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    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 & 0 \\2 & 1-2a \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)


    Edit: I've corrected the answer to 8(ii) as it had the wrong signs and 3(ii) as it was just wrong
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    Thanks Mr M.
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    (Original post by Mr M)
    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
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    (Original post by Ahmad_18)
    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
    You have probably lost 3 marks on 8ii.

    It is 150 degrees if you measure from the POSITIVE real axis.
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    Thanks for posting!
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    What's raw mark is required to gain 100 UMS for June 2013 or June 2012?
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    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.
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    (Original post by Sahil_)
    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.
    there's a lot of answers to it
    I did rotation 90 degrees clockwise then stretch scale factor 2 parallel to x axis for example

    if they get the combined transformation matrix then it's all good
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    (Original post by Mr M)
    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)
    Thanks for that. One small thing, would 8ii not give a negative answer for what you had?
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    (Original post by Mr M)
    I'm not sure what you are asking. The answer to 8ii is correct.
    But if you subbed in n=2, you'd get a negative answer :confused:
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    (Original post by Mr M)
    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)
    Mr M, for question 5 I mistakenly done the centre of my circle and half line from -2 on the y axis and not on the x axis, My circle went through the origin and I got the half line angle right, how many marks do you think I dropped?
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    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
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    Thank you very much - are you doing the m2 ocr answers by any chance?
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    (Original post by Jamesb17_)
    But if you subbed in n=2, you'd get a negative answer :confused:
    Yes sorry - I used a computer to solve it and must have had a wrong sign somewhere. I've done it by hand and fixed it now.
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    (Original post by jack0997)
    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
    Probably drop 2 on 8ii). You'll probably get 1 on 9iii).
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    (Original post by nozzelf78)
    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.
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    (Original post by Mr M)
    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.
    Agreed, I am pretty sure most people on TSR know the answers to M2 by now if they took the exam.
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    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.
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    Thanks do much for this Mr M!
    For 9ii) I got all mixed up. I put non unique for a=3 but then I proved the equations were consistent finding an exact answer, will this scrape me any marks? For part B I said unique solution but I stated DetD=0 as I mixed up my facts about determinants. You think that will get a mark?
    I hope there was error carried forward for 10 because I got u^3+16u -9 but didnt get a value for u^2. so in part ii I used the correct method but found that (-b/a)^2 was 0 this meant my final answer was -35 as I got the aby = -3. I really hope I haven't sacrificed loads of marks here when i was just on the cusp of getting them. The grade boundaries better be low!
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    (Original post by Sam596)
    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.
    I'll do C3 and C4 and maybe some others.
 
 
 
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