Mathematics Extension 1 Predictions/Thoughts (1 Viewer)

[tywebb]

So if you wrote it out in full it would be

I've heard various stories about how many marks this would get - everything from 0 to full marks.

I didn't go to NESA's HSC feedback day today which was held at UTS - but I heard that at that the HSC markers confirmed it would get full marks.

Arguments for saying stick to the syllabus is seriously weakened when many students have not been in schools in NSW for 13 years, but rather in later years come to Australia to do the HSC - when they have already been educated elsewhere in determinants, vectors including cross product, matrices etc.

So when they see a question like this it is obvious to them to use the cross product - and now according to the HSC markers would not be penalised for doing so - especially when the question said "or otherwise".

 

[Luukas.2]

I've heard various stories about how many marks this would get - everything from 0 to full marks.

I didn't go to NESA's HSC feedback day today which was held at UTS - but I heard that at that the HSC markers confirmed it would get full marks.

Arguments for saying stick to the syllabus is seriously weakened when many students have not been in schools in NSW for 13 years, but rather in later years come to Australia to do the HSC - when they have already been educated elsewhere in determinants, vectors including cross product, matrices etc.

So when they see a question like this it is obvious to them to use the cross product - and now according to the HSC markers would not be penalised for doing so - especially when the question said "or otherwise".

They could have just come from Victoria, the VCE specialist maths course includes vector cross products!

 

[tywebb]

They could have just come from Victoria, the VCE specialist maths course includes vector cross products!

So do you think it's fair to give full marks for the obviously much shorter solution - compared to these which obviously take much longer time and effort?


(from nesa mg)

 

[scaryshark09]

So do you think it's fair to give full marks for the obviously much shorter solution - compared to these which obviously take much longer time and effort?

View attachment 42564
(from nesa mg)

yeah no, i dont think that's fair
the simpler solution (3 posts ago) doesn't assess anything from the actual NSW syllabus pretty much. theres no way someone should be getting 3/3 for that.

 

[tywebb]

yeah no, i dont think that's fair
the simpler solution (3 posts ago) doesn't assess anything from the actual NSW syllabus pretty much. theres no way someone should be getting 3/3 for that.

Well they said because the question said "or otherwise" they would have no choice but to award full marks for the cross product solution, however short that may be - and regardless of anyone's opinions on the matter.

 

[epicmaths]

Love the cross products solution - another reflection of how poorly conceived the new HSC syllabus is, bring back circle geometry!

 

[Luukas.2]

@tywebb, the cross-product solution is mathematically flawless. The question did not include any direction that the cross-product method contravenes. I struggle to see any reason why it should be penalised - and especially if the solution included a statement as to what the cross-product is and how the solution thus follows. The question did strike me as strange, in that I saw multiple 'otherwise' approaches before I recognised the hence approach being suggested, but students who can see alternatives that weren't considered in advance shouldn't be penalised for greater knowledge or insight than was anticipated.

Having said that, the following question was on the 2021 MX2 HSC, q15(d), and worth 2 marks:

​

Would you give full marks for the following solution? It is valid, but also surely not what the examiners intended...

Fermat's Last Theorem, which was proved in 1999 by Andrew Wiles, states:





​

In general, questions being solvable by valid methods beyond the syllabus are a potential problem that should be considered / addressed while drafting the exams, not as a marking problem after the exams have been sat.

 

[tywebb]

...Fermat's Last Theorem, which was proved in 1999 by Andrew Wiles, states:..

No because it wasn't. It was proved in 1994 and published in 1995.

 

[tywebb]

But generally if one can give a reference for a theorem that was proved, one can go on to use it to prove other things without having to prove it again. That's how maths works.

Maybe a more succinct solution would simply be


follows as a corollary of Fermat's Last Theorem

Reference:

Wiles, Andrew (1995). "Modular elliptic curves and Fermat's Last Theorem" Annals of Mathematics. 141 (3): 443–551.

 

[Luukas.2]

No because it wasn't. It was proved in 1994 and published in 1995.

My mistake, I mis-remembered the year.

 

[Luukas.2]

But generally if one can give a reference for a theorem that was proved, one can go on to use it to prove other things without having to prove it again. That's how maths works.

Maybe a more succinct solution would simply be

View attachment 42566
follows as a corollary of Fermat's Last Theorem

Reference:

Wiles, Andrew (1995). "Modular elliptic curves and Fermat's Last Theorem" Annals of Mathematics. 141 (3): 443–551.

This I wouldn't give 2 marks for, because Fermat's Last Theorem only establishes the result for integers ... but yes, a succinct version that shows separately should be sufficient.

 

[ilovemangos]

I've heard various stories about how many marks this would get - everything from 0 to full marks.

I didn't go to NESA's HSC feedback day today which was held at UTS - but I heard that at that the HSC markers confirmed it would get full marks.

Arguments for saying stick to the syllabus is seriously weakened when many students have not been in schools in NSW for 13 years, but rather in later years come to Australia to do the HSC - when they have already been educated elsewhere in determinants, vectors including cross product, matrices etc.

