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Re: HSC 2013 3U Marathon Thread I'm going to feel so stupid for this, but here we go! (incorporation of 4u stuff >_<) \text{Imagine the bowl has been sliced perpendicular to the water level.} \text{Now, imagine a triangle formed using the radius of the hemisphere (a) as the hypotenuse...

Re: HSC 2013 2U Marathon A three line variant of the answer (despite it being just a rearrangement of the aforementioned answers is): \ \cos 90 - \alpha = \frac{x^2 + 2^2 - (2\sqrt{5})^2} \ \sin \alpha = \frac{x^2 + 4 - 20}{4x} \ \sin \alpha = \frac{x^2 - 16}{4x} God, can't split the lines...

Thank you for the results!

Re: HSC 2013 4U Marathon Sorry for being selfish or anything, but can someone post up a mechanics question? I'm dying to get more practice in that topic. Here's a conics question for those who want it: $Find the locus of the point of intersection of perpendicular tangents to the curve y = x...

Re: HSC 2013 4U Marathon Thanks, I was trying to work through that myself. Forgot to notice your fourth line of argument.

I hope you're right.

That is true, I'm someone who went through that with Economics, MX1, English, Chem, Bio and Jap. However, when Yr 12 began, I dropped Economics and picked up MX2, hence having 12 rather than 14. What I'm saying is that why would anyone have 12+ when 2+ units are going to be studied in vain...

Why are you still on 12+ units? They only count your best 8 + 2 English. Sure, 12 is fine for a buffer, but 13/14 is overkill.

Re: How many past papers have yous done ? Bet you got no marks for all of them.

The Lost Emotion (Wind Instrument Ver.) - Touhou Shinkirou Really, any song that has chimes or mallets only is a wonderful song to relax to.

Re: How many past papers have yous done ? English - 4 (last year) 2U - 15 (last year) 3U - 10 (last year), 8 4U - 7 + Crapton of questions > 200 from random trials and stuff. Biology - 2 Chemistry - 20 (What the hell am I doing?!) Japanese - 1 Need more for Japanese and Biology obviously. You...

Re: HSC 2013 2U Marathon sin (-x) cos (x) = -tan(x) EDIT: Beaten to the punch by Lord Wheels! His solution is more in-depth too! >_<

Re: MX2 Integration Marathon Nooo! If your brain is squished, how will you do well in your exam?! Then again, my brain exploded trying to find the two-line method. Explosion > Squished So, Spiral. If you may please guide us to this two-line solution, we will be very grateful!

Oi, quit trolling Meno! That's Japanese! やめてくれ！

Re: HSC 2013 4U Marathon Well, here goes! Still working on (e). a) s^7 = 1 = cis (0 + 2k[pi]), k = 0,1,2,3 s = cis (2[pi]/7) [smallest argument] b) s^7 - 1 = 0 (s - 1)(1 + s + s^2 + s^3 + s^4 + s^5 + s^6) = 0 but s =/= 1 therefore (1 + s + s^2 + s^3 +...

Oh, but you sort of simplified it for the exam (though I still couldn't get it >_<). It is a cool theorem though.

Re: HSC 2013 4U Marathon God, I need to learn how to use Latex. And find a good graphing tool.

Re: HSC 2013 4U Marathon 'Kay, here's a volumes question! A glass vase is made by rotating the region between the curves y = x0.5, (0 < x < 9)and y = 0.75 (x-1)0.5, (1 < x < 9) (They're actually equal to 0-9 and 1-9 respectively) a) Find the area by the Washer method, hence find the...

Can't think of much, maybe the proof for the derivative of a^x?

I think they mean 11d. Like the Steiner's Inequality thing you gave a lecture on?