This is the home for Further Mathematics (24/11/23 – now called General Maths) exam errors. The guidelines are given on the Methods error post, and there is also a Specialist error post. And there is also the Foundation error post.
If you suspect that there is an error that is not included in the list, or that an “error” has wrongly been included, please add a comment or contact me, and I’ll check it out.
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2026 NHT EXAM 2 (Exam here – discussed here, assessment guide here (W,I))
Q5(b) A weird typo: students were asked to show a loan balance was $598 644.07, but the correct figure is $598 644.07. The correct figure appears in the published exam. The assessment report notes, “Question stem included a typographical error which was addressed through marking”. To which the response is, “No, it was not, because you cannot quantify and thus compensate for the lost time and composure of students who struggled with the typo”. Errors happen, although God knows how this one happened. Whatever, this is not to suggest that VCAA should have or could have done more once the error was discovered, and at least they acknowledged the error, which is a vast improvement over past sleazy orthodoxy. But VCAA should not lie about something having been “addressed” when it has not and cannot be.
2025 Exam 2 (Exam here – discussed here, assessment guide here (W,I), report here (W,I))
Q4(d) (added 23/05/26) The students are asked to “explain briefly” whether a predicted sale price is an extrapolation or interpolation. The main issue here is the triviality of the (1 mark) question, and what amounts to a brief explanation. But, VCAA nitpicked, and in a manner arguably inconsistent with past practice.
Q6(b) (discussed beginning here) The question apparently has two reasonable interpretations. In a comment, Alex has informed us that VCAA will accept both interpretations. Yeah, ok, sort of; genuine ambiguities will arise, and when they arise then they should be handled honestly and decently, which VCAA has done here. Except, Alex notes,
[VCAA] have said that they were aware of both approaches when the question was set and both will be accepted as they are both valid ways to calculate a seasonal index over multiple years of data.
That sounds pretty crazy. This is not my turf and, unless somewhat insists, I am going to stay off this turf, but what is the possible argument or excuse for knowingly setting an ambiguous question? (23/05/26) Supposedly, this is a matter of (reasonable) rounding at various stages leading to different answers. That should not happen, but is not a hanging offence. Still, the VCAA clowns could get off their fat asses and clarify the issue in the exam report.
Q7(c) (added 23/05/26) The question requires students to complete a financial table, directing, “Using the values in the table …” The exam report then notes, Students were instructed to use the values in the table. Using a finance solver resulted in a different balance to the nearest cent which was not appropriate.” Once again, VCAA is simply making crap up as they go along. There is simply no indication why using a financial solver, which of course also used values in the table, was “inappropriate”. Idiots.
Q17(a) (added 23/05/26) This may be VCAA’s all-time stupidest grading decision. The students are provided a network and are then asked “Explain, with reference to the degrees of the vertices, why the gym owner’s intended route must involve some repeated edges”. The assessment guide and the report indicate two accepted answers: “Two vertices are of odd degree, and; “Not all vertices are of even degree”. However, VCAA have indicated that “There is a vertex of odd degree” was NOT accepted. Moreover, the vertex has a vertex of degree 1, making the entire thing a “well, duh” question, but point out this vertex of degree 1 was also NOT accepted. If the VCAA people who decided this are not the stupidest on the planet, it is a comment on the planet rather than the VCAA people. Utterly insane.
2024 NHT Exam 2 1 (Exam here – discussed here, report here (W, I))
Q14 (added 27/10/24) – The question asks for a six-mean smoothed value. The answer is B, but the exam report indicates the answer is D. A very odd error, since it is not obvious how to arrive at the answer D, even if one tries. (30/03/26 Apparently the exam report was updated very quickly to indicate the correct answer, B. Quite possibly the exam was graded correctly, and it was simply a glitch in the report, but it’d be nice for VCAA to confirm one way another.)
2024 Exam 1 (Exam here, marking guide here – discussed here, report here (W,I))
MCQ8-MCQ10 A peculiar use of the nth summer Olympic Games as a unit of time. The questions are workable as is, but a little odd given that the Games have not always been at 4-year intervals, and given VCAA’s previous insistence that “year” is a categorical variable.
