HSC 2016 MX2 Marathon ADVANCED (archive) (1 Viewer)

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DatAtarLyfe

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Re: HSC 2016 4U Marathon - Advanced Level

May i ask, are some of these questions simply harder problem solving question, that are considered "harder 4u" but in actuality, can be done if you sit there long enough and think about it, or does it simply require methodologies outside the syllabus? I'm not sure if i should even attempt these in case they need some special theorem and i'd be wasting my time trying to solve it.
 

leehuan

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Re: HSC 2016 4U Marathon - Advanced Level

A few are out of the syllabus, that's why I leave this thread alone and plan to come back to it after I do uni maths.
 

leehuan

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Re: HSC 2016 4U Marathon - Advanced Level

Do these questions require higher level of maths, or just intellect?
InteGrand's question just requires intellect.

Idk about Sy's. But his questions in the 3U marathon last year were 100% intellect.
 

DatAtarLyfe

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Re: HSC 2016 4U Marathon - Advanced Level

Sweet, will defs try it out tomorrow then
 

RealiseNothing

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Re: HSC 2016 4U Marathon - Advanced Level

May i ask, are some of these questions simply harder problem solving question, that are considered "harder 4u" but in actuality, can be done if you sit there long enough and think about it, or does it simply require methodologies outside the syllabus? I'm not sure if i should even attempt these in case they need some special theorem and i'd be wasting my time trying to solve it.
I don't think uni maths is required for the questions in this thread tbh.

Uni maths has quite a different flavour to high school maths.
 

leehuan

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Re: HSC 2016 4U Marathon - Advanced Level

I don't think uni maths is required for the questions in this thread tbh.

Uni maths has quite a different flavour to high school maths.
Too many of the questions, though not seeming impossible, play around with my mind a bit too much for me to bother attempting them
 

RealiseNothing

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Re: HSC 2016 4U Marathon - Advanced Level

Too many of the questions, though not seeming impossible, play around with my mind a bit too much for me to bother attempting them
Yep there's no denying they can be very hard, but still possible for a smart HSC student given they try for long enough.
 

glittergal96

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Re: HSC 2016 4U Marathon - Advanced Level

If x > 0, then x^2 < 1+x+x^2 < (1+x)^2
if x < -1 then (1+x)^2 < 1+x+x^2 < x^2.

So x=-1 or 0. (We cannot find a square strictly between two consecutive squares).

So the only integer solutions are
x=-1, y=+-1 and x=0,y=+-1.
 
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leehuan

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Re: HSC 2016 4U Marathon - Advanced Level

This is my first ever attempt at a diophantine equation, so I'm not certain it's 100% rigorous.

Can I ask how you managed to achieve the solution (2,2) by inspection? Doesn't seem so obvious.
 

Paradoxica

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Re: HSC 2016 4U Marathon - Advanced Level

Can I ask how you managed to achieve the solution (2,2) by inspection? Doesn't seem so obvious.
Compare x^3 y and 2xy^2. Suppose they are homogenous, i.e. they take on a value that achieves similar algebraic degree. As 0 and 1 have already been found, The only possibility is 2. Then since 2x2 = 2+2, (2,2) is clearly a solution to the diophantine equation and we are done.

This is all a matter of intuition. Sorry if you don't possess the same weirdness of intuition I do.
 

JusticeTackle

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Re: HSC 2016 4U Marathon - Advanced Level

I'll requote the unsolved problems from the previous marathons.
Can 2015ers not spoil the answers for these? However, anyone who is sitting the HSC in the 2016 should feel free to answer these. Also, can someone clarify what realisenothing means when he says that m is the highest integer power but contradicts themselves in the next line when they say that m doesn't necessarily have to be an integer?

Also, the two questions posted by Sy have already been resolved by previous members ages ago, so I don't see why you included those? You should remove them
 

InteGrand

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Re: HSC 2016 4U Marathon - Advanced Level

Also, can someone clarify what realisenothing means when he says that m is the highest integer power but contradicts themselves in the next line when they say that m doesn't necessarily have to be an integer?
I and another user were also a bit confused by this so we asked some questions about it on the thread where it was first posted, so you might want to read those posts: http://community.boredofstudies.org...4u-marathon-advanced-level-9.html#post6965906

(But spoiler alert, that question is solved on the next page on from that link by the user glittergal96 .)
 

JusticeTackle

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Re: HSC 2016 4U Marathon - Advanced Level

So, the only problems left for the 2016ers are Integrand's, Heroic Pandas, Lita1000's, and Dan964's.
 

glittergal96

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Re: HSC 2016 4U Marathon - Advanced Level

Related (harder): Find with proof the maximum possible value of A/P^2 where the variables denote area and perimeter of an n-sided polygon. (Find this maximum for each fixed n).

(You may assume without proof that such a maximum exists.)

b) Use this to say something about the problem of enclosing as large an area as possible with a string of unit length.
 
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