Secret 2022 Methods Business: Exam 1 Discussion

We hope the exam went well for all you students, or all your students (tick whichever applies).

We haven’t looked at the exam yet, but in any case we’ll first give others time to comment. Fire when ready.

UPDATE (03/11/22)

Exam 2 discussion is now up, here.

Thank you all for your comments. Here are our thoughts, pretty much in line with others’, but we think there are a few things still to be said, and two separate posts to write.

Globally, there are three aspects worth noting:

  • The exam appears to contain no major errors;
  • The exam is way, way too easy;
  • The writing is woeful.

On the first point, there are nonetheless one minor and two semi-major errors, as indicated below. They are not hanging offences, but they are whipping offences. These errors should not occur, and they would not occur if the exams were properly vetted.

On the second point, commenters have noted the obvious problem with the easy exam, that the better students get shortchanged, and VCAA’s inevitable nitpicking gains weight. Also, a couple of the questions are sufficiently confusing that we think it likely there will be a lottery effect; others, who know better their students and Methods-Speak, may disagree.

On the third point, we’ve decided to make a point of the point. The writing is sufficiently, gratuitously bad that we’ll have a separate post on it. Just quickly, again, proper vetting would not permit such a poorly written exam to be approved.

Here are our question by question thoughts. We’ll try to stick to the mathematics, in the main leaving issues with the wording for the dedicated post.

Q1. Routine. One would hope that the instruction to “simplify” in part (b) does not require the factoring out of the minus sign.

Q2. Part (a) is an instance where the writing is so poor that it has led to error. The question is simply not asking what VCAA thinks it is asking. Part (b) is nice (modulo wording), although 3 marks seems generous.

Q3. Pretty minus signy, but routine and fine.

Q4. A very badly structured (and worded) question. We’ve decided it’s bad enough to warrant its own WitCH, here. The question is easy, but we suspect students won’t do that well on it, simply because of the way it has been presented.

Q5. The questions are OK, but 5 marks seems very generous for a little simple algebra.

Q6. An OK question, clouded by very clumsy wording. Intrinsically a better question than Q4, but again it seems likely that some students, who would otherwise have answered the question well, will have failed to decipher parts. Part (c)(iii) has gone further and into error; the question is not asking what VCAA thinks it is asking.

Q7. A pretty silly and simple question, framed around very silly modelling, but OK. As commenters have noted, awarding Year 12 students a mark for finding the area of a 20 x 20 square is pretty damn funny.

Q8. Intrinsically a good question, but not framed well and probably in effect too cutthroat. It would have been clearer and fairer to have introduced the question by explicitly writing A(k) as the integral of f. We’re guessing many students will be confused by the initial wording, and will do poorly simply because they couldn’t get going. As commenters have noted, k = 0 should have been excluded in part (c); it is mathematically OK to include k = 0, but it is unnecessary, it confusingly jumps the scenario from continuous to discrete, and it is probably illegal within the constraints of VCAA’s curriculum.


63 Replies to “Secret 2022 Methods Business: Exam 1 Discussion”

  1. Seems like there might’ve been a mistake on the last question regarding average area – shouldn’t the domain of k should exclude zero?

    1. I agree that is an error but doubt many students will be tripped up worrying about it.

      If VCAA only makes one error in an exam, it is not too bad an exam, historically speaking…

        1. Hmm. I’m torn.

          If f(5) = 3 and f(7) = 9 then the average value of the function (with domain {5,7}) is 6. If just f(5) = 3 (with domain {5}) then the average value of the function is 3.

          So, there is no problem getting the average value of the function when k = 0, but it’s then a discrete thing.

          In summary, definitely VCAA should have excluded k = 0, but I don’t think they had to. But I’m still happy for you to argue back on the second half.

          1. The function is clearly continuous, hence I would argue the open interval is required.

            I also acknowledge that it doesn’t really matter because k=0 is clearly nonsense.

            1. Yes, it doesn’t matter hugely, but it is sloppy. The technical question is whether the sloppiness amounts to an error. I don’t think so, but I’m willing to be persuaded. I don’t understand your “clearly continuous” claim.

