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Re: HSC 2013 4U Marathon Correct, it was a really good question

Re: HSC 2013 4U Marathon P(x) $is a polynomial of degree$ \ \ n \ \ $with rational co-efficients$ $The leading co-efficient is$ \ \ a_0 \ \ $and the polynomial has roots$ \ \ \ \alpha_1, \alpha_2, .... , \alpha_n $Prove$ P'(x)=\frac{P(x)}{x-\alpha_1} +...

Re: HSC 2013 4U Marathon With the conditions above, create the variable point P(X,Y) PF=\sqrt{(X+a\cos \theta)^2+(Y+a\sin \theta)^2} The line of the tangent at D is: y-a\sin \theta = \frac{-\cos \theta}{\sin \theta} (x-a\cos \theta) y\sin \theta + x\cos \theta -a Use perpendicular...

Re: HSC 2013 4U Marathon Looking over my working for the third time, I found that when I should of multiplied by 1/a I instead multiplied by 1/a^2 which is why it only works for a=1 The result of: (X+a\cos \theta)^2+(Y+a\sin \theta)^2 = \frac{1}{a}(X\cos \theta + Y\sin \theta - a)^2 Should...

Re: HSC 2013 4U Marathon If you put in theta=0 and a=1 y^2=-4x Which is correct because the focus is at (-1,0) and directrix at x=1.... It is also correct for theta = pi/2, pi, 3pi/2

Re: HSC 2013 3U Marathon Thread Adding another part, maybe some 2012ers will remember this part if they saw the marathon last year, but here is another way to prove it using the above result: $Construct a normal to$ \ \ SR \ \ $ at the point$ \ \ S $Using the above result find$ \ \ \theta \...

Re: HSC 2013 3U Marathon Thread Yes its a typo haha, it is supposed to be a minimum, if you notice the maximum area is actually infinite so yeah there is no real max. Fixing it now

Re: HSC 2013 4U Marathon Here is something I have been working on: $(i) Prove that the parabola$ \ \ x^2=4ay \ \ $is the locus of equi-distance from a straight line and a fixed point$ \ \ \fbox{2} $Consider the circle$ \ \ x^2+y^2=a^2 $Consider the points$ \ \ D(a\cos \theta, a\sin \theta...

Re: HSC 2013 3U Marathon Thread $On the graph of$ \ \ \ x^2+y^2=r^2 \ \ \ $a line is drawn from the origin$ \ O \ $ to point$ \ P \ $which is a variable point that lies on the graph$ PO \ \ $makes an angle of$ \ \ \theta \ \ $with the$ \ \ x$-axis$ $A tangent to the graph at$ \ \ P \ \...

Alright then, I will just leave this problem alone for now, maybe I'll come back to it later. I still want to use this integral approach Thanks for the help man, really appreciate it, and excuse any mathematical garbage that is contained within these posts :P

Okay, well investigating the inequality for a bit, I found that I was a bit too hasty in establishing it and there are just way too many holes and that it is completely wrong and if I try to fix I end up with J=0 (without any influence from n) which isn't good. So I don't think Squeeze theorem...

Ok so what I need to do to fix this, is: 1) Consider domain of Alpha, I am allowed to restrict it to 0 to pi right? because that is the only alpha that I will ever deal with? 2) Consider all the cases of cos2ntheta in this domain. 3) Find inequalities for all these cases? Would that fix it?

Ok, so we can already establish that: I=\int_0^\pi \left (\left ( \frac{-\cos(2n\theta)}{2n \cdot 2\sin \theta} \right )_{\pi/2}^\alpha - \frac{1}{2n} \int_{\pi/2}^{\alpha} \frac{\cos \theta \cos(2n\theta)}{2\sin^2 \theta} \ d\theta \right ) \ d\alpha Now we can also establish: -1 \leq...

Oops, haha hopefully there are no other typos or rigour issues. If there are no rigor issues now, I will retype it in full latex with better explanation of justification of the inequality

Its just a basic locus question really, I would even classify it as a Harder 3U question. For part 4bi), what does it say? 'Show that the tangent to the hyperbola at any point T is ..... ' So its asking us to find the tangent to the parabola at point T(ct, c/t), therefore we must find...

Explain why The Traded Weighted Index is beneficial for economists and why it is not as volatile as exchange rates (3 Marks)

If you rote learn maths you will not succeed whatsoever, if you try and rote learn mathematics the maximum I would expect someone to get in 3U is a high E3, in 4U a low E3 for a rote learner, I have seen a general maths paper and went over it, it is a complete joke (it really is) I agree...

Fair enough then.

Is this directed at me?

What pragmatic skills do you learn in General Maths that isn't taught in 2U maths (at 2U maths its at a higher level), higher level geometry, trigonometry, finance, rates of change etc. Statistics is the only thing that you don't learn in 2U maths that is in general maths, and the statistics in...