A Sum of “Complex” Numbers

We really want to get on to other things, but this needs to be done. Below is pretty much a complete cataloging of Nelson‘s use of the adjective “complex” in the five recent WitCHes (here, here, here, here and here). To be clear, there is tons more wrong, and bad, in the selected excerpts in the WitCHes: the proper WitCH updating, currently scheduled for late 2029, will be long and painful. But the use of “complex” warrants particular attention. It reflects VCAA’s complex madness, and we doubt that it is a coincidence. Continue reading “A Sum of “Complex” Numbers”

WitCH 119: Poly Want a Cracker?

Last one. These are excerpts from the final section of Nelson‘s complex numbers chapter. Similar to the previous WitCHes, I’ve tried to not be manipulative material in selecting the material except, of course, in selecting the worst bits: the worked examples not indicated are standard, and in general the working is tedious but ok; a monotonous but essentially correct proof of the conjugate root theorem is included in the text.

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WitCH 118: The Chaos Factor

I was gonna go with The Sot-Weed Factor, but that was too cute a title, even for me.

We’re now getting to the VCAA-related material, which prompted this whole series. The last two sections of Nelson‘s complex numbers chapter are on factors and roots of polynomials. Below are excerpts on factorisation. (For the sake of interpretation, note that: the factor and remainder theorems are stated reasonably clearly, but of course with no hint of a proof; these two theorems are followed by two standard “worked examples”; the working of all the worked examples is painfully earnest and slow, but is close enough to correct.)

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WitCH 116: Polar Bare

This is our second WitCH on Nelson‘s chapter on complex numbers. As with our first WitCH, we have not excluded any definitions or arguments or explanations from the text that would fill apparent (and actual) gaps in the selected material; the rest of the subchapter consists of routine examples and less problematic (but far from unproblematic) exposition. Continue reading “WitCH 116: Polar Bare”

WitCH 115: Not So Complex

Last year we took a multiwhack at VICmaths, Nelson’s Year 12 Specialist Mathematics textbook, specifically at Nelsons chapter on logic and proof: see here, here, here, here, here and here. This post is the beginning of a second multiwhack, this time at Nelsons chapter on complex numbers. Continue reading “WitCH 115: Not So Complex”

One FEL Swoop: The Foundation Error List

This is the (new) newly established home for Foundation Mathematics exam errors. The guidelines are given on the Methods error post, and there is also a Specialist error post, and a (now renamed) General error post (with unchanged link).  As with General Maths, I will not look much at the Foundation exams, only posting errors as they are brought to my attention.

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2023 Exam (No exam yet, discussed here)

MCQ13 The key to the graph is confusing, and wrong. Some indication that “payment” and “interest” are cumulative had to be included.

Q1(c) There are two methods of working out the percentage increase, which give different answers. One method is unlikely to have been considered by students, but this still should not occur.

Q2(e) The question makes zero sense, since it assumes that a person cannot play both a ball sport and a non-ball sport. The question also fails to specify the percentage is of females participating in a sport.

Q6 An awfully written question, throughout confusing usage with market share. There is probably only one plausible way to answer the questions, but this is teaching Not Maths.

Q6(a) The 2022 percentages in the graph do not total to 100%. This in itself is ok, but it leads to two potential answers to (a); one answer is unlikely to be given, but this still should not occur. The graph should have been appropriately labelled.

Q11 The outer rectangle on the diagram doesn’t mean anything and was probably actively confusing.

Witch 113: Smoothing Over the Cracks

This one is a combo WitCH. The main concern is a multiple choice question from last week’s Methods Exam 2. The question may not be an “error” in the newspaper sense, but it is bad. To appreciate some (but far from all) of its badness, however, we need to see VCAA’s solution. We won’t likely see that solution, however however, for months, if ever; transparency is not VCAA’s strong suit (Section 7).

To deal with this, we’ve teamed up last week’s MCQ with a similar MCQ from the 2021 Exam 2, together with VCAA’s solution to that earlier question from the exam report. Last week’s question appears first. Continue reading “Witch 113: Smoothing Over the Cracks”

Witch 108: A Mean Trig

This one, which has been discussed a bit here, comes from the 2023 NHT Methods Exam 2. It is a little strange. There are aspects of the question we like, or at least there are some interesting ideas underlying the question. Nonetheless there is no shortage of crap, and so here we are.

Continue reading “Witch 108: A Mean Trig”