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The 3 roots of x^3 -1 are 1, w and w^2 so the common root must be One of those

i agree with the assumed uniform convergence thing, today when i went through the cssa trial in my class i had to tell my students to just swap the integral and sum notation and that you cant justify it, you just have to do it...

no that doesnt prove those are the other roots, it only proves their sum is 0.

i thought their Q8 was decent, espes the prob one

ill most likely be asleep at that time, which day is the test? besides your school is a massive trek

look carrot, you and florica had a thang going on :P Also we just need to go to a school like 1hr after test starts, cause thats when teachers get a copy, so carrot just charm your way through it

trials i have seem so far or heard about have been relatively easy, my upcoming holiday test before the HSC will be the hardest test ever, just cause i like it hard :P

my favourite

as an exercise fill in missing reasons, i numbered order i proved each angle

i had a similar q i gave to my kids using this diagram, where you had to prove XG= XB

Re: 2012 HSC MX2 Marathon Here is a 4u question from cambridge, but done in a different way:

Re: 2012 HSC MX2 Marathon to prove my method i had to construct a quarter circle contour to show the integrals were the same, so the method works, but yeh it does need proof why it works using contour integration.

I reckon usyd is better. First of all as carrot said usyd does a very rigorious treatment of the material whereas unsw just chucks a whole lot in. Having past papers from both i see that usyd's papers are a lot more theoritical, with a lot of proofs, whereas unsw is just computational stuff even...

Re: 2012 HSC MX2 Marathon yes i have a simple solution in mind, involving only 4u properties applying those 2 formulaes

Re: 2012 HSC MX2 Marathon Using the Gaussian integral: \int_{-\infty}^{\infty} e^{-x^{2}}dx= \sqrt{\pi} and Euler's identity: e^{i\theta} = cos\theta +isin\theta deduce the following special integrals: \int_{0}^{\infty} cos(x^{2})dx=\int_{0}^{\infty} sin(x^{2})dx=\sqrt{\frac{\pi}{8}}

yeh you want to use shell method here, otherwise disc method will need a x1 and x2 to be introduced and is more annoying to deal with, as you need to make x the subject.

my next holiday trial test will have a great taylor series question in it :P

For part b work out the sum of those Two and then the product and then sub Those numbers into standard form of A quadratic and you will get answer

Re: MX2 Integration Marathon who needs a substitution?