To be clear, this post is intended to be a challenge concerning VCAA’s bad writing, not a bad challenge to VCAA’s writing. But we’ll see; perhaps it will end up both.
I’ve attacked VCAA’s writing plenty often. Even when the focus of a post is some falsehood or absurdity, it is difficult to ignore when the falsehood/absurdity is wrapped in terrible writing, which is typically the case; Burkard’s and my 2022 exam critique had a section devoted to VCAA’s “poor writing”, and many other sections strayed into that territory; and I have had dedicated posts on both VCAA’s lesser and greater literary offenses. This post goes in the opposite direction; it is a challenge to identify VCAA’s good, or at least better, writing.
Some years back, I had a post premised around the conjecture that “every new idea in modern mathematics education is either trivial or false“. I was not confident that the conjecture was false but I thought it would be an interesting challenge for commenters to try to find and argue for a counterexample, and so it proved to be. I, at least, learned a lot from the discussion (and came away more confident of the conjecture). This post is presented in a similar vein, although I imagine commenters/hunters will have an easier time of it here, and the desire is more for the resulting discussion than the proof or disproof of existence.
In our critique, Burkard and I included an example of “poor writing”, where we suggested that
State the derivative of f with respect to x
would have been better written employing one word rather than seven:
Find f'(x).
VCAA’s internal response to this suggestion (courtesy of “CM”)1 was,
The authors offer an alternative wording which is equivalent, yet offers no objective or subjective gain in clarity. The alternative wording renders question purpose less explicit.
Well, you either get it or you don’t. VCAA did not.
VCAA’s exam writing has improved dramatically since 2022 but it is still not good. There are few questions that fail to make me pause, that I feel could not easily be better written. To give just one example (selected somewhat randomly just now, after a 2 minute scan), consider Q7(a) on MM Exam 1, where a polynomial f has been given in the preamble:
Verify that x = 5 is a solution of f(x) = 0.
Sure, that wording works. No one is going to go to war over it, not even me. But why not more simply write,
Verify that f(5) = 0.
To push this a little further, why is the polynomial “f”? Why not “p”? Yeah, it makes no huge difference but p is the more conventional choice and is thus the better choice. So, use it.
This kind of thing occurs over and over and over. Even when VCAA’s wording works well enough, and it certainly works better than in 2022, very often just a little thought and discernment would make it work better.2
So, to the challenge:
Find the 2025 VCAA exam lines that CANNOT be improved.
There is no prize for this challenge,3 since I’m more interested in the post as a writing workshop; I would like to see what commenters suggest as good, or good enough, VCAA writing, and then let’s see if the selections can be made better, and how.4
To indicate the parameters, let’s stick to this year’s MM1, MM2, SM1 and SM2. I’m also interested in the phrasing of single question parts, maybe with preamble; so, lesser literary concerns, not overall question structure. Examples of the type are in the Lesser Offenses post and in the “poor writing” section of the 2022 critique. There is no need to type out or screenshot the selections. Just flag the question part in a comment and then I’ll add it to the post proper.
That’s it. Just forget about all the Christmas shopping to be done and get to it.
1) Possibly Cormac McCarthy but this has not been confirmed.
2) Q7 above is a good example of this. The “f or p” thing did not occur to me until I began writing that section of the post.
3) Yes, I am aware that I have some prizewinners from previous posts still to be determined.
4) Readers may also wish to flag examples of worse writing on the 2025 exams and that’s fine; I’ll post those as well. We can ponder whatever readers wish. My main goal, however, is to get readers to think harder about “good enough” mathematical writing.
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UPDATE (17/01/25)
SRK has suggested Q1 of SM1 as a well-written question, and has pondered alternatives:
Note that John Kermond has criticised this question for the constant e4, considering it a (probably unintentional) “trick”. That may be a reasonable criticism, and good exam writing will give careful consideration to such issues, but it is not the kind of thing that this post is on about.
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UPDATE (17/01/25)
Red Five’s suggestion (I think) from MM1, with doubts about part (a):
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UPDATE (17/01/25)
Sentinel’s (very interesting) suggestion, Q2(d)(i) from MM2, with a proposed rewording. To give the context, the functions 
and 
have been given in the preamble (five pages back), and enough information is given for the students to “show that” 
and 
(in part (a)).
Methods Exam 1, Q4 parts (b) and (c).
I’m hesitant to include part (a) as I think it could have (perhaps) been improved. I like (b) and (c) because they get to the point immediately.
Sure, they are simple questions, with no real challenge to them, but the competition parameters didn’t specify a minimum length of question.
Thanks, RF, I’ll post. Just to clarify, you mean (b)(i) and (b)(ii)?
To be clear I’m perfectly fine for people to propose “can’t get much wrong” questions, not because I necessarily think VCAA got such questions wrong in 2025 but because historically they have. So, let’s check.
That is them. I think the question is OK, not great because it is too bitsy (which is unfortunately typical VCAA) because it gives all required information, gets to the point in few words and yet still gives students plenty of opportunity to make mistakes.
