Discussion of the 2021 NHT Methods Exams

This is our post for discussion of the 2021 NHT Mathematical Methods exams (here and here). See also the accompanying 2021 NHT Specialist exams post, here. See also the relevant Witches: here, here and here.

UPDATE (08/10/21) The exam reports have reappeared, as PDFs, here and here. The exam 2 report has important updates, and important non-updates; see the comments in blue, below.

UPDATE (22/09/21) The exam reports are now out, here and here (VCAA-Word-Stupid). We’ve added a couple comments below, in green.

EXAM 1 (Here)

Q2. (01/09/21) Asking for “the rule of y” in part (b) is gauche.

Q4. (01/09/21) A gratuitous and annoying framing in terms of matrices in Part (b).

Q5. (01/09/21) It is infantilising to provide the graph of the trig function.

Q7. Parts (a) and (b) have infinitely many correct answers.

Q9. A nice (if slightly misframed) question. (01/09/21) Commenters below have objected, probably correctly, to this question being on a Methods exam. The question is easy, at least with hindsight, but it is probably not the style (i.e. existence of) thinking expected in a Methods exam, particularly a Methods Exam 1.

EXAM 2 (Here)

MCQ5. There’s an issue if q is negative, but perhaps ok in context. Also, “equal to”, not “equivalent to”. (Yes, we’re the only ones who give a shit about this but it’s wrong, and we’ll keep saying it’s wrong.)

MCQ7 (22/09/21) The answer in the examination report is incorrectly given as C, instead of B. (08/10/22) Now corrected.

MCQ8. A screw up. There is no correct answer. See here.

(22/09/21) Of course there being no correct answer doesn’t stop VCAA from pretending otherwise. (08/10/22) The incorrect answer has now been deleted, with absolutely no indication that there is no correct answer. Unconscionable. 

MCQ9. Bizarre and flawed. See here.

MCQ14. Improper integrals are not in the subject, but let’s not have that stop us pushing buttons.

MCQ20. Not wrong, just stupid.

Q2. Completely nuts. See here.

(22/09/21) As indicated here, part (d)(i) is utterly ridiculous and, consequently, the solution in the examination report is utterly ridiculous. (08/10/22) Uncorrected, of course.

Q5. Part 5(b) has infinitely many correct answers.

(22/09/21) The answer to Part (d) is incorrectly given as \color{OliveGreen}\boldsymbol{1/\sqrt{a-1}} instead of \color{OliveGreen}\boldsymbol{1/\sqrt{a+1}}. (08/10/22) Now corrected.

95 Replies to “Discussion of the 2021 NHT Methods Exams”

  1. Again, have only really looked at Exam 1, but also I’m not a 12 Methods teacher.

    Question 2 b) “the rule of y”, seems like it should be read aloud in an exasperated voice. (Poor attempts at humour aside, I did find this wording very jarring.)

    Question 4 b) This just seems like a needlessly convoluted way to justify the presence of matrices in the curriculum. Why not just something along the lines of “describe a sequence of two translations that map g to f^(-1)”?

    Question 5 a) I found the presence of the graph for x 2 to be, quite frankly, pretty embarrassing. Do Year 12 Methods students really need to have these parts of the graph displayed to them if they’re any chance of sketching the graph for -1 ≤ x ≤ 2, finding the zeroes, etc.?

    Question 9. Marty, perhaps this is what you meant by “misframing”, but I think an autonomous DE question on a Methods exam is pretty unfair.

    1. Re: Q9.

      I think the DE nature of the question would have initially bamboozled most students including those doing Specialist Maths. But no calculus is ever required*, it’s basic algebra in heavy disguise (I like part (c) because “the range of f is (0, 4)” defines the domain of \displaystyle f'(x)).

      * Unless you use calculus to find the coordinates of the turning point of the parabola in part (c). Using an elephant gun to kill a fly.

      However, there is one issue that will fuck up Methods students (and maybe Specialist Maths students too) …

      The graph has NO stationary points (as any well-taught Specialist student who has met these types of DE will know). In fact, the general solution is \displaystyle f(x) = \frac{4 e^{4x}}{e^{4x} + C} (provided f(x) \neq 0 and f(x) \neq 4 which is given via “the range of f is (0, 4)”) and has two horizontal asymptotes y = 4 and y = 0.

