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Recent content by fan96

  1. fan96

    NESA Casio calculator ban debacle

    What are the other differences between this and the fx-82? Is it just being able to do arithmetic with complex numbers and the normal distributions thing?
  2. fan96


    Yep. That's the problem when you prescribe and assess the same texts year after year. If you truly want to, you'll be able to find a way.
  3. fan96


    Although I really hated HSC English (because it compulsorily counted towards the ATAR and most of it was not useful), I found the analysis skills involved to be occasionally useful - for example, when you're watching a movie or playing a story-driven game. You're never expected to be able to do...
  4. fan96

    HSC 2018-2019 MX2 Integration Marathon

    Admittedly, I went through a lengthy process (including looking up a standard integral table for \text{sech} ) and it was only at the end I realised that everything I did could be compressed into one substitution.
  5. fan96

    HSC 2018-2019 MX2 Integration Marathon

    4. \int_0^\infty \frac{x^2}{x^6+1}\,dx = \frac 13 \int_{0}^\infty \frac{1}{u^2+1}\,du \quad (u = x^3) = \frac 13 \cdot \frac \pi 2 = \frac \pi 6.
  6. fan96

    HSC 2018-2019 MX2 Integration Marathon

    I have a feeling this is not the fastest method... I = \int_0^1\left( \arcsin\left(\frac{x}{x+1}\right)\right)^2\,dx =\int_0^{\pi/6} \frac{y^2\cos y}{(1-\sin y)^2}\,dy \quad \left(y = \arcsin \left(\frac{x}{x+1}\right) \iff x = \frac{\sin y}{1-\sin y }\right) =\frac{\pi^2}{18}- 2...
  7. fan96

    Internal Course Transfer at UNSW and USYD

    For UNSW there is a difference between Adv Sci (Mathematics) and Adv Math, at least in terms of program structure. For example, MATH1081 is compulsory for Adv Math but not Adv Sci. The 2nd/3rd year core courses for Adv Sci and the Adv Math streams are also different. For the normal Science...
  8. fan96

    [HELP NEEDED] Year 11 Subject Selection

    It's whichever one you're personally interested in more. Scaling is nice, but if you don't enjoy the subject then you'll need to put in a lot of effort to get a good mark.
  9. fan96


    If one of them is clearly more convenient, then pick that one. For example, if we have the system \begin{cases} 2x+7y &= 4 \\ 4x + 15y &= 3\end{cases} Then it would be smarter to eliminate x by doubling the first equation. The alternative is to multiply equation 1 by 15 and equation 2 by...
  10. fan96


    A system of simultaneous equations is just a set of conditions. When we solve a system like this, we're simply finding and using different equations that represent the same conditions. Point being, whether you choose to do this step or that step first doesn't matter, because nothing you're...
  11. fan96

    Conflict in General Maths HSC paper 2018!?!

    Your answer doesn't work for the second equation: 3(3)-(-2) = 9 + 2 = 11 \neq 7.
  12. fan96

    Cambridge Prelim MX1 Textbook Marathon/Q&A

    \frac{1+\sqrt{1+\frac{\sqrt{3}}2}}{\sqrt{1+\frac{\sqrt{3}}2}} \cdot \frac 22 = \frac{2+\sqrt{4+2\sqrt3}}{\sqrt{4+2\sqrt3}} = \frac{3 + \sqrt3}{\sqrt 3 + 1} = \frac{\sqrt 3 (\sqrt3+1)}{\sqrt 3 + 1} = {\sqrt 3}
  13. fan96

    Weird circle

  14. fan96

    Inverse Trig and Identities Questions

    ii) The line through AP has equation y = t(x+1) . (can you see why?) Solve this simultaneously with the equation for the unit circle to obtain a quadratic in x : (1+t^2)x^2+(2t^2)x+(t^2-1)=0 This equation tells us where the line intersects the circle. You could just throw the quadratic...
  15. fan96

    HSC 2018-2019 MX2 Integration Marathon

    For k > 0, \, n \in \mathbb{Z}^+, let I_n = \int x^k (\log x)^n \, dx. Prove that (k+1) I_n = {x^{k+1}(\log x)^n} - {n}I_{n-1}. Given that \lim_{x \to 0} x^k (\log x)^n = 0, Show that \int_0^1 x^k (\log x)^n \, dx= (-1)^n \frac{n!}{(k+1)^{n+1}}, \frac 1 e \int_0^e (\log x)^n \, dx =...