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The contrapositive show be ... if sqrt(p) is rational then p is composite or 1.

That question is much more easily done geometrically. The equation is saying we are looking for points which are further from (2,0) than from (2,1).

If you are happy to time travel back 23 years you might consider doing 4 unit maths. If not, I suggest you stick to Extension 2.

They do not have the right to force you to drop to Advanced, only to strongly suggest that you drop. If they try to make you drop you have the right to complain higher up the food chain.

(1) The example in the link you gave clearly shows that isoclines are generally NOT solutions. (2) The isocline is A solution. Other solutions are indeed asymptotic to this isocline.

Perhaps the first suggestion should be to call it MATHS. We are not Yanks.

I'm not saying he was not correct, only that there was no point in mentioning it other than to discourage contributors. So I will now take my cue and contribute my part to the sorry desertification of this site by leaving and never again trying to contribute much-needed stimulus material here.

Pointing out that questions of this type (even if they involved no complex numbers) cannot be asked in the Extension 1 course.

Alternatively, we could wait for someone who hasn't seen the question before to contemplate it.

I guess this is why this site has died - too many people jumping in to discourage. I asked it here 6 years ago. Has everyone here scoured all old posts?

This is for HSCers - veterans please don't answer, at least until it's been open for a while. You are permitted to climb an n-step staircase by climbing one or two stairs with each step. For example, you might climb a 12-step staircase as follows: 2-2-1-2-1-1-1-2 Explain why the number of ways...

Looks like you got your answer.

Glad to have been able to stir up this thread again. Anyone also feel like challenging the idiocy of Adolf Trumpler?

Except that there are early manuscripts which have been edited. I believe there is one housed in an Egyptian museum (strange place to have it, I know) which clearly shows a description of the "ascension to heaven" being written over an early version which simply said that he was no longer in the...

That is what happens with any story which is initially disseminated by word of mouth over centuries. The core message doesn't change because that is the whole reason for passing on the story, but the fringe details change and become inconsistent. This is what has happened with the bible. It...

Then (a) (i) is 3^5

(a) Can't be answered unless we know whether the boxes are distinguishable, and whether the items are distinguishable.

A solution to the first question:

I thought this thread was going to be about a medical condition caused by spending too much time contemplating Combinatorics in the bathroom.

I'm quite sure HSC markers won't allow this. If you are going to use formulas from beyond the course you have to derive/justify them first.