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Re: 2012 HSC MX2 Marathon also here are some nice integration questions: \!\!\!\!\!\!\!\!\!\! 1. \; \int \frac{x+1}{\sqrt x (x^{2}-x+1)} dx \\ \\ 2. \; \int \frac{sinx +cosx}{2-sin2x} dx

Re: 2012 HSC MX2 Marathon fastest way to prove reflection property, from hsc a few years ago:

bad tutor is bad, the arrow on top is the correct way to denote vector direction

In the syllabus they say you have to know how to prove the FTA by induction, it is a fairly informal proof, but all that is required of 4u students: http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths4u_syl.pdf pg 75

i was just trolling..obv cute mouse wouldnt put such a question if the ans was so trivial

no 5=1 duh, it is defined in the question as that ;P

this is a maths problem, it is about deducing the pattern which is something you obv need to speed up on

there are 4 sub parts, so one numerical answer has no possible way of answering all four questions

i think i should be worshipping you as my god oh great 'God of Maths'

As spiral suggested, i will post this question: "Spiral was putting n letters into n envelopes and sent them off. However, Spiral not being the brighest was unsure if he sent them to the right address. Prove the probability that at least one letter went to the right address is given by : 1-...

p.s i put a new question up on the board

sprial should of only taken like 5-10 minutes max lol, over thinking it i see and i will post the letter problem now

Re: 2012 HSC MX2 Marathon For the hyperbola and ellipse use the formula To work out eccentricity and use it to deduce A nice relation. Also don't actually solve them simultaneously, let the point of intersection be P(x1,y1)

Carrot pretty diagram but it shows wrong region, question asked between y=4 and x=2

Re: 2012 HSC MX2 Marathon A hint is the reason I wrote Part one was To show you that if the hyperbola and ellipse have the Same a and b value they can't share the same Focus.

If you draw your diagram right then the region we are rotating is the one bounded by y=4 and x=2 and so the distance along the x direction will be the height when we rotate that region about the x axis. Now the length of the strip horizontally in that region is 2-x which is the height, if...

yes

Well i found another one, which i think is better: PS. carrot if you see this, let others have a go first :P

correect

i came across this and found it quite amusing, why dont you guys have a go and ill tell you the answer later: