The WitCHfest is coming to an end. Our final WitCH is, once again, from Cambridge’s *Specialist Mathematics 3 & 4* (2019). The section establishes the compound angle formulas, the first proof of which is our WitCH.

# Month: June 2019

## WitCH 16: The Root of Our Problem

This WitCH comes from one of our favourites, the Complex Numbers chapter from Cambridge’s *Specialist Mathematics 3 & 4* (2019). It is not as deep or as beWitCHing as other aspects of the chapter. But, it’s still an impressive WitCH.

## WitCH 15: Principled Objection

OK, playtime is over. This one, like the still unresolved WitCH 8, will take some work. It comes from Cambridge’s ** Mathematical Methods 3 & 4 (2019).** It is the introduction to “When is a function differentiable?”, the final section of the chapter “Differentiation”.

## Witch 14: Stretching the Truth

The easy WitCH below comes courtesy of the Evil Mathologer. It is a worked example from Cambridge’s *Essential Mathematics Year 9* (2019), in a section introducing parabolic graphs.

## WitCH 13: Here for the Ratio

The WitCH below is courtesy of a clever Year 11 student. It is a worked example from Jacaranda’s *Maths Quest 11 Specialist Mathematics* (2019):

## PoSWW 7: Power Outage

## PoSWW 6: Logging Off

The following exercise and, um, solution come from Cambridge’s *Mathematical Methods 3 & 4* (2019):

## Update

Reflecting on the comments below, it was a mistake to characterise this exercise as a PoSWW; the exercise had a point that we had missed. The point was to reinforce the Magrittesque lunacy inherent in Methods, and the exercise has done so admirably. The fact that the suggested tangents to the pictured graphs are not parallel adds a special Methodsy charm.

## WitCH 12: Duplicitous

The following WitCH comes from the VCE 2014 Specialist Exam 1:

The Examiners’ Report indicates that 81%, 48% and 45% of students received full marks for parts (a), (b) and (c), respectively.

## 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 . 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.