[Mr M]

Mr M's OCR (not OCR MEI) FP1 answers June 2012


1. (i) 21+11i (2 marks)

(ii) (3 marks)


2. (i) (2 marks)

(ii) (3 marks)


3. and (4 marks)


4. (7 marks)


5. Proof (5 marks)


6. (i) (3 marks)

(ii) (3 marks)


7. (i) Circle centre 3 + 4i and radius 4 and horizontal line through 0 + 4i (6 marks)

(ii) -1 + 4i and 7 + 4i (2 marks)

(iii) Shade top of circle above horizontal line (2 marks)


8. (i) Show (1 mark)

(ii) (6 marks)

(iii) N = 4 (4 marks)


9. (i) Shear parallel to x axis taking (0, 1) to (2, 1) (2 marks)

(ii) (5 marks)

(iii) Rotation clockwise about O by 60 degrees (2 marks)

10 (i) (3 marks)

(ii) (a) Unique solution

(b) No unique solution and inconsistent

(c) No unique solution and consistent (7 marks)

[Steve0606]

For 9(i) I put shear, x-axis invariant making an angle of arctan(1/2), would I get the mark for that? Also, how did you get Q7(ii)?

[Steve0606]

To the x-axis*

[h2shin]

I think question 7(ii) might be wrong, the centre of the circle was at 3+4i, so lines would have crossed at -1+4i and 7+4i

[As_Dust_Dances_]

For part 2ii) I don't remember getting 1/4 on the outside, think I got an 1/2 hmm..

[z95]

Pretty sure that it was 60 degrees clockwise. Not 90

[Mr M]

(Original post by Steve0606)
For 9(i) I put shear, x-axis invariant making an angle of arctan(1/2), would I get the mark for that? Also, how did you get Q7(ii)?

Sounds alright

Q7(ii) just coords of points of intersection of circle and line

[As_Dust_Dances_]

8ii) was method of differences right? I just don't remember getting an answer like that :|

[Mr M]

(Original post by z95)
Pretty sure that it was 60 degrees clockwise. Not 90

Yes typo sorry

[Mr M]

(Original post by h2shin)
I think question 7(ii) might be wrong, the centre of the circle was at 3+4i, so lines would have crossed at -1+4i and 7+4i

Oh I see. Sorry!

[Steve0606]

It's 60 degrees, and also, I'm pretty sure Q7(ii) is incorrect. It should be -1+4i and 7+4i... I think

[Mr M]

(Original post by As_Dust_Dances_)
8ii) was method of differences right? I just don't remember getting an answer like that :|

I just put it over a common denominator.

[Mr M]

(Original post by Steve0606)
It's 60 degrees, and also, I'm pretty sure Q7(ii) is incorrect. It should be -1+4i and 7+4i... I think

Yes fixed a couple of mins ago.

[As_Dust_Dances_]

(Original post by Mr M)
I just put it over a common denominator.

Oh okay, and also for the last part of the question I got N=3 as I got a decimal answer at first but then presumed you couldn't have a decimal under the sigma. :/

[Bless3d]

(Original post by Mr M)
.

what was the matrix for 9)i) please?

[cameron95]

(Original post by Mr M)
I just put it over a common denominator.

what was the unsimplified version of 8.(ii)?

[Mr M]

(Original post by As_Dust_Dances_)
Oh okay, and also for the last part of the question I got N=3 as I got a decimal answer at first but then presumed you couldn't have a decimal under the sigma. :/

No that isn't right - it came out with an exact answer.

[mathsman77]

Q4 I got the same but factorised, n(n^2 +1), I remember the question asking for it in fully factorised form so i was unsure whether they were looking for n(n+i)(n-i), i wrote both down but was thrown because i didn't they were looking for anything complex in this particular question

anyone now exactly what format they wanted the answer?

[As_Dust_Dances_]

3/2 - 1/(n+1) - 1/(n+2) or something like that is what I got for 8ii)

[As_Dust_Dances_]

(Original post by Mr M)
No that isn't right - it came out with an exact answer.

I have no idea what I have done, I did the sum from 1 to infinity which I got was 3/2 I think + the sum from n to infinity 1/(n+1) - 1/(n+2). I ended up with a quadratic but I must have simplified it wrong..