Higher Level Maths Paper 2 Option

f1dan

Does anybody know where I can learn to do the ellipse question as one of the options at the end of paper 2? My book, Text and Tests only does the further integration section. I managed to get an older copy of text and tests. which does all the options except for the ellipse section

PurpleFistMixer

The Further Geometry question seems to be done by about 0-1% of people, and finding the materials appears to be almost impossible. It's like they assume nobody will even want to do it.
I've been chasing my maths teacher about it since September still to no avail... Best I've been able to do is looking at old marking schemes for the question, but that's in no way at all sufficient.

JC 2K3

Just STFU and do Further Calculus!

Seriously though, if you're pretentious enough to want to do another option, you also really need to be bright enough be able to teach yourself it by reading the syllabus, googling and doing past papers.

Honestly, I don't think it's worth it though. Further Calculus is easy enough, and if you're interested in learning new maths concepts, join the maths society(which hopefully exists) in the university you go to next September/October. IIRC you said you're going for Maths in TCD, PFM, so you probably aren't going to miss out on anything interesting by not doing a different option to Further Calculus in the LC.

Chunky Monkey

The college you apply to isn't going to know which option you did on the paper...The whole point of the LC is get you points so you can get into college. Why bother making it harder for yourself, it ain't worth it, you don't get extra brownie points and a pat on the back.

Overheal

http://en.wikipedia.org/wiki/Ellipse

First thing I thought of. Try googling if that doesnt suit you

PurpleFistMixer

JC 2K3 wrote: »

if you're pretentious enough to want to do another option

You see wanting to do another option as pretentious. Has it occured to you that a person may be genuinely interested in the topic and perhaps may also want to give themself a choice on the day? I've not done Further Calculus yet so I don't know what it's like, but from my experience so far, unless a proof comes up in the Groups question it's very handy and quick. Also, you get to do Sudoku (see Latin Square) sometimes, whoever thought that'd happen on a maths paper.

JC 2K3 wrote: »

if you're interested in learning new maths concepts, join the maths society(which hopefully exists) in the university you go to next September/October.

Maybe one can't wait until then. Geometry is a spicy and delicious meatball, how could you blame him/her.

Chunky Monkey wrote: »

The whole point of the LC is get you points so you can get into college. Why bother making it harder for yourself, it ain't worth it, you don't get extra brownie points and a pat on the back.

How about "for the friggin' lulz"? People aren't robots. Yes, you can simplify the LC down to "learn stuffs, get points, go to college", but if somebody wants to (possibly) make it harder for themself by learning something of their own choosing, then why shouldn't they? They give you an option on paper 2, it seems ridiculous to me that one could be criticised for taking advantage of it. Education is about learning things, not just passing exams (despite what we may be led to believe in school...)

Maybe I'm just a bizarre freak, but I'd prefer to do something interesting than something easy (making the assumption that these things are in this case mutually exclusive).

Michael Collins

I would also like to know where to get this. Have you tried in a school supply centre? I might check out my local one there tomorrow.

Overheal

PurpleFistMixer wrote: »

you get to do Sudoku (see Latin Square) sometimes, whoever thought that'd happen on a maths paper.

o_0

That would have been deadly back in the good ol' days.

Yes, you can simplify the LC down to "learn stuffs, get points, go to college", but if somebody wants to (possibly) make it harder for themself by learning something of their own choosing, then why shouldn't they? They give you an option on paper 2, it seems ridiculous to me that one could be criticised for taking advantage of it. Education is about learning things, not just passing exams (despite what we may be led to believe in school...)

Maybe I'm just a bizarre freak, but I'd prefer to do something interesting than something easy (making the assumption that these things are in this case mutually exclusive).

Quoted For Truth. Points get you in the door. Understanding and a willingness to learn keep you there.

ZorbaTehZ

Iirc correctly, you can get the booklets for it through school suppliers. MathsManiac or rjt will probably be able to give you more accurate info though if they're around...

JC 2K3 wrote:

Honestly, I don't think it's worth it though.

If you've an interest in mathematics then its win win tbh. Notwithstanding that, the groups question is ridiculously easy if you can get your head around the basics.

ZorbaTehZ

Chunky Monkey wrote: »

The college you apply to isn't going to know which option you did on the paper...The whole point of the LC is get you points so you can get into college. Why bother making it harder for yourself, it ain't worth it, you don't get extra brownie points and a pat on the back.

