rote-based. Similar story...

$Your working was correct up to and including $S_n =\frac{n}{2} (19+n)$. We now just need to solve this quadratic equation. We have$ $$\begin{align*}390 &= \frac{n}{2}(19+n)\\ \Rightarrow n(19+n) &= 780 \\ \Rightarrow n^2 +19n -780 &= 0 \\ \Rightarrow (n-20)(n + 39)&= 0.\end{align*}$$ $Taking...

Re: MX2 2016 Integration Marathon $\noindent I think you accidentally differentiated at the end instead of integrated? If we have inverse tan's in the integrand, we should use Integration By Parts to get the primitive.$ $\noindent \textbf{NEW QUESTION}$ $Find $\int \sqrt{\frac{x}{1-x}}...

Was the Brouwer fixed point theorem used by Nash to prove the existence of a Nash Equilibrium in a game or something? I don't know too much about game theory haha but this was something I think I heard. And is your use of Russia as the country at all a subtle reference to this game theory of...

$\noindent Yep. Such tricks can be played with any conditionally convergent series :). Riemann showed that any conditionally convergent series can be rearranged so that the sum comes out to be any chosen real number, or diverge to $-\infty$ or $+\infty$. This is described in the link below for...