Secret Specialist Business: Exam 1 Discussion

This is our post for teachers and students to discuss Specialist Exam 1 (not online). There are also posts for Methods Exam 1, Methods Exam 2 and Specialist Exam 2.

UPDATE (10/09/21) The examination report is here (a Word document, because it’s stupider). Corresponding updates, are included with the associated question, in green, and see also here and here.

UPDATE (31/12/20) The exam is now online.

UPDATE (29/11/2020)

We’ve finally gone through the exam, we’ve read the discussion below, and here are our thoughts.

In brief, the exam is OK but no better, and there are issues. There is some decent testing of skills, but the emphasis (as in the Methods 1 exam) appears to be on fiddly computation rather than deeper concepts. That isn’t great for a 1-hour sprint exam, and commenters have suggested the exam was overly long, but of course a 1-hour sprint exam is intrinsically insane. At a deeper level, some of the questions are contrived and aimless, which is standard, but it feels a little worse this year. And, there are screw-ups.

Here are our question-by-question thoughts:

Q1. The kind of pointless and boring mechanics question whose sole purpose is to make mechanics look bad. Part (a) asks students to compute the normal force, but to no end; the normal force is not required for the rest of the question.

(10/09/21) Apparently there is an issue, every year, of whether g = 9.8, or g = g. Given VCE contains no proper mechanics (which would require g = g), we couldn’t care less. But it’s the kind of trivial matter that teachers and students must worry about, and which means they’re too busy to teach or to learn mathematics. In any case in 2020, and in 2018, g = g. In 2015 and 2016, however, g = 9.8. Go figure.

UPDATE (02/02/2022) As tom has indicated below, Part (b) is fundamentally flawed, since it is expecting students to treat the acceleration as a scalar rather than as a vector. In particular, a non-sensical remark in the examination report suggests that students who gave the negative answer were invalidly marked down. tom has also noted that 1(a) is, in some sense required for 1(b), although, more accurately, this points towards the stupid wording of 1(a).

Q2. An intrinsically nice question on integration by substitution, which shoots itself in the foot.

(10/09/21) The examiners are clearly unaware that their foot has been shot off.

Q3. A routine and nice complex roots question.

Q4. A good inequality inequality question involving absolute values. The question is not difficult but, as commenters have suggested, it seems likely that students will do the question poorly.

Q5. A pretty nice vector resolute (projection) question, sort of a coherent version of last year’s debacle. Part (a) is contrived and flawed by having to choose the integer solution from the two roots of the quadratic; it’s not a hanging offence, but it’s the kind of oddity that would make a thoughtful writer think again.

Q6. A mess. See the comments below, and here.

(10/09/21) Part(a) is a 1-pointer requiring students to “show that” the derivative of \color{OliveGreen}\boldsymbol{f(x) = \arctan(3x-6) +\pi}  equals  \color{OliveGreen}\boldsymbol{\frac3{9x^2 -36x + 37}}. The examination report provides the solution

    \[\color{Blue}\boldsymbol{f'(x) = \frac{3}{(3x-6)^2 + 1} = \frac3{\left(9x^2 -36x + 37\right)}}\,,\]

and then remarks

Students needed to demonstrate the use of the chain rule to find the (given) answer.

What does that mean? Has the report’s solution demonstrated use of the chain rule? How?

The larger issue is with Part (b), instructing students that they should “Hence” show that f has an inflection point at x = 2. The “hence” would seem to indicate some kind of first derivative argument is expected, but the report indicates a standard second derivative argument. For people who fusspot everyone to death over words, that’s pretty stupid wording. Especially so, given that the only step indicated in Part (a) is to expand the square, which is entirely irrelevant to the application in Part (b).

Q7. An OK if (for a Specialist exam) unusual integration question involving continuity and differentiability of a “hybrid function”. The wording is clumsy, since all that is required is to demand that the function be differentiable; continuity of the function is then automatic, and the demanded continuity of the derivative is irrelevant. Sure, spelling out the continuity may simply be being nice, but including the continuity of the derivative suggests the examiners don’t really get it, or are planning a sleight of hand. We’ll see. Given the most authoritative (Methods) textbook makes a complete hash of this topic, it will be interesting to see if the examination report can get it right. We wouldn’t be betting the house on it.

