FinalFantasy
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but in ext. 1 u can use ext. 2 stuff right?
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FinalFantasy
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Trev
stix
Does that mean, since 3rd derivative isn't in the syllabus it cannot be used either?
Even though it was mentioned in another thread, like FinalFantasy stated. It also appeared to me, that the student was taught this, and was using it to solve a problem - not just for extracurricular use.
Even though it was mentioned in another thread, like FinalFantasy stated. It also appeared to me, that the student was taught this, and was using it to solve a problem - not just for extracurricular use.
Captain pi
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No, sorry guys. I am almost certain that the third derivative test CANNOT be used in the HSC. Using this will result in loss of marks for that criterion.
As to using Extension 2 stuff in Extension 1, this is fine; however, if an Extension 1 question asks for a question to be solved in a particular way (e.g. by substitution [sorry Trev]), then using other techniques will result in the loss of (some) marks.
As shaqfat has said, and others have alluded to, almost anything you prove or show is a theorem or corollary; therefore, unless we require students to only use syllabus techniques, proofs can be constructed by saying "C result proven because of [Theorem outside the syllabus]."
However, these will not necessarily result in zero marks for that question, just loss of marks for that particular criterion.
*locks thread*
As to using Extension 2 stuff in Extension 1, this is fine; however, if an Extension 1 question asks for a question to be solved in a particular way (e.g. by substitution [sorry Trev]), then using other techniques will result in the loss of (some) marks.
As shaqfat has said, and others have alluded to, almost anything you prove or show is a theorem or corollary; therefore, unless we require students to only use syllabus techniques, proofs can be constructed by saying "C result proven because of [Theorem outside the syllabus]."
However, these will not necessarily result in zero marks for that question, just loss of marks for that particular criterion.
*locks thread*
My teacher was marking a 2U paper where a student was using 4U techniques.shafqat said:
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Trev
stix
Is that where I lost a mark or so in question one of the exam you marked for Mr. D?Captain pi said:
Damn, do you know how I went in the other sections?
I made the most stupid STUPID thing ever, that question where given some values you had to use l=pi*@ and A=1/2*r^2*@ simultaneously to find out 'r', from what I remember. We were given the value of 'l', yet somehow in my simultaneous equations I still had 'l' in there, so I ended up having l=r^2 or something.... *sigh's at self stupidity*
/rant
JamiL
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oh k in 3u intergration they only other thing they teach u subsitution n they give you u.. if they say int(blah blah blah) using the knowing the subsutiton u=f(x)... u cant go ad do it by parts cos that would be like using simpsons rule when asked 2 use trapizodial...
u can use 3u methods in 2u, and 4u methods in 3u, although usally on test they aviod it by makin u prove a formula or sumfing... i remeber in my trial(2u) last year, in a circle geometry question they asked us 2 prove the sin expantion graphicly... then asked hence do sumfin else using that. so realisticly a 3u student was at no advantage, other than the fact that he was more likly 2 know the proof, but its simple neway
u can use 3u methods in 2u, and 4u methods in 3u, although usally on test they aviod it by makin u prove a formula or sumfing... i remeber in my trial(2u) last year, in a circle geometry question they asked us 2 prove the sin expantion graphicly... then asked hence do sumfin else using that. so realisticly a 3u student was at no advantage, other than the fact that he was more likly 2 know the proof, but its simple neway
Slide Rule has done an excellent thing here. He's offered 2 correct solutions to this problem. His first solution follows the syllabus and is quite ghastly. His second solution uses l'Hospital's Rule and is outside the syllabus, but is much much nicer. This is an excellent demonstration of precisely why marks should not be deducted for using results outside the syllabus.
To be penalised for it just because it isn't in the syllabus, or just because the student knows more about maths than the marker means that student would be better off doing the IB instead. The HSC is a waste of time if it's just about regurgitating the syllabus, especially when this unnecessarily leads to very inelegant solutions. It should be about doing correct maths, and preference should be given to more elegant solutions, regardless of if it's in the syllabus or not.
Slide Rule's l'Hospital's Rule solution is perfectly valid and should get full marks. If he's penalised for it in the HSC, this says more about the stupidity of the HSC marking process than Slide Rule's mathematical ability.
If the HSC is all about regurgitating the syllabus, then HSC students will forever be tied down to mediocrity. Internationally, we will be seen as very crappy when it comes to mathematical education. The HSC would be an embarassment and not something I would want to be associated with.
Just imagine if Princeton University's Annals of Mathematics wrote back to Andrew Wiles saying that they can't publish his proof of Fermat's Last Theorem because it is outside the scope of a syllabus! He'd have to publish it elsewhere and the Annals of Mathematics would become such an international laughing stock, they'd have to shut it down! Ditto for the NSW Board of Studies!
