With Methods exams next week, this one’s kinda important.
We try to avoid critiquing, or even being in the same room as, third party VCE practice exams. They are invariably clunky and weird, with plenty to criticise, but they matter infinitely less than the yearly screw-ups of the official exams.
Even MAV trial exams we do our best to ignore. Yes, the MAV is (too) closely aligned with the VCAA (with a number of people in conflicted, dual roles), and so MAV has a significantly greater professional and moral obligation to maintain high standards. But still, third party is third party, and we try our best to just ignore MAV’s nonsense. On occasion, however, MAV’s nonsense matters sufficiently, or is simply sufficiently annoying, to warrant a whack.
Last week, we were shown of a copy of MAV’s 2022 Trial Exam 2 for Mathematical Methods. The exam is predictably bad, simultaneously reflective of a thoroughly perverted subject and eccentrically third party. The exam is CAS-obsessed, both in question structure and in suggested solutions. To indicate finding the extrema of the function with a couple CAS screenshots, and without a single word noting that the critical points can also easily be found by hand, is so dismissive of the notion of teaching that we cannot conceive of what purpose the authors imagine there is in any of this. The exam is also replete with absurd modelling and Magrittisms. But none of that is why we are here.
One particular question on the MAV trial exam was pointed out to us. Here it is, together with MAV’s solution:
Get to work: students have exams next week.
Thank you to everyone for the comments. It wasn’t hard, and was really more a PoSWW than a WitCH. But there seems to be some common misunderstanding of these issues, and we wanted to encourage the discussion. Here is a summary, and a couple more comments.
The first and least important thing to note is that the question is screwed, even on its own terms. The authors’ intention was to make the pdf s(x) continuous by doing the standard endpoint matching stuff, but it is impossible to do so. That is, the parameters a and b cannot be chosen to make s(x) have integral 1 and be continuous at both x = 14 and x = 16. (Two parameters and three equations, so unless you’re really lucky …)
The second and most important thing to note is that the authors’ assumption that the pdf s(x) should be continuous is completely and utterly false. Continuity is simply not required for a function to be a probability density function. Ever. It is not required even if one chants the magic words “continuous random variable”. The use of “continuous” in CRV refers to the continuity of the cumulative distribution function, , which will be true as long as the integral of s(x) makes sense in some standard manner.*
The third and unimportant thing to note is that one might argue on the basis of a given model that the CDF S(x) should be differentiable. If s(x) is continuous then that will be true, with S'(x) = s(x) continuous.** But one must argue for this, the trial exam authors don’t argue for this, and their “model” of cats sleeping is so absurd it would be impossible to argue for this.
*) In some more advanced courses the CDF of a CRV need not be continuous. See the brief discussion of MCQ14 here (in which VCAA stuffed up and then attempted to hide their stuff up). See also VCAA’s definition of “continuous variable” (Word, idiots) and ACARA’s definition of “continuous random variable” and ACARA’s other, contradictory definition of “continuous random variable”, and ACARA’s v9 definition of “continuous numerical variable” (Word, idiots).
**) Don’t say S(x) is “smooth”. The word doesn’t mean what VCAA thinks it means.
John Friend and Sai have noted in comments that the question can be reasonably fixed by asking for the set of all a-b combos that make s(x) into a pdf.