MELting Pot: The Methods Error List

UPDATE (02/11/21)

The list is now “complete”, in the sense that it includes all the errors of which we are aware. (We have given the earlier exams only a very, very quick scan.) We will update and correct the list, whenever anything is brought to our attention, and of course when new exams appear.


We’re not really ready to embark upon this post, but it seems best to get it underway ASAP, and have commenters begin making suggestions.

It seems worthwhile to have all the Mathematical Methods exam errors collected in one place: this is to be the place.*

Our plan is to update this post as commenters point out the exam errors, and so slowly (or quickly) we will compile a comprehensive list.

To be as clear as possible, by “error”, we mean a definite mistake, something more directly wrong than pointlessness or poor wording or stupid modelling. The mistake can be intrinsic to the question, or in the solution as indicated in the examination report; examples of the latter could include an insufficient or incomplete solution, or a solution that goes beyond the curriculum. Minor errors are still errors and will be listed.

With each error, we shall also indicate whether the error is (in our opinion) major or minor, and we’ll indicate whether the examination report acknowledges the error, updating as appropriate. Of course there will be judgment calls, and we’re the boss. But, we’ll happily argue the tosses in the comments.

Get to work!

*) Yes, there are also homes for Specialist Mathematics and Further Mathematics errors.


2023 EXAM 2 (Here – discussed here, report here (Word, idiots).)

MCQ 9 (discussed here) The term “smooth” is undefined in the study design, VCAA’s apparent meaning for the term is highly non-standard, and VCAA’s indicated method of proving a function “smooth” is invalid (MCQ19). (17/04/24) The proof in the exam report is bad, and badly expressed, but at least makes clear what was intended. See the updated discussion here.

MCQ 13. The pseudocode is marginally incorrect (by VCAA’s own declared style).

MCQ 18. (17/01/24) There is no correct answer. As noted by commenter LH, one of the endpoints will be a local minimum (and the other a local maximum). So, there will always be \boldsymbol{a^2 + 1} local minima. (17/04/24) The exam report is silent on the error.

MCQ 20. The compositions are undefined. (17/04/24) The exam report is silent on the error.

QB(3)(a). Limits at infinity are not clearly part of the study design. (17/04/24) The exam report whines that students “appeared to be confused by the limit notation”. FFS.

QB(3)(e)(added 18/04/24 – discussed here) The question is a mess (and is bad), asking for, “correct to two decimal places”, the “largest interval of x values” for which a function is strictly increasing. Ignoring the very clumsy language, one would assume that the rounding would need to done appropriately, to preserve the monotonicity. As it happens, the typical rounding preserves the monotonicity, so the answer indicated in the exam report is correct. But this may have been luck. The report makes no mention of the issue and then incorrectly rounds when considering the set upon which the function is decreasing. The report also simultaneously makes a separate blunder, of the type discussed here.

QB(4)(f). The question should have asked for the maximum standard deviation: asking for “the required standard deviation” is close, but is queered by the definite article.

QB(4)(j). The speed is written as “m per second” rather than “metres per second”. (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.

QB(5)(b). The preamble should have specified that the domains be maximal. (17/04/24) The exam report notes the ambiguity in the question but VCAA could have been a bit more humble about it. The solution(s) is very confusingly worded, a byproduct of not properly addressing the ambiguity. 

2023 EXAM 1 (Here – discussed here, report here (Word, idiots)

Q4. The instruction to “use two trapeziums of equal width” is vague to the point of meaninglessness. Proper reference to the trapezium rule should be made. (The word “trapeziums” is also gauche.)

Q9(b). The point P is undefined.

2023 NHT EXAM 2 (Here – discussed here, report here (Word, idiots).)

MCQ3 (added 27/10/23) There are two correct answers, since there are two given domains on which the function is strictly increasing. The exam report simply pretends that a different question was asked, that what was required was the maximal domain.

MCQ16 (added 15/08/23) The question asks for the largest domain of a composite function, but this makes no sense: in VCE, a composite function is either defined or it is not. (Which is silly.) (11/10/23 – The report is silent on the error.)

MCQ17 (added 15/08/23) The question asks for which values of a parameter a quadratic has more than one “solution” (rather than “root”). This is the kind of error which, when a student commits it, the examiners will whine no end. (11/10/23 – The report is silent on the error.)

Q2(c) (added 15/08/23) There are infinitely many answers of the required form.

Q5(e) (added 15/08/23 – discussed here) The question is sufficiently poorly worded to be regarded as incomprehensible. (11/10/23 – The report is completely silent, providing an answer but no explanation whatsoever.)

2023 NHT EXAM 1 (Here – discussed here, report here (Word, idiots).) 

Q8(d) (added 30/10/23) The second solution the exam report is incomplete and misleading. An equation sin(A) = sin(B) implies either A = -B + 2kπ, or A = (π  + B) + 2kπ. The report solution only considers the first case.

2022 EXAM 2 ((13/12/22- exam here) – discussed here) (06/04/23 – report here (Word, idiots))

MCQ9 (added 10/11/22) Asking for the “shortest distance” instead of “distance” is wrong, and wrongly suggests a max-min problem.

QB4(e)(ii) (added 10/11/22) A pointless and meaningless question. It is perfectly reasonable to consider a region to be empty, as was implicitly done in part (i), and thus all (positive) k can reasonably be considered to be in the domain.

2022 EXAM 1 ((13/12/22- exam here) – discussed here) (06/04/23 – report here (Word, idiots))

Q2(a) (added 10/11/22) Asking for “the rule of an antiderivative of g(x)” is simply not asking for the general antiderivative, which is presumably what was intended.

Q6(c)(iii) (added 10/11/22) Part (ii) requires the student to “Find the smallest positive value for a” (out of the infinitely many). This does not, however, set a to be that smallest positive value. Consequently, part (iii) is simply not asking what was intended. There are infinitely many possible domains, corresponding to the infinitely many choices of a.