To be penalised for it just because it isn't in the syllabus, or just because the student knows more about maths than the marker means that student would be better off doing the IB instead. The HSC is a waste of time if it's just about regurgitating the syllabus, especially when this unnecessarily leads to very inelegant solutions. It should be about doing correct maths, and preference should be given to more elegant solutions, regardless of if it's in the syllabus or not.
Slide Rule's l'Hospital's Rule solution is perfectly valid and should get full marks. If he's penalised for it in the HSC, this says more about the stupidity of the HSC marking process than Slide Rule's mathematical ability.
If the HSC is all about regurgitating the syllabus, then HSC students will forever be tied down to mediocrity. Internationally, we will be seen as very crappy when it comes to mathematical education. The HSC would be an embarassment and not something I would want to be associated with.
Just imagine if Princeton University's Annals of Mathematics wrote back to Andrew Wiles saying that they can't publish his proof of Fermat's Last Theorem because it is outside the scope of a syllabus! He'd have to publish it elsewhere and the Annals of Mathematics would become such an international laughing stock, they'd have to shut it down! Ditto for the NSW Board of Studies!
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Slidey
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I think you're spot on there, Derek.
For me, it's not so much about finding a more efficient solution to a problem (although that's nice, too), but learning about different ways to solve problems - learning more mathematics. To be hindered for this is absurdly nonsensical.
I have arguments with teachers time and time again about things like this. They say for example "Stick to the syllabus, don't question it, just memorise what you need to." which to me is completely ludicrous, considering that if it is not correct or if I do not understand it, I would be memorising complete garbage! That's the main reason I dropped physics.
I go to school to learn for life; not to get an arbitrary mark in a one-off test.
For me, it's not so much about finding a more efficient solution to a problem (although that's nice, too), but learning about different ways to solve problems - learning more mathematics. To be hindered for this is absurdly nonsensical.
I have arguments with teachers time and time again about things like this. They say for example "Stick to the syllabus, don't question it, just memorise what you need to." which to me is completely ludicrous, considering that if it is not correct or if I do not understand it, I would be memorising complete garbage! That's the main reason I dropped physics.
I go to school to learn for life; not to get an arbitrary mark in a one-off test.
I think we need to get teachers and academics to seriously question the purpose of the syllabus and the exams.
My view is that it's OK to have a syllabus which should be the bare minimum that needs to be covered. And it's OK to have a common external exam at the end so that students can be compared with the same thing.
However to then say that the syllabus is the upper limit of what you should learn and to say you should only be given marks for your ability to regurgitate the syllabus in the exam, is to both deny you the right to develop your skills above and beyond the confines of the syllabus, and to possibly penalise you for having a better command of mathematics than someone else who just regurgitates the syllabus.
It makes a mockery of the HSC and I sympathise with some private schools who have even threatened to dump the HSC entirely and do 100% IB.
My view is that it's OK to have a syllabus which should be the bare minimum that needs to be covered. And it's OK to have a common external exam at the end so that students can be compared with the same thing.
However to then say that the syllabus is the upper limit of what you should learn and to say you should only be given marks for your ability to regurgitate the syllabus in the exam, is to both deny you the right to develop your skills above and beyond the confines of the syllabus, and to possibly penalise you for having a better command of mathematics than someone else who just regurgitates the syllabus.
It makes a mockery of the HSC and I sympathise with some private schools who have even threatened to dump the HSC entirely and do 100% IB.
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in an ideal world mayb
but this sort of system would create other problems
different schools/teachers would teach different things beyond the syllabus
and whether students can answer questions using these techniques would become pot luck, depending on wat they were taught
anyway i think the olympiad/maths comps cater for those bright pple who need to be challenged
but this sort of system would create other problems
different schools/teachers would teach different things beyond the syllabus
and whether students can answer questions using these techniques would become pot luck, depending on wat they were taught
anyway i think the olympiad/maths comps cater for those bright pple who need to be challenged
lim x-->0 (1-cosx)/(x^2) * (1+cosx)/(1+cosx)m_isk said:Yeh thats what initally came to my mind...but then i got stuck; any suggestions wah??
= lim x-->0 (sinx)^2 // [(x^2)(1+cosx)]
split this up into
lim x-->0 (sinx)^2//(x^2) * [1/(1+cosx)]
hence
lim x-->0 sinx/x * sinx/x * [1/(1+cosx)]
sinx/x =1, sub x=0 into [1/(1+cosx)] and u get 0.5
therefore
1 * 1 * 0.5
= 0.5
Yeah. But I still like the l'Hospital's Rule method better.
Anyway, so long as everybody fully covers the syllabus, I think it's OK for people to learn different things on top of that.
Of some concern is that in some schools, they aren't even covering the syllabus properly due to a lack of qualified teachers. Also, they often are the ones who try to impose their mediocrity onto their students.
Anyway, so long as everybody fully covers the syllabus, I think it's OK for people to learn different things on top of that.
Of some concern is that in some schools, they aren't even covering the syllabus properly due to a lack of qualified teachers. Also, they often are the ones who try to impose their mediocrity onto their students.
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