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I would be penalising you for the logic of your inductive step. You should be starting with a-b (without the >0), then manipulating it until you have a >0 on the other side. Your working is similar to being asked to prove a trig identity, starting with the identity you have to prove, and...

No, I am afraid you are wrong. The division by 7 has already been accounted for, because the three neighbours have only been ordered, not placed in three specific seats.

You've got a problem there because D is not (0,1,3). It is (2,-3,3).

Re: HSC 2015 3U Marathon 11! ÷ 2 ÷ 5!

We already had the right answer.

Firstly, we only divide by 3 if we are interested only in the relative seating positions of the guests. In that case, Homer sitting in seat A, Monty in seat B and Moe in seat C is the same as Homer in B, Monty in C, Moe in A, and also the same as Homer in C, Monty in A, Moe in B. So 9P3 counts...

So ... there's no mention of it being a circular table? Then its 9P3. If it's circular, then divide by 3

Provided they justify it that way. They can't just quote the formula.

I'm afraid not. And the current syllabus was published in 1982, so unless you're more ancient than me ....

Two issues with that: (I) That formula is not mentioned in the syllabus, so you would have to first justify its use (II) If students believe they can use that formula whenever they see a cos^2 (x), they are going to get into a jam if they come across an exam question that has both a cos^2...

Why would you use t=tanx when the angle is x?

Do you really want to stand by that invitation? :) Or did you perhaps mean 'bear' with me?

Hmmm .... not sure. On a completely unrelated matter, did you realise that the fraction of females teaching 'high level' maths has increased over the last 100 years, even the last 30 years?

I know this is not an English forum, but you just wrote something that irks me every time I see it. There is no such thing as "should of". It is "should have".

You know this is not the case for the vast majority of people. Seems like I gave you an opportunity to boast.

One of the standard integrals given on the back of the paper is the integral of secxtanx. Substituting u = pi/2 - x allows you to integrate cosecxcotx using this rule. secx and cosec x can be integrated using the t-results. But Ext 1 students are not expected to come up with either of...

The later questions are nowhere near as difficult as they used to be.

Re: HSC 2015 4U Marathon Yes, my answer was wrong. I'm getting your answer in a different form: p^2 - p^2 (1-p)^3 It simplifies to the same thing, but could you explain your logic for that form of the answer.

Any f**k is a good f**k !

That depends. Are they allowing for different orderings of the rings on each finger? If so, it is not the same question. There is no ordering of the coins within each box. If they are not doing that, then their answer MUST be wrong. The MAXIMUM number of ways you can allocate the rings...