Q8(c) (added 10/11/22) The value k = 0 should probably have been excluded from the domain. It makes mathematical sense, but requires a leap from the continuous to the discrete, and appears to stray outside the VCE curriculum.

2022 NHT EXAM 2 (Here, report here – discussed here

MCQ15 (added 27/07/21 – discussed in the comments here) The question is fundamentally meaningless. One cannot define a sample proportion \boldsymbol{\hat P} without reference to a population whose members do or do not possess some attribute. No such population and no such attribute are defined, or even implied, in the question. (06/09/22. The exam report is silent).

QB5(b) (added 27/07/21 – discussed in the comments here) The question is fundamentally meaningless. The dashed curve \boldsymbol{b_2} can be any of a zillion different functions, and it is simply invalid and inappropriate to assume \boldsymbol{b_2} is a reflection of \boldsymbol{b_1}. (06/09/22. The exam report gives the expected, reflection solution, without comment.)

2022 NHT EXAM 1 (Here, report here – discussed here

Q3 (Added 29/07/22) The variable z is undefined.

Q5(c) (added 29/07/22) There are infinitely many answers of the required form (all of them pretty ridiculous).

Q6(b)(ii) (added 29/07/22) There are infinitely many answers of the required form.

Q7(b)(added 09/09/22 – discussed here) The examination report contains some confused objection to students writing “y = the inverse function”, the report claiming it to be “a contradiction of ideas”. There is no contradiction of ideas, and if students were penalised for writing some such thing, which is the implication, then that is absurd.

2021 EXAM 2 (Here, and report here – discussed here

MCQ18 (added 24/11/21) Impossible Magrittism.

MCQ19 (added 06/11/23 – discussed here and here) The exam question is fine, but the explanation in the exam report is utter nonsense. (The explanations of such material in the three textbooks are also nonsense.)

QB1 (added 24/11/21) The main issue is that the question is repetitive and aimless, but there is also an error in Part (f): the preamble states that the box’s error (18/12/22) length is twice its width, rather than that being true of the cardboard from which the box is made. (23/04/22) Not a word in the exam report to acknowledge the error.

QB5 (added 24/11/21 – discussed here) An absolute mess. The main issue is Part (f) (g), which is multidimensionally ambiguous, and under any interpretation is Magritte nonsense. Part (c) is meaningless as worded. (23/04/22) Not a meaningful word in the exam report about this screw-up.

2021 EXAM 1 (Here, and report here – discussed here

We are not aware of any errors on this exam (although the examination report might change that, once it appears (22/04/22 – indeed, it did.)).

Q1 (Added 22/04/22) The answer to Part (b) is wrong, seemingly the product of a cut and paste error. (30/09/22 – now corrected, seemingly on 22/09/22.)

2021 NHT EXAM 2 (Here, and report here – discussed here

MCQ8 (added 21/10/21) – discussed hereThere is no correct answer. The original examination report gave D as the answer; the amended report provides no answer, and provides no explanation for the lack of answer.

MCQ 9 (added 21/10/21) – discussed here. The concept of “repeated root” makes no sense for a general “continuous and differentiable function”. The question is more generally a mess (but not wrong).

QB2(d)(i) (added 21/10/21) – discussed here. The question is generally absurd but, specifically, (d)(i) is unsolvable. The solution in the examination report is fundamentally nonsensical.

QB5 (added 21/10/21 – updated 01/11/21) The answer to (b) has infinitely many correct forms. Part (f) is pretty Magrittey; the solution in the examination report doesn’t make a lot of sense, and it is difficult to know what justification can be given in Methods language.

2021 NHT EXAM 1 (Here, and report here – discussed here

Q7 (added 21/10/21) The answers to both (a) and (b) have infinitely many correct forms.

2020 EXAM 2 (Here, and report here – discussed here

MCQ20 (added 21/10/21) – discussed here. The question is incoherent and is best thought as having no answer. The approach suggested in the examination report is fundamentally invalid.

QB(5) (added 21/10/21) – discussed hereThe question is a mess. Part (c) is so vaguely worded as to be meaningless. The solution to (g) in the examination report is incomprehensible. The comment on (h) in the examination report is incomprehensible, and wrong.

2020 EXAM 1 (Here, and report here – discussed here

Q2(b) (added 21/10/21) The examination report refers to “conditional probability”, but this is not a conditional probability question.

Q3 (added 29/10/23) (EDIT: 29/10/23) This question was added, claiming the report was badly in error. That was wrong, and the answer in the report is correct. The solution is far from complete, however, and contains a minor error. To begin, the point (-1,-1) is plugged in, not (1,1) as suggested by the report. Secondly, the resulting equations for a and b are far more general than the report claims. The correct equations (unless some prior argument is made) are -a + b = -π/4 + nπ, and  a + b = π/3 + mπ. This gives many solutions for a and b, and once must then argue for the specific final answer.

Q5(b) (added 21/10/21) – discussed here and here. Among other issues with the question and the grading, there are infinitely many answers of the required form.

2019 EXAM 2 (Here, and report here

MCQ15 (added 22/10/21) – discussed here. The question asks for the derivative of an inverse function, but the direct technique is not properly part of the Methods (or Specialist) curriculum. The available alternative is to first explicitly calculate the inverse of the quadratic on the restricted domain, which is absurd.

MCQ18 (added 22/10/21) – discussed here. The question is mostly appalling, and way difficult, rather than wrong, but the diagram is also impossible.

QB(3) (added 22/10/21) – discussed here. A disastrous question. Insane throughout, but specifically (e) is incoherent, with the examination report simply ignoring the incoherence. Part (d) also includes a function g(t) being transformed in terms of x and y.

