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HSC 2014 MX2 Marathon (archive) (4 Viewers)

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nrlwinner

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Re: HSC 2014 4U Marathon

Here is a great question from the HSC a while back.

Untitled.png
 

Axio

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Re: HSC 2014 4U Marathon

a.



b.



Therefore (x+y)/2 is a closer approximation to root n than x is.
 
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sepseminar

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Re: HSC 2014 4U Marathon

Yep, that's correct, Dunjaaa. There is a slightly faster solution in which you make the substitution u=1/x. But all the deft moves are in your solution. First, the use of a substitution to equate the integral with a similar looking integral. Then the use of some basic properties to relate the two integrals together. In this case it was the fact that the inverse tan of a number and the inverse tan of the number's reciprocal is constant.
 

Fade1233

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Re: HSC 2014 4U Marathon

Capture1.PNG

Fibonacci Based Strong Induction.

Edit: Forgot to put up the condition: U(n)= U(n-1) + U(n-2)
 
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mreditor16

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Re: HSC 2014 4U Marathon

I personally enjoyed this question :)

 

mreditor16

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Re: HSC 2014 4U Marathon

btw above question was in fort street 2010

only Q3....
 

dunjaaa

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Re: HSC 2014 4U Marathon

Since nobody has answered it, I might as well do so Screen shot 2014-09-19 at 2.42.52 PM.png. Strong induction in disguise
 

Fizzy_Cyst

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Re: HSC 2014 4U Marathon

A non-real number, w, is such that |w| = 1.

If z = (1+w)/(1-w) find the locus of z as w moves on the complex number plane
 
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