Just in case anybody got the wrong impression and hoped or feared we’d turned over a new leaf, we’ll be posting a number of WitCHes in the next few days. We’ve finally had a chance to look at the 2021 NHT exams (although the exam reports have still not appeared). As usual, the exams are clunky and eccentric, and we’ll be posting a brief question-by-question overview of the exams. But, first, some highlights.
The following question is from the 2021 NHT Methods Exam 2. It seems to us more of a PoSWW than a WitCH, but we have seen the exact same issue arise in a recent SAC. So, presumably, this issue is more widely spread.
As commenters have pointed out, none of the options are correct. A function f is defined to be strictly decreasing on its domain if f(b) < f(a) whenever b > a, and this is false for all the given restricted domains. It is also standard in VCE to only apply the definition on intervals, which also kills options A, D and E. (There is no problem applying the definition on more general domains but, for the first reason given, this does not save the question.)
There is also a “local” notion of decreasing function. So, for example, one might describe a function as decreasing at x = -4, indicated, say, by the derivative at that point. But, as illustrated by the failure of option D, the global definition does not equal the sum of the local notions.
Surprising no one, the examination report simply pretends that VCAA didn’t screw up, and gives the answer as D.
John Friend has alerted us to the fact that the examination report was amended on 05/10/21. Now, the examination report suggests no answer to the question. Of course the amended report contains no explicit acknowledgment that the question is stuffed, nor that the initial version of the report was stuffed.