Secret Methods Business: Exam 2 Discussion

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

UPDATE (09/09/21) The examination report is here (a Word document, because VCAA is stupid). Corresponding updates, including the noting of blatant errors (MCQ20, and see here, and Q5), are included with the associated question, in green.

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

UPDATE (21/11/20) A link to a parent complaining about the Methods Exam 2 on 774 is here.

UPDATE (24/11/20 – Corrected) A link to VCAA apparently pleading guilty to a CAS screw-up (from 2010) is here. (Sorry, my goof to not check the link, and thanks to Worm and John Friend.)

UPDATE (05/12/2020)

We’ve now gone through the multiple choice component of the exam, and we’ve read the comments below. In general the questions seemed pretty standard and ok, with way too much CAS and other predictable irritants. A few questions were a bit weird, generally to good effect, although one struck us as off-the-planet weird.

Here are our question-by-question thoughts:

MCQ1. A trivial composition of functions question.

MCQ2. A simple remainder theorem question.

(09/09/21) 56% got this correct, which ain’t great. 

MCQ3. A simple antidifferentiation question, although the 2x under the root sign will probably trick more than a few students.

(09/09/21) 86%, so students (or, more accurately, their CASes) weren’t tricked.

MCQ4. A routine trig question made ridiculous in the standard manner. Why the hell write the solutions to \boldsymbol{\cos 2\theta = b} other than in the form \boldsymbol{\theta = \alpha + k\pi}?

MCQ5. A trivial asymptotes question.

MCQ6. A standard and easy graph of the derivative question.

MCQ7. A nice chain rule question. It’s easy, but we’re guessing plenty of students will screw it up.

MCQ8. A routine and routinely depressing binomial CAS question.

(09/09/21) 50%, for God knows what reason.

MCQ9. A routine transformation of an integral question. Pretty easy with John Friend’s gaming of the question, or anyway, but these questions seem to cause problems.

(09/09/21) 35%, for Christ’s sake. The examination report contains pointless gymnastics, and presumably students tried this and fell off the beam. (The function is squished by a factor of 2, so the area is halved. Done.)

MCQ10. An unusual but OK logarithms question. It’s easy, but the non-standardness will probably confuse a number of students.

MCQ11. A standard Z distribution question.

MCQ12. A pretty easy but nice trigonometry and clock hands question. 

MCQ13. The mandatory idiotic matrix transformation question, made especially idiotic by the eccentric form of the answers.

(09/09/21) 25%, obviously a direct consequence of VCAA’s idiotically cute form of answer.

MCQ14. Another standard Z distribution question: do we really need two of these? This one has a strangely large number of decimal places in the answers, the last of which appears to be incorrect.

(09/09/21) In the General comments, the examination report admonishes students for poor decimalising:

“Do not round too early …”

It seems their idea is actually “do not round at all”.

MCQ15. A nice average value of a function question. It can be done very quickly by first raising and then lowering the function by \boldsymbol{a} units.

(09/09/21) 36%, presumably because everyone attempted the thoughtless and painfully slow approach indicated in the examination report. 

MCQ16. A routine max-min question, which would be nice in a CAS-free world.

(09/09/21) 53%, for God knows what reason. The question is simple to do in one’s head.  

MCQ17. A really weird max-min question. The problem is to find the maximum vertical intercept of a tangent to \boldsymbol{f(x) = -log_e(x+2)}. It is trivial if one uses the convexity, but that is far from trivial to think of. Presumably some Stupid CAS Trick will also work.

(09/09/21) 42%, which is not surprising. The examination report gives absolutely no clue why the maximising tangent should be at x = 0.  

MCQ18. A somewhat tangly range of a function question. A reasonable question, and not hard if you’re guided by a graph, but we suspect students won’t do the question that well.

MCQ19. A peculiar and not very good “probability function” question. In principle the question is trivial, but it’s made difficult by the weirdness, which outweighs the minor point of the question.

(09/09/21) 15%, which is worse than throwing darts. Although the darts would be better saved to throw at the writers of this stupid question.  

MCQ20. All we can think is the writers dropped some acid. See here.