QB(4)(f)(i) (added 16/10/21) The question is more idiotic than wrong, but it is also wrong. The probability that a butterfly from a certain population has a “very large” wingspan is given as 0.0527 “correct to four decimal places”. The question then asks for the probability, again to four decimal places, that at least 3 butterflies from a random population of 36 have very large wingspans. The examination report gives the answer as 0.2947, which is simply false. The probability of very large wingspan can be anywhere from 0.05265 to 0.05275, which means the asked-for probability can be anywhere from about 0.2942 to 0.2952; as it happens, we can only know the asked-for probability to one decimal place.

Of course, the underlying idea that we might know or be able to compute probabilities in such a context to such an accuracy is ridiculous, making the set-up for this question ridiculous. The initial probability of 0.0527 comes, without explanation, from the preamble to question (d). There, it is given that the butterfly wingspans are normally distributed, with a mean of 14.1 cm and a standard deviation of 2.1 cm. This gives, to four decimal places, the probability of a “very large” – greater than 17.5 cm – wingspan to be 0.0527. It is simply absurd, however, to treat the mean and standard deviation as being exact, or to be so exact as to give a probability of such accuracy. (In any case, treating the normal parameters as exact leads to a probability of very large wingspan of 0.052719, which then gives an answer to part (f) of 0.2949.)

2019 EXAM 1 (Here, and report here

Q8 (added 22/10/21) – discussed here. The question makes no sense. For better or (in fact) worse, “maximal domain” for a composition of functions makes no sense in VCE; a composition is either defined or it isn’t.

Q9 (added 22/10/21) – discussed here. The examination report contains an error in part (b), in the exponent of e, but the massive problem is with part (f). There is no way that the report’s suggestion of a “rough sketch” is sufficient to determine the number of solutions. The question is simply way, way too difficult to answer in a sketchy 1-mark manner.

2019 NHT EXAM 2 (Here, and report here

MCQ20 (added 22/10/21) – discussed here. The same issue as with MCQ15 on 2019 Exam 2, above. The question asks for the derivative of an inverse function, the efficient technique being not part of the syllabus.

2019 NHT EXAM 1 (Here, and report here

Q3(c) (added 22/10/21) There are infinitely many answers of the required form.

2018 EXAM 2 (Here, and report here

QB(1) (added 24/10/21) For both (d) and (e) there are infinitely many answers of the required form.

QB(2)(a) (added 24/10/21) The suggested form of the answer is absurd, and there are infinitely many answers of that form.

2018 EXAM 1 (Here, and report here

Q7(b) (added 24/10/21) There are infinitely many answers of the required form (and the form is pointlessly noisy).

2018 NHT EXAM 2 (Here, and report here

MCQ20 (added 24/10/21) The solution requires the formula for the derivative of an inverse function, which is not in the Methods (or Specialist) syllabus.  

2018 NHT EXAM 1 (Here, and report here

We are not aware of any errors on this exam.

2017 EXAM 2 (Here, and report here

QB(4) (added 26/10/21) – discussed here. No explanation is provided in the examination report for the solutions to (c) and (i)(i) (sic). There may be no error as such, but it is impossible to tell. The solution to (h) is essentially correct but is missing major explanation and is in effect incomprehensible. (27/10/23) Part (i)(ii) (sic), the preamble as written makes no sense. The integrand in the exam report solution is wrong, and weird.)

2017 EXAM 1 (Here, and report here

QB(5) (added 26/10/21). For (b) and (c) there are infinitely many answers of the required form.

QB(9)(c) (added 13/11/20) – discussed here. The question contains a fundamentally misleading diagram, and the solution involves the derivative of a function at the endpoint of a closed interval, which is beyond the scope of the course. The examination report is silent on on both issues.

2017 NHT EXAM 2 (Here, and report here

Q4B(4)(e)(iii) (added 26/10/21). The required form of the answer is absurd, and there are infinitely many answers of that form.

2017 NHT EXAM 1 (Here, and report here

Q8 (added 26/10/21) – discussed here. The solutions to (b) and (c) in the examination report are fundamentally invalid.

2016 EXAM 2 (Here, and report here)

QA(11) (added 24/02/22). The first line of the exam report is completely non-sensical.

QB(3)(h) (added 06/10/20) – discussed here. This is the error that convinced us to start this blog. The question concerns a “probability density function”, but with integral unequal to 1. As a consequence, the requested “mean” (part (i)) and “median” (part (ii)) make no definite sense.

There are three natural approaches to defining the “median” for part (ii), leading to three different answers to the requested two decimal places. Initially, the examination report acknowledged the issue, while weasely avoiding direct admission of the fundamental screw-up; answers to the nearest integer were accepted. A subsequent amendment, made over two years later, made the report slightly more honest, although the term “screw-up” still does not appear.

As noted in the comment and update to this post, the “mean” in part (i) is most naturally defined in a manner different to that suggested in the examination report, leading to a different answer. The examination report still fails to acknowledge any issue with part (i).

QB(4)(c) (added 25/09/20) The solution in the examination report sets up (but doesn’t use) the equation dy/dx = stuff = 0, instead of the correct d/dx(stuff) = 0.

2016 EXAM 1 (Here, and report here)

Q4(c))(i) (added 02/11/21) There are infinitely many answers of the required form.

Q5(b)(i) (added 24/09/20) The solution in the examination report gives the incorrect expression \pm\sqrt{e^x} - 1 in the working, rather than the correct \pm\sqrt{e^x -1}.

2015 EXAM 2 (Here, report here)

QB(1)(c) (added 02/11/20) There are infinitely many answers of the required form.

QB(2)(b) (added 02/11/20) There are infinitely many answers of the required form.

QB(3)(a)(ii) (added 02/11/20) There are infinitely many answers of the required form.

QB(5)(c) (added 13/11/20) – discussed here. The method suggested in the examination report is fundamentally invalid.

2015 EXAM 1 (Here, report here)

We are not aware of any errors on this exam.

