Division by zero shock!

Tuesday 16 March 2004 at 4:35 pm | In Articles | Post Comment

It is well known that division by zero is the ultimate mistake to make in mathematics (see Dividing by 0 and Wikipedia). Different rules may apply in other advanced number systems but for use in the set of real numbers it has to be avoided. Doing so is often not easy, but one has to live with the consequences.

It is thus a shock to see division by zero hidden in a question in the AQA A Level Mathematics Specimen P4 Paper. Question 7 starts with

    The function f is defined by \begin{displaymath}\text{f} : x\mapsto\tan3x-4x \end {displaymath} and has domain 0\le x \le \frac{\pi}{6}

Where’s the division by zero? It is implicit in the definition of \tan\theta which is defined as \dfrac{\sin\theta}{\cos\theta} ,   provided of course that \cos\theta\not=0 ; so what happens in the given domain? Thus f doesn’t exist, which makes the rest of the question unanswerable, since it requires you to differentiate and integrate f 😀

The examiners should have known better. Perhaps it is just as well that the syllabus (and hence the specimen paper) will be replaced, starting in 2004.

Thanks to one of my eagle-eyed students who spotted this horror!

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