      But it won’t completely surprise me if the writers intend students to say that there are stationary points: \displaystyle f'(x) = 0 therefore f(x) = 0 or f(x) = 4 therefore two stationary points corresponding to these.

      But it’s possible that the writers will recall saying that “the range of f is (0, 4)” therefore f(x) \neq 0, 4 therefore there are no stationary points …. It’s a dirty trick to play on Methods students because Specialist students (all 12 of them in the Northern Hemisphere) w/sould know this from experience and hence have a big advantage. They should be familiar with equilibrium solutions.
      NB: The DE does not even need to be solved: https://mathematicalcrap.com/2017/11/26/the-madness-of-crowd-models/

      But at least VCAA is requiring a justification for the answer before the 1 mark is given, unlike previous years. Maybe it is listening …

      So I think part (b) is pretty unfair, but part (a) and part (c) are fair enough.

      1. Thanks, John. Can you clarify why you thought (b) was unfair? It seemed to me pretty obvious to think “stationary means f’ = 0, and what do I know about f’ …”. I’ll accept that this line of thought is likely to be much less obvious to a Methods student, but for a final question a CAS-free exam, the question as a whole seemed to me to require thought (for once) but reasonable.

        1. Well, as I commented earlier:

          1) It’s a dirty trick to play on Methods students because Specialist students (all 12 of them in the Northern Hemisphere) w/sould know this from experience and hence have a big advantage. They should be familiar with equilibrium solutions.

          2) I think that the DE nature of the question makes it unfair for Specialist students, too – it could lead Specialist Maths students down an inefficient rabbit hole that takes more than 1.5 minutes (1.5 minutes per mark).

          I really liked what SRK said: “Because it really just seems like they’re asking “how many solutions does x(4-x)=0 have, if x \in (0, 4)

          It is mutton that has been ridiculously dressed up as lamb. We will probably agree to disagree on this.

          1. Thanks, JF. I don’t think that is a fair characterisation of the question. The fact that there is a simple solution does not mean that the question is intended to be, or is, an easy question. But, probably you and SRK are correct, that it is too unMethodsy for this exam. I’ll update.

    2. Thanks, SRK. I agree on all, and will add accordingly, except on Q9. By “misframing”, I meant that it was a bit weird in the set-up, giving (almost) a definition of f, as well as a conclusion for that f. It didn’t make a lot of mathematical sense. I didn’t think of the question as unfair, and more in line with the functional equations one tends to see in the MCQ, but others here are probably a better judge, and I’m happy to add if there’s a strong enough opinion of that.

  2. Re: Q9 on exam 1. I don’t know if it is appropriate for this level. Some other comments:

    The question is set up wrong. Who comes up with this phrasing? They should set it up properly, and make it clear that f is not unique (until we set a value, i.e. after part (a)).

    (a) The information that f(0) = 1 is important. (It uniquely determines f.) The fact that it gives f'(0) is not so important. Seems a missed opportunity.

    (b) I like this part. A sketch would have been also good.

    (c) This is OK, but it’s a weird algebraic question (you can do it by just thinking about the range of x\mapsto x(4-x) for x\in(0,4).

    It feels strange to have them not solve the DE with the given condition in (a), or at least be given the solution with a free parameter that they can determine using the condition in (a). Is this a question testing DEs or polynomials?

    Is this too much for 3 marks?

    1. Hi Glen. It’s testing … hmmm … I think it’s testing polynomials and algebra.

      Solving DE’s of the form \displaystyle f'(x) = g(x) and \displaystyle f''(x) = g(x) are within the Math Methods curriculum (except they’re not called differential equations in Methods. It’s simply “Find the function f(x) such that …”).

      But the type of DE in this question is not in the Maths Methods curriculum (it’s in the Specialist Maths curriculum, however). So it’s definitely not testing differential equations. Which might not stop a Specialist Maths student from trying to solve the DE and noting that the solution has no stationary points … (A lot of work for 1 mark!). I wonder what they would think of the ‘Marty’ justification here: https://mathematicalcrap.com/2017/11/26/the-madness-of-crowd-models/.

