HSC 2013 MX2 Marathon (archive) (5 Viewers)

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cutemouse

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Re: HSC 2013 4U Marathon

I don't think Ellipses with centre other than O are in the syllabus...
 

RealiseNothing

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Re: HSC 2013 4U Marathon

I don't think Ellipses with centre other than O are in the syllabus...
I'm pretty sure they are? Unless that's only certain questions like find the centre of the ellipse given this equation etc.
 

SpiralFlex

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Re: HSC 2013 4U Marathon

I don't think Ellipses with centre other than O are in the syllabus...
Technically you see them more often in Trials than the actual HSC. They would fall under graph transformations anyway.
 

seanieg89

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Re: HSC 2013 4U Marathon

Perhaps this was a little difficult for a marathon question, although the needed tools are entirely within the HSC syllabus. I will post a solution a little later to illustrate how some different ideas in calculus interact.
 

RealiseNothing

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Re: HSC 2013 4U Marathon

I keep getting A=1 as the only possible value of A for the polynomial to have real roots.

Either something is seriously messed up with my working or it's surprisingly right.
 

Sy123

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Re: HSC 2013 4U Marathon

I keep getting A=1 as the only possible value of A for the polynomial to have real roots.

Either something is seriously messed up with my working or it's surprisingly right.
Setting A=2 B=7
Gives an equation with 3 real roots according to Geogebra.

What are the steps of your working?
 

RealiseNothing

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Re: HSC 2013 4U Marathon

Wait, I just realised, I did something stupid in my first line of working :/

I went to type it up and was like "ohhhhhhhhhhhhh... facepalm".
 

RealiseNothing

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Re: HSC 2013 4U Marathon

By inspection -1 is a root, therefore:



Equating co-efficients gives:



Solving the quadratic for real roots gives:





or

Simplifying each one gives:

or
 

Sy123

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Re: HSC 2013 4U Marathon

By inspection -1 is a root, therefore:



Equating co-efficients gives:



Solving the quadratic for real roots gives:





or

Simplifying each one gives:

or
Nice work, its easier than my method as well, I let the roots be -1, alpha, 1/alpha then used sum of roots, found the quadratic in alpha and discriminant.
 

RealiseNothing

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Re: HSC 2013 4U Marathon

Your question gave me an idea for a question, let me try it out and I'll post it if it works.
 

Sy123

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Re: HSC 2013 4U Marathon








(Just thought it was a cool result)
 

RealiseNothing

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Re: HSC 2013 4U Marathon








(Just thought it was a cool result)
I've actually played around with this result a bit before. I'll post up a question linking heaps of things together, lemme type it up as a continue on from your question if you don't mind.
 

Sy123

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Re: HSC 2013 4U Marathon

I've actually played around with this result a bit before. I'll post up a question linking heaps of things together, lemme type it up as a continue on from your question if you don't mind.
Sure go ahead.
 
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