Maths is hard.

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nova

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#3307781 11-Nov-2024 16:18

Paul1977:

ChatGPT gave the answer for height as 0.01cm shorter than the answer in the Herald.

I suspect this is because when rounding to 2 decimal places (in this case rounding down) would mean the vessel would hold fractionally less than 500ml. I wonder if they were that pedantic when marking?

The actual answer is the cube root of 250/pi , which is 4.30127, so if the herald gave 4.30 then the herald is more correct than ChatGPT. The question didn't actually state the number of decimal places, and as the answer is an irrational number

The weird with this is that the question isn't that different to the previous question on the exam, for both of them you need to understand how to find a minima using the derivative test. It seems reading the herald the complaint is that the curriculum specifies differentiating polynomials, and x^n is not a polynomial if n is negative. But the power rule for differentiating x^n is the same for both positive and negative values of n, it is always n*x^(n-1), so it is not that far out of the curriculum. It is not as if they are asking to differentiate e^x or sin(x) etc.

https://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2024/91262-exm-2024.pdf

I actually found question 1b a bit trickier, as it is an anti-derivative problem, and not a straight integration, and it took me a while to realise that the reason why my anti-derivative didn't give the right answer for the given point was that you actually needed to solve for the constant on the anti-derivative by using the given point. All up it seems like a reasonably challenging exam, but fairly narrow in scope, so if you have actually been taught the material on the exam I don't think it would be that hard.

Paul1977

5039 posts

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#3307794 11-Nov-2024 16:58

nova:

The actual answer is the cube root of 250/pi , which is 4.30127, so if the herald gave 4.30 then the herald is more correct than ChatGPT. The question didn't actually state the number of decimal places, and as the answer is an irrational number

The weird with this is that the question isn't that different to the previous question on the exam, for both of them you need to understand how to find a minima using the derivative test. It seems reading the herald the complaint is that the curriculum specifies differentiating polynomials, and x^n is not a polynomial if n is negative. But the power rule for differentiating x^n is the same for both positive and negative values of n, it is always n*x^(n-1), so it is not that far out of the curriculum. It is not as if they are asking to differentiate e^x or sin(x) etc.

https://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2024/91262-exm-2024.pdf

I actually found question 1b a bit trickier, as it is an anti-derivative problem, and not a straight integration, and it took me a while to realise that the reason why my anti-derivative didn't give the right answer for the given point was that you actually needed to solve for the constant on the anti-derivative by using the given point. All up it seems like a reasonably challenging exam, but fairly narrow in scope, so if you have actually been taught the material on the exam I don't think it would be that hard.

It was the height that ChatGPT gave a slightly different value to, not the radius. Herald said 8.61, ChatGPT said 8.60 (unrounded was 8.602540138280995).

Earbanean

937 posts

Ultimate Geek

#3307800 11-Nov-2024 17:23

My son did that exam and answered that question. When I asked him in general about how the exam had gone (prior to stuff in the media), he mentioned a question where he had to think twice about representing 1/x as x to the power of -1 before differentiating, but was then fine with the question.

I think this might not be part of Level 2 (Year 12) calculus, but my son does some Level 3 as part of an extension class. Maybe that's unfair on other Year 12s, but I guess it at least helps to spread out the range of results a bit.

As mentioned in a few earlier posts, to get the min or max of a function, you differentiate it, set the resulting function to zero, then solve that for unknown variables. For anyone interested in why that is, consider a graph of a function at a local min or local max. At the min it looks like a "u", at a max it looks like a "n". If you think about the slope of the line at the very top of the "n", or bottom of the "u", in both cases it is zero. i.e. at the instant it goes from sloping up to sloping down (or vice versa) it's flat. The slope of a line is just it's first derivative, or the differentiation of it's function. So, at the local max or min, the first derivative is equal to zero.

I remember questions back in the day about maximum paddock size for certain amount of fencing wire etc. I guess going 3-D and involving a circular area is a bit more complicated, but not excessively so.

nova

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#3307806 11-Nov-2024 17:35

Paul1977:

It was the height that ChatGPT gave a slightly different value to, not the radius. Herald said 8.61, ChatGPT said 8.60 (unrounded was 8.602540138280995).

Sorry, my mistake. Looks like ChatGPT is correct then, there is no reason to round that up to 8.61cm. The person who worked it out must have rounded the radius to 4.30cm, plugged that into the formula for height, which magnified the rounding error (since you are dividing by the square of the radius to figure out the height)

cddt

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#3307849 11-Nov-2024 20:15

blackjack17:

Schools or parents?

Possibly both. But I think that some parts of the education system have forgotten that their job is to prepare kids for the real world, and shouldn't be constantly coddled. Sure, recognise everyone's achievements, but challenge our children every day.

I would rather my daughter come home with a 50% on a tough as hell chemistry exam than 100% on an exam which she described as "a piece of cake".

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SomeoneSomewhere

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#3307896 12-Nov-2024 01:56

kiwifidget:

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

To answer the much earlier question, writing anything that's "per x" as x^-1 is very common in maths and engineering. It's pretty common to see RPM given as "min^-1", especially in European products, to avoid the anglicised 'per' or 'revolution' and thus the need to write the nameplate in a dozen languages.

MadEngineer

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#3309126 14-Nov-2024 19:46

I was helping my son with his maths a while back and I'm looking at the pages thinking I used to love this stuff but now I find myself needing to do a dodgy chatgpt to get it to teach me so I can in turn teach the lad.

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mdooher

Hmm, what to write...
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#3309128 14-Nov-2024 19:53

SomeoneSomewhere:

To answer the much earlier question, writing anything that's "per x" as x^-1 is very common in maths and engineering. It's pretty common to see RPM given as "min^-1", especially in European products, to avoid the anglicised 'per' or 'revolution' and thus the need to write the nameplate in a dozen languages.

learnt this in about form 3 eg km/h = kmh^-1 and as for 1/x = x^-1, about the same time

Matthew

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