MCQ39 A fatally ambiguous Hungarian algorithm question, discussed extensively in a comment by Bryn, and in the comments that follow. The marking guide indicates VCAA chose the less reasonable interpretation, and also the interpretation to make the question absurdly long. The marking guide will indicate how the ambiguity was handled, but this feels disturbingly like the arrogant VCAA of (one wishes) the past.
2023 Exam 2 (Here, discussed here, report here (Word, idiots))
Q7(c). The question cannot be properly answered as written.
Q7(d). There are two solutions, one of which will reportedly not be accepted as correct. (31/12/24. The exam report implies that the second solution was not accepted as correct.)
Q9(d). An extra 1 appeared in the matrix. (31/01/23. The published exam has corrected the error but with no acknowledgment of the error. This is sleazy.)(31/12/24. As indicated in the exam report, and as was reported in the news at the time, the question was invalidated.)
Q11. A poorly written question, with (at least) two correct answers.
Q14(d). There is an extra “of” in the preamble. (24/11/23) As has been point outed in a comment, since this correction was announced at the beginning of the exam, it’s not kosher to list it here as an error.
2023 Exam 1 (Exam here, discussed here, report here (Word, idiots))
MCQ26 The expression “Q multiplied by P” is absolutely fatal in the context of matrices and, if there is a clear meaning to be had, the meaning is Q x P. The question, however, requires P x Q.
2023 NHT Exam 2 (Exam here, report here (Word, idiots))
Q(3) (added 15/08/23) – The stem plot is incorrectly drawn, which can muck up the calculation of the five-number summary, asked for in part (b).
2023 NHT Exam 1 (Exam here, report here (W,I) – discussed here)
QB(2)(8) (added 03/11/25) – There is no one correct answer. The project is not sufficiently determined by the provided information.
2022 Exam 2 (Exam here, report here (Word, idiots) – discussed here)
QA(3)(a)(i) (added 27/12/22) – This is not an error yet, but it will be. The issue is whether “Day Number” (for eight consecutive days) is a “numerical variable”: based on their past idiocy, it is clear that VCAA will claim, falsely, that it is not. (15/08/23 – Yep, VCAA screwed up. The report notes, “[the answer] 6 was a common error by students who had chosen ‘day number’ as a numerical variable”.)
2022 Exam 1 (Exam here, report here (Word, idiots) – discussed here)
QA(1) (added 26/12/22) – A badly borderline question on the shape of a distribution. A really great way to start an exam.
QA(21) (added 26/12/22) – A badly ambiguous question on nominal interest rates. It is unclear whether negative rates and/or (more plausibly) periods greater than a year were to be considered.
QB(3)(5) (added 17/05/25) – A woefully written question, which demonstrably confused the hell out of students. The question concerns a cylindrical tank with hemispherical caps at each end. The “length” of the cylinder and the diameters of the caps are indicated and pictured.The “total length” of a scale model is then indicated. 24% of students answered the question correctly, with 53% answering as if “total length” meant the same as “length”. The question is not technically ambiguous, but it is damn close, and half the students were screwed because the question was written so badly. The exam report is silent on the writers having screwed up.
2022 NHT Exam 2 (Exam here, report here)
QA(2)(a) (added 27/12/22) – The report indicates that “year” is regarded as a “categorical variable”. This is absurd.
2021 Exam 2 (Exam here, report here (Word, idiots) – discussed here)
QA(1)(f) (added 24/11/21 – discussed here) The question asks for a minimum value to be an outlier, which, by definition of an outlier, cannot exist. (26/12/22 – The answer in the exam report is simply false.)
QB(1)(2)(c) (added 24/11/21 – discussed here) The indicated matrix M2 is not the square of the matrix M provided earlier in the question.
QB(2)(2)(b) (added 22/07/26 – discussed here) The question is screwed and the answer in the report is simply wrong. The question assumes that just one town will be revisited, but there is a shorter path that revisits three towns.
2021 NHT, Exam 2 (Exam here, and report here)
QA(18) (added 02/11/22) A bad question, hingeing on whether “Event”, listed as “1” or “2”, is a “nominal variable”. The report indicates that it is, which is probably best considered wrong. (Compare QA(2) on 2016 Exam 1, and the report.)