(10/09/21) Yep, they squibbed it. No indication of what is required for a function to be differentiable at a join.

Q8. An ok but ridiculously contrived volume of revolution question. Asking for the volume to be given in the form \boldsymbol{2\pi(\log_e(a) + b)} where \boldsymbol{a, b \in \mathbb R}  is needless, ill-defined and dumb.

(10/09/21) There goes the other foot.

Q9. An OK but ridiculously contrived arclength question. The introduction of the symbol \boldsymbol{s} for the arclength is gratuitous and confusing. And (reviews notes), asking for the arclength to be given in the form \boldsymbol{\log_e(m) + n\log_e(p)} where \boldsymbol{m,n, p \in \mathbb Q}  is needless, ill-defined and dumb.

(10/09/21) And there goes the third foot.

44 Replies to “Secret Specialist Business: Exam 1 Discussion”

  1. OK, I’ll start…

    I liked the exam in many ways, although I did feel it was a bit easier than previous years. Some mildly challenging partial fractions and an arc-length problem that allowed students to miss a negative in the final integration, but all in all a nice test of skill.

    The appearance of arctan(\sqrt{3}) twice was unusual in a small way, to me at least.

    I do want to see if students were expected to label the y-intercept on the “sketch the graph” question. But not holding my breath for the report.

    1. I agree, RF. I liked it too. I thought it was *mostly harmless*. I liked the necessity of partial fraction decomposition (unprompted) in Q8 (furthermore it’s been a while since an irreducible quadratic appeared in that context).

      Re: The y-intercept. It shouldn’t be required on the “sketch the graph” question since it’s not asked for in the question statement:

      Question 6(c): Sketch the graph of [\displaystyle f(x) = \arctan{(3x - 6)} + \pi] on the axis provided below. Label any asymptotes with their equations and the point of inflection with its coordinates. (2 marks)

      However, I think the y-intercept will need to be shown in the ballpark of the correct location relative to the given scale (so a bit above \displaystyle -\frac{\pi}{2} + \pi = \frac{\pi}{2}) or the ‘shape mark’ might not get awarded.

      My main gripes:

      Q1(a): What (secret) form of answer will be required? Will the substitution g = 9.8 be required?

      Q6(a): How much trivial working (for 1 mark) will VCAA require to

      “Show that [the derivative of \displaystyle f(x) = \arctan{(3x - 6)} + \pi] is \displaystyle f'(x) = \frac{3}{9x^2 - 36x + 37}“. (1 mark)

      Q6(b): Not a lot of writing space to get f”(x), show f”(2) = 0 AND show change in concavity across x = 2 ….

      I also thought the exam was a bit long – it won’t surprise me if quite a few students didn’t finish it.

      I predict Q4, although simple, will be poorly done (and I’m OK with that):

      Solve the inequality \displaystyle 3 - x > \frac{1}{|x-4|}. (4 marks)

      1. Re: 6(b)

        Hi John friend!

        I wonder if VCAA do not intend for the change in concavity to be shown/tested for? The “Hence” that prefaces the question definitely threw me.

        Does the following check? If so, could this be the intended method for solution?

        Completing the square on the denominator of part (a) allows you to show that the derivative is positive for all values of x, so f is an increasing function.
        Setting f”(x) = 0 allows us to find that x = 2 is the point of maximum gradient.
        These facts together imply that there is a point of inflection at x = 2, as an increasing function with a unique maximum derivative must change concavity.
        So perhaps you were able to get away without testing/showing concavity changes about x = 2?

        1. It will depend on the intelligence of VCAA … Hopefully some of the assessors have a brain might have raised this.

        2. MyCool, your understanding of Q6 is much clearer than that of the examiners. God knows what the examiners intended for 6(b), but note MCQ 4 of the 2014 Methods 2 Exam (and similarly on the 2007 exam), which is noted here, and which is discussed in detail here.

