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Re: Survey- Impact of mathematical education on answering simple Mathematics questio Make sure to keep in mind that correlation does not imply causation. :)

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $Let $y_1 = \cosh x = \frac{\mathrm{e}^{x}+\mathrm{e}^{-x}}{2}$ and $y_2 = \sinh x = \frac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{2}$.$ $Then$ $$\begin{align*}y_1 ^\prime &= \frac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{2} = y_2 \quad...

You'd do really well. Your 90+ (assume this is after aligning) would be your external mark. Your internal would be the highest out of all moderated external marks from your cohort, since you're first internally. This would be 90+ too. So in the end you'd end up with an overall mark of 90+...

The raw mark isn't very important, what's important is how you went relative to the cohort.

The acronym should actually be SDD (Software Design and Development). I think sirable1 just typo-ed SSD in his post. And then everyone kept saying SSD.

Re: HSC 2016 3U Marathon I think LaTeX is just messing up on this site, it happens once in a while.

Re: HSC 2016 4U Marathon I think it's messing up on the site once again (it's not working for me either).

Your school shouldn't be able to influence this, should it? Maths Extension 1 & 2 should each count as two units for your HSC.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $Yeah, maybe he thought that $\mathrm{e}^{x^k}$ means $\left(\mathrm{e}^x\right)^k$ (which, of course, it doesn't).$

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $No, but possibly appleibeats typed it wrongly and it was meant to be $x\mathrm{e}^{x^k}$ (in which case we can clearly do it using analysis of odd/even functions assuming $k>0$)? Nesting in powers is done by doing the powers...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread IBP stands for Integration by Parts, an integration technique taught in HSC 4U Maths.

$(a) Let the distance fallen in the $n^{\text{th}}$ second be $u_n$ (in metres). So $u_1 = 3,u_2 = 9, u_3 = 15$, etc. We assume the distances fallen form an arithmetic progression. The starting term is $u_1 = 3$ and the common difference is $d=6$.$ $Part (a) asks us to find the value of...

$\noindent Note that a ``pair'' is two cards of the same rank (e.g. two Queens or two Aces etc.)$ $\noindent (a) The first card on the table can be anything. For the second card, it is one of the remaining nine. Exactly one of these remaining nine cards would form the pair with the first card...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $So in summary:$ $Natural domain: $x>0$$ $Range: $y\leq 4 + \mathrm{e}^{-1}$.$

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $We have $y=f(x)=-x\ln x + 4$. Note that since we have a $\ln x$, we need $x>0$. Hence the natural domain is the positive reals $\mathbb{R}^+$ (i.e. the set of all real numbers $x$ such that $x>0$). Note that as $x \to 0^+$...

Re: HSC 2016 3U Marathon "Lattice points" is a standard mathematical term. But I agree that if this question came up in the HSC (unlikely in itself these days), instead of saying "lattice points", they would probably explain it (by saying "integer coordinates" or something), and maybe even...

Re: HSC 2016 3U Marathon $\noindent For the benefit of those who don't know, \textsl{lattice points} means points with integer coordinates. E.g. points like $(1, 0), (-5, 3)$, etc.$ $\noindent So you should have a picture like this in mind when thinking of lattice points:$...

$You're welcome! Also, Wikipedia has the derivation of the equation for $v$ given on John Baez's page. In fact, Wikipedia derives the equation for $\Delta v$, but this will just be equal to our final speed $v$ if we start with an initial rocket speed of $0$, which is what we'd expect to do.$...

Re: HSC 2016 4U Marathon It's generally not used in the HSC or school (I guess because divisibility isn't a big topic in the HSC), but it is a standard mathematical notation.

$Also check out John Baez's excellent article on this matter here:$ http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html $He discusses what we mean by a ``uniform acceleration'' and provides the useful equations, but doesn't derive them there. For a derivation, see...