Thats the med student in you talking there bud.

Ever crossed your mind that maybe there could possibly be people out there (I know it sounds crazy) that have an interest in mathematics?

JC 2K3

PurpleFistMixer wrote: »

You see wanting to do another option as pretentious. Has it occured to you that a person may be genuinely interested in the topic and perhaps may also want to give themself a choice on the day?

Nah, I'm a complete cynic. However, it should be noted that I'm also a pretentious cúnt myself.


I agree with most of what you've said though. If you really have a fascination with one of the other options then do go for it, but IMO with the lack of resources and information available on the other options it's not really worth it.

Then again, I always loved calculus and was never going to choose another option, perhaps it's just that I can't empathise with your yearning for further geometry....

rainbowtrout

JC 2K3 wrote: »

Just STFU and do Further Calculus!

Seriously though, if you're pretentious enough to want to do another option, you also really need to be bright enough be able to teach yourself it by reading the syllabus, googling and doing past papers./

How can you say that anyone is pretentious for wanting to do another option? I did the Probability and Statistics option by myself because I found Probability easy (I know it's not everyone's cup of tea). I didn't like Calculus so I didn't see why I should have to do an option I didn't like and was crap at. I didn't expect my teacher to take time out to teach me the topic or do it in class, but he wouldn't even tell me which book I could find it in, I had to do that myself and I was glad I did in the end. It's a handy option.

For what it's worth this is taken from the maths syllabus http://www.education.ie/servlet/blobservlet/lc_maths_sy.pdf?language=EN

It might make it easier to google the topics if you know what you're supposed to be looking for.


Further Geometry
1. Locus of harmonic conjugates of a point with respect to a circle. Focus-directrix definition of an ellipse; derivation of the equation of an ellipse in standard form.

2. Transformations f of the plane π which have the co-ordinate form (x,y) (x′, y′) where: →
x′ = ax + by + k1
y′ = cx + dy + k2
and ad – bc 0. Use of matrices. Magnification ratio. Invariance of ratio of lengths on parallel lines, and of midpoints. Invariance of centroid of a triangle. Invariance of ratio of areas. ≠

3. Deduction from results for a circle of similar results for an ellipse (dealing with the centre of an ellipse, tangents at the endpoints of a diameter of an ellipse, locus of midpoints of parallel chords of an ellipse, locus of harmonic conjugates of a point with respect to an ellipse (pole and polar), areas of all parallelograms circumscribed to an ellipse at the endpoints of conjugate diameters).


4. Similarly transformations, including enlargements and isometries. That similarity transformations map angles to equal angles, triangles to similar triangles, and circles to circles. Invariance under similarity transformations of orthocentre, incentre and circumcentre of a triangle.

Cokehead Mother

Further Probability and Statistics =

Overheal

Cokehead Mother wrote: »

Further Probability and Statistics =

I will agree to disagree with this statement in every way

rainbowtrout

Cokehead Mother wrote: »

Further Probability and Statistics =

+1


Link for resources on ellipses, parabolas etc

http://www.math.utah.edu/online/1220/notes/ch11.pdf

Isometries:


http://www.scienceu.com/library/articles/isometries/

Chunky Monkey

ZorbaTehZ wrote: »

Thats the med student in you talking there bud.

Ever crossed your mind that maybe there could possibly be people out there (I know it sounds crazy) that have an interest in mathematics?

Hey, I don't like it the way it is. I tried to enjoy the LC but I think we're stretched too thin to learn too little on too much. It isn't fair but to be honest I think that's the way the leaving really is. If it were like the A-levels I'd say go ahead and spend as much time as you like on whatever area of the subject you like as we allow you the time to appreciate this subject for what it is instead of being a points generating game. Do you see what I'm getting at? I envy next years medicine applicants.

rainbowtrout

I agree. I hate myself when I hear myself sometimes, when I'm starting a new topic with my 5th or 6th years and I say something like the following: 'This is important, there is a question on this topic every year on the paper'

It bugs the hell out of me. In an ideal world I would like them to be interested in the topic because it's interesting, not because it's a definite on the paper. I usually try and bring in some interest to my subjects as far as is possible in the time I have

I'm now back studying maths and stats out of interest because I like the subject and not because i need a certain amount of points in the LC, which is nice.


