2016ers Chit-Chat Thread (5 Viewers)

[InteGrand]

When was k.cos(kx) mentioned? I don't have any memories of this one...

Will have a look when I have time if you really want, don't have any high school books with me and don't have time to look through past papers right now.

Found a place summing things like k.cos(kx) came up (in the papers before 4U): 1916 NSW Leaving Certificate Exam, Question 12 of Paper I (on page 3 of this document: http://4unitmaths.com/1916.pdf ).

I'm not sure whether it's come up in HSC 4U papers, but I don't recall it being in any HSC papers from this century at least (from memory).

 

[seanieg89]

Yeah, I am sure it has come up in trials, maybe not recent HSC then.

In any case, it is definitely a trick a good mx2 student should have in his/her toolbox.

 

[leehuan]

Found a place summing things like k.cos(kx) came up (in the papers before 4U): 1916 NSW Leaving Certificate Exam, Question 12 of Paper I (on page 3 of this document: http://4unitmaths.com/1916.pdf ).

I'm not sure whether it's come up in HSC 4U papers, but I don't recall it being in any HSC papers from this century at least (from memory).

Lol. Just too bad that's gotta be the leaving certificate

 

[InteGrand]

Lol. Just too bad that's gotta be the leaving certificate

What do you mean? That was basically like the 4U of those times (in that it was the highest level of maths in NSW secondary schools at the time, I think).

 

[InteGrand]

Yeah, I am sure it has come up in trials, maybe not recent HSC then.

In any case, it is definitely a trick a good mx2 student should have in his/her toolbox.

Yeah, kind of like differentiating under integral signs, one of Feynman's favourite tricks (although this wouldn't be quickly justifiable in the HSC, unless students can just quote it, which I doubt).

 

[leehuan]

What do you mean? That was basically like the 4U of those times (in that it was the highest level of maths in NSW secondary schools at the time, I think).

.

But yeah I suppose point still stands. I just don't regard anything pre2000 anymore

 

[seanieg89]

Yeah, kind of like differentiating under integral signs, one of Feynman's favourite tricks (although this wouldn't be quickly justifiable in the HSC, unless students can just quote it, which I doubt).

I reckon it's fairly quickly justifiable in some applications, MX2 students know how to squeeze things and use the fact that the integral of something non-negative is non-negative. From here it suffices to find upper and lower bounds for difference quotients which definitely wouldn't be a stretch. (Technically this is not quite rigorous, but only because the properties of the integral are not themselves rigorously established in MX2, the argument itself is perfectly sound).

But yes, differentiation of sums is much closer to syllabus, as if we have a remainder term for the sum (like in a GP) then we are just differentiating a finite sum and there are no subtle analysis issues.

 

[leehuan]

I reckon it's fairly quickly justifiable in some applications, MX2 students know how to squeeze things and use the fact that the integral of something non-negative is non-negative. From here it suffices to find upper and lower bounds for difference quotients which definitely wouldn't be a stretch.

It's ironic though, because MX2 aren't explicitly taught the squeeze theorem. They're just taught that squeezing works because it's logical.

 

[BandSixFix]

Haven't memorized essay or creative and making up a related text for the English exam tomorrow..
Hope the BOSTES gods are in my favor...

 

[MilkyCat_]

Haven't memorized essay or creative and making up a related text for the English exam tomorrow..
Hope the BOSTES gods are in my favor...

what happened to atar aim 99.70 lmao
or are you a wizard

 

[ml125]

Haven't memorized essay or creative and making up a related text for the English exam tomorrow..
Hope the BOSTES gods are in my favor...

Lmao memorise quotes and hope for the best. Just make sure you kinda know what to write for creative and wing it

 

[InteGrand]

It's ironic though, because MX2 aren't explicitly taught the squeeze theorem. They're just taught that squeezing works because it's logical.

In fact, this can be said for most (or at least many) of the HSC maths topics, can't it?

 

[Sien]

Is anyone doing mod c people and politics

Sent from my D6503 using Tapatalk

 

[seanieg89]

It's ironic though, because MX2 aren't explicitly taught the squeeze theorem. They're just taught that squeezing works because it's logical.

