WitCH 92: The Webs VCAA Weaves

This is a continuation of a previous WitCH. To provide teachers with some guidance on the new VCE Specialist Mathematics curriculum (Word, idiots, and see comments here), VCAA had posted two webinars, on proof by contradiction and proof by induction; we WitCHed it. VCAA has now added four new webinars, which can be viewed here, and with companion documents as indicated below.

Get to work.

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WitCH 90: Tiles and Tribulations

This is late, and it isn’t very Christmasy. But it came up as part of another project, and it’s been bugging us, so Bah Humbug.

The following is a question from 2022 Mathematical Methods Exam 1. It’s been discussed some on this post, including a concerning rumour (edited 24/12/22), and we also hammered some of the wording on this post. It is clearly deserving of its own WitCH.

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The Volume of a Cone

A few days ago, we pulled on a historical thread and wound up browsing the early volumes of The Mathematical Gazette. Doing so, we stumbled across a “mathematical note” from 1896 by Alfred Lodge, the first president of the Mathematical Association. Lodge’s note provides a simple derivation for the volume of a cone. Such arguments don’t vary all that much but, however we missed it, we’d never seen the derivation in the very elegant form presented by Lodge. Here is Lodge’s argument, slightly reworded.

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The CAS Betrayal

This post will take the form of Betrayal, with a sequence of five stories going backwards in time.

STORY 5

Last year, I was asked by an acquaintance, let’s call him Rob, to take a look at the draft of a mathematics article he was writing. Rob’s article was in rough form but it was interesting, a nice application of trigonometry and calculus, suitable and good reading for a strong senior school student. One line, however, grabbed my attention. Having wound up with a vicious trig integral, Rob confidently proclaimed,

“This is definitely a case for CAS”.

It wasn’t. Continue reading “The CAS Betrayal”

WitCH 70: Troubled Relations

This is not an old one. It is from the 2019 Specialist Exam 2 and comes courtesy of student PURJ, who previously contributed to the discussion here. PURJ noted one, glaring, issue with the question below and its grading, but we think there are other issues as well. As with our previous WitCH, we’ll semi-update with excerpts from the examination report once people have had a chance to ponder and to comment.

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WitCH 64: Decreasing Intelligence

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”

WitCH 58: Differently Abled

Like the previous post, this one comes from Maths Quest Mathematical Methods 11, and is most definitely a WitCH. It can also been seen as a “contrast and compare” with WitCH 15.

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.

A Choice of Difficults

You have a choice. The two questions below come from different exams:

Each question was (arguably) last year’s most difficult exam question on the most difficult mathematics subject in that state. Each question was effectively allocated just under 20 minutes to complete (11/100 x 180 and 13/80 x 120).

Now, you must choose: which question is better, in any sense of the word “better”?

 

NSW  (Formula Marking guide and sample solution are here.)

 

VIC  (Briefly discussed here, marking guide and sample solution are in your dreams.)