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.
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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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.
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2026 NHT EXAM 2 (Exam here – discussed here, assessment guide here (W,I))
We are not aware of any errors on this exam (but we haven’t looked).
2026 NHT EXAM 1 (Exam here – discussed here, assessment guide here (W,I))
We are not aware of any errors on this exam (but we haven’t looked).
2025 EXAM 2 (Exam here, marking guide here (W,I), report here (W,I) – discussed here)
QB1(b) (added 23/05/2026) The exam report notes “The x-intercept 
was often closer to 2 than 1″. From personal communication with VCAA, it is clear that students were penalised for this, which is utterly insane. These people are mad.
QB2(d)(i) (added 23/05/2026) The functions f(x) and g(x) have been given/determined earlier, h(x) = f(x) – g(x) is defined and the question asks “Write down an expression for the derivative of h(x)”. An appallingly worded question, particularly with the atrociously inappropriate command term “write down”. As written, the answer h’ = f’ – g’ is a perfectly legitimate answer, but the exam report makes clear that this answer was not accepted.
QB4(f)(ii) (added 14/12/2025) The question asks for the minimum and maximum possible values for the y-intercept. The y-intercept, however, is a point, not a coordinate of that point.
QB4(g) The question provides the derivatives of the two functions at the endpoints. Fine, except, once and for all, VCAA must tell people that functions will always be permitted to have derivatives at the endpoints.
2025 EXAM 1 (Exam here, marking guide here (W,I), report here (W,I) – discussed here)
We are not aware of any errors on this exam.
2025 NHT EXAM 2 (Exam here – discussed here, assessment guide here (W,I), report here (W,I).)
We are not aware of any errors on this exam.
2025 NHT EXAM 1 (Exam here – discussed here, assessment guide here (W,I), report here (W,I).)
We are not aware of any errors on this exam.
2024 EXAM 2 (Exam here, marking guide here (updated 13/02/25) – discussed here, report here (W,I))
MCQ5 The bad formatting of the brackets is sufficiently annoying to count as an error.
QB(2)(a) VCAA still has to decide once and for all whether functions can have derivatives at interval endpoints. It would appear so, but VCAA has to declare it to be so. (20/04/25 The marking guide and the exam report indicates that inclusion of the endpoint was optional. That is good, and it is not nearly good enough. Students shouldn’t be having to guess.)
2024 EXAM 1 (Exam here, marking guide here (updated 16/02/25) – discussed here, report here (W,I))
Q6 There was mis-formatting of the “3” in the expression 
etc. This was subsequently corrected in the published paper.
Q9(c) Q7(c) VCAA has to decide once and for all whether functions defined on closed intervals can have derivatives at endpoints, and then tell someone. The graph in the marking guide does not make it clear what was expected, and whether or not either answer was permitted. (20/04/25 The marking guide (but not the exam report) indicates that either “open or closed circles” sufficed. That is good, and it is not nearly good enough. Students shouldn’t be having to guess.)
2024 NHT EXAM 2 (Exam here – discussed here, report here (Word, idiots))
MCQ 17 There is no correct answer. Presumably the intended answer was D, but we cannot conclude that 
. (We know that 
, but this only implies the subset conclusion if the probability distribution is discrete.) This is similar to an error made on 2014 Exam 2, although the 2014 error (and VCAA subsequently lying about it) was worse. (25/09/24) The exam report pretends that the issue does not exist: the third line of the argument in the exam report is simply invalid. For VCAA to still be doing this kind of crap is astonishing.
2024 NHT EXAM 1 (Exam here – discussed here, report here (Word, idiots))
Q3. The function f is defined with an unspecified domain D. Part (a) then asks for the maximal domain of f, which makes no sense: the domain of f is D, whatever that happens to be. Then, parts (b) and (c) require knowing D, which we do not. Throughout one can, and is probably meant to, assume that D is the maximal domain of f, but the wording is atrocious. (25/09/24) The exam report is silent on the issue. Given the intended meaning is clear enough, this is not a huge deal, but it is not exactly honest or classy.
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 
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 term “trapeziums” is also gauche.)