      2. Thanks, JF. I mostly agree. It was pretty computationally heavy, which isn’t great for a sprint exam. As with Methods 1, I wonder if this was a conscious strategy, an attempt to be “nice” to students who hadn’t had as much explanation this year; if so, I think the attempt probably failed. I agree on Q4 and the Three-card Monte of Q1. Q6 is a complete mess, which I’ll address soon.

    2. I’m surprised to hear you say that you thought it was easier than previous years. I thought it was definitely harder than last year’s exam 1 (which I thought was the easiest for some time), and no easier than the other Exam 1s from the current study design (2016-2018).

    3. Thanks, RF. I wonder if the not asking for the y-intercept was an oversight. If so, I can’t imagine the VCAA would still require it.

      1. Marty, I don’t think it was an oversight. Maybe they thought that students might (wrongly) think that there’s no exact coordinate and therefore screw up 1 of the 2 marks (a small bone tossed to them in a pandemic year). After all surely \arctan(-6) + \pi is not exact. Where are the surds …?

        Or maybe they thought that requiring it would make the question worth an extra mark – a mark that couldn’t be spared.

        I think it’s disappointing that there’s little emphasis in Specialist Maths on exact values written in symbolic form (like \arctan(-6) + \pi). What I’d love to see on Exam 1 is something simple like

        Solve cot(x) = -3 for 0 < x < 2pi

        or the same but no restricted domain.

        Save the tan(x) = Sqrt[3] stuff for the rote learners in Methods.

      2. No , I don’t think it was. A few years ago (maybe pre-2016 even) there was a question involving a trig graph and the question didn’t specifically ask for x-intercepts to be labelled. The examiners report (smugly, in my opinion) commented that a lot of students wasted time finding and labelling x-intercepts that were not specifically required by the question.

    4. Thanks, RF. Having finally gotten to go through the exam, I’m less positive on the exam, although, except for one question, I’m not strongly negative. I’ll post my question-by-question thoughts today or tomorrow.

  2. Yes, I really liked Q4 but admit that I think I accidentally helped myself by quickly sketching both graphs to get a sense of (1) how many solutions and (b) whether they were positive or negative or crossed from one to the other.

    Q1a is a permanent bug-bear. To me, g is exact, but then they say g=9.8, so I’m always puzzled as to whether I’m meant to substitute (and the examiner reports don’t help)

    Q6 – I’m not sure how harshly they will require showing the change in concavity. It is kind of obvious for a tan graph (or its reflection, in this case) – maybe?

    1. Re 1a: My understanding – and hopefully someone with more credibility can confirm this – is that (1) if no form for the answer is prescribed then leaving answers in terms of g is accepted but (2) if the question asks for the answer to be written correct to one decimal place or the nearest integer, or something like that, then you must substitute g=9.8.

      1. Sure. On paper 2 I have no issue as the questions often ask for a set number of decimal places. Paper 1 I have an issue in that:

        Either they want you to substitute 9.8 for g

        Or they shouldn’t write g = 9.8 on the exam paper.

      2. Hi SRK. Your understanding is what any *sane* person would think. But you must remember that we are dealing with idiots. Take the Specialist Maths 2015 Exam 1 Question 2(a):

        The question does not prescribe a form for the answer. But the *snort* Confidential Marking Guide (a battered copy of which blew right into my face while I was exercising on a VERY windy day and then blew out of my hands after I’d read and memorised it) *EXPLICITLY* said that an answer in terms of g is NOT to be accepted. g = 9.8 had to be substituted and the answer simplified to 220 Newtons. The deliberately deceitful and untrustworthy Examination Report fails to mention this important piece of information.

        So my understanding (based on information that VCAA refuses to disclose in its Examination Reports) is that g = 9.8 must be substituted if the resulting arithmetic calculation is not ‘difficult’. To put ‘difficult’ into perspective, the answer g/13 WAS accepted for the Specialist Maths 2018 Exam 1 Question 1(b) (and this is also stated in the Examination Report). So simplifying 9.8/13 = 98/130 = 49/65 is presumably considered ‘difficult’.

        Personally, I think VCAA just make it up each year. There is no consistency and you’re potentially damned if you do and damned if you don’t each year.

