Last month we posted a PoSWW on a 2022 Queensland MCQ exam question, for which the accompanying exam report indicated the wrong answer. It is depressingly unclear why QCAA had not been previously alerted to the error, but a couple weeks after our PoSWW appeared, QCAA updated their exam report: in the amended report QCAA indicates the correct answer (p 27), and they also indicate in a footnote that the correction had been made.
For QCAA to have done this was professional and classy. It was also important. The uncorrected report invited, effectively demanded, a mathematical misconception (on inflection points); by correcting the report, QCAA ensured that their exam-report could no longer be relied upon as an authority for this misconception.
In Victoria, it’s different.
The graph above is from a 2021 Victorian (NHT) MCQ exam question. The question asked the students for a domain upon which the function is strictly decreasing. It is clear that the intended answer was the union of the obvious two intervals upon which the function is decreasing, but the function is not decreasing on this union, and none of the suggested answers were correct. We posted a WitCH on the question.
A month after our WitCH, VCAA’s exam report appeared. The report indicated, without comment, that the answer to the MCQ was the interval union. A couple weeks after that, an amended report appeared, with the incorrect answer deleted but with nothing in its stead: VCAA failed to state that the previous report had been in error, and VCAA failed to state that the MCQ has no correct answer. For VCAA to have failed to do so was unprofessional and cowardly, and it has also had consequences: the ghost of this ridiculous exam question haunts us still.
In 2021, soon after the NHT exam appeared, we happened to see a SAC from a “top ten school”: the SAC contained a question exactly in the style of the NHT question, and exhibiting the exact same error. In October of the same year, and after the amended exam report had appeared, the same error was on the draft of a test at a second “top ten school”; the error was caught by a reader of this blog. The same error was still around in 2022, in a selection of sample questions from a third “top ten school”. If “top ten schools” are still serving this nonsense, it’s a safe bet that hundreds of not-top-ten schools are doing so as well.
We checked three current Year 12 Methods textbooks. Two of the three texts – Jacaranda and Nelson – contain multiple exercises and/or examples exhibiting the same error. Nelson sources one question to a 2010 VCAA document, a selection of sample exam questions, including the following:
If VCAA has ever flagged the 2010 error we have seen no sign of it, and the 2021 error is strong evidence that, at least until 2021, VCAA was oblivious. Others were not: itute got it right, and they could not have been alone. Presumably no one bothered to tell VCAA, presumably because no one believed that telling VCAA would have had any effect.
Whatever the history, VCAA is not now oblivious but they still refuse to state the clear truth. Which is their standard practice. There have been numerous VCE exam errors over the years, way way more than is remotely acceptable, but the number of clear and full corrections from VCAA can probably be counted on the fingers of one finger. Perhaps two.
VCAA continually produces nonsense. Then, by refusing to issue clear and proper corrections, VCAA permits, effectively demands, that VCAA be relied upon as an authority for this nonsense. This is shameful. And it has consequences.
UPDATE (02/06/23)
An update on the QCAA question is discussed here.
Thanks Marty.
And thanks QCAA for giving me hope that there is some semblance of reason within the examination bodies in Australia (outside of NSW/ACT).
The whole strictly increasing/decreasing fad (and yes I’m going to call it that as it has appeared in a number of Methods 3&4 SACs I have had the joy of proof-reading recently) is a bit self-serving it would seem: a teacher looking for ideas finds a SAC which has the phrase “strictly increasing” and it seems like a nice enough idea, so lets see how it is taught by looking at textbooks and VCAA exams… regular blog readers know too well how that story ends (assuming it has ended).
Just wait until we have functions for which
is strictly increasing but 
is strictly decreasing…
…and then there will be some confusion about whether a function defined for the interval![[a,b]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-dfd0bfaf87ada40d4af7f03a07a78a42_l3.svg "Rendered by QuickLaTeX.com")
is differentiable or not at 
and/or 
…
Considering the rest of the QCAA exam papers, I wouldn’t say there’s too much reason. Of course, it’s a positive that they acknowledged their mistake, but it unfortunately seems as if they wrote the exam questions largely with VCE math exams as a model.