Q9(b). The point P is undefined. (24/04/24 – discussed here) In the wake of the exam report, this error has been reclassified as major. It is clear that at least some students were actively confused by the lack of definition of P, and seemingly students were then penalised for VCAA’s incompetence. Beyond the arrogant framing, the solution in the exam report is incomplete and absurd. Simply, this is garbage.
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.
Q3 (added 23/02/25 – discussed here) A badly bollocksed, and very bad, question. The question makes no sense unless one assumes a > 0. But then part (c), the wording for which is independently ridiculous, makes no sense. The rectangle is also not properly specified. The wording in (f) may not quite amount to an error but it is a crime against humanity.
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. (05/05/24 – the exam and report have been amended, with the question redacted: “This question has been redacted following the findings of the Independent [Bennett] Review into the VCAA’s Examination-Setting Policies, Processes and Procedures for the VCE“.)
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. (25/09/24) As commenter Jay has noted, it seems that VCAA really did want any old antiderivative. In which case the question is fine but idiotic, and the exam report is highly confusing and misleading. For example 
is then a valid answer but the exam report gives no hint of this. It’s possible the error should be unredded, but the entire question and Report answer is so nuts, I’m gonna leave it.
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 
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 
can be any of a zillion different functions, and it is simply invalid and inappropriate to assume is a reflection of 
. (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 (W,I) – 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 (W,I) – 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 here. There 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 (W,I) – 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 here. The 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(2)(b) (added 25/09/24). The question is a borderline “error”, but there’s enough. The question is asking about the gradient of the function being strictly decreasing, but excludes the endpoint. This is (sort of) OK, if that is the convention, but VCAA is not consistent: see the discussion here. The lesser issue, but more clearly an error, is that the question asks for “the set of values” for which the gradient is strictly decreasing. This is treating monotonicity as a pointwise property, rather than a property of the function on a given interval. Which might be considered slightly nitpicky, except this confusion has led VCAA to clear error on other occasions. See, for example, here.
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)
Q6(b) (added 10/10/24) There are infinitely many answers of the required form.
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)
MCQ8 (added 02/11/24) If a = 1, which has not been excluded, there is no unique solution for x. Moreover, in this case all the provided answers are non-sensical, since logarithms to base 1 are not defined.
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 
in the working, rather than the correct 
. (25/09/24) The error has been corrected, presumably in 2021, since it is indicated that at least some amendment was made then.
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 
is the probability that a biased coin comes up heads, and where it turns out that 
. The question is fatally ambiguous, since there is no definitive answer to whether 
is possible for a “biased coin”.
The examination report answer includes both values of , 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.
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
if 
and 
if 
. Differentiating gives 
which satisfies the conditions in the question and then one last differentiation gives us that there is a change in concavity, but not 
for any x, most importantly f”(5).
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.
Ah phooey, I messed up the function in formatting… so much for a response early in the morning. Trying this again with
(with any choice for the antiderivative f) will yield that 
if 
and obviously, 
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…
Edit:
will not give you a point of inflexion on f.
No clue what’s going on with the LaTeX, my point is that
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
change sign, as you want?) The underlying question here is the meaning of “inflection point” at some 
. The standard, but not universal, notion is “change of concavity” at 
. That’s not quite a definition, since it leaves open how differentiable the function need be, particularly at 
. The 2014 exam is implicitly using a different notion.
Ah I’ve unintentionally mixed in two different ideas. One was that you don’t need to have
for a point of inflexion, only a change in concavity in some neighborhood and the other, which is that you could have 
but not necessarily a point of inflexion. The example I posted was there to suggest that you could have a change in concavity without 
as VCAA seems to think, although I’m not sure if Methods explicitly defines “stationary points of inflexion”.
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
to have an inflection point at 
, and so 
is not (usually) necessary. Also, the simple example 
shows that 
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.
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.
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?)
Thanks, AIPNH. Every error is an error. I’ll check them out.
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.
SRK, “reasonable” doesn’t cut it here.
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..
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
. The method you recommend would be 
.
Whereas I would just write
. There is no risk of “losing” solutions.
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.
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.
Marty,
Attached is the comments for Q4.
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
.
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?
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.
Thanks, P.N. I’ll look at it, although it sounds more stupid than wrong.
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?
