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Re: 2012 HSC MX1 Marathon How do you use the substitution u=x-1 when there are no x's in the expression? I did the question though using the substitution u=y+1: <a href="http://www.codecogs.com/eqnedit.php?latex=u=y@plus;1\\\frac{du}{dy}=1\\ \int y\sqrt(y@plus;1)=\int (u-1)\sqrt u\\...

Re: 2012 HSC MX1 Marathon <a href="http://www.codecogs.com/eqnedit.php?latex=(x-3)^2@plus;y^2=1 \\ (x-3)^2=1-y^2 \\ (x-3)=\pm \sqrt(1-y^2) \\ x=3\pm \sqrt(1-y^2)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?(x-3)^2+y^2=1 \\ (x-3)^2=1-y^2 \\ (x-3)=\pm \sqrt(1-y^2) \\ x=3\pm...

I won't do the whole thing for you, just give you a tip and then you can have a go... Use this: <a href="http://www.codecogs.com/eqnedit.php?latex=(x@plus;\frac{1}{x})^2=x^2@plus;\frac{1}{x^2}@plus;2 \\ \therefore x^2@plus;\frac{1}{x^2}=(x@plus;\frac{1}{x})^2-2" target="_blank"><img...

Re: 2012 HSC MX1 Marathon Subtract y^2, take the square root and then add three...

This question involves multiple angles with tan: <a href="http://www.codecogs.com/eqnedit.php?latex=tan(x@plus;y)=\frac{tanx@plus;tany}{1-tanxtany}\\ tan(x@plus;\frac{\pi}{6})=\frac{tanx@plus;tan(\frac{\pi}{6})}{1-tanxtan(\frac{\pi}{6})} \\ tan(\frac{\pi}{6})=\frac{1}{\sqrt3} \\ \therefore...

I'm assuming you're having difficulty with the first part of his solution. What he does is use double angles to get rid of the 1 at the front of the numerator and the denominator. I'll do the angles in the numerator as an example and then you should be able to do the rest: <a...

Re: 2012 HSC MX1 Marathon That's the right answer :)

Use double angles on x: x=2cos^2t-1 Square y: y^2=cos^2t Sub into the first equation I wrote: x=2y^2-1

Re: 2012 HSC MX1 Marathon New question: The region inside the circle <a href="http://www.codecogs.com/eqnedit.php?latex=(x-3)^2@plus;y^2=1" target="_blank"><img src="http://latex.codecogs.com/gif.latex?(x-3)^2+y^2=1" title="(x-3)^2+y^2=1" /></a> is rotated about the y-axis. Show that the...

Re: 2012 HSC MX1 Marathon Mate, you are a god! What did you get in the HSC for maths?

Re: 2012 HSC MX1 Marathon I like :). Don't you still have to solve the quadratic though to find the y values or is there another hack that I'm not aware of?

I don't memorise that formula, but I'll show you a way to easily obtain it, to make the solution easier. I won't solve the whole thing for you, just the layout so you can try it and then learn it much more effectively (BTW, I'm really tired so there's a good chance I made a typo/wrong...

Re: How do youse get rep powr Cheers :)

I did it but I don't think what I did was General level. Are these problems meant to involve sums of geometric sequences and logs? If you want, I can take a photo of my solution but its quite complicated...

Never round anything until the end otherwise you lose detail. The easiest way to do it is to keep it stored in your calc. When I'm doing exams, I tend to write something like 0.039 (full answer kept in calc and used) to show that marker that your working is correct to get half the moles but that...

Re: How do youse get rep powr How do you get more than one green bar?

Re: 2012 HSC MX1 Marathon Which paper was that? I can imagine a sizable number of 3U candidates doing IBP as they might have learnt it in 4U but how many 2U students have come across it (unless they were accelerated and planned to do 4U)?

If you PM me your email, I can send you Sydney Tech papers for Yr 11 tomorrow sometime. Do you want 3U or 2U?

Re: 2012 HSC MX1 Marathon Just a quick Q. If a question in a three unit paper says solve this integral using the substitution... or otherwise, can you use integration by parts or are you limited to 3U methods?

If you split the inequality, it isn't that hard. If you still can't do it, I can post my solution, but have a go first :)