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Last one: area = pi.r^2 So area = pi.r^2 + piR^2 = pi.r^2 + pi(20-r)^2 (given) = answer Find dS/dr and put = 0. Then r = 10. Show that this is a max from double derivative. So max area when r= 10, R = 20 - 10 = 10. ie they are both the same.

who_loves_maths just outlined the method I was trying to use, but I mistakenly thought AB = BC, which made it too simple lol. i guess that's what studying for exams does to you.

no i did not

I put Usyd second preference, so I never found out if I got in or not.

I think there's only one interview for that course, not numerous (well I only did one). And there isn't that much of a bottleneck, as they couldn't fill all their spots for this year I think. But they do still stick to their 99.95 cut-off.

It couldn't have been that much easier than last year's. Last year's was pretty damn doable. Even I managed a prize :eek:

sadly true although im convinced i would have enjoyed law as well

and did you do 4u maths + english, chem, phys and latin too?

My mistake. Just use that value then, the method should still work.

When a = 18, x = -3 (because of initial equation) So at t = 0, -3 = asin@ Also at t = 5pi/6, v = 12. First differentiate the expression for x: v = 3acons(3t + @) Then sub in: 12 = 3acos(5pi/6 + @) 4 = acos(5pi/6 + @) Now expand RHS using cos(alpha + beta) formula, sub in the value for...

You should end up with x^4 - 8x^2 - 20 = 0, which gives you the correct answer.

for the first one, use d/dx(v^2/2) = acceleration, then integrate. Then put v = 0 to find the boundaries of the motion

Agree completely with Idyll. Cambridge does have some strange questions for conics, but I think students should always work a little above the standard required. Most conics questions in the hsc aren't as difficult, but if you just work for past papers you may struggle with some Q6,7,8 material.

I'd disagree with that. I think very few past papers have questions up to the standard of the HSC. They are also very repetitive, using stock standard exam questions, and often don't contain questions on certain topics.

My preferences were UNSW med, Usyd sci/med, Usyd law, UNSW law, UTS law, Usyd AdvSci, UNSW commerce. Nothing interstate.

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Yes although general proofs of AM/GM arent easy, and would constitute a q7/8 question on its own.

No, most probably not. Many HSC inequality questions are themselves proofs for AM/GM in 3 terms, or similar, so assuming the result would make those questions trivial. edit: when i finish my uni assignment tomorrow, ill post up some inequality stuff for people, like general proofs of AM/GM etc

Im sorry if I offended you. Its just that many students in the past have assumed those formulae. a = -9.8 v = -9.8t + 10 x = -9.8t^2/2 + 10t To work out max height, but v = 0, and sub the value for t into x. To work out stuff at when it is 3 metres above the ground, put x = 3.

both answers are correct. your ones are in degrees, the ones above are in radians