      On reflection, I think the unfairness of part (b) to Methods students might be evened out by the fact that the DE nature of the question could lead Specialist Maths students down an inefficient rabbit hole that takes more than 1.5 minutes (1.5 minutes per mark).

      1. This is partly also a reply to your reply to my initial comment, but I’ll put it here.

        Restricting the range of f to (0, 4) in a way suggests an awareness that the question threatens to be unfair, because otherwise students would need to have some grasp of equilibrium solutions. So yes, despite the DE garb it’s not really testing DEs. But if question b) isn’t intended to test anything about DEs then what is the point of the question? To test that students know that if f has a stationary point at x then f'(x) = 0? Because it really just seems like they’re asking “how many solutions does x(4-x)=0 have, if x \in (0, 4)?”… What am I missing?

        1. SRK, you’ve hit the bullseye! Nicely said. The question is nothing more than exactly what you’ve stated! It is mutton dressed as lamb. And the dressing will have caused all sorts of confusion and trouble – for no good reason.

              1. NSW manage it, the IBO manage it (their exam questions are quite similar in nature in some ways – none of this contrived story-telling in the extended response).

                I’m not sure what the excuse is here in Vic.

                  1. Marty, I think that’s a simplistic answer and I must disagree. I believe decent CAS-Active questions can be written. I like to think I’ve written such questions this year (much to the chagrin of my students).

                    But there is a reason (not an excuse): The writers and vettors that VCAA appoint are mediocre. They have no understanding of the power of the CAS-technology, they have no solid mathematical expertise, they lack creativity, they lack appropriate literacy skills, there is an inane desire to contextualise questions in absurd ‘non-real life’ contexts … The list of reasons is extensive. The evidence can be seen in every exam.

                    Perhaps there should be a blog that runs a contest on who can write a decent CAS-Active question … I think the results would be very interesting.

                  2. John, this misses the point, and it’s a hugely important point. The question is not whether one can write a decent CAS question. We are not even discussing a CAS exam. The issue is that CAS, whatever its intrinsic merits, destroys anything that is not CAS.

                    This is fundamental, a point that Neil Postman was always hammering. Any new technology does much more than innocently provide new options. It also destroys old options.

                    1. Marty, I do understand the point. But it’s futile and useless trying to test ‘by hand’ skills in Exam 2 – unless the question is asked in such a way (such as including specific instructions) that CAS is excluded. An extreme example would be:

                      “Use calculus and algebra to find the derivative of ….”

                      and make it worth 3 marks.

                      CAS can get an answer but it can’t do the required working. And correct answers without appropriate valid working get zero.

                      But this will never happen because it’s a technology based exam and so “technology must be used”. I know you think the best solution is to get rid of the exam altogether – I disagree from a pragmatic point of view. Technology based assessment is here to stay. So I think the best solution is to make Exam 2 one hour (either all MCQ or no MCQ) and Exam 1 becomes a two hour exam. Then make every question in Exam 2 a question that requires authentic mathematical understanding before a CAS can be deployed.

                      Given that technology is here to stay, at least ensure the questions don’t use technology in a gratuitous and trivial way and that mathematical understanding still underlies its application.

                      But this will never happen either because VCAA wants the subjects to become more about using technology and less about the actual mathematical theory.

                      So we’re screwed, then we die, then a new generation comes in and mathematics is completely lost in schools.

                    2. This is a reply to JF rather than Marty, but this thread has reached its limit on reply depth:

                      JF, I gather that it’s possible to program CAS – at least on the TI, so I’d expect the same from Mathematica, not sure about Casio or HP – to give “working out” for standard processes (finding stationary points, finding a tangent line, etc, etc.) Now maybe CAS might do it’s working out in a way that no human would ever do, but that doesn’t mean it’s wrong. (In the same way that chess engines don’t play like humans, but still find the best move).

                      So forcing students to illustrate a particular method will probably make the situation worse, because then exam performance will be more about which students have learnt how to program their calculators, or have a teacher which knows how to do this, or know someone who can give them these programs, etc.

                    3. HI SRK. I don’t think we’ve reached peak fuckedness just yet, whereby “it’s possible to program CAS – at least on the TI, so I’d expect the same from Mathematica, not sure about Casio or HP – to give “working out” for standard processes (finding stationary points, finding a tangent line, etc, etc.)”

