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Since \alpha is a root then \alpha^2+\alpha+1=0 Which implies \alpha^n+\alpha^{n-1}+\alpha^{n-2}=0 Use the same argument for \beta and the result follows For the strong induction step use the property that T_{n+1}=-T_n-T_{n-1} and...

This is not true. Moderating of internal school assessment marks is based on external HSC marks within a subject. It looks at each school's internal marks and adjusts them based on their performance in the external HSC exam for that subject. There is no comparison between subjects at all in how...

Not sure where you got that from but this is definitely not true. If you look that the actual state ranks in previous years you see plenty of examples where students from lower ranked schools were placed above or tied with those from higher ranked schools

As long as it’s for educational purposes only and not for commercial sale then I think it should be okay.

See the yellow sticky which has the hyperlink and go to the relevant subject

For part a), let y = 1 + 1/z and the equation reduces to a roots of unity problem (but with one less solution as y cannot equal 1). Use some double angle manipulations when you return it in terms of z and you should get the answer.

The decomposition step is perfectly valid for integer values of x. The invalid step is the differentiation step because it is not recognising that the number of terms is also a variable.

The main flaw is that the number of terms is also a variable whereas the additivity of differentiation applies when the number of terms is fixed. A similar example is writing: x = 1+1+1+....+1 (x-times) Leading to the 1 = 0 fallacy. Another flaw is that this decomposition assumes x is an...

The scaled mark is the mark that goes into calculating your ATAR - done by UAC. The aligned mark is the mark you see on your HSC document - done by NESA. They are two independent ways to treat the same raw mark for different purposes.

If you write out Rn explicitly using the general terms of a GP you should notice that you can factorise rn. From that point the rest should follow.

Pretty much agree with this, especially the last sentence. Practicing old syllabus circle geometry questions only really helps in terms of sharpening general geometry reasoning skills (which you won’t use much of since the new syllabus has minimal geometry). It’s less relevant in helping with...

There is no “chicken-egg” thing here. Aptitude (for problem solving in this context) by definition means an individual’s innate (not learnt) abilities or natural instincts - which is clearly separate from any abilities gained from practice. It is something you and I (and anyone naturally...

So we both agree that a difficult integral can be solved either by: - calling upon prior experience; or - using problem solving skills to derive a solution from scratch How is that consistent with your primary assertion later on suggesting that having prior experience is the only way to be able...

Maybe today it looks obvious that you are drawing from your personal experience but I am pointing out that a student could never have experienced that type of ‘tricky’ integral and still be able to independently construct the solution from scratch - using only logical deduction and basic IBP...

My point was not about the application of a memorised/prescriptive strategy, but rather the construction of a strategy from scratch by analysing an unfamiliar problem and applying deductive reasoning (e.g. to arrive at the best choice of what to differentiate/integrate). Maybe you were directly...

Rote learning every single method out there is one way to be successful at integration. You can be good at integration without rote learning, especially if you are good at recognising patterns and have good foresight on what an approach will lead to. Classic example is integrating say x3ex2...

I don’t see much difference in trying to figure out a difficult integral and figuring out a difficult Olympiad problem in terms of skills drawn upon. Both require problem solving skills (i.e. the skill of applying your knowledge) which is completely separate to the method of acquisition of said...

The performance of a handful of people in an Olympiad is not necessarily representative of the population’s average.

Not sure what you mean by that? Either way, it’s hardly relevant because they’re counted in the cohort regardless and will influence the moderating of internal marks. That table is evidence that just because you’re in a top tier selective school doesn’t mean you’re guaranteed to get a high...

Not Ruse, but here is the ATAR distribution for Sydney Boys http://www.sydneyboyshigh.com/publications/document-library/doc_view/7845-atar-breakdown-2001-2018 Out of 207 students in 2018, 52 (roughly 25%) got ATARs below 90 and 25 (roughly 12%) got ATARs in the 70s or less. So basically, if...