(09/09/21) 18%. Now, what did we do with those darts? As follows from the discussion here, the suggested solution in the examination report is fundamentally invalid. One simply cannot conclude that a = 2π in the manner indicated, which means that the question is at minimum a nightmare, and is best described as wrong. Either the report writers do not know what they are writing about, or they are consciously lying to avoid admitting the question is screwed. As to which of the two it is, we dunno. Maybe throw a dart. 

UPDATE (06/12/2020)

And, we’re finally done, thank God. We’ve gone through Section B of the exam and read the comments below, and we’re ready to add our thoughts.

This update will be pretty brief. Section B of Methods Exam 2 is typically the Elephant Man of VCE mathematics, and this year is no exception. The questions are long and painful and aimless and ridiculous and CAS-drenched, just as they always are. There’s not much point in saying anything but “No”.

Here are our question-by-question thoughts:

Q1. What could be a nice question about the region trapped between two functions becomes pointless CAS shit. Finding “the minimum value of the graph of \boldsymbol{f'} ” is pretty weird wording. The sequence of transformations asked for in (d) is not unique, which is OK, as long as the graders recognise this. (Textbooks seem to typically get this wrong.)

Q2. Yet another fucking trig-shaped river. The subscripts are unnecessary and irritating.

Q3. Ridiculous modelling of delivery companies, with clumsy wording throughout. Jesus, at least give the companies names, so we don’t have to read “rival transport company” ten times. And, yet again with the independence:

“Assume that whether each delivery is on time or earlier is
independent of other deliveries.”

Q4. Aimless trapping of area between a function and line segments.

Q5. The most (only) interesting question, concerning tangents of \boldsymbol{p(x) = x^3 +wx}, but massively glitchy and poorly worded, and it’s still CAS shit. The use of subscripts is needless and irritating. More Fantasyland computation, calculating \boldsymbol{b} in part (a), and then considering the existence of \boldsymbol{b} in part (b). According to the commenters, part (d)(ii) screws up on a Casio. Part (e) could win the Bulwer-Lytton contest:

“Find the values of \color{red}\boldsymbol{a} for which the graphs of \color{red}\boldsymbol{g_a} and \color{red}\boldsymbol{g_b},
where \color{red}\boldsymbol{b} exists, are parallel and where \color{red}\boldsymbol{b\neq a}

We have no clue what was intended for part (g), a 1-marker asking students to “find” which values of \boldsymbol{w} result in \boldsymbol{p} having a tangent at some \boldsymbol{t} with \boldsymbol{x}-intercept at \boldsymbol{-t}. We can’t even see the Magritte for this one; is it just intended for students to guess? Part (h) is a needless transformation question, needlessly in matrix form, which is really the perfect way to end.

(09/09/21) This could be a horror movie: Revenge of the 1-Pointers.

Part (c) was clearly intended to be an easy 1-pointer: just note that a (tangent) line without an x-intercept is horizontal. But, somehow 77% of students stuffed it up. So, how? The examination report sermonises, thusly:

“The concept of the ‘nature of a tangent line’ was not obvious for many students.”

This suggests that the report writers don’t understand the concept of a concept. It also indicates that the report writers didn’t read their own exam. Q5(c) reads as follows:

“State the nature of the graph of ga when b does not exist. [emphasis added]”

Three sub-questions ago, ga is defined to the be the tangent to a function, and b is defined to be the x-intercept of this tangent (even though it may not exist). So, what was obviously not obvious to the students was the meaning of a vaguely worded question framed in poor notation. God, these people are dumb. And sanctimonious. And dumb.

Part (g), another 1-pointer, is concerned with the function p(x) = x3 + wx. The question asks, badly, for which values of w is there a positive t such that the tangent to p at x = t will have x-intercept at -t. 3% of students were smart enough (or lucky enough) to get the right answer, and 97% of students were very smart enough to go “Fuck this for a joke”, and skip it.

The solution in the examination report is lazily incomprehensible, but the idea was to just do the work: equate p'(t) with the rise/run slope of the tangent and see for which w there is a positive t that solves the equation. It turns out that the equation simplifies to w + 5t2 = 0, and so as long as w < 0 there will be a solution. It also turns out that specifying t positive is entirely irrelevant. Which is what they do.

