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  1. J

    MX2 Exam Thoughts

    Could you elaborate on your solution to part (ii) of the polynomials? Btw here is my solution for the part (i): x^3 + px + q = 0 (\beta - \gamma)^2 = \beta^2 - 2\beta\gamma + \gamma^2 = \alpha^2 + \beta^2 + \gamma^2 - \alpha^2 - 2\dfrac{\alpha\beta\gamma}{\alpha} =...
  2. J

    absolute values for integrals equal to log?

    \text{Let } y = \ln|x| e^y = |x| \dfrac{\text{d}}{\text{d}x} e^y = \dfrac{\text{d}}{\text{d}x} |x| \dfrac{\text{d}}{\text{d}y} e^y \dfrac{\text{d}y}{\text{d}x} = \dfrac{|x|}{x} \text{Note that the gradient of } |x| \text{ is 1 for } x>0 \text{ and -1 for } x<0 \text{ just like }...
  3. J

    2004 HSC Mathematics Extension 2 Paper

    There are several useful hints that you can look for: 1.) These part (iii) style of questions nearly always use the previous part, so it is useful to think about how you can incorporate part (ii) into part (iii) 2.) On part (iii), there are 3 terms on LHS, but 3^2 = 9 and there is a 9 on RHS...
  4. J

    Complex Number Questions

    \text{The trick for question 1 is to use trig identities to make it into a telescoping sum so that the terms cancel out:} \text{Note that: } \cos((k-1)x) - \cos((k+1)x) = \cos(kx-x) - \cos(kx+x) = 2\sin(kx)\sin(x) \text{Therefore, } \sin(kx) = \dfrac{\cos((k-1)x) - \cos((k+1)x)}{2\sin(x)}...
  5. J

    Circle Geometry Homework Help!!

    \text{(a)} OP = OT \text{ (equal radii)} \angle OTA = 90^{\circ} \text{ tangent perpendicular to radius} \cos(\alpha) = OT / (OP + PA) = 1/2 \rightarrow \alpha = 60^{\circ} \text{Then, } \gamma = 30^{\circ} \text{Now, } \angle OPT = \angle OTP = 90^{\circ} \text{ (isoceles...
  6. J

    Conics help

    Yeah I also think the question is not true, counter examples can be illustrated here: https://www.desmos.com/calculator/fhj9angyd2
  7. J

    Old HSC Question Help

    So I was doing this question from the 1967 4U HSC which is as follows: \text{Express } \dfrac{1-abx^2}{(1-ax)(1-bx)} \text{ in the form: } p + \dfrac{q}{1-ax} + \dfrac{r}{1-bx} \text{Given that } R_n(x) \text{ is a polynomial, and that:} 1-abx^2 = (1-ax)(1-bx)(1+u_1x + u_2x^2 + ...
  8. J

    Stuck on circle geo question

    A tad late, but in case anyone was wondering here is my solution: https://i.imgur.com/QO94Yx1.jpg https://i.imgur.com/5RkHkzc.jpg https://i.imgur.com/60EaPkc.jpg https://i.imgur.com/UCvTKrA.jpg https://i.imgur.com/it3NUDJ.jpg
  9. J

    Conics Help

    Not sure what you meant by sec(phi), but here's what I got anway: Part (a) https://i.imgur.com/O2Ae7sY.png Part (b) https://i.imgur.com/0tKKBM9.png