2014 EXAM 2 (Here, and report here – discussed here)

MCQ4 (added 21/09/20) – discussed here. The described function need not satisfy any of the suggested conditions. The underlying issue is the notion of “inflection point”, which was (and is) undefined in the syllabus material. The examination report ignores the issue.

MCQ14 (added 02/11/21) – discussed here. An incredible one. Or at least we thought it incredible at the time, before we got used to VCAA’s mendacity. For the intended answer to be correct, one needs Pr(X = 5) = Pr(X = 8) = 0, which is neither stated nor implied in the question. (One also requires Pr(X > 8) < 1, which is also unstated, but can be considered implied.) The examination report simply pretends that X is a continuous random variable, which is arrogantly dishonest and which doesn’t fix the problem. Disgraceful.

2014 EXAM 1 (Here, report here)

We are not aware of any errors on this exam.

2013 EXAM 2 (Here, and report here – discussed here

QB(2)(b) (added 02/11/20) – discussed here. The question assumes without statement (and unrealistically) that the probabilities are the result of a Markov process.

2013 EXAM 1 (Here, and report here – discussed here.) 

We are not aware of any errors on this exam.

2012 EXAM 2 (Here, and report here)

We are not aware of any errors on this exam.

2012 EXAM 1 (Here, and report here)

Q9(b) (added 02/11/21) The required form of the answer is meaningless, and there are infinitely many answers of that form.

Q10(a)(ii) (added 02/11/21) For no good reason, m is restricted to be rational, and thus so should the answer to thsi question. The examination report ignores the issue.

2011 EXAM 2 (Here, and report here)

MCQ 21 (added 02/11/21) – discussed here. There is no correct answer. The examination report indicates E to be the answer, but this fails to take into account the case Pr(Q) = 0. The examination report indicates that 15% of students chose E. Whether the low percentage was because the question was pretty fiddly, or because students recognised that E wasn’t correct, is anybody’s guess.

QB(3)(c)(ii) (added 02/11/21) – discussed here. The f = f-1 error. The examination report suggests only and without justification solving f(x) = x.

QB(2)(b) (added 02/11/20) The question requires computing an improper integral (via CAS), which is beyond the scope of the subject.

QB(4) (added 23/09/20) The vertex of the parabola is incorrectly labelled (-1,0), instead of (0,-1). The error is not acknowledged in the examination report.

2011 EXAM 1 (Here, and report here)

Q4(b) (added 02/11/21) – discussed here. The question asks for the maximal domain of a composition of functions, which (unfortunately) makes no sense in VCE; in VCE a function composition is either defined or it isn’t. The issue is ignored in the examination report.

Q7(b) (added 23/09/20) The question asks students to “find p“, where \boldsymbol{p} is the probability that a biased coin comes up heads, and where it turns out that \boldsymbol{p^2(4p-3)=0}. The question is fatally ambiguous, since there is no definitive answer to whether \boldsymbol{p=0} is possible for a “biased coin”.

The examination report answer includes both values of \boldsymbol{p}, while also noting “The cancelling out of p was rarely supported; many students incorrectly [sic] assumed that p could not be 0.”  The implication, but not the certainty, is that although 0 was intended as a correct answer, students who left out or excluded 0 could receive full marks IF they explicitly “supported” this exclusion.

This is an archetypal example of the examiners stuffing up, refusing to acknowledge their stuff up, and refusing to attempt any proper repair of their stuff up. Entirely unprofessional and utterly disgraceful.

2010 EXAM 2 (Here, report here)

MCQ17 (added 28/09/20) – discussed here. Same as in the 2014 Exam 2, above: the described function need not satisfy any of the suggested conditions, as discussed here.

MCQ22 (added 02/11/21) A weird question, which is almost good but isn’t. The question is also incorrect in asking for what the rule of the function “is”, rather than what it “could be”: any multiple of the indicated correct answer also works.

QB(1)(a)(iii) (added 02/11/21) – discussed here. The f = f-1 error. The examination report suggests solving any of g-1 = g or g-1 = x or g = x, without justification.

2010 EXAM 1 (Here, and report here)

Q9(b) (added 02/11/21) The required form of the answer is meaningless, and there are infinitely many answers of that form.

2009 EXAM 2 (Here, and report here)

MCQ12 (added 02/11/21) – discussed here. There are two correct answers. The examination report now indicates that “B was also accepted as it leads to an equivalent expression” (sic), but the original examination report indicated absolutely nothing. If B was accepted then it is unclear why VCAA didn’t admit it at the time. Cowards then or liars now? It’s anybody’s guess.

QB(3)(d) (added 11/11/23) The question asks for the standard deviation, but the maximal standard deviation is intended. This is reasonably understood from the question, but it should be specified. The exam report makes no mention of the error.

2009 EXAM 1 (Here, and report here)

We are not aware of any errors on this exam.

2008 EXAM 2 (Here, and report here)

We are not aware of any errors on this exam.

2008 EXAM 1 (Here, and report here)

Q10(c) (added 02/11/21) There are infinitely many answers of that form.

2007 EXAM 2 (Here, report here)

MCQ12 (added 26/09/20) Same as in the 2014 Exam 2, above: the described function need not satisfy any of the suggested conditions, as discussed here.

MCQ17 (added 02/11/20) The question incorrectly states that “the rule of the function is …” rather than “the rule of the function could be …”. There are many functions that satisfy the required condition.

2007 EXAM 1 (Here, and report here)

We are not aware of any errors on this exam.

2006 EXAM 2 (Here, and report here)

We are not aware of any errors on this exam.

2006 EXAM 1 (Here, and report here)

We are not aware of any errors on this exam.

