Another maths exam problem has gone viral after the earlier “sweets in a bag” Twitter storm. This time a Scottish Highers Maths question about crocodiles and zebras (yes!) proved insurmountable. Over and above the technical solution (see below) there were a number of interesting aspects for us English in GCSE – land.
First, the Scottish exam structure is completly different to England’s. There is no mention of GCSE or A-Level, so Higher in Scotland is roughly equivalent to A-Level in England, as it is described as a “pre-University qualification”.
Second, could such a question appear in English Maths GCSE ? Very unikely for the reason above, and because the best solution involves calculus, which is still not in the new GCSE 9-1 syallabus. Calculus is in IGCSE, but even so the crocodile problem would swallow up time as a very tricky differentiation is involved. It is, however, still just possible that a problem like this could be in our GCSE 9-1 syallabus because an alternate solution for it is through “iteration”. But solving it this way would surely eat up time, since perhaps 9 iterations might be needed with awkward square roots.
Third, it shows that quality control of questions is vital, especially when exam structures are changing. Ambiguity can be a killer. In this case many of the “descriptive” parts are not black and white (unlike the poor hunted zebra) . For instance how important is the width of the river? This makes even the first two “easy” parts tricky as you spend time understanding the English meaning. A shame – I feel the crocodile question writer (from Dundee?) crafted a potentially great question, but was let down at the end by the oversee process.
Fourth it shows there is a strong interest in Maths amongst the general public (I assume not crocodiles!) as the web post was No.1 in the charts for the BBC’s most read posts. This is encouraging!
Finally it shows there is no place that examiners won’t go to make questions less purely numeric, and more “challenging”. Another question involved toads and frogs down a well – let’s not go there.
For the record, the techncial solution (in summary!) is as follows – and it’s not a snappy answer!
(1) When x is 20, substituting in the equation for T gives T = 10.4 seconds
(2) When x is 0, substituting in the equation gives T = 11.0 seconds.
The minimum time T occurs when the dertivative (the differential) is equal to zero i.e. a turning point.
Differentiating the equation and solving, we find x = 8. Substituting back in the original equation, we find that when x = 8, T = 9.8 seconds. We can prove that this turning point is a minimum by feeding in x values either side of 8 and showing that T is above 9.8 in both cases.
And that leads to the non-calculus “iteration” method, that in theory an English GCSE pupil could cope with. But you would have to start at x = 1, evaluate T, then use x = 2 and evaluate T again, and follow T down all the way down to x = 8, and find that T reduced to 9.8, Then for x = 9 find that T begins to increase again, i.e. a minimum had been reached at x = 8.
As I said, not snappy!
In conclusion, the question would not appear in GCSE south of the border due to content, and I don’t think it would make it to A-Level becasue of ambiguity – but its a salutory lesson for examiners.