Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2016

Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2016


1. $\displaystyle \frac{n(2n+3)(n-1)}{2}$ (5 marks)


2. (i) $\sqrt{3}-3i$ (2 marks)

(ii) $\displaystyle \frac{-1+4\sqrt{3} i}{49}$ (5 marks)


3. (i) $\displaystyle \alpha + \beta = -\frac{1}{k}$ and $\displaystyle \alpha \beta = 1$ (1 mark)

(ii) $\displaystyle \frac{1}{k^2}$


4. (i) $\begin{pmatrix} 5a-3b & 10 & 0 \end{pmatrix}$ (2 marks)

(ii) $\begin{pmatrix} 6b-5 \end{pmatrix}$ (2 marks)

(iii) $\begin{pmatrix} 6a & 12 & 18 \\4a & 8 & 12 \\-a & -2 & -3 \end{pmatrix}$ (2 marks)


5. Proof (4 marks)


6. (i) $\displaystyle |z-3-3i|=\sqrt 5$ (4 marks)

(ii) Sketch (2 marks)

(iii) $2+5i$ and $4+i$ (3 marks)


7. (i) Shear with x axis invariant taking the point (0, 1) to (3, 1) (2 marks)

(ii) $\begin{pmatrix} 0 & -1 \\-1 & 0 \\ \end{pmatrix}$

Reflection in the line $y=-x$ (6 marks)


8. (i) Show (1 mark)

(ii) $\displaystyle \frac{n}{3(2n+3)}$ (6 marks)

(iii) $\displaystyle \frac{1}{2(2n+1)}$ (3 marks)


9. (i) Show (3 marks)

(ii) Determinant = 0 when a = 3 so no unique solution. The equations are consistent because 3 x equation 3 - equation 1 = equation 2. (3 marks)


10. (i) $5+4i$ and $-5-4i$ (6 marks)

(ii) Show (1 mark)

(iii) $\displaystyle \pm \frac{5}{41} \pm \frac{4i}{41}$ (4 marks)

Thanks again. Was question 3ii marks?

do you think i will lose marks for keeping the 1/41 factorised for my answer to 10 iii?

Difficulty of paper in your opinion?

Thanks so much you are a legend.
For question 2ii it said write as x+iy so shouldn't u of seperated them

It really doesn't matter.

I would be grateful if you could answer these:

For question 6i, how many marks would I lose for writing 2 instead of root 5

For my sketch, the sketch looks fine and is obviously not to scale put goes through the two points but has radius 2 instead of root 5 so many would I lose there?

For question 8ii how many would I lose for not combining the two fractions?

For the last question I didn't simplify the end result so I have 1/something. It is correct but not simplified so how much would I lose there?

I'm sorry for this but I'm just a bit worried

Thanks again for your answers - would you get ECF for the sum to infinity if you forgot to half the method of differences from 8 part ii?

Okay will I get error carried forward for the difference method as I forgot to half the first part as I didn't read it had 2 on top which means the second part is wrong?

I've just answered this for someone else. I think so.