MELting Pot: The Methods Error List

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.


2021 NHT EXAM 2 (Here, and report 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(b) (added 21/10/21) The answer has infinitely many correct forms.

2021 NHT EXAM 1 (Here, and report 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

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

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

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 1 (Here, and report here

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.

2016 EXAM 2 (Here, and report here)

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.

2016 EXAM 1 (Here, and report here)

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)

Q5(c) (added 13/11/20) – discussed here. The method suggested in the examination report is fundamentally invalid.

2014 EXAM 2 (Here, report here)

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.

2011 EXAM 2 (Here, and report here)

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.

2011 EXAM 1 (Here, and report here)

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.

2007 EXAM 2 (Here, report here and discussed 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.

53 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.

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