Further geometry(LCH)

sd123

I'm planning to teach myself the Q 11 option question before the LC, just in case i get a bad other option Q. i know that elipses and other different geometry comes up but does anyone know exactly what is required. i tried to check the sylabus but the link is currently not working. so just wondering does anyone know what you need to know and any links to notes etc. showing how to do it.
ps already have some info on elipses but could do with some more

ZorbaTehZ

Strange actually since I'm doing the same with the Groups question.

Mate of mine has one of the old T&T5 that has all the option questions in it, maybe if you ask one of your teachers they may have the same one - its an old dark-blueish one, with geometry shapes in a plane, on the front.

MathsManiac

The syllabus in on the Department's website: www.education.ie. Here's the section you want:

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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.

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None of the LC books have the material (including the old one mentioned by ZorbaTehZ above). You can get supplementary booklets on the Further Statistics option and the Groups option. If you're sure you want to do this one, your best bet is probably past papers - all papers from 1994 onwards are relevant, and that gives you a fair bit of stuff, (marking schemes for the last few years are available too) but you'll still be on a teach-yourself job. You're also unlikely to find a teacher or other grind-giver that's on top of it. You might have a bit of web-trawling ahead of you!

ZorbaTehZ

MathsManiac wrote:

None of the LC books have the material (including the old one mentioned by ZorbaTehZ above).

Interesting, because the book goes through it in detail.

MathsManiac

ZorbaTehZ wrote:

Interesting, because the book goes through it in detail.

Cool! My copy doesn't. Sorry about the misinfo.

What year is your copy printed? (I'd be interested in trying to get hold of a copy.)

Son Goku

MathsManiac wrote:

You can get supplementary booklets on the Further Statistics option and the Groups option. If you're sure you want to do this one, your best bet is probably past papers - all papers from 1994 onwards are relevant, and that gives you a fair bit of stuff, (marking schemes for the last few years are available too) but you'll still be on a teach-yourself job. You're also unlikely to find a teacher or other grind-giver that's on top of it. You might have a bit of web-trawling ahead of you!

Well if anybody wants help with the groups option, just ask around here. The syllabus for it is just a few basic facts.

sd123

yea i got a copy of that T & T 5 book from my maths teacher and it does the other three options. but not that one. this one was published in 1993. does anyone know where i'd get the additional booklet for the Q 11. it says in the preface that they published it but they probably stopped since?:mad:

sd123

maybe i'll try the groups Q. Is it difficult?

ZorbaTehZ

I don't find the Groups question difficult(very, very interesting imo). Looking at the Further Geometry question, some of it looks quite difficult - iirc there was not even a single person across Ireland who did that question in LC 2004 (Chief Examiners Report)

I don't have the book at the moment, like I said it's my mates - I'll post tomo or Saturday. Can PM you some info on it too if you're unable to get those notes.

dan719

Son Goku wrote:

Well if anybody wants help with the groups option, just ask around here. The syllabus for it is just a few basic facts.

Go ahead please, I want it to fall back on but cannot get my hands on any real notes so as it stands I am just winging it!lol

Son Goku

dan719 wrote:

Go ahead please, I want it to fall back on but cannot get my hands on any real notes so as it stands I am just winging it!lol

Cool, I'll put in a few bits to my old notes I made when I gave grinds and post them up tomorrow in a PDF, if that suits everybody.

MathsManiac

ZorbaTehZ wrote:

Interesting, because the book goes through it in detail.

Zorba, did you manage to find that book yet? (The elusive copy of T&T5 that is reputed to go into the further geometry option in detail.):rolleyes: