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Lol I'd forgotten about that feature.

Irrelevant to this thread – why post it here?

$Cube roots of unity means cube roots of the number 1.$ $The following is also true: any non-zero complex number $w$ has exactly three distinct cube roots, where a cube root of $w$ is a complex number $z$ satisfying $z^3 = w$.$ $Moreover, if $w=r\,\mathrm{cis}\,{\theta}$, where $r>0$ and...

$(b) If the two S's are together, we treat the pair of S's as one unit:$ $ [SS] O C K .$ $So this becomes like arranging four distinct letters in a row, which can be done in $4!$ ways, so the answer is $4!=24$.$ $(c) The two S's are separated by at least one other letter if and only if...

Search up Taylor's theorem.

Re: HSC 2016 4U Marathon - Advanced Level You can just do Sy123's one from the first page, since no-one's answered it yet:

Re: HSC 2016 4U Marathon - Advanced Level Another reason you don't need to assume some of them is that negative integers can be even and odd too, so you only need to know these three: odd + odd = even, odd + even = odd, even + even = even. (Or even simpler, if the two numbers being added have...

Does it have anything to do with <30 ATAR's not counting to the calculation of the median?

Re: HSC 2016 4U Marathon - Advanced Level $That's fine though. If $n$ is an integer and $n^2$ is even (that is, $n^2 = 2k$ for some integer $k$), then $n$ must be even.$

At least four subjects must count to your ATAR, so Studies of Religion must have at least one unit of it count.

$We want to say a function $f(x)$ can be written as $f(x) = c_0 + c_1 x + c_2 x^2 + \cdots $ (Taylor series centred about 0, i.e. Maclaurin series, where $|x|<R$, where $R$ is the radius of convergence). If it can be written this way, then differentiating $k$ times we have$ $$f^{(k)}(x) = 0 + 0...

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sin and cos.

A magical thing called Taylor Series.

$$1+1 = \sum_{k=0}^{\infty} (-1)^k \frac{\left(\frac{\pi}{2} \right)^{2k+1}}{(2k+1)!}+ \sum_{k=0}^{\infty} (-1)^k \frac{\left(2\pi \right)^{2k}}{(2k)!}$$

0 (mod 2).

Yeah; the only possible downside would be that high school students would find it really tedious and think matrices are pointless or get put off from studying them. But of course one needs to learn the tedious stuff before one can get to the fun stuff. Edit: oh right, pre-HSC. Yes, they should...

I think bringing in some linear algebra would be good, because currently the syllabus is mostly just calculus and no algebra.

I don't know for sure. One can see what types of matrix questions they had though here: http://4unitmaths.com/hsc1967-1974.pdf

Re: HSC Physics - Exam Paper (download) That's acceleration. Force is proportional to mass.