HSC 2016 MX2 Marathon (archive) (1 Viewer)

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wu345

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Re: HSC 2016 4U Marathon

yeah n sorry why i am so bad with latex
 

wu345

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Re: HSC 2016 4U Marathon

Interesting result, but do you know a method that involves using the binomial theorem? the above proof of palindromic polynomials seems too long to write in an exam given the question was two marks
 

Paradoxica

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Re: HSC 2016 4U Marathon

Interesting result, but do you know a method that involves using the binomial theorem? the above proof of palindromic polynomials seems too long to write in an exam given the question was two marks
The fastest way would probably be to use induction on n, Binomial expansions look tedious from this perspective.

Or maybe not, if someone can manage the cases correctly to obtain a valid expansion that doesn't use the multinomial theorem.
 

InteGrand

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Re: HSC 2016 4U Marathon

Interesting result, but do you know a method that involves using the binomial theorem? the above proof of palindromic polynomials seems too long to write in an exam given the question was two marks
Yeah I probably wouldn't do it in the above way for that Q in a HSC exam (I was just showing it as an interesting and more general result). And yeah, you can (and are probably expected to) do it via something like the binomial theorem (or you could try trinomial theorem).
 

InteGrand

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Re: HSC 2016 4U Marathon

Oops that wasn't the equation I needed help with...I mistyped it lol >>

x^2-4x+4+2i=0*
You could obtain the answer to this new one from the answer to the old one given by Paradoxica. Just take conjugates, since the new equation is satisfied precisely by the conjugates of the old one.
 

seanieg89

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Re: HSC 2016 4U Marathon

Has been a while since inequalities have been posted, so here are a couple:



 

frog1944

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Re: HSC 2016 4U Marathon

Just out of curiosity, are these questions of 4 unit material or higher?
 

seanieg89

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Re: HSC 2016 4U Marathon

Just out of curiosity, are these questions of 4 unit material or higher?
Higher really*, but some four unit students would definitely be able to do them without assuming anything wildly out of syllabus.

(*) By this I mean that the questions as stated would never be on an official MX2 exam because of the lack of guidance, but if one was to break down a proof of them into multiple guided steps, these questions are of the level that the guided steps could be fashioned into parts of a Q16. Deeper facts have definitely been proven in official exams.
 
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frog1944

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Re: HSC 2016 4U Marathon

Ok, what topic would your question come under? Or does it fit a multitude?
 

seanieg89

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Re: HSC 2016 4U Marathon

Ok, what topic would your question come under? Or does it fit a multitude?
Well inequalities are usually considered part of Harder 3U, so I would classify them as such. As for what tools from elsewhere in the syllabus are useful to attack these questions, calculus is always good to keep in mind, and the presence of symmetric sums in the latter inequality (2) indicates that some polynomial knowledge can be helpful. I am sure there are several ways of proving these other than the ways I have envisaged though.
 
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