Here you go marty, the link to the Non-CAS Maths Methods Exam 2 from 2007 (https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/2007mm2.pdf). This is slightly different to the CAS version of the same exam (https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/2007mmCAS2.pdf). 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?
Thanks, Steve. Is there a page with links for these non-CAS exams?
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.
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.
No worries, Steve. There are ways and there are ways.
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.
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.
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
, where 
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
, where 
is the same expression in part (i).
Fire away, everyone.
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.
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.
questions and dodgy solutions to dodgy 
style questions.
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
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.
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.
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:
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).
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.
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.
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.
Steve,
Following yours, another must be picked from the same year 2016, but in MM2 reports.
Thanks, PN. Up it goes.
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.
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.)
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.
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.
John and Marty，
“Lest we forget”.
Lest we forgive.
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.
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?
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.
What seven decimals? Where are you getting the probability to seven places to use?
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.”
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.
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
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!!
No, that moral doesn’t apply here. The moral here is to write comments more carefully.
I’ve added the exam question. A slightly different take to yours, but no question there is both error and idiocy there.
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.
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.
2016 Exam 2 Section A Question 11 – First line of the ‘solution’ in the Examination Report is chicken vomit.
Indeed it is. I assume just some cut and paste nonsense, but it’s an error. Will add.
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.
Thanks, L. Obviously something has gone awry, and such things happen. Still, it shouldn’t sit there for four years.
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.
Thanks, John. Fixed now (I hope).
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]”.
Thanks, John. I’ll check it out soon. (So much crap, …)
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.
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 …
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.
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 …?
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.
2011 Exam 2 Multiple Choice Question 8:
The function h = f + g is not defined because dom(f) neq dom(g).
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.
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
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
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).
Thanks, BiB. Of course the question is atrocious every which way. I’ve added a short update.
I’ve updated the list with the identified 2023 errors.
> 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
Ah, yes, good point. Thanks, Jay. I’ll cross out both, with an explanation.
If only it had been announced before the printing of the exam.
2014 exam 2 MCQ 13:
the proposed domain could have been extended to [1, a^pi]
Therefore, whilst option c is correct, I refuse to believe that the person writing it intended for it not to be the maximum possible domain, and I strongly suspect they simply forgot that cosine graphs have the range [1,-1].
Also, the wording arguably implies that it will be the maximum possible domain
EDIT: if it wasn’t referring to the maximum possible domain, options D and E shouldn’t have been included, as A is obviously a subsection of them
Thanks, Jay. I disagree.
I think it’s far from a great question but I don’t read any “maximal” in the question, and it doesn’t smell to me as if the writer got themselves confused. It seems reasonable enough that the intended domain is not maximal, particularly given the fiddliness of the question. Sure, the fact that A automatically wins over D and E means the MCQ aspect is poorly constructed, and the question can be criticised on those grounds. But I think those are the grounds.
2015 Exam 2 MCQ 22:
Why in the world is g(x) on the left and f(x) on the right? That is genuinely ridiculous, even if it’s technically not an error
Actually it’s worse: the graph of g(x) is not symmetrical, making the report’s working out incorrect, and likely also making the answer incorrect
Hi Jay, I think the question is too cute, and I don’t like the solution in the exam report, and the term is “symmetric” rather than “symmetrical”, but I think the question is ok.
The graph of g is not symmetric but the composition only depends upon g(y) for y ≥ 0, and so can reasonably be considered symmetric.
I don’t understand your concern with g being on the left.
2017 Exam 1 question 7bi:
if a is equivalent to b, is it accurate to say that a is a subset of b? If not, this question is technically flawed
Sorry, Jay, I think 7b is tricked-up nonsense but I don’t understand your question. What are a and b referring to here?
a was referring to the range of g
b was referring to the domain of f
The question was whether the range of g can be a subset of the domain of f, given they are equivalent. Basically, is [0,inf) a subset of [0,inf)? If not, the question is technically invalid
Sigh.
(i) Yes, the question is ok (at least in terms of the issue you raised). A set X is always a subset of itself.
(ii) Don’t use “equivalence” when you can says “equals”, and probably don’t use “equivalence ever. People get whipped for that around here. See here.