                      And if we have for “standard processes”, then the questions have to be made less standard. For a conscientious writer, it’s an arms race between what you want students to do and what CAS will do. It’s challenging but not impossible.

                      Given that the technology is here to stay, the task is to push for a longer non-CAS exam and a shorter CAS exam. Does anyone know why the CAS exam carries more weight than the non-CAS exam?

                    4. So none of these decisions get re-visited? New Stupid Design, new exam structure.

                      Hmmmph .. I should have thought Stacey would know better. I wonder what her views are now and whether she’s proud of her ‘legacy’.

                      Time for a new legacy.

        2. SRK, I see it as testing the understanding of a functional equation. That seems a worthwhile thing to test. Whether or not it’s fair to test it in a Methods exam, with perhaps no clear precedent, is another question.

          1. Fair enough Marty, but getting a bit legalistic here the study design has the following dot point on functional equations (included under the Algebra area of study)

            “Use of simple functional relations such as f(x+k) = f(x),\; f(x^n) = nf(x),\; f(x) + f(-x)=0,\; f(xy)=f(x)f(y), to characterise properties of functions including periodicity and symmetry, and to specify algebraic equivalence, including the exponent and logarithm laws”.

            Now of course stationary points are also in the study design, and the above dot point is fairly vague, but I’d be surprised if any teachers reading that thought functional equations relating a function to its derivative was fair game. Especially those Methods teachers also familiar with the Specialist course, they’re more likely to think “DEs are in Specialist, not in Methods”.

            But I guess nothing’s in the study design until it’s in the exam.

            1. Yes, SRK, I think you and John are correct. I like the question, but it doesn’t belong here. Already updated the post.

              1. I’m actually OK with part (a) and part (c). It’s part (b) I think is unfair.

                So if the basic premise of the question is kept, and part (b) is deleted, what else could be reasonably asked to beef it back up to 3-4 marks?

            2. “But I guess nothing’s in the study design until it’s in the exam.”

              Very nicely put, SRK. And this is one of the several major defects of the Stupid Design and of the Daft Stupid Design.

                  1. Do you mean
                    1) prove uniqueness of the solution, or
                    2) prove via a derivation of the solution, or
                    3) prove by showing that it satisfies the given functional equation?

                    At this level the style of ‘solution’ is either guess-and-check or ‘verify’ rather than using any sort of systematic technique. Entire textbooks have been written on solving functional equations but you want find any of the theory or examples of application explicated in the Stupid Design.

                    btw I don’t know why functional equations are even on the course. There might have been a good reason once upon a time, but whatever it was, it’s been corrupted and lost over time. No good reason is reflected in the sort of questions appearing on the exams nowadays. Another example of an ‘island’ appended to the Stupid Design.

                    1. I am curious to know how one derives the solution. (An outline will do.) Obviously it’s not unique; f(x) = 0 is a solution.

                      The reason that I ask is because the equation f(x+y)=f(x)+f(y) is complicated. As I recall, one needs to assume something e.g. f is continuous. In fact – and this is beautiful – if f is not continuous then its graph passes through every circle in the plane.

                    2. Both. Any. The point is to work with special choices. That restricts f. Then show that some or all of the possible f work in general.

                    3. @Marty:

                      Thanks for the clarification. The point I wish to make is that the equation f(x+y) = f(x)+f(y) in itself does not characterise a class of functions – except to say that it characterises the set of functions that satisfy the equation. Unless one knows something else (e.g. continuity), one does not know much. For example, if f is not continuous, then, as I recall, the graph of f is everywhere dense in the plane; i.e. passes through every circle in the plane. A lovely result but challenge to draw the graph.

                    4. Hi Terry,

                      I have a mountain of marking to do, so I decided to play with your question about characterising solutions to the functional equation f(xy) = f(x)f(y).

                      We need to specify a framework to work in. I found analytic functions to be a good one for this problem. That’s a fun question.

                      If we broaden the space (for example to smooth functions) then it isn’t clear to me that there is a nice result. But maybe I’m missing something.

    2. Thanks, Glen. My “misframing” was referring what you criticise in the set-up. The intention would not have been to solve the question, but to simply argue from the DE.