It is worth noting the question can also be nutted out qualitatively, if one knows what graphs like y = x3 + x and y = x3 – x look like. If w ≥ 0 then it it easy see the tangent to p(x) = x3 + wx will always hit the x-axis before crossing the y-axis, so no chance of giving a solution for the exam question. If w < 0 then look at tangents at points t between the two turning points. At a turning point the slope of the tangent is horizontal. Then as the slope goes negative the x-intercept of the tangent comes in from ∞ (or -∞), until eventually the x-intercept is 0. Somewhere along the way, there has to be a t that gives a solution for the exam question. 

Part (h), another 1-pointer, is the final question on the exam, and is a stuff up. This time, 98% of students were very smart enough to skip the damn thing. As well, as mystery student PURJ pointed out to us, the examination report is also stuffed. The question again concerns the function p. It had been noted earlier that the tangents to p at t and -t are always parallel. Then Part (h) asks, in idiotic matrix notation, how p can not be translated or dilated to so that the new function still has this parallel tangent property. Yep, the question is framed in a negative manner, and the examiners whine about it:

“The key word in this part is restrictions.”

Nope. The key word in this part is “idiotic”. (And, “ungrammatical”.) In any case, the examination report indicates that the key to solving the question is that the transformed function must still be odd. This, as PURJ pointed out, is wrong. A vertical translation is just fine but the resulting function will not be odd. The correct characterisation is that the derivative of the transformed function must be even. In sum, this means one can transform as one wishes, except for horizontal translations. Which equates to the report’s matrix answer, without any noting of the “odd”, but not odd, contradiction. 

53 Replies to “Secret Methods Business: Exam 2 Discussion”

  1. It’s far too quiet here so I’ll kick things off with some general comments on the questions in Section A:

    Q1 – Q2: Simple Methods Unit 1 questions.

    Q3: Press some buttons on a CAS. Very simple for Specialist students who would just use DSolve (in Mathematica) or similar on a CAS calculator.

    Q4: Button pushing.

    Q5: Methods Unit 1.

    Q6: Two turning points at x < 0 so only one viable option. Very obvious.

    Q7: Something that requires intelligence at last.

    Q8: Simple binomial with button pushing.

    Q9: Advantages Specialist students. Nevertheless simple if you choose f(x) = 5/4 without loss of generality.

    Q10: Trivial if you test each option.

    Q11: Trivial if you simplify to Pr(X < 259) < Pr(Z < 1.5) and solve (259 – 250)/sd = 259. Can also easily be done without intelligence using Mathematica and one line of generic code.

    Q12: Wordy but simple Methods Unit 2.

    Q13: Simple to narrow it down to E using only the translation.

    Q14: Trivial using Mathematica.

    Q15: Trivial to get the equation of each line, apply the definition and press some buttons.

    Q16: Simple Methods Unit 1 max-min problem.

    Q17: Tricky but obvious if you draw a graph of y = f(x). Nice.

    Q18: Simple Methods Unit 1.

    Q19: A bit tricky. The graph is irrelevant.

    Q20: Tricky but obvious if you see f(x) = 1 is required. Nice.

    So the way I see it, Section A can easily be finished in 30 minutes and there should only be three questions that cause a reasonable student any difficulty (Q17, Q19, Q20).

    Verdict: Benign.

    I haven't checked carefully for errors.

    1. Thanks, John. I mostly agree with you on the MCQ, although I think you might be underestimating the trickiness of some questions: the fact that there’s an easy method doesn’t mean that it’s necessarily quick or easy to find the easy method. I also found more irritants than you, but of course it’s my hobby to be irritated. I’ll post my thoughts shortly.

        1. No, the period *might* be 1/2 or 1/3 or … (in fact, anything of the form 1/n where n is a positive integer). But 1/1 is the simplest possible period that gets an answer.

              1. h = 1: If the period is 1/2 then 2 periods will take you from f(x) to f(x+1). If the period is 1/3 then 3 periods will take you to f(x+1) etc.

                h = 2: If the period is 1/2 then 4 periods will take you from f(x) to f(x+2). If the period is 1/3 then 6 periods will take you to f(x+2) etc.

                h = etc.