        1. Hi, John. The 2015 examination report does indicate the intended answer of 220, so I’m not sure how the report is being deceitful, although the extra half-line of calculation wouldn’t have killed them.

          Of course your main point is that VCAA should be clear and consistent in whether they want g or 9.8, and the whole 2015 question is weird and a little silly. To begin, 2 marks for either 20 x 9.8 or 20 x g is pretty ludicrous. Secondly, the examination report whines about students writing the force as negative, but no positive direction has been indicated in the question. Moreover, in part (b) they explicitly ask for the “acceleration of the lift downwards”; with hindsight it is clear from the examination report that they wanted the magnitude of the acceleration, but that interpretation of the question isn’t totally obvious to me.

          There’s always conventions and tricky wording with up-down acceleration problems, but this all feels very clunky.

          1. OK. They give the answer of 220 but never explicitly say that an answer in terms of g was not accepted and lost 1 mark. How hard to make this clear. Of course, VCAA engages in this sort of deceit so that it doesn’t have to answer questions such as when it is and isn’t OK to give an answer in terms of g. Because, as I noted with the 2018 exam, suddenly it IS acceptable. This is a non-trivial issue because you don’t want a student to things they don’t have to do and hence expose themselves to increased risk of making a careless error and hence needlessly losing a mark. And yet this is exactly what VCAA seems to want.

    1. It is the subject with the highest number of enrolments amongst the subjects classified as “Mathematics” by VCAA.

      Truth is, so much of what the FM exams actually test is not really Mathematics (opinion) although it could be if:

      1. The questions weren’t so repetitive from year to year (again, opinion)
      2. Calculators and notes were not allowed for every single assessment (again, opinion)
      3. The statistics section actually asked meaningful questions requiring a minimum level of thought, unlike the “memorize (or write in your bound references) these sentences and write them at the appropriate times to get full marks for the explanation” questions which are currently seen (again, opinion)

      In short: see what Marty said in response.

      1. I like the idea of the bound reference. Used well, it can be a great benefit to the student. I usually keep notes in a bound reference when I read a non-fiction book. This certainly slows me down in reading but the process helps me to understand the work.

        Some students create good bound references. Such resources don’t need to be polished or works of art to be useful.

        Some students have no idea how to do this. I have noticed that students are not particularly good at taking notes of any sort. One might blame the ubiquitous laptop for this.

        Some students buy a bound reference from students who completed the subject in the previous year.

        I have seen professionally designed bound references for Specialist Mathematics. These are in the form of semi-notes where students can fill in the blanks.

        The real value of the bound reference lies in the preparation rather than as an aid in the examination.

          1. Once upon a time, students could take in an A4 sheet of notes annotated on both sides. Then the CAS calculator was piloted. The CAS and non-CAS (graphing calculator) students did the same Specialist exam and the Methods Exam was more or less the same too. It was pointed out that the CAS calculator could store the equivalent of 100 or so pages of notes. So it was decided that everybody could bring in a bound reference in order to even out this. The CAS calculator ultimately replaced the graphing calculator but the bound reference stayed because … well I don’t know why. Either because an dickheaded moron decided it was a good idea to retain it, or a dickheaded moron was incompetent in not thinking things through. So it’s a vestigial of the Pilot CAS calculator era.

            Apart from all its other detrimental influences, the introduction of the CAS calculator facilitated the establishment of massively over-inflated reputations of many teachers as mathematical gurus that I doubt would ever have happened otherwise.

            And now you have Mathematica … students can bring in a bound set of notes AND a USB stick storing as many nb (notebook) and pac (paclet) files as they want.

  3. On Q7, I wonder if the reason why we are told that the derivative is continuous (and not merely that it exists) is so it is obvious that m, n can be found by solving m = \frac{-8x}{(1+x^2)^2} at x = 1, rather than by considering the difference quotient. In this case if the derivative exists then it is continuous, but I can appreciate that it’s better to not require students to recognise that. (Although, more generally, I did find this an odd question for a SM exam)

    1. Thanks, SRK. Yes, I think this is probably the point of the wording. “Given that” the function has a continuous derivative, then your suggested method of matching derivatives on the left and right is legitimate. But, as I was suggesting, this amounts to sleight of hand: nothing in the Cambridge text nor, I venture, in any other VCE text, clarifies the relationship between this matching of derivatives, the question of differentiability at the problem point, and the question of continuous differentiability. There will be very few students, or teachers, who will understand why the legitimate approach is indeed legitimate.