  3. Thank you to everyone who has commented so far, and also on the Specialist post. I’ll look at the comments now (while juggling home schooling), and will reply and update the post as I go.

  4. Just regarding MCQ5. I’m someone who has been known to over-use the word equivalent, but I will insist that I do know the error of my ways in the majority of cases (and have long since ceased using the phrase equivalent fractions).

    That said, I do believe that (on occasion) the word equivalent is warranted.

    This question is not one of those occasions, since p=0 kind of ruins the whole argument (of the logarithm).

    1. Another tangent:

      My motto for “equivalent” is that equivalent means equal in a sense; that is, not actually equal. If two things are actually equal, then always the word EQUAL should be used.

      🙂

      If the sense in which things are equal is made explicit, then I think again equal should be used (and not equivalent). So for example I’d say that 1 = 3 \text{ (mod 2)} and not 1 \equiv 3 \text{ (mod 2)}. However, if we were not talking about anything to do with arithmetic mod 2, then I’d probably use “equivalent” and not equal first, and then explain what I meant.

      As a result, “equivalent” comes up only if I’m talking in broad terms about a variety of things (e.g. in an introduction to a paper or something), and basically never while teaching. In fact I have a kind of “ugh” reaction when seeing the word “equivalent” in teaching materials, because I don’t like obfuscation of meaning when teaching.

      1. Regarding modulo arithmetic, I have often heard two numbers are congruent modulo p used instead of equivalent. Is this better/worse/wrong/doesn’t matter?

        Asking because I know some genuine mathematicians stalk this blog…

          1. John Groves… now that was someone who could give a lecture. Had him for 3rd year Number Theory – brilliant stuff.

        1. Yep. “Congruent” is linguistic shorthand for “equal” when talking about arithmetic mod m. It is clear enough when teaching because it was hopefully defined explicitly early in the subject and used clearly and consistently. I have no problem with it.

          Although I don’t like using \equiv as a symbol for it, if only because most people read that as “equivalent” (may be partly LaTeX’s fault). I think I’m in the minority on that. Most mathematicians don’t really worry about equal vs equivalent, IME.

          1. Mathematicians know what they are talking about. Unfortunately, many school students, and more than a few teachers, do not. They don’t know what equals means. That’s why it is so important to use the = sign and to say “equals” whenever possible, rather than a what-the-hell-does-that-mean “equivalent”.

            1. Part of the problem (perhaps?) is that (possibly thanks to CAS) there is this ingrained idea that an equation is there to be solved.

              So when you write cos^{2}x + sin^{2}x\equiv 1 at some level (hopefully) it communicates to students that this is not something to solve, but rather to use.

              Or am I giving too much credit to the CAS machines again?

              1. RF, I’m talking about a more fundamental problem, the fail to recognise that A = B means that A is the exact same quantity as B.

                But that doesn’t rule out CAS causing some other level of screw-up. Can you elaborate on what you’re thinking?

                  1. I see. I suspect the effect of CAS might be worse, that the end result might be that equations don’t mean anything.

    1. That’s pretty weird. It seems unlikely to me that the question was graded that way, but it’s also difficult to see how the report came to have the incorrect answer.

  5. Also, Paper 2, Q5d the radicand should be a+1 not a-1.

    Furthermore, I have a real issue with this being the model answer – since previous examiners reports have been really strict on not having surd denominators…!

    1. As I’ve remarked elsewhere, VCAA are NOT consistent. They are not consistent across subjects and they are not consistent within subjects. VCAA is a total disgrace. These Reports are clearly the final(?? we can only hope) legacy of a nameless disgrace.

    2. Thanks again, RF. Again, presumably just a typo in the report, but a bit weird.

      In terms of the “expected” answer, I am aware of VCAA’s surd fetish, so that expressions such as 1/√2 are, moronically, forbidden. But do they also apply the fetish rule to something like 1/√(a+1) ? That would seem sub-moronic. Can you point to an exam answer where they “rationalise” in such a case?

      1. Seriously, would sub-moronic surprise anyone?

        “previous examiners reports have been really strict on not having surd denominators”

        so teachers will draw the reasonable conclusion and train their students accordingly. But now suddenly there are exceptions. OK, you could argue that the ‘exception’ re-frames the ‘rule’ as

        No *numerical* surd denominators, surds containing a non-constant function are OK.