  2. Since there doesn’t seem to be any err love for this exam, I suppose I’ll start by saying that greater presence of explicit CAS questions (i.e questions that asked for a numerical question) was a bit unusual. I believe it could be to compensate for the probability section which is primarily CAS-active but it leads to the magic question of “did using a particular CAS, i.e Mathematica over a TI-nspire help students?”. Maybe its my inexperience with the TI-nspire since I tried using one to do this years exam with both calculators, but for various parts of SA (Q1e-f, Q2c, Q4, Q5a-e) there felt like a lot of CAS was in play. I did have a listen to the radio and it really just seems like a mishmash of “the format was unexpected” among other not so specific comments. Maybe anyone who has more expertise with these calculators can chime in.

    1. Hmpph. This whole friggin *year* was unexpected but we all just had to suck it up.

      This mishmash of “the format was unexpected”. Cry me a friggin river. Didn’t they see the Cover pages and Amended Formula Sheet? If they didn’t, then all the mewling needs to be directed elsewhere, NOT at the exam and its so-called “unexpected format”. And maybe some tough questions need to be aimed in the same direction …

    2. Thanks, Sai. I assume you mean Section B. Yes, it seemed to be swimming in CAS. Of course many students will do plenty of computations with CAS even if they can readily be done by hand. But there were lots of questions in Section B, like (most of) the questions you note, that can only be reasonably done with CAS.

  3. One thing I will say as someone who teaches at a TI school but uses Wolfram products for my computational needs (including playing around with ideas for SACs…) – a computer keyboard and interface (be it Mathematica or the TI emulator) is ALWAYS easier to use than the hand-held.

    The new TI calculators (the blue ones that have a new file format, so are pretty much incompatible with the older black model, including rendering the old docking stations useless except as charging stations…) have more memory and are a bit quicker to process things, but all the shortcomings relative to a larger screen device (computer) remain.

  4. Indeed. Far too quiet. No-one even nibbled the (unintended) bait at Q13. Simple to narrow it down to the WRONG answer of E using only the translation.

    Simpler to narrow it down to the correct answer (of A) by starting with x = 2x’ + 4. No knowledge of transformations required. Trivial with Mathematica.
    A pointless question foisted on students because of the pointless inclusion of transformation matrices.
    (Stupid in fact because:
    1) matrices are not on the course and yet they are required.
    2) it’s another disconnected piece of mathematics welded onto the course).

  5. Re Q7:

    Intelligence should one try, or to the CAS (Mathematica and the TI-nspire can just evaluate this as is).

    On the other questions, Q19 is a good question, although the graph is pointless as you said. Q17 in my opinion is just another optimisation problem the same way Q16, and one could use the fMax function (TI-nspire) or the Maximize function (Mathematica) to hammer the question without further thought. Of course, getting there could be a step of its own…

    I also had a look at a walk through of the extended response solutions courtesy of a friendly neighborhood Worm and had seen that the CASIO classpad does not capture all the solutions for an inequality (Q5dii). Now, one may argue that you could (and should) use the previous results to determine that the casio classpad was not functioning properly (in my opinion) whereas both the TI-nspire and Mathematica will return the complete inequality…. While any student would sketch a graph of this, they would have to go to the graph menu, type in the graph along with the two lines… all for one mark. From what I can see as well, it has no implication on the following questions either.

    The topic of matrices in the context of transformations annoys me a lot, since those questions feel disconnected from the other topics. Linear algebra is such an interesting topic, and the watering down of it into transformations of functions is a real injustice to the field. I would also say Further does similar things with topics such as least squares (a good use of motivating inner products) but of course all of it is button mashing.

    1. Thanks, Sai. Quick replies:

      I would assume Q7 is quicker by brain than CAS.

      Re Q19, it’s true the graph is redundant, but I assume that is the examiners being nice, and I’m fine with it. The question is sufficiently unusual that the graph could help orient students.

      Q17 is strange. I *think* I like it, just as John Friend indicated he did, but I’m not sure. I’ll indicate the nature of the problem when I update the post, so people can comment.

      I’ll think about your Section B comments once I’ve worked through it. As for transformations in VCE, it’s way beyond/beneath “injustice to the field”.

    2. Hi, Sai. I’m still digesting QB5. Do you have any sense of why the Casio screws up (d)(ii)? I didn’t test any machines, but the question doesn’t look like it’d cause such trouble.

