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

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

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..

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?

Thanks again for these mr m

what would you say 58/72 would be, b/c?

I don't like to guess but it would be closer to an A than a C!

I'm just being a pessimist then!
On finding N for the sum to infinity, if i got to the point where i'd set up a quadratic, but didn't factorise would i get a couple of marks?

You are absolutely right - I didn't notice the "fully factorised form" bit.

They want $n(n+i)(n-i)$

i just left the sum as n(n^2+1), thought this would be enough.

I didn't do that so drop one mark?

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


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

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


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

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


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


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


5. Proof (5 marks)


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

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

(iii) N = 4 (4 marks)


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

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

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

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

(ii) (a) Unique solution

(b) No unique solution and inconsistent

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

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?

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


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

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


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

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


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


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


5. Proof (5 marks)


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

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

(iii) N = 4 (4 marks)


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

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

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

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

(ii) (a) Unique solution

(b) No unique solution and inconsistent

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

You are absolutely right - I didn't notice the "fully factorised form" bit.

They want $n(n+i)(n-i)$

(9) i) I was under the impression that they wanted the term 'axis invariant'


Also, are you sure that you could just have x(x^2+1) instead of including imaginary numbers for question 4. I know it says fully factorised but those questions have come up in the past and not once has it requested it to include imaginary numbers.

Also can you put the method of differences one as the numbers you get after cancelling because that's what I have seen in some of the mark schemes, rather than making it have a common denominator.

And for the last question how far would you have to go to prove that they are inconsistent? COuld you state that z= 2-x-y and that z=1/2(2-x-y) and would that be enough.

Would you have to give the unique solutions to the last question because I think I remember seeing that in one of the previous papers where it asked the exact same thing in the question, but seeing as you had just worked out the inverse of the matrix you could write down the answer much easier. But this question was worth more marks. so?


Cheers for the answers anyway,