Stretching question

Sunday 18 June 2006 at 2:35 pm | In Articles | 13 Comments

A level maths questions these days vary little from year to year, so working through past papers is the best way to revise. Occasionally though, the examiners ask for something slightly different at the end of a question to separate the best students from the good ones.

This happened in this week’s Further Maths paper. It’s not hard, but the last part of the question may not have been seen by students before and so requires a little thought on their part.
The question started off with

    M=\begin{pmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \vspace{-2mm} \\ -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{pmatrix}

then asked for the transformation that M represents, to calculate M^2 and M^4 and then, the ‘stretcher’ for three marks, calculate M^{2006}.

It will be fascinating to see the examiners’ report on how students coped with this non-standard question.

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