Optimising novelty chocolate boxes – 2019 Higher Maths outrage

In 2018 it was the Nat5 ‘umbrella’ question that prompted tabloid outrage (see this article in the Scottish Sun ) and this year we have the ‘novelty chocolate box’ question in the Higher exam that, reportedly, has students in a tizz (the Scottish Sun, again).

Here is the worked solution for the chocolate box question taken from the Your Maths Tutor YouTube channel:

We try to keep a level head here at YMT’s Edinburgh HQ so, speaking to our students after the exam, they felt that part (a) of this question was the more difficult of the two – that is, establishing the relationship between the area of the box and the variable ‘x’. All managed to successfully answer part (b). This was great to hear as part (b) of these optimisation questions is where you gain the bulk of the marks.

Problems with proof

Proving the given relationship – part (a) – is essentially a test of how well you can manipulate systems of simultaneous equations by substitution. There may well be an issue here as at National 5 we are only really teaching Gaussian elimination, and we are not really giving students a good grounding in solving simultaneous equations by substitution (if at all). Perhaps giving students broader skills at Nat 5 will help at Higher. What do you think? Your thoughts are welcome below.