  4. Re: Update (29/11/2020) question-by-question thoughts.

    1) Well, it’s hard to do anything inspiring with mechanics given the systematic erosion of its content over the years. And the proposed Stupid Design shows why this happened.

    5) I wonder if “having to choose the integer solution from the two roots of the quadratic” was deliberate in order to nudge students towards trying to factorise the quadratic. If so, I’m not sure it was successful – I know many students who attempted to use the quadratic formula rather than attempting a routine factorisation (probably put off by the superficial difficulty of factorising). One could argue it would have been better to cook the question better so that the quadratic factorisation was more obvious.

    6) Yes, 6(b) is pure dumb-ass wording.

    7) Re: “continuity of the function is then automatic” when a function is differentiable.

    I doubt it’s automatic in the minds of many students. So I prefer your hypothesis that “spelling out the continuity [of the function] may simply be [VCAA] being nice”, rather than the hypothesis that VCAA does not understand the statement is irrelevant. I think most students would use the continuity of the function with or without the explicit nudge – but only out of desperation to get a second equation.

    Regarding the oddness. Yes, I can think of better things to ask. Alternatively, I can think of a different function to use (to *ahem* differentiate part (a) from simply being a Methods question). As written, I don’t see the point of part (a) – it belongs on a Methods exam.

    2), 8) and 9) Yep, the whole “Give you answer in the form …” instruction is really starting to wear thin. Three questions … VCAA made the most of an opportunity to shoot itself in both feet and also the hand. I think you’re right – it’s just VCAA trying to make the marking easier. But they missed a trick to be supercilious with Q8 – only the very worst students will forget the 2pi …

    Re: 8). Yes, the function is contrived. But I’m OK with that. I’m OK with using a volume question as a vehicle for testing integration and hence the function being contrived.

    1. Thanks, John. Re (1), yes the mechanics in Specialist has been fifth-columned to death. I was planning to make this comment on the draft post at some point. Re (5), you might be correct, although it feels to me more of a question that naturally gives a two-solution quadratic, and the restriction to integer was just a clunky way to specify one solution. Re (7), yes I think it likely that including continuity was conscious spelling out, and I’m basically willing to give it a pass. Although, the in-fact reasonableness of spelling it out demonstrates the whole topic is mush theory. Re (8) and (9), I’m not usually too nitpicky on contrived functions, especially for arclength and revolution. Still these were pretty damn contrived, and they concluded an exam brimful of contrivance and aimlessness.

    1. Thanks, SRK. Uni lecturers are very familiar with the difficulty of coming up with natural arclength (and surface area) questions for which √(stuff) works out nicely. As I wrote above, I wouldn’t look to beat up VCAA too much for the contrivances. But Q8 is particularly contrived, and the whole exam is full of “huh?”.

  5. Question 1 – a problem that nobody has raised?

    Teaching Specialist for the first time, so my initial venture into Specialist Exams. The first question that I read has a dubious solution. Let me remind you; given a 2 kg mass on a smooth surface with forces as shown below. Find
    (a) “the normal reaction force, in newtons, that the surface exerts on the mass”,
    (b) “the acceleration of the mass, in ms−2, after it begins to move”,
    (c) “how far the mass travels, in metres, during the first four seconds of motion”. 

    The examiners’ report for (b) says the answer is \frac 54 (2-\sqrt{3}) and then “As 10 \cos(60^\circ) > 5 \cos(30^{\circ}), a correct equation of motion was 2a = 10\cos(60^\circ) - 5\sin(30^\circ)“.

    {\em Concern 1} Acceleration is a vector. So is it left, or right, or maybe at an angle up …
    Actually there are 2 correct answers: \frac 54 (2-\sqrt{3}) to the right or \frac 54 (\sqrt{3}-2) to the left. My fear is that a student who gave the second answer has lost marks. Certainly the examiners should lose marks for treating acceleration as a scalar.