76 Replies to “MELting Pot: The Methods Error List”

  1. One example I think could be part of the inflexion point shennanigans would be MM Exam 2 2014 MCQ 4 which has a function f with no other conditions than being continuous. The problem is that you could construction a piecewise defined function, e.g f(x) =25x- \frac{5x^2}{2} if x \geq 5 and \frac{5x^2}{2}-25x+125 if x \leq 5. Differentiating gives f'(x) = \frac{5}{2} |10-2x| which satisfies the conditions in the question and then one last differentiation gives us that there is a change in concavity, but not f''(x) = 0 for any x, most importantly f”(5).

    1. Thanks, Sai, that question is definitely screwed, as discussed here, and was on my radar to include. I’m not quite sure, however, how your example contradicts the question.

      1. Ah phooey, I messed up the function in formatting… so much for a response early in the morning. Trying this again with f'(x) = - |x-5| (with any choice for the antiderivative f) will yield that f''(x) = -1 if x \neq 5 and obviously, f''(5) definitely not being equal to 0. I also found another instance in which they fucked it up, 2007 MM exam 2 (CAS and non CAS) Q12, which is the same problem, different numbers. There are no comments either on the assessors report… I would also like to note out the itute solutions posted on either occasions don’t make any comment. Make what you will of this…

          1. Hi, Sai. I tidied up your comments. (I’ve been changing settings, to deal with some spam issues, which may be confusing you and others, including me.) I added the 2007 exam as a link, because it seemed to want to be displayed, but failed. I’ll check out that exam now.

            I still don’t quite understand your example. (Doesn’t your f'' change sign, as you want?) The underlying question here is the meaning of “inflection point” at some a. The standard, but not universal, notion is “change of concavity” at a. That’s not quite a definition, since it leaves open how differentiable the function need be, particularly at a. The 2014 exam is implicitly using a different notion.

            1. Ah I’ve unintentionally mixed in two different ideas. One was that you don’t need to have f''(x) = 0 for a point of inflexion, only a change in concavity in some neighborhood and the other, which is that you could have f''(x) = 0 but not necessarily a point of inflexion. The example I posted was there to suggest that you could have a change in concavity without f''(x) = 0 as VCAA seems to think, although I’m not sure if Methods explicitly defines “stationary points of inflexion”.

              1. Hi, Sai. Hardly your fault. I don’t think “point of inflection” (stationary or otherwise) is precisely defined anywhere in the VCE material. In general, people don’t require f to be differentiable at a to have an inflection point at a, and so f''(0) = 0 is not (usually) necessary. Also, the simple example f(x) = x^4 shows that f''(0) = 0 is not sufficient. The much trickier thing is to show that the conditions of the 2014 MCQ aren’t sufficient for an “inflection point” in any change of concavity sense. That is the purpose of the example Burkard and I give in our critique of the exam.

        1. Thanks, Sai. I’ll tidy your comment soon. For latex you put the dollar signs, and right after the first dollar sign you type the word latex.

    2. 2011 Math Methods Exam 1, Q7b
      The examiner report shows that both p = 0 and p = 3/4 should be retained as valid answers.
      Even though we all know any probabilities can take values within [0, 1], it wouldn’t be a wise idea to say a tangible coin can NEVER have face up (tail). Neither does the examiner report provide a rigorous mathematical explanation that makes sense to most of the teachers, nor does it explain how those students were awarded or not – who rejected p = 0 at the end. In fact, looks like many students who cancelled p^2 at the first place were penalized, and it was expected on students – expanding both probabilities, rearranging and use null factor law to get “both solutions”.

      Same year – 2011, paper 2: ERQ4, the point (-1, 0) was labeled, instead of (0, -1), though it should not have impeded students from getting some work done (seemingly, but who knows?)

      1. Re: MM 2011 Exam 1 7b. I’d have to work through the question thoroughly, but my initial reaction is that p = 0 is a reasonable solution, since that would represent one of the two extreme cases of a biased coin: a two-tailed coin.

        The point about cancelling p^2 is interesting (to me). I have taught my students that it would be fine to divide by p^2, but this assumes that p^2 ≠ 0, in which case one should also consider the equation p^2 = 0 and what solutions (if any) that has. This seems just as valid an approach as moving all the unknowns to one side with 0 on the other, then factoring, etc.

        1. SRK,
          You are right. However, cancellation of common terms will definitely get them penalised for some questions in spesh (in particular certain scenarios in exam 1s).

          Examples includes:
          – 2012 SM 1 Q2 (3 marks) If student cancelled cos(x) both sides after using compound angle formula, award maximum 1 out of 3 marks
          – 2017 NHT SM1 Q6 (3 marks) If student cancelled tan(x), also maximum 1 out of 3 marks
          – 2019 SM1 Q4 (3 marks) If student presented any evidence of cancellation of “t” both sides when they equate the x components such as drawing a slash on “t”s, then deduct 1 mark, whether it be right final answer or not.

          Even though the marking procedures vary from time to time, I still believe it is safer for the kids to perform the following procedure in any Methods or Spesh exams:
          1. Expand both sides.
          2. Don’t do any cancellations. Rearrange everything to one side, making RHS=0
          3. Take out any common factor and factorise “properly”.
          4. State all solutions from above, and see if there is any solutions to be rejected. If any needs rejection, state the reason.
          That’s what I really emphasize with my students every year, in the hope they don’t lose any extra mark and play safer..

          1. P.N. I’m aware of the 2019 question you mentioned; I raised this issue at the Meet the Assessors earlier this year, and the response I got was the one you just gave. I wasn’t persuaded then, and I’m still not persuaded.

            Consider t^3 = t. The method you recommend would be t^3 - t = 0 \longrightarrow t (t^2 - 1) = 0 \longrightarrow t = 0\; \textrm{or}\; t^2 - 1 = 0.

            Whereas I would just write t^3 = t \longrightarrow t = 0\; \textrm{or, if}\; t \neq 0,\; t^2 = 1. There is no risk of “losing” solutions.

            1. Yes SRK,

              Honestly I was not persuaded too (when I was informed by someone in Nov last year)

              I feel your second solution is also great. When term 4 starts I will show my students your method.