2021 NHT, Exam 1 (Exam here, and report here)
QA(18) (added 02/11/22) Madness. A multiple choice question on compound interest, for which none of the available answers is correct (or even close). The examination report indicates no answer, simply noting
As a result of psychometric analysis, the question was invalidated.
Some psychometric analysis is probably in order, but VCAA appears to be pointing their psych gun at the wrong target.
2019, Exam 2 (Exam here, and report here)
QA(1)(a) (added 27/12/22) The question asks which of the two variables in a table is “ordinal”. The report indicates that “day number” (for fifteen consecutive days) is ordinal. Given the other choice was “temperature”, there wasn’t much alternative, But the better answer, and only properly correct answer, is “neither”. The exam report notes “A small number of students answered ‘neither’ “, without indicating whether this answer was deemed correct.
2019, Exam 1 (Exam here, and report here)
QB(6) (added 21/09/20) The solution requires that a Markov process is involved, although this is not stated, either in the question or in the report.
2018, Exam 1 (Exam here, and report here)
MCQ4 (added 02/11/24) The question fails to state that the graph is connected, which is required for the expected answer to be unique.
2018 NHT, Exam 1 (Exam here, and report here)
MCQ 3, Module 2 (added 21/09/20) The solution requires that a Markov process is involved, although this is not stated, either in the question or in the report.
2017 Exam 2 (Exam here, and report here)
Q1(c)(ii) (added 13/11/20) – discussed here. The question is fundamentally nonsense, since there are infinitely many 1 x 3 matrices L that will solve the equation. As well, the 3 x 1 matrix given in the question does not represent the total value of the three products as indicated in Q(c)(i). The examination does not acknowledge either error, but does add irony to the error by whining about students incorrectly answering with a 3 x 1 matrix. (30/10/22) The examination report has finally been amended to acknowledge the obvious error, albeit in a snarky “no harm, no foul” manner. The fundamental nonsense of the question remains unacknowledged. As commenter DB has noted, the examination report also makes the hilarious claim,
The overwhelming majority [of students] answered the question in the manner intended without a problem.
We’re not sure the “minority” of 72% of students who scored 0/1 on the question would agree.
2017 Exam 1 (Exam here, and report here)
MCQ11 (added 13/11/20) – discussed here. None of the available answers is correct, since seasonal indices can be negative. The examination report does not acknowledge the error.
MCQ6 Module 2 (added 05/09/22) – discussed here. The intention of the question is reasonably clear, but the expression “how many different ways” is, at minimum, clumsily ambiguous, and one can argue for either C or D or E being correct. The intended answer was E, but many also students answered C or D. The examination report suggests that the incorrect answers were due to “simple counting errors”, which is possible but far from definite. The report also writes “Most students answered option B, C or D”, which is contradicted by the statistics; presumably the statistics are correct and the sentence is wrong, but it is unclear.
MCQ8 Module 2 (added 02/11/24) The question is a jungle, and the solution in the exam report is a mess, but the question is also wrong. The intended answer is B, with minimum cut B for x = 2, but there is a lower cut for x = 2.
2015 Exam 1 (Exam here, and report here)
MCQ9 Module 2 (added 30/09/20) The question refers to cutting a wedge of cheese to make a “similar” wedge of cheese, but the new wedge is not (mathematically) similar. The exam report states that the word “similar” was intended “in its everyday sense” but noted the confusion, albeit in a weasely, “who woulda thought?” manner. A second answer was marked correct, although only after a fight over the issue. 14/12/23. The similarity argument in the report refers to d – 8, rather than 8 – d.
2011 Exam 1 (Exam here, and report here)
MCQ3 (added 23/11/22). The question asks for the “closest” value for the median, but this cannot be determined from the provided histogram; two of the provided answers (B and C) may be correct. The examination report is silent on the issue.
2007 Exam 1 (Exam here, and report here)
Module 5 MCQ6 (added 14/02/25). The graph apparently contained an undirected rather than directed line segment (hte exam would appear to have been amended). The exam report indicates that two answers were awarded as correct.
Thanks, Terry. This issue is common, isn’t it? Feel free to list all such occurrences that you can find.
2018 NHT Further Maths Exam 1
Module – Data Analysis Q4.
