Mathematics Extension 1 Predictions/Thoughts (1 Viewer)

[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.

 

[Average Boreduser]

What r predictions looking like for next yr?

 

[WeiWeiMan]

What r predictions looking like for next yr?

u mean this yr?

 

[Average Boreduser]

u mean this yr?

mb this yr

 

[WeiWeiMan]

mb this yr

prob harder than 2022
my guesses:
7 marker in 2 parts vectors (kinda like 14c from 2023)
4 mark long ass stats question (like last qn from 2022)
5 mark long ass projectile question (like second last qn from 4u 2021)
4 mark hard induction question

 

[SMARTYPANTS_SINGH]

prob harder than 2022
my guesses:
7 marker in 2 parts vectors (kinda like 14c from 2023)
4 mark long ass stats question (like last qn from 2022)
5 mark long ass projectile question (like second last qn from 4u 2021)
4 mark hard induction question

I’ve never seen a “hard” 3U induction question other then in BOS trials cause they manage to somehow make the most aids tests

 

[WeiWeiMan]

I’ve never seen a “hard” 3U induction question other then in BOS trials cause they manage to somehow make the most aids tests

there's a first for everything

 

[K2Trappy]

I’ve never seen a “hard” 3U induction question other then in BOS trials cause they manage to somehow make the most aids tests

ye I think hard in induction would just be some long ass algebra in which ur likely to make a small error cause in 3u they cant really do much unless they make some weird thing to do with the inductive step idk

 

[bruhmoment.]

I’ve never seen a “hard” 3U induction question other then in BOS trials cause they manage to somehow make the most aids tests

bruh for some of them, i cant even prove n = 1.

 

[bruhmoment.]

there's a first for everything

idk a hard induction question just seems like a trig induction (maybe similar to 2006 hsc - i think thats the trig induction year i forgot) but idk it cant really go harder than that, excluding bos trials. This year's independent had a q14 induction question but that was piss easy.

 

[bruhmoment.]

prob harder than 2022
my guesses:
7 marker in 2 parts vectors (kinda like 14c from 2023)
4 mark long ass stats question (like last qn from 2022)
5 mark long ass projectile question (like second last qn from 4u 2021)
4 mark hard induction question

wouldnt u say vectors as a hard question is unlikely since we got it last yr. If u look at the trend, they have never rlly repeated a topic 2 years in a row. I guess one example is 2021 and 2022 which both have q14 stats questions.

 

[bruhmoment.]

prob harder than 2022
my guesses:
7 marker in 2 parts vectors (kinda like 14c from 2023)
4 mark long ass stats question (like last qn from 2022)
5 mark long ass projectile question (like second last qn from 4u 2021)
4 mark hard induction question

im thinking volume or a logistics (differential) question but idk.

 

[Average Boreduser]

im thinking volume or a logistics (differential) question but idk.

hopefully thats gonna b the case