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

Decent exam, can't complain about confusing questions really.

Only irritation was that I ballsed up question 9 slightly. Got the first part with the shear, but calculated the determinant of the inverse of the shear as -1 instead of 1, which has annoyingly given me the wrong answer, despite my method being fine. I realised this with about 30 seconds to go and didn't have enough time to change it. Will I still get some method marks and a Mark for stating 'rotation' in part 3 despite not getting the right angle? (120 degrees anticlockwise, exactly opposite).


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How many marks would you lose roughly if you made a small calculation error in the process of factorising. e.g +3 instead of -3.

Everything else was fine, method etc.

Could you possible break the marks to this question down as much as possible?

Thanks in advance.

does anyone remember what z and w were on the 1st question?

For the second part of the first question, I have no idea what I did (though I'd assume I got confused with positive i^2 and negative i^2) and instead of (26 - 29i) / 41, I got (26 - 29i) / 29, so had 26/29 + i. I'm more concerned about how I did that as opposed to how many marks I'd lose of the three (I'd assume I'd lose 2 of them?), so I was just wondering if anyone could tell what I did?

For the second part of the first question, I have no idea what I did (though I'd assume I got confused with positive i^2 and negative i^2) and instead of (26 - 29i) / 41, I got (26 - 29i) / 29, so had 26/29 + i. I'm more concerned about how I did that as opposed to how many marks I'd lose of the three (I'd assume I'd lose 2 of them?), so I was just wondering if anyone could tell what I did?

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)