The assessor’ report states that option ABC are all accepted because:
“ The best estimate of the IQR from this histogram is 1.5, therefore option B.
Under particular conditions it would be possible for the IQR to be as small as 1.0 or as large as 2.0, therefore options A and C were also accepted.”
What are the “particular conditions”?
That is an interesting phrase to be sighted in the official exam report.
Huh. That’s pretty damn weird. Thanks, P.N., I’ll check it out.
In fact, (one of) the author of this NHT paper exposed himself somewhere.
(I am not sure whether it is a good idea to do so – shouldn’t any (previous or future) member in exam setting panel stay confidential?)
Interesting. I think it’s arguable that examiners should be permitted to remain anonymous, and perhaps wise. I’m not I see it should be mandatory.
2015 Paper 1 Geometry module Q9.
The use of the word “similar” in the question is wrong, misleading and insanely inappropriate.
Yes, the infamous cheese question. Will add soon.
This one has a history, some of which I can repeat, and some I cannot. Here is the history I can repeat.
Two weeks after the exam was held, Burkard and I and the MAV were contacted by an upset teacher, all of whose students had misinterpreted the question. The teacher had been fobbed off by the Examinations Unit, which took two weeks to come back with an idiotic, “nothing wrong” reply. The teacher was then hoping the MAV and/or the Caped Crusaders (whatever) might go in to fight.
The MAV did … wait for it … nothing.
I did not do nothing. I emailed the Examinations Unit, and also got a bullshit reply, although they indicated the Examinations Unit was, two weeks after the exam, “continuing to monitor student responses to this question”. (No such indication had been given to the teacher.) I slammed the reply for the crap that it was, and requested the contact information for the Boss. After a couple emails back and forth, the Boss indicated the resolution, as indicated in the post above.
Why did the grading get changed? It’s unclear, and I don’t want to take undue credit. But, it is clear that two things did *not* get the grading changed: (1) The Examination Unit’s knee-jerk willingess to fob off teachers; (2) The MAV’s knee-jerk willingess to do nothing.
Yes, the MAV … Once again, providing “a voice, leadership and professional support for mathematics education” (its words, not mine). Bravo.
On the 2021 NHT Exam 1 Question 18, the scenario involved an investment that was compounding quarterly and the value of the investment after n years was modelled using a recurrence relation. Students had to find the value of R in the recurrence relation, but none of the options were correct.
On the Examiners Report, the problem was addressed thus:
Question 18
As a result of psychometric analysis, the question was invalidated.
That’s hilarious! (Well, not for the students …)
Thanks, Damo. I’ll check it out.
“As a result of psychometric analysis, the question was invalidated.”
VCAA code for “VCAA made a mistake but will NEVER admit this.”
I’ve seen the “psychometric analysis” phrase used a few times – the first time I saw it (and yes, it was in the context of VCAA responding to an error) I honestly thought it was made up gobbledygook. I now know better, it’s real gobbledygook.
That’s an unbelievable response. I’ve now added it to the list.
2011, Exam 1, Question 3. I believe this question is erroneous, because – for all that we know from the histogram – the median could be 17.5% and as such it’s not possible to state which value the median *is* closest to (of 15% or 20%)
I suppose it could be rewritten as “the median *could be* closest to”, but then options B and C should be accepted as correct, and the question is still stuffed for that reason.
(A similar issue exists in 2018 NHT Exam 1, Question 4. In this case at least all three possible IQRs (A, B, C) were accepted).
Sigh. I need a holiday.
Thanks, SRK. I’ll confirm and add.
Thanks, SRK. I finally got a chance to look at these. The 2018 error was already listed. You’re obviously correct about the 2011 error, and I’ve added it.
I never cease to wonder about such decade-old errors. It can’t be that no one has noticed them previously. So, is it simply that in times past no one bothered to tell VCAA when they stuffed up? Or just that no one demanded they fess up?
A copy of the exam is made available to teachers 30 minutes after reading time. In times past, you could find an error while the exam was still in progress and report it to VCAA. VCAA would send a correction out to all schools, which then got passed on to the invigilator. The invigilator would stop the exam and announce the correction. So I think some errors were reported back in the day and ‘corrected’ while the exam was live (*). But the culture has always been to deny errors in the Examination Reports (**).
