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Yeah, I never thought that the geo q in last year's paper was actually difficult but that's probs becos I had the intuition to solve those probs.

indubitably

Pretty sure this is an old Tournament of Towns problem but wasn't too difficult (maybe IMOSL G1?)... It is a bit of a pain to convert to directed angles so left as an exercise to the reader. If direction: We construct midpoints N, P, Q of BC, AC, BD respectively. Also, let AB \cap CD = R, AB...

yeah my bad, good job

No, you can have the case where they flip the same number of Heads.

$\noindent Let $\mathcal{P}$ be a parabola with focus $F$. Suppose distinct points $A$, $B$, $C$ are on this parabola. Let the tangents at $A$, $B$, $C$ enclose triangle $XYZ$. Show that $FXYZ$ is a cyclic quadrilateral.

Your symmetry argument unfortunately fails, as pointed out by blyatman. I gave this prob to my year's 4u class and most agreed this answer made sense at an intuitive level, but proving it rigorously was much more of a struggle.

I thought this was a very nice problem outlining the utility of symmetry: $\noindent After both have flipped $n$ coins, let $p_A$ be the probability Amy has flipped more Heads than Ben, $p_B$ be the probability Ben has flipped more Heads than Amy, and let $p_D$ be the probability they flipped...

Well, our school has compulsory participation in the Australian Maths Comp for yr 7 and 8. I did it in yr 7 and got 131/135, which was equivalent to a medal (top 0.03% or smth), and was invited to the Australian School of Excellence. This is a maths camp designed specifically for ppl who are...

$\noindent Amy and Ben are flipping $n$ fair coins and $n+1$ fair coins respectively. What is the probability that Ben flips more Heads than Amy?

Look at BOS Trials for hard papers.

Well, I only recently started looking at uni maths because I'm too old for the comps now. Nothing official, but I've done some of my own research work. I haven't done much tho becos rest of HSC cancer (especially with new science and english courses)

Yeah, my school let me accelerate 4 unit maths because I was in the Australian competition maths stream.

The only mark I lost in 2017 was the very last q because I made an arithmetic error ffs :(

I'm quite sure since I know I got 99 raw in 4 unit and 98 raw in 3 unit that year, and that paper I found was significantly easier that year. :(

For 2017, I know for a fact you needed 100 for State Rank, because I got 99 raw and that wasn't State Rank. :(

wut

Re: HSC 2018 MX2 Integration Marathon We can prove series expansion of $e$ using 4U maths.

Re: HSC 2018 MX2 Marathon Trivially, $\noindent P(x)=(2x^2+3x-2)(x^2+2x-1)=(x+2)(2x-1)(x+1-\sqrt{2})(x+1+\sqrt{2})$.

I'll be able to make it for MX1.