WitCH 90: Tiles and Tribulations

This is late, and it isn’t very Christmasy. But it came up as part of another project, and it’s been bugging us, so Bah Humbug.

The following is a question from 2022 Mathematical Methods Exam 1. It’s been discussed some on this post, including a concerning rumour (edited 24/12/22), and we also hammered some of the wording on this post. It is clearly deserving of its own WitCH.

19 Replies to “WitCH 90: Tiles and Tribulations”

    1. You have many fish to fry Marty, so to quote Charli Hebdo, “All is forgiven.”

      There is also an awful lot of crap this year to unpick. Just wait until the examiners reports come out…

  1. 1. and 2. below are bad, but what I’m explicitly damning as the baddest of the bad is the following rumour (if true):

    “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. Different question (or did I miss something?).

      Agree though – that would be the middle finger to rule them all (if true – which I doubt we could ever prove; ironic really since VCAA now wants students to prove things…)

      1. Probably this is already noted earlier (sorry I’ve not been up to speed with the blog) but the question doesn’t say that tiles need to be placed without rotation, does it? Or that they need to line up perfectly? Maybe I missed it. (This affects the value of a part and also the last part, because if you allow rotation then a “continuous pattern” can’t be guaranteed for all ways in which tiles “can be placed”.)

  2. There is something about this question that I don’t think I ever realised…

    (apologies to anyone and everyone who may have pointed this out earlier).

    Condition 2 states that the tiles must form a continuous pattern. However, the example given the lack of a domain for any of the “rules” you could argue that the pattern will never be continuous unless only the trigonometric option is chosen.

  3. Ahhh the tile question. It is all so easy and weird, I worry for the marking.

    For example, part c… do students need to consider the cases:

    AA
    AB
    BA
    BB

    explicitly and say that in each case the boundary points are equal? Or do they then need to also argue that a row will consist of a union of such pairs? Do they need to explicitly state that f and g are continuous?

    Or can they simply note the boundary values (assuming the a is as specified in an earlier part…. another issue) and then say, clearly it’s all fine.

    I’d be stressing in the extreme doing this question.

    1. I think all four permutations are covered by the f(0)=f(20)=g(0)=g(20) statement, but I never know for sure unfortunately.

      As for rotations… I think this was raised on the exam discussion post.

  4. OK, I’ve deleted a number of comments, which then also resulted in a number of replies being deleted.

    Forget the rumours about the grading, no matter how solid. The question is sufficiently appalling as it is. Issues with the grading can wait for the examination report. Issues with the absurd waiting time for the examination reports will be part of near year’s campaigning (and is already underway).

  5. Just to be clear, commenters are permitted to hammer “VCAA”. Hard. But I don’t want any comments, even oblique comments, aiming at individuals. Even if these comments are objectively fair and objectively reasonable.

    I might let some such comments through, and might make them myself at times. The more a person is in charge and/or is a public representative of VCAA or ACARA or whatever, the more the person is fair game. But the default position is that comments containing implicit or explicit personal attacks will be deleted.

  6. Somehow in part b), looking at my statement of marks, one examiner gave me 3/3 and the second examiner gave me 2/3. And I can bet I’m not the only one to lose half a mark on it… I remember I set up the integral and everything, purposefully avoided any shortcuts (eg. since the equation is a cubic, if the leftmost and rightmost point on the tile are halfway up the height of the tile, and have the same gradient sign, half the area would be shaded; I think this is a decent argument (correct me if I’m wrong) but I pictured VCAA not following/accepting it so I did the stupid integral) and I showed my calculations for the size of the square and everything. And it must have all been correct calculation for one assessor to give me full marks… I’d been concerned about ‘show that’ questions for weeks leading up to the exam, its never clear how much needs to be shown. I suppose nothing is trivial to VCAA (I’m inclined to say its because they’re stupid and bad at maths). Maybe they’re mad I didn’t quote the formula for the area of a square.

    Of course the problem isn’t just a personal one: it’s that so many students are sitting there in the exam, and rather than being occupied by, y’know, year 12 maths, they’re stressing about whether they need to state how to find the area of a square. VCAA can’t discriminate between top students using hard questions (maybe they couldn’t answer such questions themselves) so instead they’re just really, really petty. (It was the only mark I lost on the exam).

    1. Thanks, student. I don’t understand your non-calculus cubic approach. Presumably the examination report will indicate what trivia VCAA decided to whine about, which resulted in your lost mark. Forgive my ignorance, but what happens when two graders disagree? They just average the two scores?

      1. The exam has 40 marks, but you get a mark out of 80 for the exam which is the two scores added together (so yeah, they average the results, unless they differ significantly then I think they get a third examiner in, which is much more of an English thing than Maths). In hindsight my cubic approach was missing the necessary (and possibly sufficient?) condition that the cubic’s point of inflection was in the middle of the tile. Should have thought that through a bit more before posting, sorry about that. I hope the exam report will indicate what the problem was, but I’m not so optimistic…

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