              Some pelnaties in spesh or methods marking are not well known. And it varies from year to year. However, common penalties come from pedantry.

            2. SRK and P.N., I’m too busy to chase down such leads right now. But if there is clear evidence in the examination reports of such obviously valid methods being penalised, please give the precise references in the comments here and I will check them out.

                1. Hi, P.N. Sorry for being obtuse but I don’t see how this connects to SRK’s valid (but declared invalid?) method of solving t^3 = t.

                  Of course it is valid to “cancel out” a t or a cos x or whatever, as long you consider the possibility of the cancelled term being 0. Is there any direct evidence from the examination report and/or assessor solutions that VCAA considers otherwise?

  2. 2007 MM (NO CAS) Exam 2
    Question 2 Tasmania – Insects being deadly.
    The very last part was intended to test whether students could use the graph of trig function to find the points of intersection. However, the ambiguity of “insects being deadly” is definitely NOT a good example of authentic mathematical modelling, and it is really the pain in the arse – could our students create some magics from the air – to link the concentration level with insects being deadly – and then determine the safe period(s) of total time for comparison? I will say this question was excruciating and notoriously absurd.

      1. Jesus. That is monumentally stupid. But, I don’t think it qualifies as “wrong”.

        PINOF, you also refer to the question as “NO CAS”. Is the non-CAS version, on this question or in general, different from the CAS version, and is that the no-CAS version available?

        1. Here you go marty, the link to the Non-CAS Maths Methods Exam 2 from 2007 ( This is slightly different to the CAS version of the same exam ( The only difference I can see in Question 2 is the marks allocated to part f (i.). In the Non-CAS version it is 3 marks whereas in the CAS version it’s 2. Presumably due to CAS cutting out some portion of the working?

            1. Marty,

              Unfortunately these old collection pages are gone, following the big update of VCAA exams last year.

              Luckily I know where you can still access them.
              These Mathematical Methods (No CAS) papers can be accessed somewhere else. I will email you the link.

            2. Unfortunately not marty. I only found that link by using the Google terms “2007 MATHEMATICAL METHODS Written examination 2” and looked carefully at the URLs in the search results – one was 2007mm2.pdf and the other 2007mmCAS2.pdf and that was enough to get it.

              Not sure where you could head to, to find the page with these exams (in the same way you can find the current exams on the VCAA site). As VM has said below, there may be one but I’m not aware of the link personally.

  3. 2012 MM2 Q4b exam report:

    This Tasmania question is intended to ask students “showing that” the tank will be empty when after 20 minutes.

    Great question but poor exemplar answer on the report. This suggested approach is “verify”,not “show” (which is also highly relevant to one recent discussion “verification code”)

    In my opinion, despite being a one mark question, the proper way is to set h(t) = 0, write a fully factorised equation in terms of t, derive two t values and then state why the negative t is rejected as t>0, thus concluding that the tank is empty at t=20.

    1. Huh. Sauce for the goose.

      NLP, the question is stupid rather than great, and the answer is problematic in a directly relevant manner to the MitPY verify/show/prove discussion. But the issue here is whether the question+solution contains an error. I don’t think it does.

      Plugging in to “show that the tank is empty when t = 20” is, at least on Planet Earth, valid and sensible. The fact that the VCAA on a singular occasion demonstrated a glimmer of common sense doesn’t make their sense then an error.

  4. My contribution to the MELting Pot stems from the post Bernoulli Trials and Tribulations and some of the comments that ensued, specifically those by JF, for those following along at home.

    However, my contribution pertains to commercial, third-party trial exams, specifically MAV, and I’m not sure on the copyright implications of discussing and/or posting screenshots of the offending questions. In that vein, I’ll simply mention the exam’s year and question number, and those with access to the exam can add their responses accordingly.

    Both exams are MAV Trial Exam 1s – the first is the 2020 exam and the second is the 2011 exam.

    In the MAV 2020 MM Trial Exam 1, Question 3 involves a definite integral of the form \int \frac{f'(x)}{f(x)}, where f is *quadratic* rather than the usual *linear* that is usually seen in Methods.

    In the MAV 2011 MM Trial Exam 1, Question 1(b) involves an “integration by recognition” type question – where part (i) involves the derivative of the sum of an exponential and linear term, and part (ii) involves, as before, the antiderivative of the form \int \frac{f'(x)}{f(x)}, where f is the same expression in part (i).

    Fire away, everyone.

    1. Everyone, please hold your fire.

      Thanks, Steve. As it happens, I am just writing a post now on the 2020 Methods 1 trial exam. The focus is different, but I’ll mention that question and it’ll be the natural place to comment on that issue.

      In general I’ll keep the error posts for the formal VCAA exams. But, it’s hard to know what to do with the MAV twilight zone.

      1. Hi Marty, here’s a suggestion for what to do with the MAV twilight zone:

        It’s common knowledge that the MAV has an unhealthy cosy relationship with the VCAA.
        It follows that impressionable (for many reasons) teachers will see MAV trial exams as reflecting some sort of special VCAA-insider knowledge or special/subtle interpretation of the Study Design (VCAA sanctioned “natural connections”).
        As a consequence it follows that many such teachers will get bad-influenced and stressed by MAV trial exam bullshit such as dodgy \displaystyle \int \frac{f'(x)}{f(x)} dx questions and dodgy solutions to dodgy f(x) = f^{-1}(x) style questions.

        For this reason I propose that MAV trial exam questions and solutions be treated the same way (or perhaps be given their own similar blog) as VCAA questions.

        Obviously there are many commercial companies writing all sorts of bullshit but none of it has quite the ‘special status’ that MAV bullshit has.

        1. Thanks, JF. That pretty much captures it. I don’t think one can treat MAV (or any) trial exams the same way as offical VCAA exams: screw ups in the latter directly cause problems. But MAV-VCAA is like a really bad TV crossover episode, and MAV products must accordingly be considered to have, at minimum, a heavy VCAA tinge to them.