              1. Function f is drawn as a continuous function, so asking for an average value over a discrete set seems a bit… wrong(?)

                Also, VCAA does not mention “average value” except as an application of integration, so again I would argue that continuity is implied.

                Is it an error? I think so. Does VCAA think so?

                (Maybe the word “so” is misplaced here)

                1. Well, the diagram doesn’t illustrate the endpoint case, but I don’t think that is an intrinsic problem.

                  For example, if you have a volume-of-a-box problem, and even if you draw the box, I think it is still ok (and preferable) to include the endpoint cases, where the “volume” of the “box” is zero. True, VCAA doesn’t tend to do that, and so it can be an issue for them, but it’s not for me.

                  Does VCAA not explicitly consider the average value of a discrete function? If not, then they’re stuffed.

                  1. I’ve never seen them do it.

                    Since the only mention of average value in the study design is as an application of integral calculus and VCAA only considers continuous functions for integrals…

                    I rest my case.

        1. Maybe, but in cryptic VCAA-waffle over 4 paragraphs, no doubt. Takes me longer to understand what they’re asking me to do than to do the actual maths to solve the question. -.-

  2. My thoughts:

    Q1 – typical

    Q2 – part b was weird but ultimately OK.

    Q3 – typical

    Q4 – interesting that the fraction given was not simplified. That should imply that answers given do not need to be simplified.

    Q5 – typical

    Q6 – part c was excessively wordy and I had to read it twice before understanding what they were actually asking, after that, not difficult, but weird.

    Q7 – not sure how much working will be expected for part (b). Part (c) was actually nice, although there was no consideration of rotated tiles…?

    Q8 – part b was weird but easy enough once you realise what the question is trying to ask (in a really odd manner). I suspect a lot of students could guess part (c) easily enough. Not sure the domain for k should include zero, but VCAA may have a definition of average value which means a, b must be different numbers (there may be a rule that b>a somewhere, I haven’t bothered looking for it).

    Overall, it felt shorter than previous years and largely an OK exam. By VCAA standards.

    1. Hi, Dave (and everyone). The paper tends to get scanned and starts to circulate pretty quickly, but I don’t want anybody to post it here. If anybody finds it on one of the standard maths discussion sites, I’m fine with them posting a link to it in the comments.

      Unfortunately, VCAA takes way too long to post the exam, although they’ve improved in the last couple years.

      1. Apparently VCAA’s legal team has to sign off on all the copyright issues. For a maths exam this can obviously take many months, and the team may well be occupied with all sorts of other matters.

        (In NSW the similar process only takes a few weeks. Probably something to do with the inverse relationship between exam quality and time needed).

        1. No, that’s garbage. I know VCAA gives that as the excuse, but it is simply an excuse, as evidenced by the NSW system you noted.

          If VCAA cared they could do it quicker, and in fact they have begun to do it quicker. Proving that before they did it quicker they had no excuse to not do it quicker. It is simply a question of the extent to which VCAA gives a stuff, which is not much and not often.

          1. Yeah, I know. When written, my sarcasm sometimes loses it nuance.

            VCAA does give the copyright excuse and I agree that it’s garbage.

  3. Question 4b,c seems poorly worded. Unclear if a card is drawn, which is given to be blue, then 3 more are drawn OR if simply 3 are drawn, the first of which is given to be blue. Regardless of the interpretation, the final answer happens to be the same in part c but not part b.

    1. Further to this I remember in a discussion of a previous methods exam (likely exam 1) on this website, a similar thing was criticised, I believe the wording was along the lines of “use of the word given despite not using conditional probability formula” does anyone remember which year this was?

      1. Hi, Anonymous. Maybe you’re referring to Question 2(b) on 2020 Exam 1? The exam report noted “Students generally recognised the conditional probability”, but report’s solution (and anything I could think of) contained no conditional probability.

    2. I don’t think it’s ambiguous. For others who don’t have the paper, the wording is “given that the first card drawn is blue, find the probability that exactly two of the *next* three cards drawn will be red…” (my emphasis).