(iii) If you’re looking to nitpick VCAA, it’s not great to do so with such a sloppy question, with “a” and “b” introduced with zero explanation. I appreciate people detectiving the exams, and I try to answer whatever anybody asks, but this is tiring work. Please don’t make my job harder than it need be.
Not sure where a better place to post this is, but is i just me or is the Methods formula sheet (https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/mathmethods1-formula-w.pdf) ridiculously over-complicated? Like why are so many integrals written as (1/b)a instead of a/b
This is as good a place as any. So, you’d prefer, for example,
rather than 
?
Yeah, it’s a little more cumbersome, but I’m ok with the constant
having a little extra prominence. I’m irritated by the gratuitous parenthese around the 
, and I really don’t like formulas for 
.
I don’t understand either complaint tbh
Are you saying that sinax is better than sin(ax)? Also, would you remove the +b from all the formulas? Is there something incorrect about it, or is the issue that it discourages mathematical thinking (I don’t see how though)?
Thanks, Jay. Yes, I much prefer
to 
. The brackets are unnecessary clutter.
The ax + b thing is more complicated. The problem is that students do this autopilot thing where they see a as the derivative of ax + b, and conclude that a similar formula holds more generally, for f(non-linear thing).
The blame, however, lies not really with the formula sheet but with the curriculum. The fundamental idiocy is that Methods does not have integration by substitution.
> 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.
The report doesn’t include +c in the answer, making me think that they actually were indeed asking for “an anti-derivative” as opposed to the general anti-derivative
Sheesh. Would it have been that hard for you to have also indicated the exam?
Anyway, to your point, yes i think you may be correct, but I’ll leave it as an error and adjust the wording. Any which way you look at it, the question and/or answer is bad. Either the question is in error, or the wording is appalling, or the question being asked is really damn stupid and the exam report is wrong. Note that
is a valid answer as you, and seemingly VCAA, are interpreting the question, but the exam report gives no hint of this. It is thus hellishly confusing for any teacher or student who is not fluent in VCAA-Speak.
Sorry for not including the exam. For future reference, it is 2022 exam 1 question 2(a).
I agree that asking for “an integral” is inherently stupid, however, rightly or wrongly, it is something that is taught in the Methods curriculum. To quote the Jacaranda textbook:
“If you are asked to find ‘the’ anti-derivative of an expression, then the ‘+c’ component must be part of the answer. However, if you are asked to find ‘an’ anti-derivative, then you can choose what the value of c is. The convention when finding ‘an’ anti-derivative is to let c equal 0.”
Furthermore, I’d argue that the same issue would apply for the general antiderivative: (3/2)log(2x-3)+c is a valid answer, but wouldn’t (3/2)log(2x-3)+98+c also technically be valid?
Yes, I’ve made the note. But: (a) this is insane; (b) the exam report is wrong, in that it suggests *particular* antiderivatives as correct and privileged.
Random thought-(3/2)log(4x-6) is correct, and had they asked for the general anti-derivative, (3/2)log(4x-6)+c would be correct, despite it not being the obvious answer and appearing to be an incorrect answer
(the reason it’s correct is because (3/2)log(4x-6)-(3/2)log(2x-3) is a constant, and hence the difference gets cancelled out by the +c)
There’s actually infinite possible correct answers which will appear incorrect at first glance, which, in my opinion, is a major problem, since I’d bet that numerous VCE students will have been cheated out by integration questions over the years
I think VCAA would have allowed any of the valid answers. My concern is that the question is so stupid and the report so unclear on the stupidity, that students and teachers reading the report will either be flummoxed or misled.
> 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}.
According to https://www.vcaa.vic.edu.au/assessment/vce-assessment/past-examinations/Pages/Mathematical-Methods.aspx, that report was amended on 9 June 2021, and I can’t find that mistake anymore
Thanks, Jay. Probably corrected. I’ll check it out, and will look at all your posts, tomorrow. I fthe error has been corrected, I’ll add a note to that effect.
Yes, the error has been corrected, and I’ve added a note to that effect.
Again, please don’t be lazy with the comments: include the year, and don’t be lazy with LaTex code.
2017 exam 1:
> QB(5) (added 26/10/21). For (b) and (c) there are infinitely many answers of the required form.
