Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2015

Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2015


1. $2(x^2+y^2)$ (3 marks)


2. $\frac{n}{2} (2n-3)(n+3)$ (4 marks)


3. (i) $\frac{1}{2} \begin{pmatrix} 1 & -a \\0 & 2 \end{pmatrix}$ (2 marks)

(ii) $\begin{pmatrix} 1 & 2a \\2 & 2a+1 \end{pmatrix}$ (3 marks)


4. Complete proof (5 marks)


5. (i) Circle centre -2 + 0i radius 2 and half line starting at the centre of the circle 30 degrees above the negative real axis (4 marks)

(ii) $-2-\sqrt 3 + i$ (2 marks)

(iii) Shade sector inside circle between half line and negative real axis (2 marks)


6. (i) A' = (0, -1) B' = (2, -1) C' = (2, 0) (3 marks)

(ii) One possible combination is stretch in y direction scale factor 2

$\begin{pmatrix} 1 & 0 \\0 & 2 \end{pmatrix}$

followed by rotation 90 degrees clockwise about the origin

$\begin{pmatrix} 0 & 1 \\-1 & 0 \end{pmatrix}$ (4 marks)


7. (i) $\pm (3+2i)$ (5 marks)

(ii) $x=-1-2i$ or $x=5+2i$ (5 marks)


8. (i) Show (2 marks)

(ii) $\frac{1}{n+1}+\frac{3}{n}-\frac{7}{2}$ (6 marks)

(iii) $\frac{5}{4}$ (2 marks)


9. (i) a = 5 or a = 1 (6 marks)

(ii) (a) Unique solution

(b) Inconsistent equations (4 marks)


10. (i) $u^3+8u^2+16u-9=0$ (3 marks)

(ii) 29 (7 marks)

Firstly thank you Mr M for posting the answers.

For question 8ii on method of differences i could not spot and cancel out the term, how many marks do you think I've lost.
And for 5i i wrote 150° instead of 30°
Thanks again

For the transformation question, could you do a reflection in the line y=-x followed by a stretch scale factor -2 parallel to the x-axis, because if you multiply those two matrices you get the transformation matrix.

Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2015


1. $2(x^2+y^2)$ (3 marks)


2. $\frac{n}{2} (2n-3)(n+3)$ (4 marks)


3. (i) $\frac{1}{2} \begin{pmatrix} 1 & -a \\0 & 2 \end{pmatrix}$ (2 marks)

(ii) $\begin{pmatrix} 1 & 2a \\2 & 2a+1 \end{pmatrix}$ (3 marks)


4. Complete proof (5 marks)


5. (i) Circle centre -2 + 0i radius 2 and half line starting at the centre of the circle 30 degrees above the negative real axis (4 marks)

(ii) $-2-\sqrt 3 + i$ (2 marks)

(iii) Shade sector inside circle between half line and negative real axis (2 marks)


6. (i) A' = (0, -1) B' = (2, -1) C' = (2, 0) (3 marks)

(ii) One possible combination is stretch in y direction scale factor 2

$\begin{pmatrix} 1 & 0 \\0 & 2 \end{pmatrix}$

followed by rotation 90 degrees clockwise about the origin

$\begin{pmatrix} 0 & 1 \\-1 & 0 \end{pmatrix}$ (4 marks)


7. (i) $\pm (3+2i)$ (5 marks)

(ii) $x=-1-2i$ or $x=5+2i$ (5 marks)


8. (i) Show (2 marks)

(ii) $\frac{1}{n+1}+\frac{3}{n}-\frac{7}{2}$ (6 marks)

(iii) $\frac{5}{4}$ (2 marks)


9. (i) a = 5 or a = 1 (6 marks)

(ii) (a) Unique solution

(b) Inconsistent equations (4 marks)


10. (i) $u^3+8u^2+16u-9=0$ (3 marks)

(ii) 29 (7 marks)

I'm not sure what you are asking. The answer to 8ii is correct.

Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2015


1. $2(x^2+y^2)$ (3 marks)


2. $\frac{n}{2} (2n-3)(n+3)$ (4 marks)


3. (i) $\frac{1}{2} \begin{pmatrix} 1 & -a \\0 & 2 \end{pmatrix}$ (2 marks)

(ii) $\begin{pmatrix} 1 & 2a \\2 & 2a+1 \end{pmatrix}$ (3 marks)


4. Complete proof (5 marks)


5. (i) Circle centre -2 + 0i radius 2 and half line starting at the centre of the circle 30 degrees above the negative real axis (4 marks)

(ii) $-2-\sqrt 3 + i$ (2 marks)

(iii) Shade sector inside circle between half line and negative real axis (2 marks)


6. (i) A' = (0, -1) B' = (2, -1) C' = (2, 0) (3 marks)

(ii) One possible combination is stretch in y direction scale factor 2

$\begin{pmatrix} 1 & 0 \\0 & 2 \end{pmatrix}$

followed by rotation 90 degrees clockwise about the origin

$\begin{pmatrix} 0 & 1 \\-1 & 0 \end{pmatrix}$ (4 marks)


7. (i) $\pm (3+2i)$ (5 marks)

(ii) $x=-1-2i$ or $x=5+2i$ (5 marks)


8. (i) Show (2 marks)

(ii) $\frac{1}{n+1}+\frac{3}{n}-\frac{7}{2}$ (6 marks)

(iii) $\frac{5}{4}$ (2 marks)


9. (i) a = 5 or a = 1 (6 marks)

(ii) (a) Unique solution

(b) Inconsistent equations (4 marks)


10. (i) $u^3+8u^2+16u-9=0$ (3 marks)

(ii) 29 (7 marks)

But if you subbed in n=2, you'd get a negative answer

Hi Mr M, thanks for posting.

On the method of differences, i got 5/2 - some terms with n in that i cant remember, but I found a full cancelling pattern and considered integers for r and n-1 and n - how many marks could I pick up for method marks here?
Weirdly I obtained 5/4 for the sum to infinity question with a wrong previous term - would I still gain the marks?
Thanks again

Thank you very much - are you doing the m2 ocr answers by any chance?

I looked in another M2 thread and saw a list of answers so I thought I probably wouldn't bother. If there is some debate I can do. I have a paper in my bag.

By this, looks like I've lost around 10 marks :/.

Thanks Mr M though! If I may ask, what OCR papers will you be able to put up a mark scheme for this year? I've still got C3, C4, FP3, S1, S2, and D2 to come.