It is of course a very simplistic “do you know this specific concept/skill” type question which does make it low-hanging fruit in many regards…
Thanks, RF. Of course the question (all questions) are flawed by being bitsy, but that’s not the issue we’re discussing here. I’ll give some thoughts on all the suggested questions tomorrow.
Posted now. I assume this is the question you mean. I have thoughts but will give others a go first.
Hi, RF. I’ll give my thoughts now, first on (b).
Yeah, (b)(i) and (b)(ii) are fine. It is difficult for them not to be but no matter: the point is to ask clear and direct questions in a clear and direct manner, and VCAA have done so.
The one change I would definitely make is to replace “Let k = 15” with “Suppose that k = 15” in (b)(i). We already have a probability distribution from part (a), so k is given; we just don’t know what k is, and there are only two possibilities. Using “Let” implies that we are choosing k, but we are not.
Part (a) is also basically ok, although the “where k is a positive real number” at the end is a little awkward. There is no purpose in specifying that k is “positive”, I’m not sure “discrete” is required or helpful, and “given by” is definitely preferable to “given in”. All in all, I think a better wording is,
Consider the probability distribution for the random variable X given by the table below, where
.
I’m still not really pleased with that, because of the k business at the end. But, given the artificiality of the question, I’m not sure there’s a better wording.
Just want to say I hate the font they use for the questions.
Thanks, OT. Yeah, off topic but worth mentioning. I’m not a big fan of the font either, although I’m not sure why. I normally prefer sans fonts. In any case, I think the font change was a Bennett suggestion (or maybe Deloitte), with the idea that the exams be easier to read.
I’m going to defend Spec Exam 1, Question 1. I can think of a couple of ways of making the question more concise, but each has drawbacks.
1. Rewrite the whole thing as “Find the equation of the tangent to the curve with equation …. at (4,-2)”. But with this many prepositional phrases, I think it is preferable to break it up in the way the examiners have: here’s the object to consider, here’s what we want you to do with it.
2. Rewrite the whole thing as “Find the equation of the tangent to at (4, -2)”. While it is obvious what is intended, I don’t think equations have tangents. A similar thing could be said about rewriting the question as “Find the tangent to the curve with equation …” – we want students to ultimately write down an equation for the tangent.
If I’m missing another way to improve the question, or if my judgement on these adjustments is awry, I’d be keen to hear it.
Thanks very much, SRK. A very good example.
Clearly, the wording works and any criticism is going to be nitpicky. But that is the point, to consider what goes into a well-worded question and can one go from well-worded to best-worded. (Of course “best” will stray well into subjective considerations.) Do your suggested rewordings not work as well?
I have thoughts but I’ll let other people have a go first.
Hi, SRK. Here are my thoughts on SM1 Q1. In sum, I agree with you. I might make two very minor changes, as indicated below, but I think the question is very well worded.
On your first possible modification, I strongly agree that it is better to have the question split as has been done. There is absolutely no value in cramming the background information and substantive question into one sentence, particularly with the information coming second. VCAA used to have this format much more, and still uses it too often, and it is usually bad, or worse.
On your second possible modification, I again agree. There is something over-definitiony about a lot of VCAA wording, and I’ve been looking to sort it out in my mind and attack it (maybe here, maybe a separate post), but I don’t think one can write “the tangent to [equation]”, even if the meaning were understood.
One minor change that I would make is to change “with” to “given by”. Yeah, I’m not gonna beat up anybody for using “with”, but naturally the equation comes first and then we interpret the equation as giving or represented by a curve. There’s a logical/chronological order here, and “with” clouds that.
The other change I would make is to leave out “the point”. This is definitely a judgment call; the phrase is redundant but one can still argue that “the point” makes the question read more easily. But, i think probably not. In general, if words are not technically required in an exam question then one needs a good argument to include them.
ERQ2di
. Give your answer in terms of 
. “
Could‘ve been phrased as
“Find
Thanks, Sentinel. Posted now, and interesting choice. How did you come to consider that one?
Does the “give your answer in terms of
” add anything of substance? One would assume this was clear enough. OK, maybe “hope” is better than “assume”.
Looks like the examiners wanted to see an explicit expression this time rather than implied form
…
Judging by the marking guide, or do you have other information?
OK… question for this one: given the way it is written, does any *reasonable* person see a reason why writing
would be marked as wrong? (likely such a statement would have been marked as wrong, but I’m not convinced the wording of the question makes such an answer wrong at all…)
An excellent question, RF. I don’t know if that’s why Sentinel nominated the question, but Sentinel’s rewording goes towards eliminating the ambiguity, which is undeniably there.
Yes Marty.
SRK [Marty edit: it was Red Five] mentioned exactly the same point I would love to flag as an issue.
Thanks, Sentinel. I *think* I know what you’re on about but it’s a little cryptic so far. What is the “exactly the same point” that SRK made, and where did they make it?
I’ll comment on this question but I’d first like to get straight your angle on it.
