Oxford MAT Test - 5th Nov 2014

Can anyone help with this question?

I don't know how to prove the square of an arithmetic progression... I can only do it in a roundabout sort of way which takes a while.

Is there a way for you to rewrite the series in terms of an arthrithmetic progress (Hint, consider the difference of two squares)

I'm stuck on the last multiple choice question on the 2013 paper..
I'm not sure if I understand it, does it have a 'stair' shaped graph? I just did the geometric sum and the answers all look alot more complicated -.-'

So I've split it into n(n+1)/2 and two arithmetic progressions (+(1+3+5...) and -(2+4+6...)).

But I end up with -n^2(n+1)/2...

Well for example,

you see that $1^2-2^2=-3, 3^2-4^2=-7, 5^2-6^2=-11$ etc.

You then see that you have a sequence of -3, -7, -11 etc. where you will have n terms.

Can you see what you can do from here and the other terms?

Would PAT papers help MAT?

Please can someone explain why the area isn't maximised when Q and R are very close to P so that nearly all the circle is shaded?

Please can someone explain why the area isn't maximised when Q and R are very close to P so that nearly all the circle is shaded?

"Dirty" method:

When theta = pi/2, QR is a diameter, and the area of triangle QPR is clearly maximized when the triangle is isoceles, at which point we see it's area is 1 (right angled triangle with base = height = sqrt(2)). The remaining area (the curved bit) is the area of a semicircle (radius 1), so equals pi/2.

So any correct answer must = 1 + pi/2 when theta = pi/2. The only option that matches is B.

why would theta being 0.5pi imply QR is the diameter?

GCSE geometry:

http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/circles2hirev5.shtml

Does anyone know are we allowed to use extra paper for the MAT if we use all the space? The instructions can kinda suggest that we can't but i'm not sure - "Answers to questions 2-7 should be written in the space provided, continuing on to the blank pages at the end of this booklet if necessary. Each of Questions 2-7 is worth 15 marks." I REALLY hope we can use extra paper or i'll have to be much more careful with how much space I use :/

No extra paper. They will only mark what is in the answer book.