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.)

VCAA’s Draft Feedback Due TODAY

We’ve been remiss in not writing further on VCAA’s draft for the new mathematics VCE subjects. It’s just, for reasons we’ll explain briefly here and flesh out elsewhere, we’ve struggled to face up to this new nonsense.

But, feedback is due TODAY (midnight? – see links below), and we really oughta say something. So, here are our brief thoughts and then, after that, why we believe none of it really matters:

  • “Computational thinking and algorithms” is pure snake oil.  Inevitably, it will be nothing but wafer-thin twaddle for the training of data monkeys.
  • The increased weight on these meaningless, revolting SACs is insidious.
  • If we read it correctly, more weight will be placed on the non-CAS Methods/Specialist exams; it is not remotely close to enough, but it is good.
  • Statistics was and is and will always be an insane topic to emphasise in school.
  • Foundation Mathematics: Who Cares?
  • General Mathematics: Who Cares?
  • Mathematical Methods: same old swill.
  • The deletion of mechanics from Specialist Mathematics is criminal, but the topic had already been so bled to meaningless that it hardly matters.
  • In principle, the inclusion in SM of “logic” and “proof and number” and “combinatorics” is a good thing. We’ll see.
  • Similarly, in principle the making of SM12 presumed knowledge for SM34 is good; in practice, it is almost certainly bad. Currently, a good teacher at a good school will take the freedom in SM12 to go to town, to show their students some genuine mathematics and real mathematical thought. In the future, that will be close to impossible, and SM12 will likely become as predictable and as dull as MM12 (and MM34 and SM34).

And now, why doesn’t any of it matter? Because, fundamentally it doesn’t matter what you teach, it matters how you teach. What matters is the manner in which you approach your subject and your students, and none of that will change in other than a microscopic manner. Nothing in VCAA has changed, nothing in the general culture of Victorian education had changed. So, why the Hell would twiddling a few dials on utterly insane subjects assessed in an utterly insane manner make any meaningful difference?

Everything VCAA touches, they will turn to shit. That will continue to be true until there is a fundamental cultural shift, in VCAA and generally.

I hate this place.


  • The current (pre-COVID) study design (pdf) is here.
  • The draft for the new study design (word) is here.
  • The key changes overview (work) is here.
  • The link for feedback (until March 9, 2021) is here.

WitCH 56: Fuzzy Dots

Has it occurred to anyone else that these WitCHes are a blogging Ponzi scheme? As long as we keep posting new WitCHes, no one bugs us about not polishing off the old WitCHes. What the hell; we’ll keep going until someone calls the Blog Cops. And, to continue with the scheme, this WitCH comes from the Cambridge text Specialist Mathematics 1 & 2, in the section titled Linear Diophantine equations. Happy hunting.

WitCH 52: Lines of Attack

Yes, we have tons of overdue homework for this blog, and we will start hacking into it. Really. But we’ll also try to keep the new posts ticking along.

The following, long WitCH comes from the Cambridge text Mathematical Methods 3 & 4 (including an exercise solution from the online version of the text).

UPDATE (07/02/21)

Commenter John Friend has noted a related question from the 2011 Methods Exam 1. We’ve added that question below, along with the discussion from the assessment report.



WitCH 49: Trigged Again

The question below is from the second 2020 Specialist exam (not online), and was flagged by commenter John Friend in the discussion here. John has spelled out the problems, but the question is bad enough to warrant its own post, and there’s arguably a little more to be said.

WitCH 48: Thesis Not Good

This combo WitCH comes courtesy of mystery correspondent, tjrb. They flagged three multiple choice questions from the 2018 Algorithmics exam (here, and examination report here), and we’ve added a fourth. tjrb also remarks, “There are probably a lot more errors in this paper (and the other algorithmics papers), but these were the most strikingly incorrect”.

For Q2, the examination report indicates that 41% of students gave the intended answer of A. By way of explanation, the report then remarks,

“Cobham theorised that problems that are feasibly computable (also known as easy problems) are those that are decidable in polynomial time.”

For Q6, the report indicate that both A (51%) and C (33%) were “accepted”, but is otherwise silent.

The report is silent on Q12 and Q16, except to indicate the intended answers: C (94%) and A (66%), respectively.