Maths is hard.

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kiwifidget

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#317718 9-Nov-2024 10:24

NCEA L2 students in tears over this one...

https://www.nzherald.co.nz/nz/the-level-2-ncea-maths-question-that-knocked-the-confidence-of-our-top-students/QDISMTPN4BDD3OUELHUZ25EFOI/

Answer:

Click to see spoiler(s)

I can follow the answer up to the highlighted bit and then it turns into dark magic for me.

But it's all irrelevant really, because real life experience has taught me that a straight cylinder is the second worst/second best shape for keeping hot liquids warm as long as possible.

A receptacle that is wider at the top than the bottom is the worst.

A receptacle that tapers in at the top is the best, but I imagine the maths for that is even harder.

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#3307131 9-Nov-2024 11:02

It’s always been interesting seeing the uproar when students feel they are entitled to answer every question correctly. I see it as a good life lesson for them - what you plan for is not always what you expect.

Anyway for this question you need to find the first derivative with respect to radius. The trick (or controversial aspect) is knowing to rewrite 1/r as r^-1. Then you set the derivative to zero and solve for r.

kiwifidget

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#3307134 9-Nov-2024 11:29

Nate001: Anyway for this question you need to find the first derivative with respect to radius. The trick (or controversial aspect) is knowing to rewrite 1/r as r^-1. Then you set the derivative to zero and solve for r.

ie dark magic

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SirHumphreyAppleby

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#3307136 9-Nov-2024 11:59

kiwifidget:

ie dark magic

Not really. While I am very out of practice, that's how we did it back in the day.

eracode

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#3307137 9-Nov-2024 12:08

It’s good to see that, despite what we hear in the media, NZ school maths doesn’t appear to have been excessively dumbed-down.

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#3307140 9-Nov-2024 12:29

eracode:

It’s good to see that, despite what we hear in the media, NZ school maths doesn’t appear to have been excessively dumbed-down.

except that what they're taught in classes are. which is why every year we have this on stuff complaining about the exam.

RunningMan

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#3307202 9-Nov-2024 13:04

It's an old question. Sometimes framed as wanting to minimise the material used to make it to minimise cost. Some thing, just different wording.

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yitz

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#3307209 9-Nov-2024 13:22

I'm guessing the problem is due to the last bullet point below found in the current/2007 curriculum document - the equation to be differentiated is not from the class of polynomials functions but rational (which they are required to understand under the Equations and Expressions sub-heading).

The wider problem seems to be the narrowing in scope of successive curriculums written by the bureaucrats in Wellington, compared the above 2007 curriculum document to the below 1992 it appears the later curriculum focuses more on being able to solve real world problems and use extended abstract thinking yet at the same time limit applications to only polynomial functions when previously this was merely a suggested context. I say good on the government on outsourcing parts of the maths curriculum to text book companies as they have done for primary school / end of Year 8 maths.

Curriculum documents published
(2007) https://nzcurriculum.tki.org.nz/content/download/1109/11992/file/Charts2.pdf
(1992) https://nzcurriculum.tki.org.nz/content/download/62998/504260/file/MATH_NZC.pdf

k1w1k1d

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#3307257 9-Nov-2024 13:43

Does h include the thickness of the cap?

cddt

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#3307258 9-Nov-2024 13:43

As an extremely formulaic question I would have assumed 6th form maths students would have practiced similar questions many times before.

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#3307276 9-Nov-2024 14:54

To be fair, as an adult, I wouldn't even know where to start with that question. Admittedly it's been a GOOD many years since I would have faced something like this.

Behodar

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#3307290 9-Nov-2024 15:59

networkn:

To be fair, as an adult, I wouldn't even know where to start with that question. Admittedly it's been a GOOD many years since I would have faced something like this.

I've been working on a project recently that forced me to remember how to do trigonometry. It's been a while, and there were some false starts.

"Why is sin(0.25) not giving me 1? A sine wave goes 'up, middle, down, middle' so a quarter of the way through should be 'up'!"

It took me an embarrassingly long time to remember that the functions go from 0-360, not 0-1!

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cddt

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#3307295 9-Nov-2024 16:14

Behodar:

I've been working on a project recently that forced me to remember how to do trigonometry. It's been a while, and there were some false starts.

"Why is sin(0.25) not giving me 1? A sine wave goes 'up, middle, down, middle' so a quarter of the way through should be 'up'!"

It took me an embarrassingly long time to remember that the functions go from 0-360, not 0-1!

Depends how you have your calculator set... technically they go from 0 - 2*pi radians. And everyone doing any remotely serious maths uses radians rather than degrees.

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neb

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#3307307 9-Nov-2024 18:06

networkn: To be fair, as an adult, I wouldn't even know where to start with that question. Admittedly it's been a GOOD many years since I would have faced something like this.

Just channel your inner millennial, "Hey Siri, I need to minimise the surface area of a cup ...".

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#3307308 9-Nov-2024 18:08

cddt: As an extremely formulaic question I would have assumed 6th form maths students would have practiced similar questions many times before.

I don't remember ever getting anything like that, it was all just differentiate this, solve this integral, differentiate something else. The single most useless educational topic I've ever encountered (or possibly the most uselessly-taught topic).

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#3307309 9-Nov-2024 18:13

Not being a math person these days, I do like to have fun with these types of questions from a physics/science perspective.

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