  6. Q.19 I think the graph was to possibly spark symmetry in the heads of students?

    ER Q5dii… solving the inequality…

    TI inspire gives the correct intervals… CASIO Classpad is missing one of the intervals…

    How can they have this on the exam? Surely it should be tested beforehand… 98% of students using a CASIO will not pick up on this given the previous question… Very unfair… and how will it be marked?

    1. There are on-going issues with the non-level playing field of technology.

      VCAA has gives assurances that all exam questions are tested with all three CAS calculators (the TI-Insipid, the Crapio, and the Spewlett Hackard) for ‘equity’. This is obvious bullshit ( and your comment is the latest evidence. Furthermore, Mathematica leaves the calculators for dead (, but VCAA does not care (for obvious reasons – it wants Mathematica Methods not Mathematical Methods).

      1. Imagine getting those teachers who already can’t teach methods or spesh, to then learn mathematica! They shy away from the basics of a CAS calculator… and would never consider writing a small program….

        Some schools have a mini orgasm when they find out that you can use both the TI Inspire… and CASIO and…. mathematica…

        I figure that if they force it on you, you may as well become competent in it!

        I would love to have a two hour exam on both that was harder, but they have more time to work on the paper…

        I dont know if you guys know of a student called Alex Gunning? He got a perfect score in Mathematics in the international olympiad, yet he could never finish a paper in specialist or methods… and got about ~40 in both subjects….

        1. He’s currently studying mathematics (Masters) at Trinity College, Cambridge. Probably because of his Olympiad success, no thanks to the VCAA exams.

          More proof of how stupid the VCAA exams really are (although getting 40’s in Methods and Specialist indicates something, I suppose). Answering a bunch of questions within *unrealistic* time constraints is just plain dumb. But *apparently* the exams are subjected to a blind review, which among other things is meant to check that the exam is of an appropriate length for a reasonable student. Either more bullshit from VCAA or the blind reviewer gets ignored. It’s my experience (given the number of errors in the exams each year) that the VCAA vettors have been asleep at the wheel for many years.

          What I’d like is the VCAA exam writers, vettors and DuLL to all sit one of *my* exams under normal examination conditions.

          The Methods exams were not overly-difficult, the format was not the big surprise many are alleging, and there were no questions outside the scope of the Adjusted 2020 Study Design. But Exam 1 was undoubtedly too long (by my estimate, about 6 marks = 10 minutes more time was needed) – I blame the VCAA vettors.

          I haven’t worked through Exam 2 Section B but I think Section A could easily be done within 30 minutes by a reasonable student (therefore not too long).

          1. I completely agree…

            There was a new head of the panel in Methods this year… I would suggest that they probably thought they knew best…

            1. So you mean a ‘knew head’ …

              A tough year to be new (whether it be teacher, HoD or exam setting panel), although I’m sure work had started on the 2020 exam before the pandemic struck. If exam 1 had been shorter (by deleting a couple of the 1 mark questions and distributing those marks to other questions), I’d say that the ‘knew head’ had done pretty well.

        1. Thanks, John. I haven’t yet worked through the comments on this post, and the article is weirdly vague, but I gather this is the issue Worm raised? I’ll post the link above as well.

          1. The newspaper report is related (I remember this – there was a big uproar). The report was evidence that that VCAA aren’t doing the technology checks it claims to be doing – the Crapio seems to fall short relative to the TI-nsipid on some VCAA exam questions. Worm has raised ER Q5dii from the 2020 exam – it adds to this evidence.

            And we certainly know that VCAA have no clue (or don’t care) about the huge advantage Mathematica-using students have relative to CAS-calculator using students.

            1. Ah, I see. Stupid me, and I’ve corrected the update. I’ll check out the 2020 issue, and the whole exam, in the next day or so.

      1. Hey Marty,

        I’m pretty sure it’s just the algorithms and accuracy of the iterative methods in the CAS…

        It may only go to 1 or 2 decimal places which isn’t sufficient in this case.

