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n=2k where k is an integer should be a starting point...

Thanks for that. Looks exactly how I predicted after the 2U/4U exam. ie. Projectile motion, Rates of change, SHM and proving binomial identities... Doesn't look that hard though. But what is their obsession with first order ODEs this year?

Definitely SHM and Projectile motion...

Not this year probably. And yes they do come up occasionally.

Well, they usually don't ask that in 4U anyway.

Um, if I haven't been mistaken the Balls 1-7 question was a binomial probability? Note, that I haven't actually done that question so I could be wrong... Oh and there could also be a question proving nCr results. I think the 2004 paper has a good question on that if you want to revise.

Judging by the 2U and 4U paper... Loan repayments was asked in 2U, so it probably wont be asked in the 3U paper. Also, 4U contained a bit of binomial probability so it is likely that the 3U paper won't contain such probability questions. 2U contained quite a bit of probability as well, so maybe...

Looks quite straightforward... Had some 1st year uni ODEs in it... and the Q7 conics was basically taken from Coroneos...

Yeah you could do something like x=(1/2) sec^2 theta, I guess... although I haven't tried that way for this q...

Use the subs. x=1/u ...

You will never get ln(-1) as your final answer. You might get something like ln(-1) - ln(-2), which combines to be ln(-1/-2) = ln(1/2), ie. the negative signs cancelling out after applying log laws...

Well, you can use absolute values. If you don't and you get a negative value inside the function and you recombine the expression using log laws then you should get a positive value inside the log function (ie. the -ve's will cancel).

1/n! = 1/(n(n-1)(n-2)...(3)(2)1) < 1/(2*2*2*...*2*2*1) = 1/2^(n-1) for n>=3. QED

It happened to the old Physics courses once I believe. They just changed a few questions.

You need to show working though. It said in the marker's comments that some students just wrote the answer without any working, and that doing so did not give full marks.

I found that one of my favourite subjects... It was just 4U mechanics with a twist to it IMO.

No, because firstly, in that year many students who were involved with various maths clubs had seen that question before and therefore could do it easily. Whilst those who hadn't seen it before couldn't do it. And it doesn't really test the course IMO.

Q8 HSC 1989. Stupid question IMO.

They're not "crappy". They're just a bit irrelevant sometimes... Yeah if I was teaching 4U then I'd do that too.

What Trebla said and in addition Put cos theta + sin theta in the form R cos alpha and then using the symmtery property (ie. integral from 0 to a f(x) = integral from 0 to a f(a-x)) and then use log laws. Btw, where did you get that question from?