While the medicine revamp is an improvement I can't see it alleviating the problem all that much, more will be able to apply and 480 is a lot more achieveable than 580, so I can see the focus turning to 'how to score highly on the aptitude test'

It does leave it open to a wider group of people which is good, but there will be more competition.

Overheal

Look on the bright side: it keeps Ireland as one of the highest ranking education systems in the world. You could be in america learning the joys and wonders of Creationism.

ZorbaTehZ

To say that a student doesn't have enough time to learn an extra topic or two during the leaving, be it math's questions or Physics or whatever is imo totally ludicrous. Even if you are going for Medicine. At the risk of derailing the thread, I'll leave it at that.

JC 2K3

rainbowtrout wrote: »

While the medicine revamp is an improvement I can't see it alleviating the problem all that much, more will be able to apply and 480 is a lot more achieveable than 580, so I can see the focus turning to 'how to score highly on the aptitude test'

It does leave it open to a wider group of people which is good, but there will be more competition.

Not really. When the points for Medicine go down, less people will apply for it. It'll no longer be "the course to do" if you can get the points.

Chunky Monkey

If I didn't personally know several people who applied for medicine just because it has the high points requirement I'd be inclined to agree with rainbowtrout but there's the evidence so I have to agree with JC. I wonder what aptitude test they'll use. There was a big hooha in the UK over the UKCAT. They discounted the personality and abstract reasoning sections though I'm not complaining, it brought my average right up But there were people who got full marks in the AR and said it was because they 'studied' for it. To my understanding you're not supposed to study for an aptitude test.

To say that a student doesn't have enough time to learn an extra topic or two during the leaving, be it math's questions or Physics or whatever is imo totally ludicrous. Even if you are going for Medicine. At the risk of derailing the thread, I'll leave it at that.

That really depends on the student Zorba-how many subjects they're taking, at what level and how many extra curricular activities they're involved in. I think it's healthy to get involved in activities other than study. I realised after my first post on this thread that the OP wants to do maths, so I apologise for that.

I hope they bring in mandatory work experience for the medicine and I think everyone should do some work as a HCA and get to know the dirty side of healthcare and become more aware of their fellow workers so they don't ignorantly block doors when we're trying to get through with a patient in a chair. 'Nuff said

rainbowtrout

Chunky Monkey wrote: »

If I didn't personally know several people who applied for medicine just because it has the high points requirement I'd be inclined to agree with rainbowtrout but there's the evidence so I have to agree with JC.

i would totally agree with this, there are loads of people out there who apply for medicine, dentistry,veterinary, physio etc because it seems like the thing to do - it has high points and seems to be a prestigious course, just like there are people who think ITs are rubbish and the courses they run are useless just because the points are low. This is also not true.

What I would really be basing my opinion on, is the fact that medicine isn't like business studies where there can be hundreds in a class and every college has a course in it. There are only a few medical courses in the country, they don't have a huge amount of places, so while there may be a slight drop in points as it won't be seen as prestigious as before, I can't see it dropping by a lot. And there aren't really any other courses to take it's place in that category. The graduate entry medical courses will ease things a but not a lot.


I've always thought it was wrong anyway that students can repeat the LC having got the requirements the first time round in the science subjects and then take a combination such as Geography, Business, Ag Science, French, History etc to get 'easy honours' to get the points for the course (No disrespect to any of the above subjects, there is no such thing as an easy honour). I know there isn't an easier way out and this particular course shouldn't be singled out from the points system but a near perfect set of grades in the Leaving Cert in a random list of subjects does not make a good doctor. The aptitude to study - yes, the aptitude to retain information - yes, a good beside manner - not necessarily so.

Chunky Monkey and JC have made a good point about students applying because it's high points, I had one of those student last year, she got 500, is repeating for Medicine this year. She's a lovely girl, intelligent, hard working, but I would not ever want to be treated by her as a doctor, she just doesn't have the manner or confidence for it in my opinion, and while she might change over the years and I wish her well I have my doubts. But she does have a cousin doing medicine so she has to compete with her unfortunately.


I did my LC in 1996 and Medicine was achievable with 530-540. And everyone back then thought that was crazy. But it was still the course everyone aimed for.

Chunky Monkey

I did my LC in 1996 and Medicine was achievable with 530-540. And everyone back then thought that was crazy. But it was still the course everyone aimed for.

Looking back on past papers though they were a lot harder so I can understand the increase in the requirement, it's a lot easier to achieve an A now.

