FP1 OCR (not MEI) 1st June Exam Discussion

Put very quickly:
1) the answer is only 2+i because of the arg being between 0 and pi/2. Only the 2+i will give an arg of this, -2-i will be in the bottom left of the graph, indicating that the angle is greater that pi/2.

2) for the last bit, the rule is as follows, if w^3 is the conjugate of z^3... ie if (z^3)* = w^3, then w = z*.

You have that w^3 is 2-11i, again relating to the arg of w being negative therefore 2-11i is the answer, not 2+11i as this would be in the positive region of the argann diagram.

So we can see that w^3 is the conjugate of z^3 and therefore w is the conjugate of z.

As z is 2+i, you use the conjugate of this to find out that w = 2-i

Hope that helped

thank you, it's so simple when you know what to do! i hope i don't get thrown off like that in the real thing.

@NathDragon5

These answers are great. But I think there are a couple of mistakes in the matrix question.
For the final answer (finding X^-1)
I think you multiplied the determinant by -1 by mistake in the last part. Also I think the final value should be a^2-4 instead of a^2 +4.
But I could be wrong.

Quite possibly, but I am prone to making incredibly silly errors myself even after checking twice or three times.

Quite possibly, but I am prone to making incredibly silly errors myself even after checking twice or three times.

Okay, in regards to the determinant, in 9 part i, I got it wrong by multiplying it all by -1. So in effect, the determinant should read -a^2 -9a +10.... I'll go correct it now.

Secondly, I seem to have mistyped that, indeed it should be a^2-4

Sorry!

Any other problems with the answers?

No I did the paper this morning and all our other answers are the same.

Oh god don't tell me this! XD

If you like I'll send you this file I've made which basically has all the FP1 papers from 2012 Jan to 2005 June with all the questions organised into chapters (excluding Ch.1 which I've kind of mixed with Chapter 10).

Good luck with your studying regardless

M1 was pretty easy IMHO 'Maphs'!
And ahhh guys I think i'm one of the weird kids who gets induction, but I HATE HATE HATE the roots of equations involving all the Alpha beta gamma stuff + substitution into them.. and the weird Loci stuff! Yeuck!

But yeah good luck guys P.S.

But also dude...

Please upload this or whatever! It would help sooooooo much! It'd save me soooooooooo much time! Ha!

when you end up with your sum to infinity, a series will converge usually if n is on the bottom of a fraction, since as n approaches infinity the value of that fraction will get ever smaller, and so tends to another value

e.g 3 - (1 / n)

as n gets larger it tends more towards 3, so the sum to infinity is 3, it converges to 3.

Cheers man, Also I don't suppose you could help explain January 2012 10ii) ... I never get these smelly questions! ? :P