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Edexcel FP3 Tommorow

How prepared are you?
After finding FP2 average but not great I'm probably going to revise way too much.
Just one question, it is at 1.30pm right, or afternoon session?
I would never forgive my school if they printed out the wrong time etc. even though its never happened.

Anyway, if you want to discuss some FP3 stuff here, do that too, I could do with some tips.
My biggest problem is complex numbers. The nth roots of anything take me a while to work out and I have no idea if I'm doing it right, the transformations are horrible, and I forget the loci all the time.
Everything else seems fine, vector questions are sometimes worded in a horrible way, and some of the words for matrices catch me out, such as singular in a solomon paper. I knew it meant no inverse, but forgot that meant Determinant=0.
Good luck anyhow!

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Reply 1

mikeleeds

benwellsday

My biggest problem is complex numbers. The nth roots of anything take me a while to work out and I have no idea if I'm doing it right, the transformations are horrible, and I forget the loci all the time.
Everything else seems fine, vector questions are sometimes worded in a horrible way, and some of the words for matrices catch me out

Im the same.
Most of the time if I knew what they wanted me to do I could do it but its just trying to figure our what they want doing!

Amd Loci in the complex plane I HATE more then anything! Vectors can be nasty too sometimes.

Reply 2

benwellsday

I can remember the circle one
|z| = 9 is a circle, I think radius 9 because using z=x+iy gives
x^2 + y^2 = 81 which is a circle equation
but thats about it.
The one where its has two arguements, something like
arg (z/z-2) = pi/4
arg z - arg z-2 = pi/4
are horrible. I know its part of a circle, but which part, and where is beyond me. The explanation in lessons never really made sense. Hopefully expanding arg (f(z)/g(z)) to arg f(z) - arg g(z) will get me one mark if it comes up!

Reply 3

mikeleeds

benwellsday

Yep I can do modus ones too, transformations in w/z planes I dont like either i just cant get rid of stuff thats meant to go...
And I completely agree RE:Args when theres 2 and there both complicated i never seem to get the right answer, unless I draw a good picture and do it via trig and stuff, which is never how youre suposed to!

Reply 4

x_reggg

benwellsday

How prepared are you?

i haven't finished chapter 2 and onwards.
that's how prepared i am :3
i did okay in FP2, i'm not that freaked out, but i still need to do good because D2 was just weird x______________________x;

here comes an all-nighter :biggrin:

Reply 5

fisix

x_reggg

Lol i literally cant believe some one is in the same boat as me!!!I have only done some matricies and Proof, I haven t done any of the other chapters yet. you guys better love me for bringing down the boundaries

Reply 6

mikeleeds

fisix

Youre a godsend

Reply 7

benwellsday

lol, chapter 2, 3 and 4 are the killers in my opinion. Chapter 1, series, is like the binomial expansion mixed with differentiation, and occasionally a differential equation. Complex numbers is hell, de Moivre's theorem is the only easy bit, and that can take up 10 minutes if they do a "Express cos7x in terms of ascending powers of cos x" question. Chapter 3 isn't too bad, memorising how to inverse, and how to do the orthogonal diagonal thingy is most the work. Transformations fit in somewhere but I still don't get them, the papers make them look very different from the book. Vectors is horrible, just loads of formulas which you need to know how to apply. Chapter 5 is simple, its basically iteration + differentiation, and can be matched with chapter 1 style questions. Proof is usually alright on the papers. I don't like the inequality proofs, but usually its alright if you apply true for n=k, so true for n=k+1, and do some algebra.
After checking the FP2 thread I'm fairly confident I got an A, which would mean I'd need about 10% marks in FP3 for an A overall, so I'm not rushing to learn every possible style of question.

Reply 8

fisix

benwellsday

I dont care too much about it because it doesnt form any part of my offer... the uni told me to do it cos it would be halpful next year, I'm aiming for a B-C my mechanics went well so i should be ok I think :s-smilie:

I know I will be doing Fmath over the summer just to keep the old grey matter sharp. Gap years dont half make you dumb

Reply 9

x_reggg

fisix

haha i'll bring them down with you :biggrin:

matrices are killing my brain.. all i remember about proofs from flipping through the book was like n=k and n=k+1. and the fact there were no answers for it :frown:

i'm aiming for an A in further maths too :p:

Reply 10

silent ninja

The only topic that I am a little concerned about is matrices. I'm not always doing the image questions properly and some of the eigenvector stuff mixed in with invariant lines can be a little confusing.

I dont mind the w plane stuff anymore. I identified that as a tough section a few weeks back and have made an effort to understand it, so it should be okay.

