## WitCH 67: Rooted

Our final 2021 NHT WitCH is the final question from the Specialist Exam 1.

## UPDATE (29/08/21)

Sigh. We really hate updating WitCHes.* We have about a hundred of these things to do, and we’re generally thinking of the updating as a task for retirement or, better, for a reincarnation. However these NHT WitCHes, and this one in particular, have highlighted a degree of confusion. So, alas, it seems worthwhile sorting out the issues while the issues are in mind.

## WitCH 37: A Foolproof Argument

We’re amazed we didn’t know about this one, which was brought to our attention by commenter P.N.. It comes from the 2013 Specialist Mathematics Exam 2: The sole comment on this question in the Examination Report is:

“All students were awarded [the] mark for this question.”

Yep, the question is plain stuffed. We think, however, there is more here than the simple wrongness, which is why we’ve made it a WitCH rather than a PoSWW. Happy hunting.

UPDATE (11/05) Steve C’s comment below has inspired an addition:

## Update (20/05/20)

The third greatest issue with the exam question is that it is wrong: none of the available answers is correct. The second greatest issue is that the wrongness is obvious: if lies in a sector then the natural guess is that will lie in one of three equally spaced sectors of a third the width, so God knows why the alarm bells weren’t ringing. The greatest issue is that VCAA didn’t have the guts or the basic integrity to fess up: not a single word of responsibility or remorse. Assholes.

Those are the elephants stomping through the room but, as commenters as have noted, there is plenty more awfulness in this question:

• “Letting” is sloppy, confusing and pointless;
• The term “quadrant” is undefined;
• The use of “principal” is unnecessary;
• “argument” is better thought as the measure of an angle not the angle itself;
• Given is a single complex number, “the complete set of values for Arg()” will consist of a single number.
• The grammar isn’t.