  5. Another example. The pedant in me (all VCAA-induced pedantry I’ll add) picked up on this immediately.

    VCAA 2016 Exam 1, Question 5(b)(i) – the Assessor’s Report has wrong working (on the surface it could be construed as a minor typo, however if a student/teacher were to present this working in an actual exam, it would be crucified until the cows come home).

    Here’s the question, with the offending “solution” following:

    View post on

    View post on

    Notice the “not big enough square roots” in the second-last and third-last working steps.

    Have a field day, ladies and gentlemen (and marty).

    1. First, lets deal with marty being placed in the “other” category …

      Steve, yes of course it’s just a silly typo or TeX error or whatnot. But it doesn’t matter. It’s wrong.

      1. Just a bit of lighthearted humour there Marty – no offence intended at all.

        But yes, given that these assessor’s reports by their very nature must be vetted by multiple assessors, seeing a stupid error like this flow through (and not corrected 4 years later – I imagine they’ve been emailed about it querying this?) is not on. When you’re an organisation whose (sole) focus is to pick on small errors and so forth, and then you go and deal out this crap, it doesn’t bode well for everyone confiding in you.
        Anyway rant over, I could go on all day and night.
        Marty, looking forward to your next post on the trial exam.

        1. As was my response.

          And you’re exactly right. OK, having a typo on the solutions is no big deal, and doesn’t compare to their exam screw-ups. But it *should* have been caught, and it definitely should have been corrected by now.

  6. Something that I found when I was practicing for Methods was a rather annoying NHT question (2018, MCQ 18). I don’t believe it completely is an error, but the premise is that you’re given 5 transformations along withe the start and end graph. You’re also told that the two graphs have the same scale. The ridiculousness is that if you were to apply transformation C or D, you would obtain identical graphs, although one is dilated in comparison to the other, at which point you’d need to carefully distinguish which one is which.

    1. Jesus H. Christ. No, it’s not an error, but “fucking dumb” doesn’t begin to cover it either. Who thinks up such a question? Who signs off on it?

      (ps Sai, I did a little edit of your comment, to make the exam a link. The PDF link seemed to want to display but fail.)

  7. We better not forget the dodgy ‘pdf’ on 2016 Exam 2 Q3 (h). If errors were an Olympic event, this one would be on the podium.

    1. Of course that one is on the radar. At this stage I’m just posting errors as people suggest/remind me of them, but a bunch of the exam WitCHes, and a bunch of others will eventually get posted.

  8. 2019 Maths Methods Exam 2 Question 4 part (f)(i):

    The question asks for an answer correct to four decimal places and the preamble provides the value necessary for the calculation to only the same accuracy (four decimal places). This leads to a significant rounding error in the final answer: Using the VCAA value gives 0.2947, whereas the answer correct to four decimal places is actually 0.2949.

    In Examination Reports VCAA mewls about students not using sufficient accuracy during a calculation to get a final answer that is correct to the specified accuracy. And yet it lets an idiot write a question that deliberately forces students to make this very mistake.

    1. Thanks, John, but I don’t understand your comment. I agree that the question is screwed (and ridiculous), but how are you claiming the “actual” answer to four places is 0.2949?

      1. If you use four decimal places of accuracy (the value given by VCAA in the question) in the calculation, you get the answer 0.2947. If you use seven decimal places of accuracy in the calculation (ignore the given VCAA value, calculate your own value and use it to 7 dp accuracy), you get the answer 0.2949. The latter answer IS correct to four decimal places, the former answer clearly is NOT.

        So saying that 0.2947 is the answer, correct to four decimal places, is bullshit. It’s an error. The error is in the question – the value in the question should have been given to more than 4 dp accuracy if an answer correct to 4 dp is required. Alternatively, an answer correct to 2 dp should have been asked for.

        I can post the calculations if more clarity is needed.

        Another idiot exam writer.

          1. OK … More clarity is needed so here are the calculations:

            The preamble to part (f) (i) says:

            “Each year, a detailed study is conducted on a random sample of 36 Lorenz birdwing butterflies in Town A. A Lorenz birdwing butterfly is considered to be very large if its wingspan is greater than 17.5 cm. The probability that the wingspan of any Lorenz birdwing butterfly in Town A is greater than 17.5 cm is 0.0527, correct to four decimal places.”

            Earlier in the question (preamble to part (d)) it says:

            “The wingspans of Lorenz birdwing butterflies in Town A are normally distributed with a mean of 14.1 cm and a standard deviation of 2.1 cm.”

            So the probability “that the wingspan of any Lorenz birdwing butterfly in Town A is greater than 17.5 cm” can be calculated to a greater accuracy than the four decimal place value given by VCAA. For example, 0.0527185, correct to 7 decimal places.

            The question then asks:

            (f) (i) “Find the probability that three or more of the butterflies, in a random sample of 36 Lorenz birdwing butterflies from Town A, are very large, correct to four decimal places.”

            The required probability is calculated using the binomial distribution:

            Number of butterflies ~ Binomial (n = 36, p = …)

            If you use p = 0.0527 (the value given by VCAA) you get a probability of 0.2947, rounded to 4 dp.
            If you use p = 0.0527185 (the more accurate value that I calculated using Mathematica), you get a probability of 0.2949, rounded to 4 dp.

            VCAA asked for an answer that is correct to 4 dp. 0.2947 is NOT correct to 4 dp. The answer, correct to 4 dp, is 0.2949.

            In general, it should be bleedingly obvious that if you want an answer correct to x decimal places, you have to use MORE than x decimal places of accuracy during the calculation. (I advise students to use at least 3 more decimal places).

            So … as I said above:

            “In Examination Reports VCAA mewls about students not using sufficient accuracy during a calculation to get a final answer that is correct to the specified accuracy. And yet it lets an idiot write a question that deliberately forces students to make this very mistake.”

