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

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


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

(ii) 2629i41\frac{26-29i}{41} (3 marks)


2. (i) (52136)\begin{pmatrix} 5 & 2\\13 & 6 \end{pmatrix} (2 marks)

(ii) 14(62135)\frac{1}{4} \begin{pmatrix} 6 & -2\\-13 & 5 \end{pmatrix} (3 marks)


3. a=8a=-8 and b=25b=25 (4 marks)


4. n(n+i)(ni)n(n+i)(n-i) (7 marks)


5. Proof (5 marks)


6. (i) 5u2+11u+8=05u^2+11u+8=0 (3 marks)

(ii) 85\frac{8}{5} (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) n(5+3n)2(n+1)(n+2)\frac{n(5+3n)}{2(n+1)(n+2)} (6 marks)

(iii) N = 4 (4 marks)


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

(ii) 12(1331)\frac{1}{2} \begin{pmatrix} 1 & \sqrt{3}\\ -\sqrt{3} & 1 \end{pmatrix} (5 marks)

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

10 (i) a34aa^3 - 4a (3 marks)

(ii) (a) Unique solution

(b) No unique solution and inconsistent

(c) No unique solution and consistent (7 marks)
(edited 11 years ago)

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Reply 1
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)?
Reply 2
To the x-axis*
Reply 3
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
For part 2ii) I don't remember getting 1/4 on the outside, think I got an 1/2 hmm..
Reply 5
Pretty sure that it was 60 degrees clockwise. Not 90
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
8ii) was method of differences right? I just don't remember getting an answer like that :|
Original post by z95
Pretty sure that it was 60 degrees clockwise. Not 90


Yes typo sorry
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!
Reply 10
It's 60 degrees, and also, I'm pretty sure Q7(ii) is incorrect. It should be -1+4i and 7+4i... I think :biggrin:
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.
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 :biggrin:


Yes fixed a couple of mins ago.
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. :/
Reply 14
Original post by Mr M
.


what was the matrix for 9)i) please?
(edited 11 years ago)
Reply 15
Original post by Mr M
I just put it over a common denominator.


what was the unsimplified version of 8.(ii)?
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.
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?
3/2 - 1/(n+1) - 1/(n+2) or something like that is what I got for 8ii)
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..

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