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It is not a matter of which is better - you are not permitted to write them down without proof. The only exception is the chord of contact formula (or of course if they ask a multiple choice question on the topic). And ..... in Australia we do maths.

Re: MX2 2015 Integration Marathon A relation that just involves In, Jn, Kn would not be a recurrence relation. It would have to involves smaller values of n.

Is there supposed to be a restriction on x in this question?

When you say "your case is not very believable" you are implying that everyone should come to the same conclusion. Clearly you are the only person outside the teachers who have that opinion. When expressing you own opinion, say "I don't believe it".

"Transition probability matrix" ?? I think this should be moved out of the 2 unit thread.

Re: 2015 permutation X2 marathon I don't want to give my calculation because it is supposed to be for HSC students. But for the tetrahedron, and only for n>3, I get an expression which simplifies algebraically to: \frac {n^2(n^2+11)} {12} I can't see a logical way to go straight to...

Re: 2015 permutation X2 marathon Why are you dividing by 4 ?

Re: 2015 permutation X2 marathon Wouldn't the answer depend on whether or not n>3 ?

Re: 2015 permutation X2 marathon You would have to get seriously stuck into Inclusion/Exclusion

Re: 2015 permutation X2 marathon (I just want to get this question out while it's still in my head, so don't forget the previous question) In a 12 sided convex polygon, how many diagonal intersections lie inside the polygon? (ie. not counting the vertices themselves) [Assume that no...

Re: 2015 permutation X2 marathon I really don't think it is a good idea to give out your name on this site.

Re: 2015 permutation X2 marathon A special chessboard has 25 squares by 25 squares. In how many ways can a knight move from the top left corner to the bottom right corner if it only moves down and to the right? Answer: 12870

The distractors in a multiple choice question are typically designed to attract people who go with their gut.

\int x dx = \int x . \frac{d}{dx}(x) dx = x.x - \int x.\frac{d}{dx}(x) dx = x^2 - \frac{x^2}{2} = \frac{x^2}{2}

Because that scenario is exactly what addition of velocity vectors is all about.

I'm afraid this is not even a calculus question. It is just addition of vectors.

Actually, the form the equation was given in originally is general form.

Re: 2015 permutation X2 marathon Actually, it is not something HSC students need to know. I asked the question on the basis that this result would have been derived in an earlier part.

Re: 2015 permutation X2 marathon Let T_n be the number of ORDERED subsets of n distinct objects. Show that as n approaches infinity, T_n approaches e.n!