        Simple enough. But when the exception arises for the first time, how are you meant to know without the benefit of hindsight that it *was* an exception …? VCAA makes up the rules as it goes along, there’s no consistency, no clarity, no certainty, NO *trust*. Maybe the NHT exams are non-canon when it comes to the November exams (the stupidity on the NHT Specialist Exams has us hoping so …)

        Two ‘typos’ (if we’re to be charitable) in the one Report – obviously the same idiots who vet the exams are vetting the reports. It’s not “a bit weird” or “pretty weird”. At best, it’s sloppy. At worst, it’s incompetence.
        Maybe this is why Reports are now being published as word documents – to facilitate do-it-yourself corrections. So in that spirit, I’ve made the necessary amendments and passed on a correct report to my students (and they should get a laugh from it).

        The ‘new broom’ has a lot of mess to try and sweep clean.

      2. I can’t find an example in a VCAA exam as yet, but textbooks are full of them – rationalising denominators, making denominators real in the case of complex numbers… two sides of the same coin as far as I’m concerned.

        1. RF, it seems that in this instance I must defend VCAA. There are three instances I can find (including NHT exams) since 2002 of answers in Maths Methods with a surd in the denominator:

          1) 2012 Q6(a). Both answers were accepted according to the Report.

          2) 2015 Q10(d). \displaystyle \frac{6}{\sqrt{3}} was required to be simplified to \displaystyle 2 \sqrt{3}, which can be reasonably argued is a simpler form.

          3) NHT 2017 Q1(b). Answer was left as \displaystyle \frac{1}{\sqrt{3}}.

          In all answers involving the surd of a function in the denominator, rationalisation was not required.

          So “since previous examiners reports have been really strict on not having surd denominators…!” might be somewhat of an urban myth.
          Then again, what’s in the Report may not match the secret marking scheme (see my comments about Lami’s Theorem in at least two different places

          Hard SEL: The Specialist Error List

          ACARA’s Terms of Reference


          The Report suggests using Lami’s Theorem is OK). VCAA is untrustworthy enough to give this credence.
          Or maybe you heard it in camera at one of the ridiculous ‘Meet the Asses’ sessions.

          As for textbooks … they are often UNexemplary and VCAA can’t be held responsible for their content. Last time I checked, the Cambridge Specialist textbook still had plenty of questions involving the coefficient of friction – which has not been in the Specialist course since 2016 … And of course there are all those questions requiring approximate answers but no hint given of this in the questions …

          1. Thanks, JF. Does that mean that, for example, 1/√2 would be regarded as in acceptable form? That’s good if true, and also astonishing. I have never heard any teacher *not* worry about the rationalising crap.

            1. Marty, my answer is yes. What’s good for the 1/√3 goose is good for the 1/√2 gander. I’d love to see VCAA try and weasel its way out of that one if it wasn’t. And yes, it’s a good thing. And I’ve never worried about the “rationalising crap”, except to point out that things like 6/√2 etc. can be ‘simplified’, and I’m sure I’m not alone.

              RF is probably correct in suggesting that this “rationalising crap” has its origins in textbooks. And it’s probably also a vestigial of Yr 9 (and Yr 10) surds, where students are initially given stuff like 1/√3 and asked to rationalise the denominator. The problem is that this then gets ‘normalised’ in the eyes of (some) teachers as something that must be done all the time. And how many tables of exact trigonometric values of special angles do you see in Yr 11 and Yr 12 textbooks with 1/√2 = √2/2 and 1/√3 = √3/3. Pointless redundancy that further perpetuates the ‘myth’.

              And no doubt some fool at one of those ‘Meet the Money-Grabbers’ sessions has said something at some stage that has further entrenched this “rationalising crap”.

              Speaking of pointless redundancy, I’ve previously noted the stupid redundant use of brackets around integrands. Reviewing the Reports, I’ve noticed an even greater stupid redundancy: VCAA’s persistent habit of writing things like \displaystyle \log_{e} \left( \left | x - 1 \right | \right ) rather than \displaystyle \log_{e} \left | x - 1 \right |. If only VCAA could have the same zeal for important details. I’d have seen this sort of shit many times in the past, but my jaded eyes generally just wash over these Reports and it’s only when I’m looking for something in particular or when something is spectacularly stupid or wrong or both that I consciously see anything.

