HSC 2012 MX1 Marathon #2 (archive) (1 Viewer)

bleakarcher

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Hey guys, for fun's sake and ofcourse the sake of the HSC, I've decided to start a new marathon thread (after the last one died). Answer the questions then post your own :). To encourage MX1'ers of any level of ability to take part, please rate your questions in terms of difficulty. To start off:

For what values of x will 1-tan^2(x)+tan^4(x)-tan^6(x)+... have a limiting sum where x lies between 0 and 2pi? (Easy-Medium)
 

Carrotsticks

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Re: HSC 2012 Marathon :)

Might I add, graduates are generally discouraged from answering questions UNLESS the thread died because nobody could do the question (unlikely, we have quite a few bright ones here).
 

barbernator

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Re: HSC 2012 Marathon :)



i will post solution and new question upon confirmation
 
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deswa1

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Re: HSC 2012 Marathon :)

This was from our last 3U test- Prove that the smallest diagonal of a rectangle occurs when the rectangle is a square (medium?- I'm not very good at estimating, maybe someone else can give a judgement)
 

mirakon

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Re: HSC 2012 Marathon :)

This was from our last 3U test- Prove that the smallest diagonal of a rectangle occurs when the rectangle is a square (medium?- I'm not very good at estimating, maybe someone else can give a judgement)
I'd say you are right in this question being medium
 

Carrotsticks

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Re: HSC 2012 Marathon :)

This was from our last 3U test- Prove that the smallest diagonal of a rectangle occurs when the rectangle is a square (medium?- I'm not very good at estimating, maybe someone else can give a judgement)
I think a Medium is suitable.

Reason is because you're giving the question straight out as opposed to breaking it up into parts ie: a) Show that the diagonal is XXXX, b) Show that the derivative is XXXX etc etc.
 

barbernator

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Re: HSC 2012 Marathon :)

This was from our last 3U test- Prove that the smallest diagonal of a rectangle occurs when the rectangle is a square (medium?- I'm not very good at estimating, maybe someone else can give a judgement)
smallest relative to perimiter or area or what?
 

deswa1

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Re: HSC 2012 Marathon :)

smallest relative to perimiter or area or what?
Sorry, what do you mean? The question is saying that when a rectangle is a square, that is the shortest possible diagoncal length- i.e. as you stretch a square out into a rectangle, the diagonal becomes longer. Now you have to prove that.
 

qrpw

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Re: HSC 2012 Marathon :)

Two poles, 12m and 10m, are 8m apart. Wires stretch from the top of each pole to the foot of the other. Find the height of the point where the wires cross. (medium-hard)
 

barbernator

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Re: HSC 2012 Marathon :)

defining the lines as y=5x/4 and y=-3x/2 +12. We solve simultaneously to obtain 60/11 m.

next question.... draw the graph of y=x^3/x. (easy)
 
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Deliriously

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Re: HSC 2012 Marathon :)

parabola

next question:
simplify :
sin(A+B)sin(A-B)+cos(A+B)cos(A-B)
 

Deliriously

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Re: HSC 2012 Marathon :)

dont forget that there is a hole at x=0, thats why i posted it :)
ohh is it so? hmm interesting
but if you simplify it ..

EDIT: actually il take your word for it , it does make sense.
 
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