      What I found strange about these two parts is why they bothered to include the “given that…” bit, since above we are told that “the colour of any drawn card is independent of the colour of any other drawn card”.

      Otherwise, a very very easy paper, not good for giving the stronger students an opportunity to show their ability.

        1. Maybe the wording could have been a bit better but I don’t think any of Q4 is confusing.

          Maybe VCAA wanted to test whether a student understood that the outcome for the first card doesn’t affect what happens with the next three cards (although I would have made the question worth 2 marks in that case – take the charity third mark from Q2(b)). That the word “given” doesn’t automatically mean conditional probability.

          Having said this, better wording \displaystyle might have been:

          “After the first card is drawn and replaced, find the probability …”

          But I’ll bet that would have ‘tricked’ some students too.

          Ditto for part (c). (But I would have preferred to see something different to part (b) being tested – maybe a ‘without replacement’ question).

          But I don’t have an issue with the wording VCAA used. All of Q4 question was clear in my view. Marty, I think the “drunk monkey” comment below is a bit harsh and deserves some explanation …. In fairness to VCAA, it is often hard to write a clear but unambiguous probability question.

          As for the “this is way too easy”. “Maybe VCAA just want to play with our heads”. VCAA want to trick us. VCAA want to confuse us … VCAA does have a lot to answer for regarding the paranoia it creates in the minds of students and teachers. But my advice is to play the question, not the man. Take the question for what it is and answer it. Don’t second guess motives.

          1. No. The wording is appalling. It also seems to me that question is deliberately framed in order to trick students. Perhaps it tricked me, and I will look carefully before posting. But I think Q4 is pretty awful.

    3. The question does suffer from absolutely awful wording (although for me the fourth and fifth sentences in the question stem were the worst). But parts (b) and (c) do seem clear to me. In every part four cards are drawn. In parts (b) and (c) the colour of the first card drawn is blue.

    1. That got me a good laugh. No seriously, why is it there? It’s just the area of a square… Sure you could argue that it’s used for the following parts, but it’s so basic that you may as well have left it out, or just stated it.

        1. A new methods teacher, so I’m still learning VCAA speak. O_o Questions are very wordy these days and I, myself, have a habit of not reading every detail of the question which catches me out a bit. My students found the exam very accessible, but it probably didn’t give my stronger students enough scope to show off. We will see what today offers.

          1. I see. Thanks, B. I don’t think “very word” begins to describe the awfulness of the writing. I also agree, the exam was way too easy. I don’t think students will do all that well on Q4 and Q8, but mostly because of poor wording. So it’ll be mostly a lottery. I don’t think it’ll do much to separate good from bad kids.

    2. Me who over-thought the question and took the area for half a tile…

      Honestly though, in my mind I was thinking “this is way too easy”. Maybe VCAA just want to play with our heads.

      1. Oh, Torrada. That’s funny. I feel sorry for you, but it’s funny. I hope the rest of it went better.

        Once, on a vectors exam, I asked:

        Spell “independent”.

        One of my students spelled it “independant”. He said later he thought I was trying to trick him. (I gave him the mark anyway.)

    3. The discriminator will be whether the unit of sq cm was included. No unit, no mark. I’ll guess at least 25% of students will get zero for this reason.

  4. Exam definitely felt easier than many of the previous years’. I’m thinking a 36/40 or 35/40 needed for A+

  5. student here. felt this exam 1 was extremely trivial – finished it with roughly 15 minutes to spare, which is unusual for me. the only question i had difficulty with was that domain transformation one, simply because i hadn’t completed a question similar to it before (not sure if previous exams had it since i spent most of my time practicing specialist)
    hope the graded distribution isnt too heavily skewed towards the high range.

  6. Thanks everyone for your comments. I’ve now gone through the exam. I think there are a few things to note, but I’ll wait until I’ve slept and can write it in semi-polite language.

    Good luck to you and/or your students on tomorrow’s Exam 2.

