Correlation between Complex Locus and Circle Geometry (former harder 3u) (1 Viewer)

[lolzdj]

Currently, the most efficient way to study locus problems; and the wide variety of rules/properties you may be asked to prove is to:
1. Grind out problems.
2. Identify what circle geometry property is being used.
3. Learn it and move on.
I'm still not super convinced with how thorough this method is though. To what extent did the former circle geometry topic (4u) help with overall geometry problems throughout the entire course? Also, my 4u teachers basically set out all of 3u circle geometry from the old syllabus (in focus) in preparation for locus next term, is it worth spending the time doing?
Cheers.

 

[fan96]

I'm not familiar with the new syllabus but I can tell you how it was in the older syllabus.

In the older syllabus, circle geometry problems were pretty limited in scope - some diagram involving circles is given and you have to bash out those circle geo-specific theorems you memorised to prove a relationship between some angles and lines.

The geometry problems outside of the circle geo topic rarely involved circles at all, usually either polygons and/or lines, or other conic sections (parabola, hyperbola, ellipse). They generally favoured algebraic approaches as well. If a circle was involved there wasn't too much going on with it - it's not often you need to deal with angles inscribed inside circles or subtended by chords.

So, the circle geo theorems were basically only useful for circle geo questions. There wasn't much overlap between circle geometry and other geometry.

(But as always, one thing that does carry over is the development of mathematical skills in solving problems.)

 

[Drdusk]

Currently, the most efficient way to study locus problems; and the wide variety of rules/properties you may be asked to prove is to:
1. Grind out problems.
2. Identify what circle geometry property is being used.
3. Learn it and move on.
I'm still not super convinced with how thorough this method is though. To what extent did the former circle geometry topic (4u) help with overall geometry problems throughout the entire course? Also, my 4u teachers basically set out all of 3u circle geometry from the old syllabus (in focus) in preparation for locus next term, is it worth spending the time doing?
Cheers.

I didn’t really think 4U circle Geo really helped much with any locus geometry problems. Grinding out problems really is usually the way to go imo but you should always stop and think in every locus problem ‘What does this mean geometrically?’ even if the question doesn’t ask for it. I don’t really see any other way tbh. Maybe all the math gods on here could provide some more enlightenment..

 

[Trebla]

I'm not familiar with the new syllabus but I can tell you how it was in the older syllabus.

In the older syllabus, circle geometry problems were pretty limited in scope - some diagram involving circles is given and you have to bash out those circle geo-specific theorems you memorised to prove a relationship between some angles and lines.

The geometry problems outside of the circle geo topic rarely involved circles at all, usually either polygons and/or lines, or other conic sections (parabola, hyperbola, ellipse). They generally favoured algebraic approaches as well. If a circle was involved there wasn't too much going on with it - it's not often you need to deal with angles inscribed inside circles or subtended by chords.

So, the circle geo theorems were basically only useful for circle geo questions. There wasn't much overlap between circle geometry and other geometry.

(But as always, one thing that does carry over is the development of mathematical skills in solving problems.)

Pretty much agree with this, especially the last sentence. Practicing old syllabus circle geometry questions only really helps in terms of sharpening general geometry reasoning skills (which you won’t use much of since the new syllabus has minimal geometry). It’s less relevant in helping with locus problems in this context.