Well that's the same with the intermediate value theorem and the fundamental theorem of calculus. Theres no point formalising things and naming them properly if students aren't doing rigorous analysis. (Which they cannot even begin to do without proper construction of the reals and discussion of limits, which is not at all feasible for a secondary school course).

What is important though, is that everything done in HSC mathematics CAN be made rigorous with sufficient knowledge. This is why they consult with academics when it comes to writing HSC MX2 exams.

 

[BandSixFix]

Lmao memorise quotes and hope for the best. Just make sure you kinda know what to write for creative and wing it

Yeah that's what I'll do - hopefully I can tank my rank since this is only worth 10%. I know like the main themes of the texts and a few quotes/techniques rip. I'll try and forge a plot for a creative aaaaaaaaaaah

what happened to atar aim 99.70 lmao
or are you a wizard

Well. I certainly hope I am

 

[InteGrand]

Well that's the same with the intermediate value theorem and the fundamental theorem of calculus. Theres no point formalising things and naming them properly if students aren't doing rigorous analysis. (Which they cannot even begin to do without proper construction of the reals and discussion of limits, which is not at all feasible for a secondary school course).

What is important though, is that everything done in HSC mathematics CAN be made rigorous with sufficient knowledge. This is why they consult with academics when it comes to writing HSC MX2 exams.

What do they ask academics when writing the HSC MX2 papers? Do they basically just want to make sure that everything in the paper can be made rigorous with sufficient knowledge? Also, wasn't a HSC MX2 Q once written by an academic in fact (maybe this is even a common thing)?

 

[seanieg89]

What do they ask academics when writing the HSC MX2 papers? Do they basically just want to make sure that everything in the paper can be made rigorous with sufficient knowledge? Also, wasn't a HSC MX2 Q once written by an academic in fact (maybe this is even a common thing)?

I assume so, am not familiar with the exact process.

Yes, the question about the irrationality of pi was provided by a lecturer from UNSW. (p brown) (I think the original proof was just a short article written by someone else, but the lecturer parsed it into a form suitable for an MX2 question).

I do not know how common an occurence this is, but most of the Q8/16s seem to be written by pretty knowledgable people.

(Note that it is harder to write a good MX2 Q8/16 question than it is to solve one, given the delicate balance between mathematical correctness, appropriateness of difficulty, it being interesting etc).

 

[InteGrand]

I assume so, am not familiar with the exact process.

Yes, the question about the irrationality of pi was provided by a lecturer from UNSW. (p brown) (I think the original proof was just a short article written by someone else, but the lecturer parsed it into a form suitable for an MX2 question).

I do not know how common an occurence this is, but most of the Q8/16s seem to be written by pretty knowledgable people.

(Note that it is harder to write a good MX2 Q8/16 question than it is to solve one, given the balance between mathematical correctness, appropriateness of difficulty, it being interesting etc).

Ah yeah, that was the Q. I was thinking of (the irrationality of pi one, I think it's from 2003).

 

[Paradoxica]

Yeah, kind of like differentiating under integral signs, one of Feynman's favourite tricks (although this wouldn't be quickly justifiable in the HSC, unless students can just quote it, which I doubt).

Hm. I do wonder if I could use that.

My Head teacher says he once wrote a question which only made sense to one student on his class (who would later to go on and get almost 100% raw mark), so he removed it from the paper. The student transformed the given hyperbola into a rectangular hyperbola and proving whatever statement it was would hold true under transformation (in this case, using projective geometry)

He also did short work of a question which involved proving a modified form of Pascal's theorem, by simply quoting the theorem.

I hope he accidentally puts in an integral which is too difficult for everyone else.

*coughcough*

 

[InteGrand]

Hm. I do wonder if I could use that.

My Head teacher says he once wrote a question which only made sense to one student on his class (who would later to go on and get almost 100% raw mark), so he removed it from the paper. The student transformed the given hyperbola into a rectangular hyperbola and proving whatever statement it was would hold true under transformation (in this case, using projective geometry)

He also did short work of a question which involved proving a modified form of Pascal's theorem, by simply quoting the theorem.

I hope he accidentally puts in an integral which is too difficult for everyone else.

*coughcough*

Did he get the marks for the Pascal's theorem one? Since he basically assumed the result if he just quoted the theorem as his proof.