Conics Q (1 Viewer)

[CM_Tutor]

Originally posted by CrashOveride
Tangent at P(x1,y1) to ellipse 9x^2 + 16y^2 = 144 meets the directricies at T and T' respectively. S and S' are foci, prove that PST and PS'T' are both right angles

I usually do these things the long way....i was thinkign just find the co-ords of T' and T and fine all the neccesary gradients and then do the m1.m2 = -1 thingo and thats how i can show it. Any quick short cuts?

I don't see an immediately obvious short cut, although it isn't necessary to prove both results, as ΔPST ≡ ΔPS'T', as PS and PS' are equally inclined to the tangent TPT', and, PSS' = PMM' = PTT'.

Edited to correct an error.

 

[CrashOveride]

Thanks

Just had my 4unit test then, thanks for all your help CM ! It was pretty easy and I finished with like 1/4 of time to spare

 

[CrashOveride]

Hmm CM Tutor, could i get your opininon on something as you;ve been a marker ?

I had two volumes questions in the test...for one i put in the "c.u." part at the end but for the other i *think* i may have left it out. Does that warrant deduction of marks? See because our teacher was saying stuff about leaniancy and in previous tests no marks were taken off for leaving out the +C in indefinate integration.

Also, to check my answer to one question I used pappus' theorem (which i dont think is in the 4u syllabus) and it worked out. Just i left out the "c.u." part and also i left the comment "via pappus theorem... blabla... thus i am correct below"

Does that souind arrogant ? Arghh im stressing about it now coz i had so much time left

 

[CrashOveride]

I feel like shooting myself.... someone say something positive :'(

 

[ToO LaZy ^*]

...no one's stoppin ya mate ..
nah..jks..

umm..something positive...ok, here goes..HSC isn't the be all, and end all...there's always TAFE ...

 

[:: ck ::]

Originally posted by CrashOveride
Hmm CM Tutor, could i get your opininon on something as you;ve been a marker ?

I had two volumes questions in the test...for one i put in the "c.u." part at the end but for the other i *think* i may have left it out. Does that warrant deduction of marks? See because our teacher was saying stuff about leaniancy and in previous tests no marks were taken off for leaving out the +C in indefinate integration.

Also, to check my answer to one question I used pappus' theorem (which i dont think is in the 4u syllabus) and it worked out. Just i left out the "c.u." part and also i left the comment "via pappus theorem... blabla... thus i am correct below"

Does that souind arrogant ? Arghh im stressing about it now coz i had so much time left

soz but my tutor sed u can't apply pappus' theorem for hsc.. =\

only use it to check ur answers

 

[CrashOveride]

I said i used it to check my answer

Did u just call ur tutor and ask him?

 

[:: ck ::]

oh i think its ok to use as checking then.. soz for not reading

nah i heard it like two months ago

 

[CrashOveride]

Hmm im gona argue about it with him tomorrow, as i dont think its a reallllll grounds for penalty considering past events

 

[sammeh]

u can use pretty much whatever u want in hsc. be assured that the examiners will go to absurd lengths to justify your working.

for instance, my physics teacher encourgages me to use 4u methods specifically particle dynamics and graphical solutions of complex numbers (vectors) in my physics work to save time in studying. he's been marking hsc papers in phys, chem and bio for years, so i'd like to think he's to be trusted :] anyway, its a risk u have to choose to take.

u would probly lose 1-2 marks tops for an exemption like that tho. well for leaving out the constant of integration you should, because it doesnt give a correct answer otherwise but dont stress, its no biggie really :]

anyway, i hope that this reply has been remotely relevant.

 

[CM_Tutor]

Originally posted by CrashOveride
Hmm CM Tutor, could i get your opininon on something as you;ve been a marker ?

I had two volumes questions in the test...for one i put in the "c.u." part at the end but for the other i *think* i may have left it out. Does that warrant deduction of marks? See because our teacher was saying stuff about leaniancy and in previous tests no marks were taken off for leaving out the +C in indefinate integration.

This is a judgement call for a marker. Some people may take the view that if they are mostly correct, then don't penalise. However, another approach is to pick a point in the paper and say "I am going to check units on this answer", and then only mark it at that point, and ignore it elsewhere. I think you'll probably be OK, but take it as a warning to be careful in the future.

Also, to check my answer to one question I used pappus' theorem (which i dont think is in the 4u syllabus) and it worked out. Just i left out the "c.u." part and also i left the comment "via pappus theorem... blabla... thus i am correct below"

Does that souind arrogant ? Arghh im stressing about it now coz i had so much time left

If you want to use something like Pappus Theorem to check an answer, that is OK, but I would write something like "So, my result is consistent with the result from Pappus Theorem" rather than "So I'm right...". Leave it to the marker to mark - some won't care, others may not like it much.