I agree with SRK [Marty edit: it was Red Five] – the response
shouldn’t be marked as incorrect in line with the wording of the question “write down the derivative …”
I am not convinced too – if this was marked zero. But a number of students who obtained their statement of mark raised this issue – they did get zeros.
You mean Red Five? I can’t see where SRK commented on this question.
Much more importantly, you had “a number of students” who answered f’ – g’ and received 0/1? Have they complained or appealed or whatever one does?
Sorry – I meant RF in my previous posts. Are you able to fix my posts above?
The inspection process takes long…usually it has a small cost to inspect the paper…and maybe this time it’s not worth the 26 bucks for inspection and appealing…obviously they didn’t accept that form…
No big deal, re SRK/RF, but I added little notes.
I don’t see that it’s worth inspecting the paper. As you say, pretty clearly VCAA didn’t give the point for f’ – g’.
What is your opinion on that? Yes, the flaw lies in the question, and something like your wording was required, but do you think nonetheless students should have realised what was expected?
I have a feeling that they were trying to be awarding and inclusive when the marking guide was set (if you look at the published guide – even accepting
)- but they didn’t like the special case discussed above.
…
I believe the largest majority of the MM students gave what was expected. Still there must be a small proportion of them, just looking at the command term ‘write down’ and giving this expression
One argument around this could be whether they really *attempted* differentiation…so they wanted to see evidence of a difference between two explicit derivatives…
On the other hand, this year’s MM exams (both) were much easier than the 2023 and 2024 exams… so there was not much room for the kids who were aiming for high 40s; imagine some good students just missed on this mark – it basically implies one mark off on their study score.
A Pandora’s box again …! If the question stem was not set unambiguously, you always see some loopholes or flaws. All sorts of issues will be creeping in then.
Thanks, Sentinel. I’m replying to your latest comment here, since the thread was getting narrow. And sorry to be slowly teasing out why you flagged this question and your thoughts on it, but this question had already been flagged to me and I wanted to know your thoughts before weighing in.
To begin, the question is obviously fatally ambiguous. Putting aside the insanity of setting such 1-mark micro-questions, it is reasonable for the examiners to expect an explicit answer, in terms of x. But, they have to damn well ask for it. And, not only did these nitwits not ask for that, they asked students to “write down” their answer. That command term points in exactly the opposite direction of computing or combining or whatever, for a 1-mark question.
In short, the examiners screwed up and they should definitely have awarded the mark for f’ – g’. It is pretty clear that they didn’t because they are assholes who always refuse to take responsibility for their stuff-ups, but they should have.
There is another MM2 question I have in my sights for somewhat similar reasons, and I plan to write on both (and an insane GM question) in the near future.
As for how to reword the question – the reason why we’re here – it is difficult because the question is so microscopic and so stupid. But, your suggestion works well enough, and you need something along those lines. You must use a more forceful, “do some work” command term, like “find” or “determine”; and, you must have an “in terms of x” directive. I’d probably go with
“Determine an expression for h'(x), in terms of x.”
But, I’m not sure I can argue my version is better than yours.
Further to your previous post on the “Utterly predictable dickishness”… let me offer other two suggestions to:
1. MM2 ERQ1d
2. SM2 ERQ1a
They should really use the key term “draw” or “plot” in lieu of “sketch”!
Thanks, Sentinel. I’m not sure the suggestions belong on the writing post but no matter. I’ll look at both soon.
Hi, Sentinel, I’m puzzled by both these suggestions.
SM2 EQ1a is the subject of the Dickishness post. Did you intend to flag some other question?
Do you mean MM2 ERQ1b? (i.e. not 1d) If so, I cannot see an issue with either the question (taking as a given that it is pointless CAS crap) or the grading. There are no gridlines suggesting some unwarranted accuracy, and nothing in the marking guide suggests this. Do you know or suspect something further?
As for the command term, it definitely must be “sketch”. The solution is not to harden the command word but to soften the command.
Thanks Marty, yeah I meant ERQ1b for MM2.
Imagine a negative quartic graph students produced on the paper that flattened too much, bumpy and twistly, swirlled away…would you say it’s good enough for 2/2…?
I mean, if the examiners really want the students to take extra care when producing any kind of graph, they should explicitly spell out their expectations, rather than using a softened language like ‘sketch’, while their actual intention was ‘plot’.
I like the black one.
Obviously there’s a limit to how sketchy a sketch should be permitted to be, and there will always be judgment calls. I wouldn’t be too fussed if the main features were there and correctly placed relative to each other. I’d be amused by the black graph and I probably wouldn’t mark it down, but semi-fair enough if VCAA/teachers demand something less wormy. (As long as this demand is not being driven by a “copy your CAS better” fetish.)
But I think you’re trying to correct the mismatch between “sketch” and the assessors’ expectations by focussing on the wrong target. Yes, IF “if the examiners really want the students to take extra care when producing any kind of graph” THEN whatever. BUT, the examiners are simply cretins for wanting that and I’m not going to accept the “IF” for even hypothetical purposes. VCAA should simply be told that this is all fucking insane.