I’d argue that there’s only one correct answer, and that an unsimplified fraction would be incorrect. My reasoning is below (sorry it’s long, I tried to condense it as much as possible):
Claim 1: answers must be fully evaluated if a form isn’t specified
Example: Part A asks what the probability is that Jac does not log on to the computer successfully. It has the answer 17/125, based on evaluating (3/5)^3. The report mentions that “students erred with the arithmetic evaluation”, but doesn’t state anywhere that students should leave their answers in the form (3/5)^3 to avoid arithmetic mistakes. I’m very happy it doesn’t state that, as, in my opinion, it would be beyond stupid if it did. I think claim 1 follows on from that opinion.
Claim 2: unsimplified fractions aren’t fully evaluated
No evidence for this. It’s an opinion that I assume you’ll agree with, but if not I’d be very curious why…
Claim 3: Specifying the required form doesn’t change whether the answer has to be fully evaluated
Feel free to disagree with this claim. I just don’t see any argument for the contrary claim (specifying the required form changes whether the answer has to be fully evaluated)
Thanks, Jay. In brief, you’re wrong. But I understand that this “more than one answer” thing is something that people don’t really get (and VCAA doesn’t get at all). It’s worth a post, which I’ll try to do in the not too distant future.
Thanks, I look forward to the post
Is 2019 exam 1 question 6b wrong, because there’s infinite answers of the required form, such as (830078125/2176782336)*1^1
For instance.
Thanks, Jay. Added. Somehow “wrong” seems the wrong word, but the question is flawed.
Your very funny example is a good illustration of why I find this VCAA phrasing so absurd. (So maybe I don’t have to write the post now.)
I would assume my answer would also be considered correct, but maybe it wouldn’t be
Tbh I’m still not quite sure why specifying a restriction on the answer’s form makes the answer suddenly need only one form. Is it the fact that it’s asking you to solve for a, b, and c, even though it’s impossible to individually solve for any of them?
Jay, I wouldn’t worry much over this. This “answer in the form of” thing is gratuitous and bad mathematical style, but I don’t think in practice it is of too much consequence.
I don’t think VCAA are demanding one specific answer (of the given form), but I think they are generally *expecting* one specific answer (of the given form). And usually this is the answer a student would naturally obtain, or would obtain after natural simplification. So, the gist of what VCAA is requiring is “simplify in the natural manner”.
Whether a weirdo answer likes yours would be accepted is a very theoretical question, but also a very interesting question. Less weirdo but valid answers may arise, and I don’t think it’s a safe bet that VCAA would always award these answers the full marks deserved. VCAA has had plenty of history being assholes on such matters, as well as being wrong.
I’m guessing a slightly weirdo answer would be ok, but I’m only guessing.
2023 Methods sample 1 (https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/mathmethods1-samp-w.pdf) question 7:
Infinite answers of form. Also, I hate that they wrote “elsewhere” instead of t<0
Thanks, Jay. Yeah, the “elsewhere” is pretty damn lazy.
Things like sample problems I won’t normally attack, or list (although see here).
If I may have a slight exception to that rule, I’m wondering whether sample question 2c makes any sense? It’s a problem that often appears in Methods practice exams (eg MAV), but I’m completely puzzled how g(h(x)) could only exist if it always exists?
The wording of 2(c) is utterly atrocious, but I think the intended question is within VCAA’s rules.
(I understand the type of objection you’re making, and definitely VCAA has screwed this on occasion, and 3rd party exams do frequently enough, but I don’t know exactly the objection you’re making.)
2014 exam 2
> 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.
I am really confused. A point where a function’s gradient is 0 can be defined as a “stationary point”, which according to https://en.wikipedia.org/wiki/Stationary_point#Classification will either be a “point of inflection”, a minimum, or a maximum.
Furthermore, according to https://en.wikipedia.org/wiki/Inflection_point, “the condition f” = 0 can also be used to find an inflection point”. It is obvious that the second derivative will be zero, because it is a turning point in the derivative function. Furthermore, the second derivative test (https://en.wikipedia.org/wiki/Derivative_test#Second-derivative_test_(single_variable) ) dictates that the second derivative must be zero if a critical point is neither a local maximum nor a local minimum
I also don’t quite understand the counter-example in the blog post. Doesn’t it simply prove that the function can have infinite points of inflection?
