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!
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(b) (added 21/10/21) The answer has infinitely many correct forms.
Q7 (added 21/10/21) The answers to both (a) and (b) have infinitely many correct forms.
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.
Q2(b) (added 21/10/21) The examination report refers to “conditional probability”, but this is not a conditional probability question.
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.)
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.
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.
Q3(c) (added 22/10/21) There are infinitely many answers of the required form.
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.
Q7(b) (added 24/10/21) There are infinitely many answers of the required form (and the form is pointlessly noisy).
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.
We are not aware of any errors on this exam.
Q9(c), Section B (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.
Q3(h), Section B (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).
Q4(c), Section B (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.
Q5(b)(i) (added 24/09/20) The solution in the examination report gives the incorrect expression in the working, rather than the correct .
Q5(c) (added 13/11/20) – discussed here. The method suggested in the examination report is fundamentally invalid.
MCQ4 (added 21/09/20) – discussed here. The described function need not satisfy any of the suggested conditions, as discussed here. The underlying issue is the notion of “inflection point”, which was (and is) undefined in the syllabus material. The examination report ignores the issue.
Q4, Section 2 (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.
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.
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.