MitPY 10: Square Roots

This MitPY comes from a student, Jay:

I have a question relating to polynomial equations. For context I have just finished Y11 during which I completed Further 3&4, Methods 1&2 and Specialist 1&2.

This year during my maths methods class we covered the square root graph, however I was confused as to why it only showed the positive solutions. When I asked about it I was told it was because the radical symbol meant only the positive solution.

However since then I have learnt that the graph of \boldsymbol{y=x^{0.5}} also only shows the positive solution of the square root, while \boldsymbol{y^2=x} shows both. I am quite confused by why they aren’t the same. The only reason that I could think of is that it would mean \boldsymbol{y=x^2} would be the same as \boldsymbol{y^2=x^4}, and while the points (-2,-4) and (2,-4) fit the latter they clearly don’t fit former.

Could you please explain why these aren’t the same?

ScoMoFo Meets PingMoFo

Zhao Lijian, who has been hilariously described as a “diplomat“, has posted a mean tweet.

Zhao, who is, of course, a hypocritical little toad, posted a faked image of an Australian soldier with a bloodied knife over the throat of an Afghan kid. The image was created by Lu Yu, another hypocritical little toad, and hilariously described as a “political computer graphic artist“. Lu Yu’s image is outrageous, and so ScoMoFo sprang into action and confected outrage.

Let’s remind ourselves what this is about. Zhao’s post was in reference to the Brereton Report into alleged crimes by the Australian Defence Force, which ScoMoFo is already undermining. Specifically, Zhao was referring to an alleged incident raised by Dr. Samantha Crompvoets, a sociologist specialising in military culture. In 2015, the Special Operations Commander Australia appointed Dr. Crompvoets to undertake a “cultural review” of the Special Operations Command, which resulted in two documents referred to in the Brereton Report (pp 119-121): “Insights and reflection” (January, 2016); and “Perceptions reputation and risk” (February, 2016). In her January report, which is short and which should be read by everyone, Dr. Crompvoet records a number of specific incidents reported to her by military personnel (p 120 of the Brereton Report):

“A specific incident described to Dr. Crompvoets involved an incident where members from the [Special Air Service Regiment] were driving along a road and saw two 14-year-old boys whom they decided might be Taliban sympathisers. They stopped, searched the boys and slit their throats. The rest of the Troop then had to ‘clean up the mess’, which involved bagging the bodies and throwing them into a nearby river. Dr Crompvoets says she was told this was not an isolated incident.”

In regard to incidents such as the above not being isolated, Dr. Crompvoets wrote,

The gravity of these descriptions does not simply come from the details of particular events, it comes from the emphasis that most often accompanied these stories – ‘it happened all the time’.  

The above is the incident latched onto by Toad Lu and Toad Zhou. Which leaves us with a choice. On the one hand, we can consider the probable murdering of kids by Australian military personnel, and we can ponder just how often such horrors occurred. Or, as ScoMoFo would prefer, we can focus on a couple of toads and a fucking mean tweet. Take your pick.

WitCH 48: Thesis Not Good

This combo WitCH comes courtesy of mystery correspondent, tjrb. They flagged three multiple choice questions from the 2018 Algorithmics exam (here, and examination report here), and we’ve added a fourth. tjrb also remarks, “There are probably a lot more errors in this paper (and the other algorithmics papers), but these were the most strikingly incorrect”.

For Q2, the examination report indicates that 41% of students gave the intended answer of A. By way of explanation, the report then remarks,

“Cobham theorised that problems that are feasibly computable (also known as easy problems) are those that are decidable in polynomial time.”

For Q6, the report indicate that both A (51%) and C (33%) were “accepted”, but is otherwise silent.

The report is silent on Q12 and Q16, except to indicate the intended answers: C (94%) and A (66%), respectively.

Feeling VCAA’s Draft: Discussion

It seems the VCAA has just released their draft of the new study design for Mathematics:

  • The current (pre-COVID) study design (pdf) is here.
  • The draft for the new study design (word) is here.
  • The key changes overview (work) is here.
  • The link for feedback (until March 9, 2021) is here.

We haven’t yet looked at the draft, because we’re scared. But, don’t let that stop others. May the discussion and the throwing of brickbats begin.