            1. Brevity, John!

              But thanks. I didn’t realise that the probability arose from earlier information. (Not that the normal data can be assumed to be sufficiently exact to give 7 (or 4) places of accuracy.) I’ll add to the post.

              1. Well, once you put the coin in the slot …
                (I know your busy but you needed to scull a vodka and then read the whole question! The moral to the epic (that some students are slow to learn) is that later parts of a question often link to earlier parts).

                I understand why VCAA gave a value of p – if it wasn’t given, tracking the consequential marks in all four subparts of (f) would be a nightmare. But do it right and give an appropriate value!!

                1. I’ve added the exam question. A slightly different take to yours, but no question there is both error and idiocy there.

  9. I’ll be updating this post as much as I can throughout today, with errors from WitCHes and other errors that people have flagged. I’ll also try to take a quick look at the older exams. I’m not sure how much I can get to, but will do what I can. Sorry for mistiming my run.

    1. OK, I’ve updated what I’m going to do. I’ve added all the errors I know. My guess is there is a decent amount of forgotten or undiscovered nonsense in the early exams, but I’m not going to hunt for it.

  10. 2016 Exam 2 Section A Question 11 – First line of the ‘solution’ in the Examination Report is chicken vomit.

      1. Regarding this typo, I feel like the original entries might come from an older version of MathType – the MathType equations could be originally edited on a higher version (at the time possibly 6.0+), once the word doc/docx file is opened on another machine with older version of MathType, then it would not be recognised correctly and then blury, unedited images containing the equations generated…This causes a lot of trouble if further amendments are required.

        1. Thanks, L. Obviously something has gone awry, and such things happen. Still, it shouldn’t sit there for four years.

      2. Hi Marty. You made a small typo (VCAA-itis can be contagious but luckily you only caught a low load … A shame there’s no vaccine).

        “QA(1)) (added 24/02/22).” should be QA(11).

        PS – Lancelot. Calling this error a typo is very generous of you. That’s like calling appendicitis a stomach ache. It’s what we’ve come to expect from VCAA – lazy, careless, insouciant proofreading.

  11. Maths Methods 2019 Exam 1 Question 6 (b) – another error I only just came across today:

    The question obviously intends that the binomial approximation be used (the Examination Report confirms this).
    But the Binomial approximation is only valid for the first few boxes that are packed. If we look at, say, the 400th box, the population that the pegs were chosen from for this box will be so depleted (due to the previous 399 boxes getting packed) that there is no chance the binomial approximation will still be valid. (Think of the extreme case where we look into the very last box that was packed, where the population the pegs were chosen from has depleted to, say, 16 …)

    A small quibble I know. And easily fixed by asking “Find Pr(…) [for the first box that is packed]”.

    1. John, I’ve looked at I’m not sure I understand your objection. Maybe I’m being obtuse but isn’t a box of pegs a box of pegs? I don’t see how it matters if it’s the last box of pegs, if along the way the pegs have been chosen randomly.

      1. OK. Let’s suppose there’s a population of 18,000 pegs and 3,000 are defective.
        You choose 12 pegs and put them in a box. Clearly the number of defective pegs chosen can be approximated by a binomial distribution.
        You do this for a few hundred boxes. The population is getting smaller.
        At some stage the population you’re choosing from will be, say, 20. The number of defective pegs in the box chosen at this stage will not be approximated by a binomial distribution.

        What happens when the population has shrunk to 20 and maybe there are no defective pegs left and you choose pegs for your box of 12 … What’s the sampling distribution for that box …?

        The binomial approximation is only reasonable when applied to the boxes where pegs were chosen while the population was large.

        A box of pegs is not a box of pegs. Each box is actually chosen in a slightly different way due to the shrinking of the population. And of course, if you decide to choose a random box after all the packing is finished, that’s a whole different problem …

        1. I don’t think this makes sense. You have 1500 boxes of pegs. The boxes are either opened or they aren’t. If boxes 1-1499 are opened, then you know exactly what is in box 1500. If the boxes are unopened, then you have no greater or lesser knowledge about box 1500 than you do about box 1.

          1. OK, I think I see what you’re saying.
            But what happens if you know the box you’ve been asked to calculate the probability for was the last box to be packed? Are you saying that the distribution of defective pegs in this last box will follow the same distribution (approx binomial) as the number of defectives in the first box that was packed? So it doesn’t matter what box you’re calculating the probability for, as long as you don’t know when it was packed?

            Maybe I’m the one that’s obtuse …?

            1. Yes. I’m saying if you don’t open the boxes then you may as well label the boxes Peter and Bob and John and so forth. There’s no meaningful sense of first box and last box.

  12. 2011 Exam 2 Multiple Choice Question 8:
    The function h = f + g is not defined because dom(f) neq dom(g).

    1. Thanks, A. The question is ok (if you one ignores the appalling grammar). There are different conventions, but the convention then (and I think still) in VCE is that f + g is taken to be defined on the intersection of the domains.

  13. 2017 Exam 2 Section B Question 4 part (i) (ii) – Examination Report: The formula for the area contains two errors:

    1) The integrand uses the wrong notation, it should be \displaystyle g_k(x) not f(x). We note that the taking the limit makes no sense as a consequence.

    2) The integral expression for the area is not correct, it is missing a multiplying factor of 2. We are also puzzled why \displaystyle g_k^{-1}(x) - g_k(x) is not used as the integrand.

    The errors are minor and inconsequential to getting the answer. Nevertheless they are errors (of the sort that VCAA loves to penalise and pontificate about when made by students).

    We note in passing the ridiculousness (and confusion) of having a part (i) that contains subparts (i) and (ii).

    1. > QB(4)(j). The speed is written as “m per second” rather than “metres per second”.

      I think it’s important to note that this issue was announced at the beginning of the exam, similar to the general typo

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