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Physics is full of relentless rote learning sometimes little to do with the actual Physics course. Although this is similar to HSC Chemistry in a way, Physics is no better. HSC Physics is a horrible subject In terms of contribution to humanity overall, it is difficult to compare both as they...

Re: HSC 2013 4U Marathon Yep HeroicPandas, that's pretty much it, that is 7 marks from a school trial (ascham 2005) === $Suppose$ \ \ a,b,c > 0 \ $and$ \ abc= 1 $It is known that$ \ a+b+c > \frac{1}{a}+ \frac{1}{b} + \frac{1}{c} $Prove that exactly one of the numbers$ \ a,b,c \ \ $is...

Re: HSC 2013 2U Marathon Since x=a is a minimum of the function f(x) for any value of x > 0 Then if we pick say x=1 (if a=/=1) then f(1) > f(a) right? If you sketch the graph of f(x), then when x=a, it is a minimum value and the rest of the function is greater than or equal to it. Its like...

Re: HSC 2013 4U Marathon $For positive real values$ \ a, b, c \ $it is given$ \ a+b+c \geq 3\sqrt[3]{abc} \ \ \ $and$ \ a+b+c = 1 $i) Prove$ \ \frac{1}{a} +\frac{1}{b} + \frac{1}{c} \geq 9 $ii) Hence find the minimum value of$ \ \ \left( \frac{1}{a} - 1 \right ) \left(\frac{1}{b}- 1 \right...

Re: HSC 2013 2U Marathon Yes x=a is the minimum of the function, this means that f(x) > f(a) However we aren't proving equality, we are proving the inequality here. Try and use the fact that f(x) > f(a)

Re: HSC 2013 2U Marathon Not really, I just thought since maxima/minima is a big part of the 2U course, they might as well utilise it. And I'm divided in 2U whether to just ask it straight away or to give a hint (Using (a-b)^2 > 0 etc)

Re: HSC 2013 2U Marathon HINT: If you look at the function given and the inequality that you need to prove, it seems that through differentiation we need to prove that f(x) \geq 0

Re: HSC 2013 3U Marathon Thread $i) Verify that$ \ \ a^n + b^n = (a+b)(a^{n-1} + b^{n-1}) - ab(a^{n-2}+ b^{n-2}) $ii) A sequence$ \ u_1, u_2, u_3, \dots \ \ $is such that$ u_n = u_{n-1} + u_{n-2} \ \ $and$ \ u_1 = 1 \ u_2 = 3 $Using the result from part$ \ (i) \ $prove that$ u_n =...

Re: HSC 2013 2U Marathon For the above answer, when differentiating ln(y) with respect to x you get: \frac{y'}{y} instead of \frac{1}{y} It is correct except for the 1 on the LHS, it should be y' And for your solution, it is correct except for the part where you assume the area if a...

Re: HSC 2013 2U Marathon $i) Let$ \ f(x) = (a+x) - 2\sqrt{ax} $for positive constant$ \ a \ $and$ \ x>0 $Prove by differentiation$ \ \ (a+x) \geq 2\sqrt{ax} $ii) A farmer has$ \ P \ $metres of fencing to fence in a flat rectangular area of land$ $Prove that if the area to be fenced in...

Re: MX2 Integration Marathon I'm afraid I don't understand your second step, could you please explain it? EDIT: NVM, I get it, nice!

Re: MX2 Integration Marathon My friend conjectured: \lim_{t \to 1} \int_{\sqrt{t}}^{t} \frac{x^{n+1}}{x^n - 1} \ dx = \frac{1}{n} \ln(2) For integer n, it works for n=2, 3 and 19 by computation Any ideas on how to prove/disprove this?

Re: MX2 Integration Marathon Yep You need to insert the LaTeX code into the tags [.tex] and [./tex] (without the dots) For example if you quote this post to see coding used: $Hello$ and \frac{\pi }{\sqrt{2}} Commands such as \frac and \sqrt are used, a small guide is stickied in these...

He edited his answer :)

Re: MX2 Integration Marathon A cool result: \lim_{t\to 1} \int_{\sqrt{t}}^t \frac{x^3}{x^2- 1} \ dx

Re: HSC 2013 4U Marathon $Prove for some positive$ \ x \ $and$ \ a \geq 1 x^a + \frac{1}{x^a} \geq x^{a-1} + \frac{1}{x^{a-1}} $For what values of$ \ x \ $and$ \ a \ $does equality hold?$

13c3 = 286

1. Coming last in english first task, mainly due to lack of effort, I was able to crawl up considerably though 2. Not trying hard enough for Chemistry 3. Spending too much time on maths 4. Spending too much time on video games 5. ^Similar to Eg's one I too did 14 units for entire first 2 terms...

good luck

I would not consider 8 hours to be 'cramming' That is enough time to go over all notes multiple times, even time to make notes from scratch and do exercise questions for each chapter many times over 3 hours is cramming, and even then....