A Tale of Three Cities

This is kind of a WitCH, but there’s plenty of non-crap as well. It is also properly a tale of two states and a planet, but the title was difficult to resist.

A few months ago a teacher-reader sent me three recent assessment questions from three different sources: NSW’s HSC Extension 2 Exam, the World’s IB Higher Level Analysis Exam, and Victoria’s VCE Specialist Mathematics Sample Assessment Tasks (SACs). All three questions involve integrating functions of the form \boldsymbol{x^ne^{kx}}, and the teacher-reader had suggested that there was a smell of plagiarism about it all. We weren’t convinced of that; the functions are very natural fodder for senior mathematics questions, and if there is arguably some borrowing, it is definitely not a Harvard standard of plagiarism. Indeed, the three questions are notably different in, um, style. That seemed worthy of a post.

Here are the three questions. Readers can have at it. Continue reading “A Tale of Three Cities”

A Scaffold for Nothing

It’s been fun VCE times down here in Victoria, but reportedly there have also been issues up north. While our students have been lamenting their inability to calculate the area of a 20 x 20 square (Murdoch, paywalled), New South Wales’ HSC students have been struggling with projectiles subject to air resistance. Same same. Continue reading “A Scaffold for Nothing”

A Choice of Difficults

You have a choice. The two questions below come from different exams:

Each question was (arguably) last year’s most difficult exam question on the most difficult mathematics subject in that state. Each question was effectively allocated just under 20 minutes to complete (11/100 x 180 and 13/80 x 120).

Now, you must choose: which question is better, in any sense of the word “better”?


NSW  (Formula Marking guide and sample solution are here.)


VIC  (Briefly discussed here, marking guide and sample solution are in your dreams.)