        After using the TI-Inspire and CASIO, it’s clear that generally the algorithms handling inequalities on the CASIO are far inferior to those on the TI…

        I knew this when doing the exam, hence, I knew there was every chance that it would give the wrong solutions…

        1. Geez. Next question: how is it possible, if at all, for the VCAA to not catch this? If they claim that they checked the question on all three standard paltforms, would that claim be a provable lie?

  7. Question 4eiii
    For the TI-nspire CX CAS when equating areas and solving for n without inserting a domain the calculator returns 1.087 to 3 decimal places, but when inserting the domain 1<n<3, it returns 1.088. Will both answers be accepted?

    1. Who knows. VCAA probably tossed a coin last Sunday (assessor training day). It seems to be how it does most things.

    2. Ryan, what happens if you set the TI to return, say, five or six decimal places? To how many places do the two answers (with or without domain) agree?

  8. Re: Q5 part e.
    The values of a are found from the equation 5 a^2 = 1.
    We’re told in the preamble to part (a) that a \in R so it would follow that \displaystyle a = \pm \frac{1}{\sqrt{5}}.
    But the positive solution for a makes no sense in the context of the graph given in the preamble to part (e) … Is it my imagination or are we meant to now *assume* that a < 0 for part (e)?

    And here's a question about part (f):

    Does the word "Find" mean that an answer with some working is required? As opposed to "State", where clearly only an answer is wanted? So will a student who simply writes w < 0 (maybe as a hopeful guess) get the 1 mark or is some working required to justify this answer. We know VCAA says

    "In questions where more than 1 mark is available, appropriate working must be shown."

    But does this mean that NO working is required in a question worth 1 mark where students are asked to "Find" …?

    In a 1 mark question, is there a difference between "State" and "Find" in terms of what VCAA expects??

    1. And if anyone would like to opine on Q5 part (h) …

      My interpretation (and that of some others) is that the tangent at x = t is parallel to the tangent at x = -t and therefore there *can* be vertical translation of p.

      However, I’ve seen arguments for the interpretation that the tangent at t cuts the x-axis at -t and therefore there *cannot* be vertical translation of p.

      I’m curious what others think and if the question might be ambiguous.

      And … it’s a 1 mark “State …” rather than a 1 mark “Find …” question. I’m still curious whether others think VCAA might attach a different meaning to each word (in the way discussed in my previous comment). (If VCAA does, my blood will boil).

      1. OK, drunk enough now. John, I don’t think the question is ambiguous, and that clearly vertical translations will also work. Part (e) is maybe leading people to look at the question in the other way, but I think (h) is worded clearly, give or take the ridiculous matrix formulation.

        1. Yes, I thought the same.

          It will be very interesting to see the MAV solutions for this exam. Since 2019 all MAV exam solutions have been written through the cracked VCAA lens of an assessor – I have found their clarity and mathematical rigour very poor (based on last years solutions I wouldn’t use them if you paid me to). It’s an interesting insight into the mind of VCAA.

          On the topic of written solutions – I thought some of the free solutions currently available were not nearly as good as they’ve been in the past. I’ve found errors and a very noticeable lack of clarity this year (particularly for some of the MCQ and many of the 1 mark questions in Part B). I find this very interesting because if the people who write these solutions are struggling to present clear and accurate solutions, I can only wonder what the solutions written by the exam candidates look like. Maybe that’s why some of these parts are only worth 1 mark – too hard to explain and justify answers …?

          Which brings me back to how very interesting it will be to see the MAV solutions for this exam.

          I’m still pondering on whether VCAA sees a difference in the meanings of “Find” and “State” in 1 mark questions … Does “State” mean an answer requires no justification but “Find” means a justification is required? If there’s no difference, why are two different words used to mean the same thing??

          1. Because as we have seen countless times, VCAA likes to give its own special meaning to words … Can anyone shed any light on whether VCAA might or might not attach a different special meaning to ‘Find’ versus ‘State’ in a 1 mark question?

    2. Thanks, JF. I don’t see the graph as misleading for part (e). Perhaps graphing the case where \boldsymbol{a<0} subliminally suggests this is to be assumed or concluded, but I don’t know what one can do about it.

      I assume your other query is about (g)? Yeah, the word “find” for that 1-marker made no sense to me. Even ignoring the single mark, I haven’t convinced myself there’s an easy way to see \boldsymbol{w<0} always works, other than by traditional Methods logic: “It’s a 1-marker, and so …”.