Hopefully as that girl gets more experience with patients her social skills will improve. I really hope it doesn't turn out to be a huge disappointment for her after repeating to get in. I stand by the HCA work idea. When I first started I was very shy and terrified of dealing with patients. Now it's like second nature to me and I feel it's helped big time.

MathsManiac

Getting back to topic:

First, nearly on topic:
There are booklets on the groups option and the further probability option available to accompany each of the main textbooks (Oliver Murphy's, Aidan Roantree's and O.D. Morris's). I've looked at them all and they're all perfectly good, so the one corresponding to your own textbook is probably the best one to get, just so that you're used to the style and layout. If you want the booklet for any option and you can't find it in your local shop, ask them if they can order it for you, or contact the relevant publisher and see if you can get it directly.

Second, completely on topic:
Up until the time I stopped teaching, nobody had published a booklet on the Further Geometry option, and I haven't heard of one since, so I'd say you're out of luck. However, you could try learning from past papers and marking schemes and the web, and you can always ask for help with any specific problem on good old boards.ie. When the syllabus was first introduced, NCCA published teacher guidelines that included a section on this topic, but I don't know whether they still stock it. Anyway, it didn't take a very accessible approach, and the few people I knew who taught this topic didn't really use it. If you can get it though, it might be better than nothing.

If you look at the past papers and solutions you'll see that to succeed at this topic you need the following:
- know the basic stuff about the equation of the ellipse in standard position, (incl. what a, b, and e are and how they're related.)
- get an intuitive understanding of affine transformations, so you know which things are invariant and which aren't (you'll need to be able to justify some results here)
- get the hang of which additional things are invariant under a similarity transformation, (and justify them too)
- be able to use a transformation between the ellipse and the unit circle in order to prove hard things about an ellipse by instead proving the corresponding but easier thing about a circle (and showing that the result carries over in the transformation).

For completeness, you'd also need to be able to handle "pole" and "polar", but questions on this seem pretty rare.

(And by the way, the calculus option is grand for engineers and other such blinkered plodders, but for people who enjoy mathematics, all the really interesting stuff is in the other options. )

Chunky Monkey

How about looking at A-level material? They might be covering it. Or on their further maths course. And then practise questions from past papers so you know the format for that particular section.

EDIT: Hodges and Figgs on Dawson Street sell lots of A-level material.

annie19

ye all love ur math
my advise is if there isnt a good book, gets grinds or just know ur option inside out so u can do it with ur eyes closed. then u will have nothing to worry about.:cool:

MathsManiac

f1dan wrote: »

Does anybody know where I can learn to do the ellipse question as one of the options at the end of paper 2? My book, Text and Tests only does the further integration section. I managed to get an older copy of text and tests. which does all the options except for the ellipse section

Michael Collins wrote: »

I would also like to know where to get this. Have you tried in a school supply centre? I might check out my local one there tomorrow.

Might one infer from the above comments that, in the event that some decent notes (or other suitable resource) on this topic were to magically appear on the internet, somebody might actually be interested in looking at them?

Michael Collins

MathsManiac wrote: »

Might one infer from the above comments that, in the event that some decent notes (or other suitable resource) on this topic were to magically appear on the internet, somebody might actually be interested in looking at them?

One may indeed infer that!

MathsManiac

Then one must see what one can do.

(Perhaps we will all wish very hard and see what happens...)

xxshaunaxx

hey..... by any chance did anyone's teacher give ye the 2007 mock exam for extra study??? because my maths teacher has decided to give us the 07 mock iinstead of the 08 mock!!!:(

its deb by the way!!!

x

PurpleFistMixer

Did you even read the thread TITLE, let alone the first post?

MathsManiac

You SHALL go to the ball!

Here you go:
http://homepage.eircom.net/~mathsmaniac/geometry/geometry1.htm

Yours sincerely,

Fairy Godmother (a.k.a. MathsManiac)

Chunky Monkey

Ah I was wondering what was with the pandying about. Fair play on the site

PurpleFistMixer

Wow, many thanks!

Michael Collins

MathsManiac wrote: »

You SHALL go to the ball!

Here you go:
http://homepage.eircom.net/~mathsmaniac/geometry/geometry1.htm

Yours sincerely,

Fairy Godmother (a.k.a. MathsManiac)

Excellent work there. This is the only complete source of information for that question as far as I can tell. Much obliged.