WitCH 10: Malfunction

It’s a long, long time since we’ve had a WitCH. They have been not-so-slowly accumulating, however. And now, since we’re temporarily free of the Evil Mathologer, it is the WitCHing hour.

Due mostly to the hard work of Damo, all of the outstanding WitCHes have been resolved, with the exception of WitCH 8. That one will take time: it’s a jungle of half-maths. Our new WitCHes are not so tricky, although there is perhaps more to be said than indicated at first glance.

The first of our new batch of WitCHes is from the VCE 2018 Specialist Exam 1:

The Examiners’ Report gives the answer as \int_0^{\frac34}\left(2-t^2\right)dt. The Report also indicates that the average score on this question was 1.3/5, with 98% of students scoring 3 or lower, and over a third of students scoring 0.

Happy WitCHing.

5 Replies to “WitCH 10: Malfunction”

  1. I feel like this doesn’t get to the heart of the matter, but I’m not convinced that the distance travelled by the particle in “three quarters of a second” is given by an integral with lower and upper limits of, respectively, 0 and 0.75. Couldn’t it be any integral with lower and upper limits of x and x + 0.75?

    1. I felt the same thing, but was willing to throw VCAA a bone and assume that out of all the possible 3/4 second time intervals, they were specifying the one from t = 0 to t = 3/4.

    2. Thanks, SRK. Of course you are correct. Yeah, it’s not the main point and the required answer makes clear the time interval. But the wording is simply wrong, and needlessly wrong.

      And, true, one might consider, as John does, to throw the VCAA a bone. But think about it. This is lazy “Who gives a shit?” wording from the same nasty obsessives who self-righteously nitpick students to death. So screw it. Throw the bone at them.

      1. Indeed. It would have been no skin off their chin to have added two simple words and said “… in *the first* three-quarters of a second….”

        1. Exactly. I can completely understand a harried teacher writing such a sloppy expression. And at times there is a tricky balancing act to be made between accuracy and clarity. But not here. Here, it is just laziness. Or idiocy. Or both.

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