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

[bleakarcher]

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]

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]

Re: HSC 2012 Marathon



i will post solution and new question upon confirmation

 

[deswa1]

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]

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]

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]

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]

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.

 

[lolcakes52]

Re: HSC 2012 Marathon

smallest, lowest length.

 

[Carrotsticks]

Re: HSC 2012 Marathon

smallest relative to perimiter or area or what?

He means with respect to the other sides.

 

[qrpw]

Re: HSC 2012 Marathon

 

[qrpw]

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]

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)

 

[Deliriously]

Re: HSC 2012 Marathon

parabola

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

 

[barbernator]

Re: HSC 2012 Marathon

parabola

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

dont forget that there is a hole at x=0, thats why i posted it

 

[Deliriously]

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.

 

[deswa1]

Re: HSC 2012 Marathon

ohh is it so? hmm interesting
but if you simplify it ..

Your are right. There is no 'hole' at x=0

 

[barbernator]

Re: HSC 2012 Marathon

Your are right. There is no 'hole' at x=0

lol there goes my logic.

 

[AAEldar]

Re: HSC 2012 Marathon

lol there goes my logic.

No you're right, it isn't continuous at x=0.

 

[bleakarcher]

Re: HSC 2012 Marathon

Your are right. There is no 'hole' at x=0

How? In the original function, x can not be 0.