Thanks, Y. I’ve barely skimmed the QLD exams, but from a brief skim, I’d agree: the QLD exams look appalling, similar to the VIC exams.
There are pre-exam awfulnesses that cannot be ignored, but dealing just with the exams, there are, at least in Victoria, a number of separate aspects:
a) Out and out errors, both big and small;
d) Poorly conceived questions;
c) Atrocious writing;
d) An overall triviality, with a microscopic grading scheme;
e) Opaque grading, which appears to lean to the prissy and pointless;
f) Reporting that is thin and poor and arrogant and misleading, when not outright dishonest.
Of these issues, I think the existence of outright errors is of least concern. However, the existence of these errors points to a general dysfunctionality in the writing and vetting of the exams. And, VCAA’s refusal to own up to these errors is evidence of VCAA’s unwillingness to admit to this dysfunctionality, at least publicly. Plus, as I’m arguing in this post, it demonstrates VCAA’s lack of concern for a teaching founded on truth.
I focus on the exam errors and their reporting because I regard it as VCAA’s weak spot. VCAA either admits the errors and thus publicly acknowledges the exam flaws. Or, VCAA obfuscates, or worse, and then at least I can highlight the undeniable absurdity of this situation.
I don’t see how the exam errors can be diminished without a fundamental change in the manner of the exams’ creation, possibly implying that entirely different people would be involved. If that were to happen, other, more fundamental improvements, are imaginable.
As someone who went to a “top ten school” for better or for worse, it doesn’t surprise me at all that teachers would repeat VCAA’s error. In fact, they probably went out of their way to repeat the error. The goal of my “top ten school” and I assume the other high ranking schools, was not to teach but rather to get the best possible VCE marks. In fact, one of my teachers (not in mathematics) explicitly admitted that some of what he was teaching was incorrect, but that we should learn it regardless in order to get good marks.
Thanks again, Y. I know the game, that all schools play, and that “top ten schools” play better.
There are some aspects of VCE maths being “incorrect” that are more egregious than others. I am not against, for example, a light and dodgy take on theory for the purpose of focussing on solid technique. Such teaching is not remotely “incorrect” in the manner of this post’s nonsense.
The above question asks for “
subset for which…”. This suggests that there is only one such subset. Students who read examination questions carefully will be aware of this subtle suggestion.
Indeed. Which is why I wrote “error(s)”.
The “the” in “the subset” is VCAA-speak for ‘the largest’ or ‘maximal’ (whatever any of that means because the cardinality of any continuous interval is the same as any other). Whos on first!? (take youre pick)
Alexander Pope – To err is human, to forgive divine, to refuse to issue clear and proper corrections is VCAA.
Thanks, A. However:
(i) Being VCAA-speak doesn’t make it either English or correct.
(ii) I can’t be bothered confirming, but I’m pretty sure VCAA often asks for the “maximal” or “largest” domain for this or that function. So, even if it is VCAA-speak, it is inconsistent VCAA-speak.
VCAA-speak is a language and so evolves over time (for better or for worse) just like any other language. So it is unsurprising that 2010 VCAA-speak is inconsistent with 2021 VCAA-speak. So I dont think such inconsistency should be held against the 2010 question. And we see that the wording on the 2021 NHT MCQ doesnt have the ‘ambiguity’ that Terry Mills notes.
2012 SM1: “Find the largest set of values of x ∈ R for which f (x) is defined.”
Touche. If only we new what ‘largest set’ means, I havent seen it defined anywhere by VCAA. I think I prefer it when they ask to find the ‘maximal domain’.
To forgive is not VCAA policy…
You really would think VCAA would get its act together here, given whats at stake in these exams. Until reading this blog I just assumed they knew what they were doing. Incredible that they’d let sit uncorrected exam errors. But then again, this is typical of the mostly lazy and inefficient victorian public service; just like the Victorian Institute of Teaching etc.
Thanks, Harry. It’s an interesting question. I have theories, some more substantiated than others, but I’ll leave it for now.