  9. Re: Update 09/09/21 and the observation “[the examination Report is] a Word document, because VCAA is stupid”.

    I’ve had a lot of fun with the 2020 Report for Specialist Exam 2 (I called it the Reality Report) … I was tempted to attach it but VCAA would undoubtedly think I (and hence you) had crossed the line in publishing it (excessive quoting of copyright material without permission). Even though every change I made in it was correct and can be defended … An excerpt from Q2(b):

    “It was stupid that the question gave a ray whose terminus is at u since this creates ambiguity in how to label a point with both a closed circle (Question 2a.) and open circle (Question 2b.). Confusion among students was evident but students are reminded that VCAA questions are often defective in some way and that students just have to suck it up and do their best. The diagram below shows the solutions to Question 2b. (the points and line) and Question 2di. (the ray). Students should note the weaselly way in which the point u is labelled. VCAA makes no apology that the ray has no arrow-head and looks like a line segment”

    It was pure gold watching the looks on teachers faces as I passed the Report around and asked them to read it …

    1. Well, I’m glad you resisted the temptation to link. The Specialist updates will appear shortly, so please save your ammo.

      1. Now that I think about it, I made my edit quite a while ago (back in the olden days of face-to-face teaching) and remember sending a copy to VCAA as a demonstration of the stupidity of publishing Examination Reports in word format. I didn’t get a reply. Clearly my Reality Report was not compelling enough, so maybe the alterations I made are harmless enough after all …

  10. As per the Report, students lost marks for Question 1f for having “incorrect inequality signs”. I wonder then if students who rounded down to 3dp and thus used < instead of ≤ were therefore penalised – I really hope not, but…

    1. Interesting thought, Lemon, and I although I doubt it in this case. Both positive endpoints happen to get rounded down. So, even if one were to switch to strict inequalities, which would be a little weird, you’d do it for the lower endpoint but not the upper.

  11. The Examination Report says that the answers to Question 3 part (c) can be found by solving the equation \displaystyle \int_{-4.5}^{0.5} \frac{1}{4 \sqrt{2 \pi}} e^{\frac{-(t-k)^2}{2 \times 4^2}} = 0.4648.

    Since 0.4648 is only a decimal approximation of Pr(-4.5 < T2 < 0.5)*, this equation can never give the exact values of k (the exact values can only be found using symmetry). But the solutions have been stated to 1 decimal place without explanation, dishonestly suggesting that these are exact solutions to the equation.

    I wonder whether VCAA accepted answers such as k = -2.503 and k = -1.497 (found by rounding the solutions found using the equation to 3 dp) or whether students were required to round to -2.5 and -1.5.

    You only know exact answers exist by using symmetry. But if you use the equation then you're not using symmetry so you don't know that exact answers exist …!!

    * T2 is the new random variable "delivery time under new model".

    1. John, the question is a mess, and I sort of understand what you’re getting at, but I can’t see it’s a big deal and you’ll have to say it a lot clearer than you have. The question is not asking for the exact values of k, so what is your objection?

      1. yeah, that was my bad. It asked for one decimal place. I realised that a few minutes ago. A combination of complete distrust of VCAA and getting so many questions from students due to errors or shit in the questions and errors or shit in the Reports and substandard solutions (I can’t complain, they’re free and mostly OK).

        The amount of work VCAA creates for teachers through its incompetence, stubbornness and dishonesty is significant at this time of year.

        I’ve had a lot of questions about this question and after doing it using symmetry I didn’t read it properly that a one decimal approximation (which turns out to give the exact answers) was asked for.

        I wonder if the 1 dp was expecting that students would push buttons rather than use symmetry and get the values ‘by hand’.

        Anyway, VCAA get you to the point where you expect mistakes and so sometimes see them even when they’re not there.

        1. No problem. The post is for discussion. And, there is something a bit odd about having the choice between a (purportedly) exact approach and an approximation.

  12. MCQ8 is at least a practical problem that arises in industry. People who are charged with solving these sorts of problems in industry often have little in the way of mathematics education. I was asked to solve problems like this by a manufacturing business because the accountant had a vague recollection from his business degree that this sort of problem is easily solved with mathematics.

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