Hard SEL: The Specialist Error List

This is the home for Specialist Mathematics exam errors. The guidelines are given on the Methods error post, and there is also a Further error post.

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2006 EXAM 2 (Here, and report here)

MCQ20 (added 24/09/20) The notation F_1, F_2, F_3 refers to the forces in the question being asked, and seemingly also in the diagram for the question, but to the magnitudes of these forces in the suggested answers. The examination report doesn’t acknowledge the error.

35 Replies to “Hard SEL: The Specialist Error List”

  1. OK, I’ll have a go with 2006 Multiple Choice Q17.

    85% of students gave the intended answer of B and I agree that B is mostly correct, although I would prefer the question to say the *acute* angle or something similar just to avoid ambiguity (if this were a paper 1, would students be marked wrong for writing 315 degrees?)

    Also, is the assumption that the vectors are tails together when the angle is measured?

    Possibly not a “mistake” in the true sense, but the VCAA-induced pedant in me is looking for these things a lot more now.

    1. Hmm. Good question. Obviously not a hanging offence. (Last year’s projection question was a hanging offence.) It’s a matter of convention: what does “angle between vectors” mean in Specialist?

      1. I can’t recall if I’ve been asked this by a student, but the way I think of it: in Specialist we think of vectors as arrows free to move around in space, so first we move both vectors so their tails are at the same point, and then the size of the angle between them is the smallest anti-clockwise rotation required to superimpose one of them upon the other.

        1. And normally I would agree, but this is VCAA.

          Because it is a multiple-choice question, there probably is not a need, since there is only one correct answer given.

          But if it were not multiple choice, I would have liked some more guidance.

        2. Thanks, SRK. Definitely one has to think of vectors with tails at the same point. The only question is whether “angle” between v and w automatically means “acute angle”.

          1. I would like some statement somewhere to say that “angle” refers to the non-reflex angle in the absence of the adjective “reflex”.

            Specifying acute or obtuse in some cases may be considered giving too much of a hint.

            OK, back to the 2007 Papers. SM Paper 1s seem (for the most part) error-free. It is the Multiple choice that I feel may be the major source of errors, with more than one correct answer being the most common “error”.

            1. Sure. again, it’s not a hanging offence, but if VCE convention suggests they should have specified acute, then they should have.

  2. I would also question whether VCAA would mark as wrong all of the following answers since there are no modulus signs in use and the vectors are clearly all different…

    Again, pedantic, so possibly not “wrong” as such.

  3. OK, here is another one that I’m not sure about (the question is fine, it is the report that I don’t like):

    SM 2006 Paper 1 Q5a (4 marks): Show that tan(\frac{\pi}{8})=\sqrt{2}-1

    Examiner’s report: “Quite a few students whose working was correct failed to complete their solution, giving no proper explanation as to why the negative answer should be rejected, or not mentioning the negative answer at all.”

    Now… seriously??? 0 \leq \frac{\pi}{8} \leq \frac{\pi}{2} so surely it is obvious that tan(\frac{\pi}{8}) is positive…???

    OK, if you use a half angle formula there is a *possibility* that the half angle will have a different sign, but not for angles in quadrant 1.

    1. Jesus, this gets old.

      RF, it’s not an “error” by my reckoning, but it is moronic. Yet another example of a decent question turned to trash by the “show that” formation.

      1. OK, so I agree with you in the sense that the question itself is fine.

        The way the question was marked (according to the report) I feel is wrong, or at least hideously unfair to students who would look at this and say “well, of course it is positive” and move on with the exam.

        1. It’s a judgment call, and I’ll think more about it.

          Obviously the intrinsic problem is fine. The question is, what is reasonable to expect as answer given they asked the problem in ‘Show that’ form. The best answer to that is “Don’t fucking asking stupid fucking ‘show that’ questions, you dumb shits”. But, they did.

          Given they did, there is the reality that more than a few students will have bluffed some of the quadratic work.

          1. Agreed. There was no need for it to be a ‘Show’ or ‘Prove’ question. It would have been great as a simple ‘Find’ question.

            And if you’re that worried about students not explicitly rejecting extraneous answers, it could have asked to find the value of tan(7pi/8). Yes, a bit trickier because the half-angle is not as obvious, but surely tan(7pi/8) = -tan(pi/8) is not asking too much of a reasonable Specialist student …?

            Part (b) uses the value of tan(pi/8), but in a totally gratuitous way. Part (b) works just as well if tan(pi/8) is replaced with any other comparable value.

            Is it a VCAA requirement to have a direct link between the two parts of a two part Exam 1 question? Surely a link by topic or theme is sufficient? The ill-conceived motivation to link the two parts via the value of tan(pi/8) is what wrecked what could have been a good part (a) question.

    2. Compare, from the same year, Exam 2, Section B, 5(b), which is more or less the same question (but with cos rather than tan), but in this case students are explicitly told to explain why any values are rejected.

      See also 2009 Exam 2, Section B, 4(c) for this issue in a non-trig context.

      Agreed this is not an error, but it is definitely mixed messaging for students / teachers.

      1. Hi SRK.

        Re: 2009 Exam 2, Section B, 4(c).