              1. Thanks JF and Marty,

                A couple of comments I will make (opinion, not fact):

                1. Just because an examiners’ report gives an answer in a particular form does not mean this is what was marked as correct since VCAA has (to the best of my knowledge) NEVER released a marking scheme.

                2. Further to point (1) VCAA’s own rules (study design, examiners’ reports) can be so damned VAGUE that teachers HAVE TO guess what is and is not acceptable. Asking a question at “meet the assessors” is no help because of point (1).

                3. Writing \frac{1}{\sqrt{2}} as \frac{\sqrt{2}}{2} is possibly therefore the SAFER option.

                4. Textbook authors (especially VCE textbooks) one would hope take their guidance from somewhere…

                1. This makes no sense. Why doesn’t someone simply ask VCAA if, for example, 1/√2 is acceptable? Also, on 3, the fact that something is “safer” doesn’t make it free. Compliance costs add up very quickly.

                  1. You are assuming we haven’t asked.

                    I have asked many questions of VCAA over recent years, my favourite was the response I got when I asked if the coefficient of static friction was required in Specialist… the response I got made me feel temporarily stupid for asking.

                    The answers raise more questions than they solve.

                  2. Furthermore… I went as far as to ask a colleague who was marking for VCAA in a particular year. I was told that they were not permitted to speak about the marking scheme.

                    I’m not convinced this was really the case, but it seemed pointless to argue.

                    And before anyone suggests that the solution is to apply to VCAA to be an assessor myself – I gave up after the third “no thanks” letter.

                    1. Isn’t that just a completely unacceptable, untenable position though? How can they not release a marking scheme? How can they not answer a straightforward, earnest question of “How many marks would this answer receive”?

                    2. a) Because no one complains to the authorities. Maths heads are sheep.

                      b) Because it’s not all that important. Who needs a marking scheme for a 2-mark question. VCE maths is 90% such triviality.

                      c) Marking schemes are pseudomathematical garbage, in school and at university.

                    3. RF, VCAA want stooges, not people with intelligence and integrity who will call out crap when they see it. Be proud that you’ve been rejected by VCAA. Be proud that you’re not tarred with the same brush as your idiotic so-called colleague.

                      @Glen: VCAA gets away with it for the simple reason that the vast majority of teachers are either apathetic, stupid, or afraid.

                      (I’m sure the teachers union could do something about it if it had the back-bone. But, after the current EBA negotiation, it will be more of the “Peace in our time” rhetoric that it has spewed out for the last few decades)

                  3. Sorry, but you’re being ridiculous. You ask clear, straight questions to DLL or, now, his temporary replacement. If he doesn’t give you a straight answer, or if he gives you an answer that later turns out to be false, then you complain to his boss. Loudly. And/or you can tell me.

                    If you put up with shit then they will give you shit.

                    1. Who would ever have associated the word “temporary” with bad news.

                      (And “bad news” is probably understating how most feel).

                      Some people just don’t have the decency to crawl under their rock and stay there.

                    2. I can’t seem to reply to Marty directly but… I disagree re: marking schemes. I use them all the time. When leading a team of people in a large subject, they are crucial to having some semblance of consistency in the marking.

                      I imagine for exams taken by orders of magnitude more students, with many more markers (maybe), they would seem to be also important.

                      Unless there is some weird jargon version of “marking scheme” that you’re taking aim at?

                    3. Yes, Glen. I definitely agree. The importance of the marking scheme is to ensure consistency. It’s a huge shame (and a disgrace) that
                      1) the consistency is kept secret,
                      2) the consistency changes from year-to-year.

                    4. Marty, it’s only your comment b) that is (partially) wrong:

                      “b) Because it’s not all that important. Who needs a marking scheme for a 2-mark question. VCE maths is 90% such triviality.”

