WitCH 11: Impartial

The following WitCH comes from the (CAS permitted) 2018 Specialist Mathematics Exam 2:

The Examiners’ Report indicates that about half of the students gave the intended answer of D, with about a third giving the incorrect answer B. The Report notes:

Option B did not account for common factors and its last term is not irreducible, so should not have Dx in the numerator.

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.

WitCH 9: A Distant Hope

This WitCH (as is the accompanying PoSWW) is an exercise and solution from Cambridge’s Mathematical Methods Units 1 and 2, and is courtesy of the Evil Mathologer. (A reminder that WitCH 2, WitCH3, Witch 7 and WitCH 8 are still open for business.)

Update

As Number 8 and Potii pointed out, notation of the form AB is amtriguous, referring in turn to the line through A and B, the segment from A to B and the distance from A to B. (This lazy lack of definition appears to be systemic in the textbook.) And, as Potii pointed out, there’s nothing stopping A being the same point as C.

And, the typesetting sucks.

And, “therefore” dots suck.

WitCH 8: Oblique Reasoning

A reminder, WitCH 2, WitCH 3 and WitCH 7 are also open for business. Our new WitCH comes courtesy of John the Merciless. Once again, it is from Cambridge’s text Specialist Mathematics VCE Units 3 & 4 (2019). The text provides a general definition and some instruction, followed by a number of examples, one of which we have included below. Have fun.

Update

With John the Impatient’s permission, I’ve removed John’s comments for now, to create a clean slate. It’s up for other readers to do the work here, and (the royal) we are prepared to wait (as is the continuing case for WitCh 2 and Witch 3).

This WitCH is probably difficult for a Specialist teacher (and much more so for other teachers). But it is also important: the instruction and the example, and the subsequent exercises, are deeply flawed. (If anybody can confirm that  exercise 6G 17(f) exists in a current electronic or hard copy version, please indicate so in the comments.)

WitCH 7: North by Southwest

Our new WitCH, below, comes courtesy of Charlie the Enforcer. Once again, this WitCH is from the 2018 SCSA Mathematical Methods Exam (here and here): it’s the gift that keeps on giving. (And a reminder, WitCH 2 and WitCH 3 still require attention are still unresolved.)

Question 11 and the solution in SCSA’s marking key are below. Happy hunting.

Update

John has pretty much caught it all. The killer issue is the use of the term “deceleration” in part (c) which, the solution implies, refers to the drone speeding up in the southerly direction. This is arguably permissible, since deceleration can be (though is far from universally) defined as a negative acceleration, and since way back in part (a) it was implied that North coincides with the positive x direction.

Permissible acts, however, can nonetheless be idiotic: voting Liberal or Republican, for example. And, to use “deceleration” on a high stakes exam to refer implicitly to increasing speed is idiotic. Moreover, to use “deceleration” in this manner immediately after explicitly indicating the “due south” direction of motion is truly ruly idiotic. Still not as idiotic as voting Liberal or Republican, but genuinely special-effort idiotic.

That’s enough to condemn the question, even by SCSA standards. But, the question is also awful in many other ways:

  • The question is boring and butt ugly.
  • No indication is given whether exact or numerical solutions are permitted or required.
  • Having a drone an arbitrary 5m up in the sky for a 1D problem is asking for trouble. For example:
  • The “displacement” of x(0) = 0 for a drone 5m up is pretty stupid.
  • “Where is the drone in relation to the [mysterious] pilot?” Um, kind of uppish?
  • “How far has the drone travelled …” is needlessly wordy and ambiguous. If you want a distance, for God’s sake say “distance”.
  • Given the position function x(t) is at hand, part (c) can easily and naturally be solved by hand. But of course why think about things when you can do mindless calculator crap?