WitCH 89: Proof Negative

VCAA’s new version of Specialist Mathematics contains “Proof” as a topic (which says everything one needs to know about VCE mathematics). A few commenters have alerted us to the fact that VCAA have now provided two videos: on induction (transcript and slides); and on proof by contradiction (transcript and slides). There are issues.

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WitCH 88: Unwarranted Confidence

One more from the 2022 Specialist Mathematics Exam 2. Belatedly, we’ve decided this one deserves its own post. It’s probably more of a PoSWW. But, for those weirdos who like to think about this stuff, there are probably also aspects to discuss.

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WitCH 87: Cannery Row

(The title is very clever, but you have to think about it.)*

This one is the last part of the last question of 2022 Specialist Mathematics Exam 2 (not online). It sparked a lot of discussion on the exam post, but seems worth its own WitCH. The question is clearly a mess, but what was intended, and how to think about the mess is not so clear, at least to us. (We showed the question to a professor of statistics, whose first reaction was “Ow!” We’ve applied the smelling salts, and we should be in possession of the professor’s second reaction soon.)

For clarification, we are (kinda sorta) told in the question stem that the masses of the empty cans are normally distributed, but we are told nothing else relevant, other than what’s given below.

Go for it (again).

*) Proving that the title is not really that clever.

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WitCH 85: The Continuation of MAV’s Trials

With Methods exams next week, this one’s kinda important.

We try to avoid critiquing, or even being in the same room as, third party VCE practice exams. They are invariably clunky and weird, with plenty to criticise, but they matter infinitely less than the yearly screw-ups of the official exams.

Even MAV trial exams we do our best to ignore. Yes, the MAV is (too) closely aligned with the VCAA (with a number of people in conflicted, dual roles), and so MAV has a significantly greater professional and moral obligation to maintain high standards. But still, third party is third party, and we try our best to just ignore MAV’s nonsense. On occasion, however, MAV’s nonsense matters sufficiently, or is simply sufficiently annoying, to warrant a whack.

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WitCH 83: A Viral MAS Question

8 √∑ 2(2 + 2) = ?

This is really a PoSWW. Except, there are a lot of words.

Above is one of those stupid BODMAS things, which appear in the media about once a month. Except, this one has just been sorted by a couple of Canadian Maths Ed professors, in a Conversation article titled The Simple Reason a Viral Math Question Stumped the Internet. Regular readers will be aware of our method of resolving such questions, but we think there are aspects of the Conversation article that warrant specific whacks.

Have fun.

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WitCH 81: Pointed Criticism

This is another one courtesy of Mysterious Michael. We’re not quite sure whether it’s a WitCH, or a PoSWW, or one for the error list, or simply a roll-your-eyes-and-ignore. In any case, it’s a question from the notorious 2016 Methods Exam 2 (report here), and we’ve expanded slightly from MM’s stated concern. (We could’ve expanded to include the entire question, as a Road to Nowhere, but decided not to lose too much of MM’s original focus.)

Have fun.

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WitCH 80: External Forcing

Yep, it’s Golden Ratio Day here at Mathematical CrapLand.

This is a weird one. It might be trivial, or very hard, or non-existent. We’re not 100% sure. (OK, we are sure, but it took a while.) Anyway, it’s a research paper appearing in a (not the)¬†journal published by Nature, and so can tolerate a little extra scrutiny. The paper, titled The golden number seen in a mechanical oscillator, appeared a couple weeks ago in the open access Nature journal, Scientific Reports; the paper can be downloaded here. Here is the begining: Continue reading “WitCH 80: External Forcing”