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9(9^{k+1} - 1) - 8(k+1) \\= 9(64P + 9 + 8k - 1) - 8(k +1) \\= 9.64P + 64k + 64

Yeah, looks like it is broken at the moment

Note that P'(x)=4x^3+2Ax and P''(x)=12x^2+2A. P(x) is concave up with a minimum turning point at (0,B). Hence, P(x) > B > 0 so no real roots.

State rank is not the same as a first in state. To be first in state (i.e. where you actually get notified to be given an award) it is almost a pre-requisite you come first internally. However, that is not necessary for a non-first state rank (where there is no notification, you just find out...

Just realised the x and y axes are differently orientated. Is that a typo? Or is that deliberate?

MC updated with working

Converting a mark out of 70 into a mark out of 100 will lead to decimal places.

Imagine showing that picture out of context...

Also, slightly controversial, I quite liked the sample proportion question as it really tested whether you knew your stuff conceptually. Most sample proportion questions are pretty generic just blindly plugging numbers into formulae.

My personal view was it more like what you “expected” from the HSC i.e. pretty stock standard questions until you dive into Q13 onwards or last couple of multiple choice (I was very surprised they went very easy on perms/combs though). The thing about last year’s paper was that the combinatoric...

Q11 updated with working

The distribution of exam marks of the cohort are meant to be the "benchmark" for moderating the internal marks to be consistent across the state. A student who ranks first internally obviously has to get the highest internal mark (it wouldn't make sense otherwise) regardless of what he/she gets...

Fixed. Thanks.

So I thought I would have a go at doing solutions to the full Maths Ext1 HSC paper, particularly in LaTeX. Turned out to be way more time consuming than expected doing it with LaTeX....(also ceebs with graphs/diagrams). Disclaimer: These answers may contain errors, so feel free to point any...