Mr M's OCR (not OCR MEI) Further Pure 2 Answers June 2013

Mr M's OCR (not OCR MEI) Further Pure 2 Answers June 2013

7. (i) x = -1, x = 7, y = 1 (3 marks)

Thanks for the answers Mr M. By the looks of it I may have gotten what I needed for my university offer which is great! (well assuming my sketches and show that's are all valid, and the extra paper I used doesn't go missing haha )

How did you find this paper in comparison to other FP2 papers out of interest?

Thank you very much for the great work as per usual Mr. M - I'll miss your posts next year when I have nowhere to look up answers

Just a couple of questions,

Q2.ii, I forgot to put plus/minus in my answers. Will it cost me 1 mark or 2 marks?

Q3, I only managed to find the first derivative of f(x). How many marks will I lose there out of 6?

Q5.iii, I would have assumed that the answer would be that the NR method will lead to the positive root rather than the negative root. Am I incorrect/discredited of marks for saying this?

thanks in advance

2ii) drop 1

3) drop 4

5iii) yes that's right, I'll change my wording to improve my answer

for part 3ii) would i lose a mark if i put tanh^-1(1/3) instead of 0.5ln2?

If I put all of these but also y=0, would I still get all 3 marks?

I wasn't sure from the working of the question, we're we supposed to give x2 and x3 to 5dp as well as alpha or just alpha?
I gave the other to greater accuracy and alpha to 5, hope I don't lose makes for that


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No you are supposed to give them to more figures than 5 d.p. (I didn't write them down to more and couldn't be bothered to do them again!).

Mr M's OCR (not OCR MEI) Further Pure 2 Answers June 2013


1. 1 (5 marks)


2. (i) Show (3 marks)

(ii) $x=\ln (2 \pm \sqrt {3})$ and $x=\ln (3 \pm 2 \sqrt 2)$ (5 marks)


3. (i) Show (6 marks)

(ii) $\frac{1}{2} \ln 2 - \frac{x}{2} + \frac{x^2}{4}$ (4 marks)


4. (i) Show (5 marks)

(ii) $\frac{256}{693}$


5. (i) Show (3 marks)

(ii) $x_2 = -0.72652$

$x_3 = -0.72611$

$\alpha = -0.72611$ (3 marks)

(iii) $x_1$ is to the right of the stationary point sending the tangent away from the negative root and this means NR will find the positive root(2 marks)


6. (i) Show (3 marks)

(ii) $\frac{3}{n} \sum_{r=1}^n \ln (\ln (3+\frac{3r}{n})$ (1 mark)

(iii) 1468 (4 marks)


7. (i) x = -1, x = 7, y = 1 (3 marks)

(ii) $(-3, \frac{1}{2})$ and $(\frac{1}{3}, -\frac{1}{8})$ (5 marks)

(iii) $(-\frac{4}{3}, 1)$ (3 marks)

(iv) Sketch (3 marks)


8. (i) $r=1+\cos \theta$ (3 marks)

(ii) Sketch (2 marks)

(iii) 1 : 3 (6 marks)

Sorry if this is a stupid question, but for 7i) why is y=0 not an asymptote? Since it's x^2 + 1 on top surely it is impossible to get y=0?

Hi Mr M, thanks for the answers! Regarding the last question, I made a fatal horror error in writing the formula x^2+y^2 = r compared to r squared. I therefore didnt get the correct equation and therefore my sketch etc were wrong as well. Will I lose all the marks for the question i.e. 0/11