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

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    (Original post by Mr M)
    Do you mean a = 3 so the determinant = 0? Get 1 mark if you said that.
    Thanks, also another question: For Question 8 iii.) if I stated the wrong evaluation of sum to infinity, and thus did not add a sixth to the answer, however stated the correct summation at the start (Sum of n to infinity = Sum of 1 to infinity - Sum of 1 to n-1). The only thing I missed was the sixth, so how many marks would I lose for this?
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    (Original post by Mr M)
    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} (5 marks)


    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)
    Just wondering how many marks I would lose in 2 ii) as I didn't see the conjugate parts so I used the part I got in part i) but I did everything else on that question right only used the non conjugate z how many marks would I lose?
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    (Original post by deadroad)
    Thanks, also another question: For Question 8 iii.) if I stated the wrong evaluation of sum to infinity, and thus did not add a sixth to the answer, however stated the correct summation at the start (Sum of n to infinity = Sum of 1 to infinity - Sum of 1 to n-1). The only thing I missed was the sixth, so how many marks would I lose for this?
    Probably just 1.
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    (Original post by getjdhwgebrixow)
    Just wondering how many marks I would lose in 2 ii) as I didn't see the conjugate parts so I used the part I got in part i) but I did everything else on that question right only used the non conjugate z how many marks would I lose?
    Either 1 or 2.
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    (Original post by Mr M)
    Either 1 or 2.
    Thank you
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    What was the last question?
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    I know this post was a while ago, but I've been doing this paper as practice for next weeks exam. I was wondering how to get the answer to 7)ii) I've tried a lot of things but I'm still not sure! Thanks
 
 
 
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