(The preamble for this post is now a post-amble, at the end.)
Our final 2021 NHT WitCH is the final question from the Specialist Exam 1.
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.
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. Continue reading “WitCH 64: Decreasing Intelligence”
The following comes courtesy of frequent commenter, John Friend. It is an exercise and solution from Cambridge Specialist Mathematics 3&4.
It’s not fun, but we gotta do it.
Below is Hannah Stoten, one of the review authors and future kidnap victim, launching the review. An excellent review, and a well-spoken author. What could go wrong?
Well, that’s not good:
Nonetheless, we’re willing to assume that Hannah is innocent here, and plans to kidnap her and bring her to Australia are proceeding apace.
Subsection 13.2.5, below, is on “differentiability”. The earlier part of chapter 13 gives a potted, and not error-free, introduction to limits and continuity, and Chapter 12 covers the “first principles” (limit) computation of polynomial derivatives. We’ve included the relevant “worked example”, and the relevant exercises and answers.
The following is just a dumb exercise, and so is probably more of a PoSWW. It seems so lemmingly stupid, however, that it comes around full cycle to be a WitCH. It is an exercise from Maths Quest Mathematical Methods 11. The exercise appears in a pre-calculus, CAS-permitted chapter, Cubic Polynomials. The suggested answers are (a) , and (b) 81/32 km.