        I dislike the “giving reasons for rejecting any solutions.” prompt in this question. The extraneous solution in this case is less obvious than it is for the tan(pi/8) question – but it’s obvious enough and I’d want students, particularly Specialist students, to recognise the existence of extraneous solutions without prompting. Such recognition and rejection without prompting is what’s worth the 1 mark in my book. And surely part (d)(ii) contains a subtle prompt …. (negative volumes, anyone?)

        But I totally agree with the mixed messaging.

  4. OK, I’ll toss my hat in the ring with something that still makes my blood boil 12 years later.

    2008 Exam 1 Q7: The question asks for the exact value of F. No required form for this value is given.

    Using Lami’s Theorem you get the exact value of 120 \sqrt{2} \sin (165^0).

    This answer was NOT accepted. Only the exact surd value of 60 \sqrt{3} - 60 was accepted
    (which you get by either:
    1) resolving forces, or
    2) spending another 6 minutes using a compound angle formula to get the value of \sin (165^0) = \sin (15^0) in surd form, substitute into 120 \sqrt{2} \sin (165^0) and then simplify)

    (I know this because a little birdy told me).

    The Examination Report does not mention any of this, except to make the following snide comment: “Those who correctly used [Lami’s Theorem] usually could not go on to find F”.

    I have no problem with requiring an exact *surd* value – but it’s an error of omission (and dishonest) not to declare this in the question. And it’s an error of omission (and deceitful) not to comment on this in the Report. Either *completely* specify the required form (exact surd value), OR use angles where this issue won’t occur. The stupid thing is that if this question had been on Exam 2, there would be no issue.

    (It’s the same with Specialist questions that want equations of lines, don’t ask for any particular form, but then only accept an answer given in the form y = mx + c).

    1. Not accepting sin(165^{\circ}) is crazy on two fronts:

      1. It IS an exact answer.
      2. Lami’s theorem is so often the more efficient way of solving problems with triangle of forces that to not allow it is penalising students for being efficient and seems totally wrong.

      1. RF, I hate to play assholes’ advocate here, but the fact that a certain technique is sometimes or commonly more efficient/successful doesn’t mean it always is. The question is to what extent, and how, should exam questions be designed to have students handle such issues.

    2. I’ll have to think about this one. The expression “exact value” is more problematic that is commonly understood; the \sqrt{\phantom{3}} in \sqrt 3, for example, is cloaking our general inability to deal with real numbers in an “exact” manner. It’s not really a value, let alone an exact value. And, how can a value be “inexact”? Nonetheless, \sin 165 feels less answerish to me.

      1. @Marty: I agree that 120 \sqrt{2} \sin (165^0) feels “less answerish”. Nevertheless the issue is whether or not it answers the question that was asked and, if not, on what grounds does it fail. I wonder whether \displaystyle 120 \frac{\sin (165^0)}{\sin (45^0)} would have been accepted (and if not, why not).

        @RF: I totally agree. I don’t move in the ‘right circles’ but every now and then I do meet little-names who know things. It’s a total disgrace that you can only find these things out by accident. The default required form of a line is one that really gets up my nose – you won’t find it written anywhere in a Report.

        In the Lami’s Theorem case, info from a little-name led to me chasing a big-name down a walkway at a 2008 conference, yelling for an explanation (big-name sought refuge in a packed lecture theatre and unfortunately the talk taking place was not about the social benefits of gladiatorial contests). But apparently we’re meant to know that ‘hybrid’ answers are not acceptable (whatever the hell a hybrid answer is).

        Nowadays I tell my students to only consider using Lami’s Theorem
        1) in Exam 2, or
        2) if they can see (during reading time in Exam 1) that only special angles are involved. So valid methods get held hostage by VCAA-idiocy.
        Otherwise resolve the forces.

        @RF (again): I totally agree that using efficient methods should not be penalised if they give ‘less preferred’ answers. It’s up to the writer to make sure things like this don’t happen. In reality, is 120 \sqrt{2} \sin (165^0) any less practical/useful/meaningful than 60 \sqrt{3} - 60?

        1. JF, I’d make the tu quoque response, is 120\left(\sin\left(\frac{\pi}{3}\right) - \cos\left(\frac{\pi}{3}\right) \right) any less practical/useful/meaningful than 60\sqrt{3}-60?

          Personally, I’m not too bothered by this one. Using compound angle formulae to calculate trig ratios of multiples of \frac{\pi}{12} is something that I’d expect all Specialist students to be familiar with from Year 11, and then return to in a variety of contexts in Year 12 – circular functions, complex numbers, vectors, dynamics. One could even throw it in when calculating a definite integral and angle between tangents. (It’s a bit like \sqrt{x^2} = \lvert x \rvert, you know the students will forget, so regular spaced reinforcement is required). So while these don’t quite have the hallowed status of the 30-45-60 values, I think it’s fair game for Specialist. I also don’t think this view overgeneralises, since \sin\left(\frac{\pi}{12}\right) can be calculated in one line from a single use of a compound angle formulae from the “special” angles, unlike more recherche cases like \sin\left(\frac{\pi}{10}\right).

