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You can find info about Lines of Best Fit on this thread: http://community.boredofstudies.org/18/physics/335522/line-best-fit.html

Yes, there's essentially no maths in HSC or Prelim. Chemistry apart from things like basic addition, subtraction, multiplication, division (and using logarithms for pH in Year 12 HSC Chemistry, which for this subject doesn't require much understanding of logarithms usually anyway).

$\noindent Yes, the divide by 4 is correct. This is because the area of a circle with diameter $d$ is given by $A=\frac{\pi d^2}{4}$. You probably know that if the radius is $r$, the area is $A=\pi r^2$. Since the radius is half the diameter, $r=\frac{d}{2}$. So$ $$\begin{align*}A&= \pi...

But memorising colours isn't that fun, is it? That's basically just a pointless test of memory.

Re: HSC 2016 3U Marathon The theorem itself is in the HSC, but somehow they don't seem to give it a name (in the HSC). So instead of referring to its name (Power of a Point Theorem) in the HSC exam, you should just write something like "product of intercepts of intersecting secants are equal"...

Re: HSC 2016 3U Marathon "Power of a point theorem" is a real name, but isn't used in the HSC as far as I know. So don't write that in the actual HSC. You can read more about it here: http://www.cut-the-knot.org/pythagoras/PPower.shtml .

Spot on! :)

Re: HSC 2016 3U Marathon Haha, why is that question funny?

Re: HSC 2016 3U Marathon $\noindent There are simpler ways to do this, for example, recall that $\phi$ is the positive solution to $x^2- x -1=0$. Then via products of roots, the other solution is $\psi := -\phi ^{-1}$. So$ $$\begin{align*} \phi^2 + \phi ^{-2} &= \phi^2 + \psi ^2 \\ &=...

Re: HSC 2016 3U Marathon You can have an A.P. with common difference of 0, but Paradoxica said in the question that that was a trivial one, implying that he wanted you to find the other solutions.

Re: MX2 2016 Integration Marathon $\noindent Technically it does matter. The primitive I gave has the integrand as a derivative for all $x\neq 0$, but the function has a (jump) discontinuity at 0 and so is not differentiable there.$ $\noindent Let $F(x) =...

Re: MX2 2016 Integration Marathon $\noindent Let $I=\int \frac{x^{2}}{1+x^{4}}\text{ d}x$, so$ $$\begin{align*} 2I &= \int \frac{x^2+1}{1+x^{4}}\text{ d}x + \int \frac{x^2-1}{1+x^{4}}\text{ d}x \\ &= \int \frac{1+\frac{1}{x^2}}{\frac{1}{x^2}+x^2}\text{ d}x + \int...

$\noindent Let $y=f(x)=\left( \ln x\right)^2$ ($x>0$), then $f^\prime (c) = 2\ln c \cdot \frac{1}{c}$. The point on the curve at $x = c$ is $\left(c, \left(\ln c\right)^2 \right)$. So using point-slope form, the equation of the tangent to the curve here is $y -\left(\ln c\right)^2 = \frac{2\ln...

Re: HSC 2016 2U Marathon $\noindent The denominator of the original expression (the one they asked us to simplify) is $\frac{1}{x}-x$. This is undefined iff $x = 0$ and equals $0$ iff $x =\pm 1$ (and the numerator is defined for all real $x$ except $x =0$.) Hence for the original expression...

I think Paradoxica might have been being tongue-in-cheek when he said that comment. Or at least, I thought he was being tongue-in-cheek when I first saw the comment (thought he was just jokingly taking a jab at English maybe), not sure now upon seeing his reply to your post I quoted.

Correct, 1 is not prime.

For two solutions (Q.1), we can also have k > 9.

$\noindent 6. Bit rushed since I need to go for a bit but I hope it's right. We have $f:\mathbb{R}\to \mathbb{R}$, with $f(f(x)+y) = x+y$, for all $x,y\in \mathbb{R}$.$ $\noindent Let $y=0$, then $f(f(x)) =x$ for all real $x$. Hence $f$ is an involution from $\mathbb{R}\to \mathbb{R}$. In...

Pretty sure every year people get state ranks / 99.95's etc. without coaching. Different things work for different people though. And I'm not sure whether or not the majority of HSC Science / maths state rankers had coaching, but I think it is quite likely to be the case.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread There isn't much to this question other than following through with the algebra and not making silly mistakes. Maybe post your working? It might just be a silly mistake you made.