An article titled Mathematica and the Potential Gaming of VCE has just appeared in the MAV’s journal Vinculum (and we have posted it here). By Sai kumar Murali krishnan, who completed VCE last year and who we previously mentioned in this post, the article delivers what the title promises (noting the “Potential” is redundant): Sai demonstrates how Mathematica’s huge library of functions and extremely powerful programming can be used, and has been used, to trivialise VCE maths exams. We believe Sai’s article is very interesting and very important. (For anyone interested to do so, Sai can be contacted by email here.)
Also likely to be of interest, at least to readers of this blog, is the story of the long and weird battle to have Sai’s article appear. Roger Walter, Vinculum’s editor, deserves a hell of a lot of credit for seeing that battle through and ensuring Sai’s article survived, largely unscathed. And a disclaimer: we played a role in Sai choosing to write the article, and we were also involved in the subsequent battle. We intend to write on all of this in the near future.
The problem is to determine Pr(X > 0). Here is Sai’s solution, utilising standard Mathematica functions:
The point is, of course, that the application of functions such as Area and Polygon requires very little sense of the mathematics involved. For an example requiring no mathematical sense whatsoever, consider the following multiple choice question, which appeared on the 2017 Mathematical Methods exam:
The question is of a standard type, and for these questions Sai created the Mathematica function FTest. The following is Sai’s complete Mathematica working to solve the question above:
A final example, again from the 2019 Mathematical Methods exam:
Here is Sai’s Mathematica working for this question, using two functions he created, FInfo and TangentLine:
Sai’s Vinculum paper contains a number of other examples, and Sai has created a huge library of incredibly sophisticated functions to tackle VCE questions, a library which he shared with his fellow VCE students. Sai’s work raises obvious issues, not least of which is the grossly unfair competition between the majority handheld-CAS students and the few Mathematica-powered students. The original version of Sai’s article ended with two paragraphs, which the MAV Publications Committee demanded be cut:
Whatever naivete may exist, I believe it is unlikely to last. Nothing precludes the marketing of Mathematica packages designed specifically for VCE testing and, if Mathematica becomes widely available in VCE, I believe this commercialisation is inevitable. Such a development would turn VCAA’s implementation of Mathematica, which is already very problematic, into an obvious farce.
Of course the MAV having cut these paragraphs, along with every single reference to the VCAA, doesn’t make their content any less true, any less obvious or any less important.
We intend to write more later in the week.