          None of this is to disagree with the broader point about the lack of clarity and transparency from VCAA about is considered an acceptable form of a final answer, when none is specified.

          Also, putting aside the merits of this question as an *exam* question, I did find it an instructive example to go through with my students, just on this point of how to decide between resolving forces into rectangular components or using sine / cosine rule.

          1. Hi SRK. My only objection to 120\left(\sin\left(\frac{\pi}{3}\right) - \cos\left(\frac{\pi}{3}\right) \right) is that there’s probably some arcane VCAA convention known to maybe 12 people in the world that requires trig(special angle) to be simplified:

            For many years many of us knew anecdotally (thanks to little birdies) that VCAA did not accept numerically correct answers such as 0.23/0.47. It had to be 23/47. Only in the last few years has VCAA deigned to include this important information in a Report. So who knows what other arcane VCAA bullshit lore is out there.

            Your proposed answer answers the question so it has to be accepted. Or an explanation given as to why it’s not accepted.

            Now here’s the problem – there are clear and numerous precedents where VCAA explicitly prescribe/micro-manage the form in which they want an answer. OK, I’m fine with that. But when this doesn’t happen in a question, there’s a very reasonable expectation that any reasonable form (within the parameters specified by the Reports) is acceptable. Except this is not what happens. It gets decided behind closed doors that only one form of answer is acceptable and all other forms are wrong. In the question under discussion, some idiot retrospectively decided that only exact *surd* form was acceptable, and didn’t have the guts to explain in the Report *why* the simple ‘hybrid’ form obtained from Lami’s Theorem was wrong.

            All of the above applies to:

            1) Questions where the equation of a line is the answer. Even when it’s not stated in the question, only the form y = mx + c is accepted, apparently. How is the average teacher expected to know this? From the Report, you would hope. Nope. Unless they’re an assessor or meet a little birdy, they won’t know and will blithely think the slope-point form y - y_1 = m(x - x_1) is OK.

            2) Questions where g appears in the answer. In the absence of an instruction, when to substitute g = 9.8 and arithmetically simplify and when not to …? Surely both should be accepted, particularly when the exam DEFINES g = 9.8. Except sometimes they’re not both acceptable. It should state in the bloody question!

            VCAA has shown on numerous occasions that it can be a petty pedantic prick. But it never seems to be pedantic for important things like specification of syllabus in a Study Design, exam questions, Reports …

            This is wrong, unfair, unjust and stupid.

  5. …and another thing that annoys me, while we are on the topic…

    All these “a little bird told me” snippets are really useful and very interesting, but it does sort of imply that unless a teacher moves in the right circles (MAV may suggest that their “meet the assessors” sessions are the right circles, but recent evidence on this is… inconclusive) they do not learn these very valuable insights and their future students suffer as a result.

    I have no doubt it happens in a lot of subjects, but is it FAIR?

    1. The broader and ultimate unfairness is that VCAA is not transparent in how the exams are marked. I do not understand how VCAA gets away with not making the marking scheme available.

      If the MAV did not have such an unhealthy incestuous relationship with the VCAA, it could be a genuine voice of Victorian Mathematics Teachers and demand the marking scheme be made publicly available.

  6. Could this be an error – NHT 2018 Exam 1, Q8c
    Any ray passing through the centre will be perpendicular. (Or does “in the form Arg(z)=a” imply rays starting from the origin?)

    1. It is my understanding that Arg(z)=\theta means the ray starts at the origin, whereas Arg(z-z_{1})=\theta means the ray starts at z_{1}

      Again, though, I have never seen this formalised in a VCAA report or curriculum document.

      1. A couple of clarifications:

        1) Marty’s comment (below) could be misconstrued as implying a definition.

        “Arg(z) always refers to the (appropriate) angle that the line from O through z makes with the positive real axis.”

        is a mathematical fact. Consider Arg\displaystyle (z) = \frac{\pi}{4}. So you want values of z that have a principal argument of \displaystyle \frac{\pi}{4}. Clearly they lie on the line y = x with x > 0, noting that if x = 0 is on this line then z = 0 and Arg(0) is not defined, so this value is not included and you have a ‘hole’ at the origin. In other words, the part of the line from (but not including) O through z that makes an angle \displaystyle \frac{\pi}{4} with the positive real axis.

        In a similar way, Arg\displaystyle (z) = - \frac{\pi}{4} defines values of z lying on the line y = -x with x > 0. In other words, the part of the line from (but not including) O through z that makes an angle \displaystyle - \frac{\pi}{4} with the positive real axis. Note that the negative in \displaystyle - \frac{\pi}{4} means clockwise form the positive x-axis. Pick any value of z lying on this ‘half-line’ (that is, ray) and it will have a principal argument of \displaystyle - \frac{\pi}{4}.

        2) For Arg(z - z_1) = \theta, the value of z such that z - z_1 = 0 is the terminus (starting point) of the ray but is NOT included (open circle) because at that point you have Arg(0) which is undefined.

    2. Hi, BWS. The question is fine (and nice, but with poor sentence construction). Arg(z) always refers to the (appropriate) angle that the line from O through z makes with the positive real axis.

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