This one is on a question and a half from the 2025 Western Australian “calculator assumed” Mathematics Specialist Exam (not yet posted). One of the questions was queried because Haese apparently screwed up a similar question, and the query was whether WACE might screw up similarly. We’ll have to wait and see. However that query plays out, regular readers will quickly spot the entirely separate reason to be here.
UPDATE (11/02/26)
I’ve updated the capture for 10(a) from the published exam, which makes clear that the ‘locus” is the region bounded by the curve (and including the curve). And, the marking key has also been published: see below.
This is hilarious and, beyond being hilarious, 10(a) has a bonus WitCH.
Visited 78 times, 1 visit(s) today
Is the first graph meant to be symmetrical about
?
It does not appear to be, but it that was the intention…
Actually, stupid me… of course the graph is not symmetrical. It cannot be given the asymptotes and axial intercepts.
There still seems to be infinitely many possible rules for
though.
Yes.
On its face, the range of possibilities for f(x) in #9 does not make this a good question for a quick answer examination. What sort of experience students are expected to have that makes them think “aha — that is what the graph of that function I know about might look like”. The second question that I have is how students actually answer such a question, and this is where teachers who debrief the candidates can be helpful — what is the probability of a student saying “geez — I don’t have a clue” and is this a reasonable probability for this sort of test? if a question is too easy, too hard or too badly designed, then the examiners don’t get useful information. Do we know the mark distribution for this question?
Neither question is a good question, and for the same reason, even for a slow answer examination. They both teach the principle that what you perceive is what you have: “This looks like X, and X is all I can think of, therefore this must be X”.
As for how students did/do on Q9, I don’t know. The exam has not been published yet, much less a grading scheme or mark breakdown. I don’t know the WA exams but I suspect that this type of nonsense may be pretty standard, meaning that students will attempt, better or worse, the autopilot expected.
Perhaps examiners expect something along these lines. “This looks like X, for the following reasons, and therefore this could be X”, or better still “This looks like X, for the following reasons, and therefore this could be X, but one can’t be certain from only a sketch of the graph.”
.
The examiners cannot expect anything sensible since the question is not asking anything sensible. But everybody will perform the ritual, so all good.
So the assumption is that students look at the asymptotes and intercepts and get
.
However, just going on what the graph looks like, it suggests the right part of the curve doesn’t cross the horizontal asymptote but the graph of the equation above does.
There is a lot to assume.
Thanks, Potii. (I fixed up your TeX.)
I’m not sure I understand your point. I was just focused on the Magritte idiocy. Are you suggesting that, even on the question’s own terms, the graph is misleading?
I was thinking the same thing as Potii.
Yep. Thank you, both. as often occurs with the WitCHes and PoSSWs, I post for one reason and you then sharp-eyed guys find further madness.
Ah, I see. That is very funny.
Yeah, it is very slopy work. Someone just didn’t even look at the graph properly when creating the question.
Or the writer thought, that that part of the graph passing through the horizontal asymptote, if shown, would confuse students and should be left out. As,
, then who cares what side the the graph approaches the asymptote (probably what the writer thought).
Either way it is not good.
“slopy work” is a very funny typo.
I think it’s probably the latter, that the writers assumed, probably correctly, that including the crossing of the asymptote and the second turning point would confuse the students. But leaving them out certainly adds to the madness of the question.
Haha yeah that was a good typo, I mean intentional pun.
This could easily have been mitigated with “Part of the graph of …” rather than “THE graph ….” As worded, I think the question can justifiably be called defective.
As for Magritte, labelling the features that are shown (with coordinates and equations) would mitigate this.
No, nothing fixes the Magritte.
You clearly forgot to add
to your 
.
You’re doomed, As are we. Anybody who comes up with a question like # 9 (number 9, number 9, number 9) should be . . . no, I’m not going to say it. If I had been given a problem like this when I was 18 I would have said it’s y =x, just very badly drawn.
That’s hilarious. Franz wins.
Question 10 offers delightful possibilities for bush lawyers. Can I get away with equations or inequalities based on the real and imaginary parts by simply disguising the real part as
and the imaginary part as 
? Is the use of 
forbidden in my answer?
Thanks, Barry. Yes, apart from the Magritte nonsense, the prohibition in 10(a) of using Re(z) and Im(z) is absurd and close to meaningless.
Curious about it all. 2024 wace has part 1 tech free, for a total of 47, i think, 50
minutes as indicative time. Q9 is worth 5+4 =9 marks. It is heavy. Part of the
graph beyond x=4 or 5 seems deceptive – going below y=2 affects the range asked for in part b…
But the whole question is worth almost 20% of this section, with around 10 minutes to spend on it.
Could we have it checked? I think it is part with no cas
I just checked. It’s “calculator assumed”:
Q9 asks for “a” defining rule with justification. I would interpret this to mean that the examiners are prepared for a number of answers with justification.
That does not save the question.
I can see that it is useful for students to look at a graph and surmise possible functions that might give rise to it. However, I do not think this test is a good place for it for two reasons. First of all, I agree that Potil’s suggestion was what the examiners were fishing for, and therefore it invites an uncritical rote response that students can be prepared by their teachers to give. However, the main difficulty in my mind is that it is without either mathematical or pedagogical context. For example, one might look at an application for which a graph exists and wonder whether one could describe it by some function. In this way, students can come to understand the characteristics and significance of some standard functions — polynomials, exponential, logarithm, trigonometric, etc.
Pedagogically, I think the best setting for a question like this is a class or small group discussion where suggestions can be put forward, tested and maybe some interesting questions raised such as whether the graph crosses the horizontal asymptotes.
Any curriculum that includes the graphing of functions with horizontal asymptotes, and certainly diagonal asymptotes, is incompetently taught if it is not taught that graphs can cross such asymptotes. And such a curriculum is defective if such cases are not explicitly included in it. It makes me white hot angry when I hear teachers ‘teaching’ that “a graph cannot cross an asymptote”.
And I wonder whether students get taught that if f(x) has a vertical asymptote x = a, then the graph of 1/f(x) will have either an x-intercept or a ‘hole’ at x = a and that some further investigation is required. Again, in my opinion a curriculum is defective if such cases are not explicitly included in it.
The above defects are among the many, many defects of the current VCE Mathematics Study Design.
John, you’re shoehorning an agenda again. Victoria’s curriculum has much more and much more importantly bad/absent than the treatment of asymptotes.
The 1/f thing is interesting, and I vaguely alluded to it in the post. Q9(a) was initially flagged because apparently a Haese book incorrectly gives the range of such a 1/f as including 0: that is, the “hole” was incorrectly filled in. (I haven’t seen the error to confirm it, and I don’t know which book.) The question, then, was whether WACE was going to make a similar error in the grading of 9(a). (My WA source does not seem to think this is likely.)
Exactly. Even in the schoolroom setting I think there are issues with such questions, and the framing matters a lot. It would be natural and beneficial, for example, to ask as well for both underdetermined and overdetermined functions (within a given class). But a question like this should be nowhere near an exam.
I’ve updated the post with a clearer picture of 10(a) from the published exam, and the excerpts from the marking guide, including a bonus WitCH. No words are required.