I dont need many marks either, did FP2 last year, but would like to finish off on a high. I see no point in going through the material only to sabotage my efforts on the last hurdle.

Reply 11

benwellsday

I just did a past paper, january 2006, got 61/75 so I'm fairly confident. Lost 2 marks for forgetting to add 0.5pi and finding a 6th root which I didn't need (5th roots of i). Then I lost another 3 for a sketch of the infamous loci, the one with 2 arguements. It was arg (z-2i / z+2) = pi/2 . My first thoughts were points (0,-2) and (2,0) on the diagram, then some sort of circle joining them. The mark scheme didn't show a diagram but somehow you can work out that it is part of a circle with radius root(2) and centre (-1,1). Any ideas how you do that algebraically? I can't think of anything except z-2i / z+2 = tan(pi/2) which is undefined which means z = -2, which doesn't particularly help.

Reply 12

gyrase

benwellsday

It was arg (z-2i / z+2) = pi/2 . My first thoughts were points (0,-2) and (2,0) on the diagram, then some sort of circle joining them. The mark scheme didn't show a diagram but somehow you can work out that it is part of a circle with radius root(2) and centre (-1,1). Any ideas how you do that algebraically? I can't think of anything except z-2i / z+2 = tan(pi/2) which is undefined which means z = -2, which doesn't particularly help.

arg((z-2i)/(z+2)) = pi/2
=> arg(z-2i) - arg(z+2) = pi/2

therefore;
arctan((y-2)/x) - arctan(y/(x+2)) = pi/2
=> arctan((y-2)/x) = pi/2 + arctan(y/(x+2))
=> (y-2)/x = tan(pi/2 + arctan(y/(x+2)))

Use the identity; tan(pi/2+z) = -cot(z)

=> (y-2)/x = -(x+2)/y
=> 2y-y^2 = x^2+2x
=> y^2-2y+x^2+2x = 0
=> (y-1)^2+(x+1)^2 = 2

circle; centre (-1,1), with radius rt2.

Reply 13

benwellsday

Ok that makes sense although I've never seen that tan identity before. Is there any way to show that identity through algebra etc. I can't seem to think 'why' it works, which usually makes it harder for me to remember.

Reply 14

gyrase

If you want to prove that identity, then do as follows;
tan(x-pi/2)
= sin(x-p/2)/cos(x-pi/2)
= (sinxcos(pi/2)-sin(pi/2)cosx)/(cosxcos(pi/2)+sinxsin(pi/2))
= -cosx/sinx = -cotx

Reply 15

benwellsday

Thanks. I'll probably remember it tommorow anyway but if not I know how to work it out which I seem to be better at remembering.

Reply 16

silent ninja

That question is made simpler if you recognise that the argument of pi/2 means you have a semi-circle, with the two given points each side of the diameter. You can find the centre and radius without algebra easily.

You dont need to remember that identity. Just replace z with z=x+iy then multiply top and bottom by the conjugate of bottom. Next, since you have pi/2 on the right and arg(a+ib) = tan^-1(b/a) and tan(pi/2) is not define, you know that the real part must be 0. So set that to zero and you'll find you have the circle in cartesian form.

Reply 17

benwellsday

Actually I saw that in the mark scheme about a semi-circle. Thinking about it makes sense, the two points meet at an angle of pi/2, so they must be apart by the diameter of the circle. Thats the sort of thing I always forget in mocks and usually remember right at the end of a real exam. Even though that type of loci seems pretty simple now, I still hate complex numbers and their loci.

Reply 18

xinolisss

I hate transformations
I really hate transformations
I really really hate transformations... both as matrices and as complex numbers... I don't get them generally... but on the whole, really it's OK, I've got 291 out of 300 in my AS hence, I would only need another 189 for an A therefore not much work needed on this one since I've already nailed FP2 and M4... :biggrin:

Reply 19

benwellsday

Matrix transformations are alright in the book but the questions are usually worded annoyingly. I've learnt that if a matrix maps a line onto itself then you do Matrix * xi + yj (+ zk) = eigenvalue * xi + yj (+ zk). If it maps a point onto itself then its easier.
Transformations in complex numbers are horrible but the technique I use now is if it gives you w=f(z) and asks for the loci of w in the z plane of some previous formula then find z as a function of w, and stick it into the formula. It works out easier rather than expanding to x + iy and u + iv straight away as usually stuff will cancel. Other times the transformation is too hard and I just make a mess.
Tonight I have learnt how to find the vector for a point on a line that is closest to the origin, and how to find the line from the intersection of two planes.
So its afternoon tommorow?
I'll be revising from 10am onwards.