Have I misunderstood something?
Thanks, Jay. Yes, you’ve misunderstood something, and I’ll try to de-misunderstand you. But the first thing is, don’t stress it. The counterexample I gave is very standard for those who do these things, but it is way outside the world of mathematics teachers and standard VCE.
An inflection point is where you go from concave down to concave up, or vice versa. The thing with the counterexample is that it switches its concavity infinitely often near 0: note the little bumps. So, although overall the function has the “vibes” of going from concave up to concave down at 0, *nothing* of that kind actually occurs at 0.
I’d have to double-check the properties of the function, and others I could create, but I’m pretty sure:
*) The stationary point classification is wrong.
*) The inflection point page I *think* is saying something simple, that IF there is an inflection point then that point must be somewhere where f” = 0. But it’s not saying anything about whether those points are in fact inflection points. (If it is, it’s wrong.)
*) Ditto the second derivative test. It’s telling you where to look, but not what you might find when you look there.
(I know this is outside the scope of VCE, it’s just fun to look into this kind of thing when I’m taking a break from studying. Feel free not to respond if it’s to time consuming to try to explain why I’m wrong)
Anyway, after re-reading that Wikipedia page you are definitely right that it mentions a necessary by not sufficient condition of f’’(x)=0
However, it mentions “A sufficient existence condition for a point of inflection in the case that f(x) is k times continuously differentiable in a certain neighborhood of a point x0 with k odd and k ≥ 3, is that f(n)(x0) = 0 for n = 2, …, k − 1 and f(k)(x0) ≠ 0. Then f(x) has a point of inflection at x0.”
(In other words, if I’ve understood correctly, the first non-zero derivative of f(x) must come from differentiating an odd number of times)
That obviously means that the first non-zero derivative must come from differentiating f‘(x) an even amount of times. In that question we’ve been told that f’(5) is a maximum, so I’m pretty sure that, based on the higher order derivative test (https://en.wikipedia.org/wiki/Derivative_test#Higher-order_derivative_test) we can conclude that the first non-zero derivative will indeed come from differentiating f’(x) and even number of times, in other words differentiating f(x) an odd number of times. The only exception is if there are infinite zero derivatives. My assumption is that that’s impossible since f’(x) isn’t a straight line, but I could be wrong about that
Side note: isn’t the counter-example, and by extension all it’s derivatives, undefined at x=0? Is there some rule that means that actually the derivative is 0?
Also, thanks for explaining what a point of inflection is. Methods just teaches “stationary points of inflection” (which seems to be referring to the thing that everyone else calls “stationary points”)
Thanks again, Jay. Rushing, but quick responses:
*) Yes, in general a sufficient condition for an inflection point must involved a non-zero derivative.
*) In the exam question, we have f’ is a max at 5, but i think the sufficient is considering higher derivatives. (I’m rushing.)
*) The counterexample is explicitly defined to be 0 at 0.
*) No, a stationary point of inflection is both a stationary point and a point of inflection. It’s an absurd camel of a topic. It’d be like a zoologist studying brown horses and only brown horses.
2017 Methods exam 2 (https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/2017/2017MM2-w.pdf) multiple choice question 8 should probably state that a≠1. As it currently stands the equation is perfectly valid for a=1, but none of the solutions are defined for it
EDIT: I guess that could possibly be intentional to prevent people solving it using a CAS
I’m puzzled. Logarithms base 1 don’t make sense. Are you saying that the CAS spat out something?
EDIT: Sorry, was being dumb. Of course you’re right. Definitely an error: I’ll ponder how red to make it.
I see you wrote for the 2014 error
> The examination report simply pretends that X is a continuous random variable, which is arrogantly dishonest and which doesn’t fix the problem. Disgraceful.
If X is a continuous random variable, isn’t there a 0 probability of x being any specific value? We were taught that Pr(x>1)=Pr(x≥1), for example, since there’s 0 chance of x being exactly 1
EDIT: Obviously the exam contains a mistake, since it only states “continuous random variable” in the final report. I’m just curious about why stating that in the original question wouldn’t fix it?
I was being a bit technical and snarky. It’s a question of how you define “continuous random variable”. Maybe look up the definitions and see what you think.