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What do they ask academics when writing the HSC MX2 papers? Do they basically just want to make sure that everything in the paper can be made rigorous with sufficient knowledge? Also, wasn't a HSC MX2 Q once written by an academic in fact (maybe this is even a common thing)?

In fact, this can be said for most (or at least many) of the HSC maths topics, can't it?

Yeah, kind of like differentiating under integral signs, one of Feynman's favourite tricks (although this wouldn't be quickly justifiable in the HSC, unless students can just quote it, which I doubt).

What do you mean? That was basically like the 4U of those times (in that it was the highest level of maths in NSW secondary schools at the time, I think).

Found a place summing things like k.cos(kx) came up (in the papers before 4U): 1916 NSW Leaving Certificate Exam, Question 12 of Paper I (on page 3 of this document: http://4unitmaths.com/1916.pdf ). I'm not sure whether it's come up in HSC 4U papers, but I don't recall it being in any HSC...

If you're curious about the mathematics of triangulation (it's much simpler), you can read about it here: https://en.wikipedia.org/wiki/Triangulation#Distance_to_a_point_by_measuring_two_fixed_angles . A combination of trilateration and triangulation is triangulateration, used in surveying...

GPS uses trilateration. You can read about the mathematics of it here: https://en.wikipedia.org/wiki/Trilateration

Yes, you need to use the inductive hypothesis to make it a proof by induction. If you didn't make use of it, then you have essentially proved the statement without induction.

$\noindent The solutions aren't just $x_1,x_2,x_3\in \mathbb{R}$. That would be saying that ANY triple $\left(x_1,x_2,x_3\right)$ would satisfy those equations, but that's not the case (instead, we need to choose triples from the plane described by those equations. This is what the given answer...

$\noindent The 13 (b) one is a special case of a classic physics problem known as \textit{The Monkey and the Hunter}:$ https://en.wikipedia.org/wiki/The_Monkey_and_the_Hunter $\noindent Basically, if a hunter aims his gun so that it faces a monkey in a tree in a straight line, and fires, and...

$\noindent Are these both within the realms of inspection?: $\infty ! = \sqrt{2\pi}$, $\sum _{k=1}^{\infty} \frac{k^3}{2^{k}}=26$.$

Re: HSC 2016 2U Marathon Try splitting up the LaTeX code in half. :)

Re: HSC 2016 3U Marathon $\noindent Note $z=Ay^{-10}+B \mathrm{e}^{y}$. So $\frac{\mathrm{d}z}{\mathrm{d}y}=-10Ay^{-11}+B \mathrm{e}^{y}=-\frac{10A}{y^{11}}+B \mathrm{e}^{y}$.$

$\noindent Call the first equation (1) and the second one (2). From (1), since $a_{11}\neq 0$, we have $x_1 = \frac{b_1 - a_{12}x_2}{a_{11}}$. Now, sub. this in (2):$ $\noindent $a_{21}\cdot \frac{b_1 - a_{12}x_2}{a_{11}} + a_{22}x_2 = b_2$.$ $\noindent Multiply by $a_{11}\neq 0$: $a_{21}b_1 -...

What about colours for ion tests (and the ion tests themselves)? Wouldn't they have needed rote learning?

$\noindent The answer is that $f(x) \to \infty$ as $x \to 1^{+}$ This follows from the epsilon-delta definition of ``$f(x) \to \infty$ as $x\to a^{+}$'', where $a\in \mathbb{R}$. For your reference, the definition is that for any $K>0$ there exists a $\delta >0$ such that whenever...

I think one of the reasons behind why a lot of people hate HSC Chemistry is due to the level of rote learning involved.

Complete the squares.

The second one is completely normal, the first one is based on Riemann-Zeta 'magic'.

$\noindent What about the ``$\infty ! = \sqrt{2\pi}$'' or $\sum _{k=1}^{\infty} \frac{k^3}{2^k}=26$ results? Would you consider those ones worthy of being memorised?$