VCAA would be aware of many of these old errors but steadfastly refuses to amend the Examination Reports unless absolutely forced to. (Even then, the amendment never uses the word error).
I would posit that since 2011, VCAA has rubbed teachers up the wrong way to such an extent that finding errors on exams became a blood sport for some (and their students (***)). And old errors have a habit of rising up from the slime when you get a bright and hard working student who works through those old exams (**) … (Show me the teacher that willingly goes back to ‘old’ exams, works through them, and re-discovers these errors)
These days, VCAA prefers to think that errors on old exams are irrelevant (because the exams are, like, you know, old) and not even worth a mealy-mouthed amendment the Reports. Having said this, it’s interesting to note the number of amendments made to multiple choice questions – a second correct option suddenly appearing without comment (see multiple choice Q12 here: https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/mmcas2_assessrep_09.pdf ), ‘correct’ options deleted without comment ( https://mathematicalcrap.com/2021/08/24/witch-64-decreasing-intelligence/ ) etc.
Errors on VCAA exams is the big VCAA cover-up.
* I doubt this happens anymore, for several reasons.
** And because the Reports are deceitfully silent on errors, you would think that the error went unnoticed.
*** Getting students to find the VCAA error in a question can be a fun and useful way teaching (the danger is overdoing it because there are sooooo many errors). VCAA’s right-triangle with a hypotenuse smaller than one of the other sides ( https://mathematicalcrap.com/2020/02/14/witch-35-overly-resolute/ ) still entertains. As does the strictly decreasing with a union of intervals ( https://mathematicalcrap.com/2021/08/24/witch-64-decreasing-intelligence/ )
Hey idk if anyone checks this anymore but theres an error in VCAA 2021 E2 Q2b of NETWORKS
the question states that the shortest path going through every vertex has exactly one town thats passed through twice, and students were instructed to find that town
problem is, with questions like these it seems like even VCAA themselves cant find optimal solutions properly, because their intended solution is wrong and nobody actually called it out
The question intends for the path GHIKJONKLM = 269 km, in which K the only repeated vertex, HOWEVER
there exists GOGHIKJKLMNM = 254 km, which is indeed the shortest path from G to M that passes through all vertices, and it repeats 3 different towns (G,K,M)
shout out to lazymaths udf for finding this
Thank you “anonymous” (but, in future, *please* put in a name of some sort). I never look at FM/GM unless someone flags it, and no one flagged this one. Do you have an explanation of how VCAA came up with the wrong answer? In any case, I’ll look.
aha mb
it looks like vcaa just didnt check enough paths before releasing this question, like the “obvious” answer seems to just be traversing K twice through the route GHIKJONKLM, however the actual shortest path is not so trivial to find and and was only recently found with algorithm through a UDF
Its worth noting that nobody actually noticed this at the time, due to the difficulty of finding the actual shortest path, and (basically) everyone followed the “shortest” intended path that goes through all the homes as its easy to spot, and repeats the vertex once.
Nevertheless, as this is still an assessable question, VCAA has to be careful when writing out these questions or just not assess shortest route questions at all, if they cant even get the correct solution to it
Thank you, Hussain. I have little doubt that you (and “anonymous”, if a different person) are correct, but I check these things out myself before adding.
But I am puzzled: what is a student generally expected to do with such a question? Just guess for the “obvious”?
The question says that the shortest path passes through exactly one town twice, which was wrong, but VCAA didnt notice. And it seems like nobody else in the 2021 cohort noticed either cause theres no discussion about this anywhere
the actual shortest path (passing through 3 vertices) was just too difficult to find by hand and nobody in their right mind would think to look for that.
I see. So the procedure is “look for the obvious path to double”, and that procedure didn’t work here. Thank you. I’ll check and then add.
Just to be clear, you’re “anonymous”?
Yep, and thanks for taking time to look into it
Thank you very much for raising it, Hussain. It is definitely worth flagging anything from the past that is wrong, and really definitely when it is that wrong.
Added now. Thanks again, Hussain.
I’ve updated the post with the identified 2023 errors (and given the post a new name).