So when they see a question like this it is obvious to them to use the cross product - and now according to the HSC markers would not be penalised for doing so - especially when the question said "or otherwise".

wouldn't you have to derive OOS formulas such as the cross product, scalar triple product, etc.?

 

[tywebb]

wouldn't you have to derive OOS formulas such as the cross product, scalar triple product, etc.?

They didn't say that you need to derive it. They said because the question said "or otherwise" you can use ANYTHING including oos stuff.

It is silly to have to derive well known things like that.

Do you derive Pythagoras' Theorem every time you use it?

 

[liamkk112]

So do you think it's fair to give full marks for the obviously much shorter solution - compared to these which obviously take much longer time and effort?

View attachment 42564
(from nesa mg)

i think its fair because if you are willing to take the time to learn beyond the syllabus then you should be rewarded. in other subjects like physics there's no issue if you learn all of the deeper details about how motors work, the standard model and so on, and students are rewarded for the added detail, so i don't see why math should be any different.

also you run the risk of making a mistake and potentially getting lesser marks than other in syllabus solutions. my teacher (a hsc marker) said that while for example you could use l'hospitals rule for evaluating limits, if you make a small mistake or fail to give enough detail or justification as to why your method works, then the HSC marker could decide that your solution isn't worth as much as another solution with another mistake (as they decide what "equivalent merit" is). so while the cross product in this case would potentially save time, if you didn't say that the magnitude of the cross product gives you the area of a parallelogram formed by the two vectors and that the area of the triangle formed by the two vectors is half the area of the parallelogram, you risk potentially losing marks (and you can't predict how much justification you need as obviously there are no past questions on the method you are using to indicate the level of detail required). this also might be why some students recieved lower marks than others although they used the same solution method.

 

[ilovemangos]

i think its fair because if you are willing to take the time to learn beyond the syllabus then you should be rewarded. in other subjects like physics there's no issue if you learn all of the deeper details about how motors work, the standard model and so on, and students are rewarded for the added detail, so i don't see why math should be any different.

also you run the risk of making a mistake and potentially getting lesser marks than other in syllabus solutions. my teacher (a hsc marker) said that while for example you could use l'hospitals rule for evaluating limits, if you make a small mistake or fail to give enough detail or justification as to why your method works, then the HSC marker could decide that your solution isn't worth as much as another solution with another mistake (as they decide what "equivalent merit" is). so while the cross product in this case would potentially save time, if you didn't say that the magnitude of the cross product gives you the area of a parallelogram formed by the two vectors and that the area of the triangle formed by the two vectors is half the area of the parallelogram, you risk potentially losing marks (and you can't predict how much justification you need as obviously there are no past questions on the method you are using to indicate the level of detail required). this also might be why some students recieved lower marks than others although they used the same solution method.

i was wondering what do you mean by students are rewarded for extra detail in subjects like physics? I thought physics marking guidelines were strict for what they want you to say in short answer as with chemistry. so going into too much detail would produce a convoluted response.

 

[liamkk112]

i was wondering what do you mean by students are rewarded for extra detail in subjects like physics? I thought physics marking guidelines were pretty strict for what they want you to say in short answer right? same with chemistry. so going into too much detail would probably produce a convoluted response.

well for example q21 in 2023 hsc physics, you were asked to identify two variables that determine the luminosity of a star. most students are only exposed to the HR diagram so would have probably written the size and the temperature. however, the power output is a variable that also determines the luminosity, and this isn't in the syllabus, but is still a fact that is rewarded. The formula for luminosity is also not in the syllabus, however it is a very good idea to know this and I'd say many physics students probably know this anyway because of questions like this and other relevant formulas to stars that aren't in the syllabus (i did memorise the luminosity formula myself).

question 33 in 2023 hsc physics is another example. it pretty much asks you to list off experiments related to quantum physics and/or particle physics that made new discoveries in these areas, and how these experiments relate to fields. a student with out of syllabus knowledge could talk about the higgs boson, discovery of quarks, etc. and be aptly rewarded (and afaik some schools also teach these concepts), just as much as a student who would talk about thomson and the electron, chadwick and so on.

my point wasn't so much that every single question has an out of syllabus response, moreso that if it does, students are still rewarded for providing one and this is sometimes even in the marking guidelines like q21 in 2023 physics, so i don't see why math should be treated any differently with regards to out of syllabus content

 

[Luukas.2]

i was wondering what do you mean by students are rewarded for extra detail in subjects like physics? I thought physics marking guidelines were strict for what they want you to say in short answer as with chemistry. so going into too much detail would produce a convoluted response.

Marking guidelines are strict about what is required in an answer but much more flexible about the content used to meet the requirements. An "assess" question that does not make a judgement, based on discussed evidence, will not score highly. However, there are many questions where what the judgement is and what evidence is discussed in support of it is quite open.

For example, a question seeking an assessment of the importance of X to Y may have full-mark responses ranging from X is crucial to X is of little importance, but each conclusion must be supported by the evidence discussed. On the other hand, a fifteen sentence response describing X and its implications for Y in detail, but lacking an assessment of X's importance, will be penalised even if everything written is accurate and relevant to making such a judgement.