    {\em Concern 2} The examiners seem to imply that one must decide whether 10 \cos(60^\circ) > 5 \cos(30^{\circ}) in order to obtain a correct equation of motion. A physicist would approach this problem by first defining a coordinate system, basically deciding which direction to take as positive. If we take a displacement axis to the right in the diagram then the equation of motion results as the one given. If we take it left, then we get
    2a = 10\cos(5\sin(30^\circ-60^\circ) ). A Year 12 student is supposed to learn that either way is correct; an acceleration of 50 m/{\mbox s}^2 right is the same as -50 m/s^2 left. It is one of the great achievements of algebra that we do not need to consider which force component here is greater. This enables us to easily handle more general questions, say where the two forces shown have arbitrary magnitudes.

    I also find myself disagreeing with Marty’s comments.
    1: “The kind of pointless and boring mechanics question whose sole purpose is to make mechanics look bad”
    The question requires one to know that the horizontal and vertical components of motion may be considered independently. This is one of Galileo’s great discoveries. So I feel this question has more depth than any other.

    2: “Part (a) asks students to compute the normal force, but to no end; the normal force is not required for the rest of the question.”
    On the contrary, if the reaction turned out to be negative, then the resultant force is actually upward. So the body would leave the surface. This means that the acceleration required in part (b) would have an upward component.

    1. Thanks very much, tom, and I’m sorry it took so long for your comment to appear. I’ve been very busy, and just noticed now your comment was stuck in the spam box.

      I agree with you, that 1(b) is screwed. I also agree that the remark in the exam report is idiotic, and the remark strongly suggests that students who gave the negative answer, \boldsymbol{\frac54}(\sqrt3 -2), were incorrectly marked down. I will add an update above, and add an entry to the Specialist Error List.

      As for disagreeing with my comments, I think you are mostly correct to slap me, but I think you have the wrong ends (?) of the stick:

      (i) You are correct, that in effect one must compute the (possibly mythical) normal force, to see whether the block leaves the ground. But what this really indicates is the woeful wording of 1(a). it is not the “normal force” that matters, but rather whether the vertical components of the indicated forces win against the gravitational force.

      (ii) The fact that one must consider (something akin to) the normal force to properly answer 1(b) is clearly not expected by the examiners. That is, 1(a) has no meaningful input into 1(b) for the purposes of the exam question.

      (iii) Galileo-Shmalileo. Your florid praise doesn’t change the fact that the question is boring and goes nowhere.

      1. I’ll make a couple of comments here:

        1) VCAA has a shameful history of lazily asking for a ‘vector’ when what it actually wants is a ‘scalar’. The evidence is in the Examination Reports, where ‘scalars’ are given as the answers for ‘vectors’. The 2020 Report delivers the same slop.
        Obviously Tom is correct in asserting that acceleration is a vector. The question should have asked for the size or the magnitude of the acceleration. Then there would be no problem (about from banality). It’s worth noting that the motion is linear and therefore the direction of the acceleration is defined by deciding which direction is the ‘positive’ direction (and therefore which is the ‘negative’ direction). The Report implicitly takes the positive direction as the direction of motion. This is the natural choice but, as Tom points out, it’s not the only choice. The answer given by VCAA (or a student) is meaningless until the positive direction is defined.

        2) Finding the \displaystyle size of the normal reaction force (to make the appropriate correction to the question) is obviously relevant to later parts because it establishes the fact that the object stays in contact with the surface. But, as Marty credibly suggests, the writers probably didn’t think of this. They probably included part (a) simply to have something to ask on a topic that has been systematically laid to waste by VCAA.

        3) Re: Galileo’s great discoveries. I’m with Marty here. And I doubt the writer(s) of the Exam (or the Stupid Design) would be familiar with Galileo and his insights. We may as well say that a banal graphing question represents one of Descarte’s great discoveries and so should feel that such a question has more depth than any other …

        The question is yet another fine showcase for the ‘competency’ of the writer(s).

