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Re: HSC 2013 2U Marathon $The displacement $x$ metres at time $t$ seconds of a particle moving in a straight line is given by:\\ \\ $x = 1+2\cos^{2}t \\\\ $If $v$ and $a$ are the respectively the velocity and acceleration of the particle at time $t$, $find:$\\ i) $v$ and $a$ in terms of $t$.\\...

yes from memory around 40%-30% of prelim maths can be in the test.

I am in the process of answering, but did you notice the mistake in the question?

woops

No, probability in mathematics is exactly the same as you are doing now, you'll have 2 years to practice your 'so-so' trig and geometry skills algebra and coordinate take up huge portions of the syllabus, so you are basically fine.

re: HSC Physics Marathon Archive Not really a HSC type question but it fits into physics outcomes. Here is a string of comments from this youtube video: http://www.youtube.com/watch?v=tAUXIEr-VzM Assess the information presented by James Ede, and create a reply to his comment.

'r' is a constant so treat it like an ordinary number. It is like differentiating f(x)=(2^2 -x^2)

y & = & (r^{2}-x^{2})^{\frac{1}{2}}\\ \\ Let\ u & = & r^{2}-x^{2}\\ \\ \frac{du}{dx} & = & -2x\\ \\ \frac{dy}{du} & = & \frac{1}{2}u^{-\frac{1}{2}}\\ \\ \frac{dy}{dx} & = & \frac{dy}{du}\cdot\frac{du}{dx}\\ \\ & = & -x(u)^{-\frac{1}{2}}\\ \\ & = & -x(r^{2}-x^{2})^{-\frac{1}{2}} Chain rule

:s its better if you write it out on paper and take a picture

Knock yourself out. $A smooth narrow tube of, length $L$ is fixed at an angle of 30º to the horizontal. A particle is fired up the tube, from the lower end, with initial velocity $u$. When the particle reaches the upper end of the tube, it continues its motion until it returns to the same level...

Re: HSC 2013 3U Marathon Thread I guess~ I can't really find any logical faults. But another way you can do it is by dividing A^{n}-B^{n} by A-B And you'll get (A-B)(A-B)(A^{n-1}+A^{n-2}B+...+b^{n-1}) which then makes the whole process so much more clearer

Re: HSC 2013 3U Marathon Thread Found this in one of the most underrated textbooks. $It is given that$\ A>0,\ B>0,\ $and $n$ is a positive integer. \small $ a) Divide $A^{n+1}-A^{n}B+B^{n+1}-B^{n}A \ $by $A-B$ and deduce that A^{n+1}+B^{n+1}\geq A^{n}B+B^{n}A \small $ b) Using (a), show by...

^agreed

Re: HSC 2013 2U Marathon Since I am doing probability in class the rest of you must also suffer $The probability that a cityrail train arrives on 1:08 pm Saturdays is 0.19.$ $If$ \ n \ $is the number of weeks that pass$ $How many weeks must pass until it is 0.98 certain that the train will...

weird question o.o what is the answer?

Re: HSC 2013 3U Marathon Thread $i) Prove that$: \sqrt[x]{x} = e^{\frac{ln{x}}{x}} $ii)Hence show that the maximum value of $f(x)=\sqrt[x]{x} \ $occurs at $ x=e Not sure if this belongs to the 2U or 3U so i'll post it here~

I have no idea what is 10.1 (maybe his class number) but 5.3 is the advanced course for year 10 maths. To op go for it, I didn't even do 5.3 and got into extension 1 maths. If you feel that it is too hard, don't give up until half way year 12

re: HSC Chemistry Marathon Archive Fair enough~ I agree so here is a better question. $ A student carried out an investigation to analyse the sulfate content of lawn fertilizer. The student weighed out 1.0g of fertilizer into a beaker, added water and then stirred. 50 mL of 0.30 mol\cdot...

re: HSC Chemistry Marathon Archive I'm not too sure how you manage to get away answering like that. :L But anyhow I asked you explain the statement not, list the process of how cfc disintegrate the ozone. So I'll give you a 3 out of 5, one for not actually explaining the statement, and another...

re: HSC Chemistry Marathon Archive I think it is only for Industrial chem. Explain the following statement: "The release of CFCs into the environment devastate the ozone layer, due to its endless chlorine catalytic cycle." Include all relevant equations in your answer. (5 marks)