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Re: HSC 2015 4U Marathon $ Ah cool. I used some relationship that didn't even know existed. Just drew it out and inferred. $ arg( \frac{-1}{z}) = \frac{-2 \pi}{3} arg(-z) = \frac{2 \pi}{3} arg(z) + \pi = arg(-z) \therefore arg(z) = \frac{- \pi}{3} \therefore $ z must have...

Re: HSC 2015 4U Marathon I got z = 1 - sqrt3 i?

Also the MX2 Permutation marathon

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $ An obvious way would be to let $ \frac{dA}{d \alpha} = 0 $ and then test with the second derivative. $ $ But you can also do it via inequalities $ $ A $ = \frac{4 \tan ^{2} \alpha + 4 \tan \alpha + 1}{2 \tan \alpha}...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $ A $ = \frac{1}{2}d^{2}\cos ^{2}\alpha \sin \alpha $ To find maximum or minimum, differentiate and let that equal zero $ $ But first, use the fact that $ \cos ^{2}\alpha = 1 - \sin ^{2} \alpha ($Didn't want to use...

$ Use complementary probability $ $P(no-one winning) + P(at least 1 person winning) $ = 1 $P(no-one winning)$ = \frac{3}{4} * \frac{5}{6} * \frac{3}{5} = \frac{3}{8} $ Hence, P(at least 1 win) $ = 1- \frac{3}{8} = \frac{5}{8} \Rightarrow $ D $

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Re: HSC 2015 4U Marathon Just a minor thing, why does the equality get removed?

Re: HSC 2015 2U Marathon If v*a > 0 particle is increasing speed. If v*a < 0 particle is decreasing in speed. Makes intuitive sense because if v <0 it wants to travel left. If a < 0 then it wants to increase velocity in the NEGATIVE direction hence allowing it to become faster travelling...

In I and II, aren't they the same? Just rotations of each other? (In 3 dimensioms)

Maybe I've missed a few things but the one I remember that wasnt completely correct was a MC in physicswhere there were 3 conductors and it asked for the order of which the magnet passed through. The question didn't account for small eddy currents when a section of the conductor was removed...

https://9eeba4054ee764a743f35bb25b5f907e66151207.googledrive.com/host/0ByEFYhkkDQBKUmxzb0Q4MEswQ3c/Year%2012%20-%20HSC/Chemistry/Past%20Trials/Sydney%20Grammar/Sydney%20Grammar%202004%20Chemistry%20Trials%20&%20Solutions.pdf On page 42/57 of this PDF, question(ii) notes say not to use O3 as...

Re: HSC 2015 2U Marathon It will work (but the bounds are 0 to 3 or else it'll give a negative for the integral)

The lead/dry cell one for 3-4 marks. 3-4 marks on precipitation reactions Industrial: 5 marks on saponification or the cells

Re: HSC 2015 4U Marathon ____________________________________________ $ New question $ $ let $ f(x) = x^4 + ax^3 + bx^2 + ax + 1 = 0 $ If f(x) has at least one real root for real numbers a,b then find the minimum value of a^2 + b^2 $

Re: HSC 2015 3U Marathon $ By using the fact that $ \int_{0}^{\infty} \frac{\sin x}{x} dx = \frac{\pi}{2} , $ Evaluate $ \int_{0}^{\infty} \frac{\sin (x^{2015})}{x} dx

The argument is 3pi/4. Draw up the complex number z1-z2 on an argand diagram and label it z1-z2. You'll notice that it lies in the second quadrant. So the argument of it should be pi/2 (since coordinate axes are equal) + angle between the vector z1-z2 and the y axis which is arctan((sqrt3 -...

Yes, you could do it that way if you were using polar form ( rcis(theta)). Preferably, I would just do what mentioned, because z1-z2 and z1+z2 have 'weird' real and imaginary parts, that probably wouldn't give a 'neat' value for their respective arguments when taking the inverse tan. (I haven't...

You should find the simplified expression for both z1+z1 and z1-z2, then multiply both numerator and denominator by the conjugate of the denominator.

Re: HSC 2015 4U Marathon When you say there are 'np' minutes, does that mean there are n multiplied by p minutes or {n}{p} minutes