                      Even a 2-mark question requires a marking scheme to ensure the first mark is allocated consistently. The triviality of VCE maths might make the allocation obvious, but it’s nevertheless needed. And 3-mark questions definitely require a marking scheme to ensure consistency. But no-one is disputing that the marking scheme might be idiotic. Unfortunately, we cannot judge this directly because the marking scheme is kept a secret. Nevertheless, Examination Reports sometimes reveals this idiocy – a good example is that 1-mark “Show that … is a solution to …” question on a Specialist Exam 1 a few years ago. Four lines of work was required, and at least one of those lines was so trivial and obvious that most students would not have included it. Which would explain why the average mark for the state was surprisingly low. (And this is why VCAA don’t want people like RF as assessors)

                      “c) Marking schemes are pseudomathematical garbage, in school and at university.”

                      I’d include the word “usually” in the above observation.

                      “a) Because no one complains to the authorities. Maths heads are sheep.”

                      Maths heads generally don’t want to rock the boat because of the flack they’ll get from above. And some of these Maths heads are VCAA stooges or wannabe stooges.

                2. Important fact 1:
                  The unfortunate consequence of all this is that if you have a correct answer but decide to be ‘safe’ by changing its form, you are potentially ‘over-engaging’ with the question and

                  1) at best you waste valuable time, and

                  2) at worst you waste valuable time AND make a mistake doing something that was unnecessary and therefore lose the answer mark you would otherwise have obtained.

                  Fact 2:
                  The ‘Meet the Money-Grabbers’ sessions is a huge con job. But there seems to be an endless supply of suckers who waste their school’s money by attending.

                  Fact 3: RF, your so-called colleague is a sycophantic idiot. S/he is NOT a colleague. They’re a VCAA stooge. When s/he – inevitably – needs something from you, make sure you say that you’re not permitted to speak.

                  Fact 4: The textbooks always have at least one idiot on the writing team that has delusions of grandeur and likes to look like a guru and give the impression of having ‘inside knowledge’. They are often stooges of VCAA.

                  Fact 5: “the response I got made me feel temporarily stupid for asking.” When this happens, it is nearly always because the person you ask is an idiot who either doesn’t know the answer or is afraid to give an answer or an opinion. In the case of the Asses, this is a certainty. And, to avoid being pinned down and exposed as a charlatan, they will generally follow-up by saying that there’s more to get through and they need to move on. I’d love to see a united front from all attendees when this happens, a demand from everyone present that the question get answered properly. A lack of solidarity (due to apathy and stupidity) is why these fraudsters get away with doing this.

                  Finally a recommendation: You will likely get a timely response to your questions if you send your email straight to the top. Try the Executive Director of Curriculum of VCAA: Say that you’ve had no satisfactory response from the fools in the Mathematics Unit and could your query be forwarded to someone competent and honest. This creates a chain of accountability (but you risk getting a reply that no such person exists in VCAA).

  6. 7/October/2021

    VCAA has published new examiners’ reports with the previously mentioned errors corrected. No mention of “updated” anywhere, which is unusual (this seemed to happen with the November papers).

    1. Yes, I noticed that too. Maybe the number of mistakes in these Reports, given:
      1) how long it takes for them to be published, and
      2) they pretty much only contain answers (some of which are wrong),
      has become too embarrassing for VCAA to publicly acknowledge.

      Maybe you should email VCAA and ask why … It’s a shitful act by VCAA because teachers who downloaded the old reports for their students will not know that the reports have been amended due to errors.

      And notice that the Reports for ALL subjects are now available in both word AND traditional pdf formats …

      1. And now the pdf copies have been taken down for all subjects … But no mention of the update to Methods Exam 2 Report. I think VCAA has a work experience student handling this.

        1. And now the pdf copies are back again for all subjects. I’m getting dizzy. And the amendment has been tagged. If I had to guess, I’d say that some new chum is overseeing this process.
          I’ve noticed recent govt documents all seem to be published in word format (like roadmaps to freedom etc.) – I wonder if this explains why Examination Reports are in word format …? Dumbness decreed from above …?

    2. Thanks, RF. I’ll update the post.

      One hopes that the lack of an “update” flag is simply an oversight, although I doubt it. Worse, to simply delete the incorrect answer to MCQ8, without any acknowledgment that the exam question is plain wrong, is unprofessional and cowardly. And, of course there is no acknowledgment that the solution (and any solution) to B(2)(d)(i) on Exam 2 is complete nonsense.

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