Don't stress about finishing early, that just gives you time to check your work.

 

[CM_Tutor]

I'd be very careful about using anything to exotic in an HSC exam. Some markers will take the view:

I don't recognise this - I better check with some other people, and see if this is valid.

I consider these the good markers, who generally have enough confidence in their own ability to feel comfortable saying that there is something that they do not know. Other markers will take the view:

I am a teacher. I know more than any other person alive. I don't recognise this, therefore it must be wrong.

Ok, I am exaggerating, but you (hopefully) can see my point. Remember the discussion on the third derivative method.

 

[CrashOveride]

Thanks for your input guys
So basically u cant actually answer a question with anything outside of the 4u syllabuys? just use it as a "checking mechanism" ?

 

[CM_Tutor]

Originally posted by CrashOveride
Thanks for your input guys
So basically u cant actually answer a question with anything outside of the 4u syllabuys? just use it as a "checking mechanism" ?

I am not (quite) saying that. An answer is better than no answer, so if the only way you can see to do something is using non-syllabus information, then do so. A blank page is a guaranteed zero. However, if you can do it by a syllabus method, then keep your non-syllabus short cuts for checking.

If you are going to use something outside the syllabus, or if you think that there is a danger that you will not be understood, you can always sketch out the justification. ie. State that you will be using Pappus Theorem (in this case), and then state what that is - maybe describe in a line or two how it could be proved (assuming you know that for the case in question). It makes it a lot harder to treat as "I've never heard of this therefore is made up". Be polite if you do this - you aren't trying to get into a slanging match with the marker, and writing as if they are stupid is starting a battle that you won't win. You are providing information so that your answer is clearer. I have done this in exams - stated things like "this question can be interpretted as X or Y, and I am taking it to mean X" - I got one assignment back that had a note from the marker - "It actually means Y, but I accept your stated assumption". I was the only person in the class with the X interpretation that got all the marks. I also described some theory outside the syllabus (with a proof) in a Uni Maths exam, and got the marks.

 

[CM_Tutor]

Originally posted by buchanan
CM_Tutor, what's your view on third derivative method?

I even teach it to 2 unit students (but also the testing either side of the point method because sometimes it's necessary).

As surprising as this might sound, I had not come across this method prior to hearing about it on BOS. I have never come across a student that used it / wanted to use it beyond here.

Do I think it is valid? Yes, the justification of it makes sense, and you have an honours degree in Maths, and so are well qualifed to know - much better qualified than I am in this area, as I only have a maths minor.

Would I teach it? No, as I don't think that the benefits outweigh the risks (using it at Uni would be a different story) that a marker will reject it - unless I was specifically asked to discuss it. However, it seems to me that it can be reasonably argued that it is a decision for the student. I would have no problem with a teacher teaching both, saying that it'll be accepted in the trials, and explaining the pros and cons re use in the HSC, and leaving it to the student to make the call.

Should it be rejected? No, as it is valid, and is also a logical extension of the syllabus material. Furthermore, I have seen far too many answers where people solve d²y/dx² = 0, and then assert that there are inflexions without further work. To me, it is these answers that are in need of penalisation, and it doesn't make sense to penalise a student who has (correctly) tested to establish the presence of an inflexion, even if the test is not the usual one used by students. After all, we allow two methods of testing the nature of a stationary point, why should we refuse to recognise a second method of testing the nature of an inflexion?

 

[CrashOveride]

Hmm another thing...i got some feedback today that i stuffed up a volumes question...and im pretty sure i can recall why...i was using the washer method and to obtain the cross-sectional area i had to use pi(r₂² - r₁²) except for the r1 part i forgot to square it. Everything else i did was correct but because i made that little error at the start, my answer ultimately was wrong. THhe question was worth 4 marks, do i still earn maybe 1 or 2 D) marks for like say recognising how to do the question or something of that nature ?

 

[ngai]

pappus theorem...haha the markers might also not like the fact that u knocked over the question in one line..
try not to use it unless u have like 10 secs left or sumfink

hmm, 1 or 2 marks...
well, depends on the question...if not squaring that r1 meant that ur integration was totally easy, then u'll probably lose 2 marks
if not squaring that r1 hardly changed the difficulty of ur question, then u shoudl get away with losing one mark only
getting 1/4 just coz u forgot a little 2 is quite harsh...i'd definitely be arguing if i lost marks like that

 

[CrashOveride]

It turned out good, it was only a 1 mark deduction = p