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HSC 2013 MX2 Marathon (archive) (5 Viewers)

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Carrotsticks

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Re: HSC 2013 4U Marathon

Hmmm...I got 2*log(2)-1. Are you sure your answer is correct?
My mistake Sean, the question was supposed to be an ACUTE ANGLED triangle, but I didn't type out the 'acute angled' part.

Your answer 2ln(2) - 1 is however correct. My method was to determine a set of inequalities which made a 'hyperbolic triangle', then found the area of the triangle either through a non-linear transformation or playing around with a bit of geometry and integration etc.

What you have worked out is not the answer to the question. Your answer is for forming a right angled triangle. Now I see why the probability is so low.
Read above. Fus Ro Dah is not mistaken, I sent him the correct question privately via PM whereas I typed down the wrong one here on the thread, which is why he acquired his answer. My fault for the typo.

This is going to be good.
My typos strike again!
 

Carrotsticks

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Re: HSC 2013 4U Marathon

Here's a question more accessible to the majority of MX2 students.

 

Carrotsticks

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Re: HSC 2013 4U Marathon

Here's a slightly different question to what you would normally see. It is a fairly well-known problem.

Some pirates wish to bury their treasure on an island. They find a tree T and two rocks U and V. Starting at T, they pace off the distance from T to U, then turn right and pace off an equal distance from U to a point P, which they mark. Returning to T, they pace off the distance from T to V, then turn left and pace off an equal distance (to TV) to a point Q, which they mark. The treasure is then buried at the midpoint of PQ.

Years later a treasure hunter, who has the exact instructions for the location of the treasure, visits the island but finds that the tree T has disappeared! Being rash, he finds a random rock and decides to pretend that is the location of T, then proceeds to follow the instructions as usual. Use Complex Numbers and an Argand Diagram to determine if this treasure hunter get rich in the end.
 

jyu

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Re: HSC 2013 4U Marathon

(x-1)(x-3)(x-6)(x-9)=252, find x
 

bleakarcher

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Re: HSC 2013 4U Marathon

For C, we just do

t_k (k in N) are the roots.

For R, we simply add the conjugates and express as quadratic factors.



For Q, am I right in saying:

I don't think the factorisation over Q is correct. You are not given whether n is even or odd.
 

Sy123

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Re: HSC 2013 4U Marathon

I don't think the factorisation over Q is correct. You are not given whether n is even or odd.
Ah yes, my factorisation only works if n is odd. My bad.
 

Trebla

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Re: HSC 2013 4U Marathon

 
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