  7. Re Question 7 (of which part a is the the infamous question to find the area of a square with side length 20 cm):

    A little bird told me: For part b. (“Show that a Type B tile meets condition 1” – ie. that the area under the curve is half of the area of the tile) students who calculated the definite integral of g(x), from 0 to 20, and got 200 were not awarded full marks – the final answer mark required students saying something like “200 is half of 400, so meets Condition 1”.

    For part c. Calculating f(0) and f(20) and g(0) and g(20) was insufficient to get full marks. Students also needed to say something like “f(0)=f(20)=g(0)=g(20) so meets condition 2”. And apparently a few lines of working for g(20) was required – mental maths is verboten.

    And yet, for Question 1b. students will be awarded a method mark if they wrote down some combination of ±e^x * sin(x) and ±e^x * cos(x) in the numerator of a fraction, whether or not the signs were correct – nevermind that the quotient rule and derivatives of cos(x) and e^x are on the formula sheet. And for Question 5 (solve 10^(10x-13) = 100), students will be awarded a method mark if they wrote 10x-13 = 10.

      1. One more bit of insanity. For question 3 (finding k such that the pair of linear equations have infinitely many simultaneous solutions), writing the equation k^2 + 8k = -15 is not sufficient for the 2nd method mark, students needed to write k^2 + 8k + 15 = 0.

        1. That’s FUBAR.

          That crap is totally on the Chief Assessor. I don’t understand why the Assessors didn’t walk out on VCAA en mass. Does your birdy know if anyone in that ‘Training Day’ meeting had the brains, guts or integrity to powerfully prosecute the argument that:

          Using the determinant: \displaystyle k(k+8) + 15 = 0.

          Using gradients:

          \displaystyle \frac{k}{5} = \frac{3}{k+8}

          \displaystyle \Rightarrow k(k+8) = 15

          and that any one of these three equations should receive the method mark.

          Seriously, Assessors acquiescing to
          “writing the equation k^2 + 8k = -15 is not sufficient for the 2nd method mark, students needed to write k^2 + 8k + 15 = 0.”
          is one of the more spineless acts I’ve come across.

      2. Assessors may (sometimes do) argue vehemently about the marking scheme one way or the other, but the Chief Assessor has the final say on the marking scheme. I doubt the bird was drunk.

        So for Q1 (b) there’s 1 mark for an attempt to apply the correct technique and 1 mark for the correct answer. It makes a strange kind of sense given the question is only worth 2 marks … but I think what the bird has said suggests a reasonable argument that the marking scheme for each question should be in increments of 1/2 and you round down to a mark out of 40 at the end. Certainly Q7(c) makes a strong argument for this (VCAA wants 5 things for 2 marks). And the required statement for Question 7(b) should only be 1/2 mark.

        Re: “And apparently a few lines of working for g(20) was required – mental maths is verboten.”

        Following from what I said above, g(20) should only be 1/2 mark. I’d expect to see no more than

        \displaystyle g(20) = -\frac{8000}{100} + \frac{1200}{10} - 40 + 10 = -80 + 120 - 40 + 10 = 10.

        I don’t see how most students could get 10 without writing this down, nevertheless I’d give the 1/2 mark simply for stating g(20) = 10.

        Re: “And for Question 5 (solve 10^(10x-13) = 100), students will be awarded a method mark if they wrote 10x-13 = 10.”

        I totally agree with this.

        The bottom line is that VCAA will \displaystyle always get its spread of results. The ‘easier’ the exam, the more pedantic VCAA will get to achieve this.

        1. I’m not in principle opposed to awarding a method mark for recognising that using the quotient rule is a reasonable way to differentiate cos(x)/e^x, even if the rule is misapplied – although for a 2 mark question, it seems overly generous. I agree – more fine-grained marking here seems useful.

          But it’s insane to award a mark to students who show that (minimal) level of understanding, but deny it to students who can correctly use a definite integral to calculate the area under a curve but omit mentioning that their answer is half of 400. That’s not something that a more fine-grained marking scheme will help.

          You’re right, and this was something people noted immediately after the exam, that with an easy exam VCAA will achieve the required spread of results just by marking perniciously.

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