        1. Thanks, John. I’m sure you are correct, that plenty of other exam questions are flawed with the same scalar-vector confusion. (I’ll happily add any such occurrences that people note to the Error List.) I think what got under tom’s skin (and my skin) with this example is the ridiculous remark in the examination report, seemingly trying to justify the *not* giving full marks for the negative answer.

          1. There’s a strong \displaystyle implication that VCAA did not accept the negative answer, but this is never explicitly stated. In fact, a charitable interpretation of the wording that *a* “correct equation of motion …” (rather than *the* “correct equation of motion …”) might suggest that the negative answer was also accepted … But we’ll never know of course because of the secrecy VCAA imposes on its marking scheme (which, by the way, is a total disgrace).

            Be that as it may, VCAA can’t hide the fact that it incompetently treats vectors such as acceleration as scalars.

            2019 Exam Question 9 asks for the tension rather than the size or magnitude of the tension. (I’ve always considered tension a force, but I’m happy to be told that ‘tension’ means the scalar and ‘tension force’ is the vector …) This type of error will have many entries (and only a masochist would look for them all), so if you’re going to add to the Error list, I’d suggest a simple generic ‘Treating a vector quantity as a scalar quantity’ entry with a couple of recent examples.

            1. Thanks, John. I’m not troubled by the tension one, even if technically sloppy (and I’m not sure).

              In terms of the Error List(s), I’m really not fussed, and I’m definitely not going to hunt for further errors. But I like the format of the list as it is, with errors listed exam by exam. That would be muddied by indicating as well categories of errors.

      2. Thanks Marty 😉

        I was tidying up the format of the post for about 5 minutes when it disappeared – certainly not the normal time allowed. Having spent a long time on the original wording, I did not have the energy to submit again. Glad to see you found it.

        Looks like we differ on what makes a good question. I’m sure most teachers just treat dynamics questions with a rote method, without wondering where did the method come from, and what are the assumptions. But isn’t that true for every topic? I try to follow the historical development where possible. Thinks: Is it possible to write a question that brings out the independence of the components of motion?

        1. “I’m sure most teachers just treat dynamics questions with a rote method, without wondering where did the method come from, and what are the assumptions.”
          I agree, and that gets passed on to students. But VCAA’s systematic destruction of mechanics brought mechanics to a point where that’s all it was – nothing more than applying (step by step) a rote learnt recipe.

          Tom, \displaystyle every mechanics question brings out the independence of the components of motion. I don’t think the sort of question you’re really thinking of (getting students to ponder \displaystyle why this can be done) belongs in Specialist Maths, certainly not under any of the Stupid Designs (in other words, not during VCAA’s tepid reign). It more naturally belongs in physics (along with questions like why does the motion of the center-of-mass model the motion of the entire system of particles etc)

          The reality though is that many things are treated with a rote method (statistics, anyone?)

          1. Of course I did not claim that such a question belongs in Specialist Maths. Just dreaming – how would one examine such understanding? But even with the current subject I hope that there are good teachers out there that discuss this point when progressing from 1D motion to 2D.

        2. tom, as you must know, the dynamics in HSC Applied Mathematics was deep and beautiful. Given that background, given VCAA’s cultural criminality in destroying a beautiful topic, I have absolutely no idea how you can refer to the above aimless and trivial nonsense as “good”.

            1. Tom, I think you and Marty actually do agree. Marty said that the 2020 mechanics is not good You’ve also said that the question was not good.

              It’s not good because it’s impossible to write a good mechanics question due to the wanton mathematical vandalism and destruction committed by VCAA and its apparatchiks. Yes, answering the question requires deep ideas – but these ideas have been reduced to superficial rote learnt recipes. Making the question banal and shallow. A question can only be as good as the syllabus allows. VCAA’s Stupid Design does not allow much mathematical goodness.

              I think we’d all agree that good mechanics questions were possible back in the days of HSC Applied Mathematics under VCAB (see p74 onwards of attachment for a glimpse, and before VCAB, VUSEB). But VCAA have wrecked what were once great mathematics subjects.

              Believe it or not, there was a time – pre-VCAA – when mathematics in Victoria was easily superior to mathematics in NSW. How the worm turns. What we have now is a credit to NSW and a damning indictment on Victoria.

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