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Mr M's OCR (not OCR MEI) FP1 answers June 2012

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    (Original post by As_Dust_Dances_)
    3/2 - 1/(n+1) - 1/(n+2) or something like that is what I got for 8ii)
    i got this too, would it be okay?
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    Thanks again for these mr m

    what would you say 58/72 would be, b/c?
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    (Original post by As_Dust_Dances_)
    I have no idea what I have done, I did the sum from 1 to infinity which I got was 3/2 I think + the sum from n to infinity 1/(n+1) - 1/(n+2). I ended up with a quadratic but I must have simplified it wrong..
    the quadratic factorised to (11x + 17)(x - 4) if i remember correctly, so the answer was n=4.
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    (Original post by mathsman77)
    Q4 I got the same but factorised, n(n^2 +1), I remember the question asking for it in fully factorised form so i was unsure whether they were looking for n(n+i)(n-i), i wrote both down but was thrown because i didn't they were looking for anything complex in this particular question

    anyone now exactly what format they wanted the answer?
    You are absolutely right - I didn't notice the "fully factorised form" bit.

    They want n(n+i)(n-i)
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    (Original post by gpsmith26)
    Thanks again for these mr m

    what would you say 58/72 would be, b/c?
    I don't like to guess but it would be closer to an A than a C!
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    I'm not too sure if I got the induction question right, I remember getting the 6 on the outside part from 18-12, out of the 5 will you get 2 just for putting n=1 and n=k into the equation?
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    (Original post by Mr M)
    I don't like to guess but it would be closer to an A than a C!
    I'm just being a pessimist then!
    On finding N for the sum to infinity, if i got to the point where i'd set up a quadratic, but didn't factorise would i get a couple of marks?
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    (Original post by gpsmith26)
    I'm just being a pessimist then!
    On finding N for the sum to infinity, if i got to the point where i'd set up a quadratic, but didn't factorise would i get a couple of marks?
    Yes
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    (Original post by Mr M)
    You are absolutely right - I didn't notice the "fully factorised form" bit.

    They want n(n+i)(n-i)
    I didn't do that so drop one mark?
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    i just left the sum as n(n^2+1), thought this would be enough.
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    (9) i) I was under the impression that they wanted the term 'axis invariant'


    Also, are you sure that you could just have x(x^2+1) instead of including imaginary numbers for question 4. I know it says fully factorised but those questions have come up in the past and not once has it requested it to include imaginary numbers.

    Also can you put the method of differences one as the numbers you get after cancelling because that's what I have seen in some of the mark schemes, rather than making it have a common denominator.

    And for the last question how far would you have to go to prove that they are inconsistent? COuld you state that z= 2-x-y and that z=1/2(2-x-y) and would that be enough.

    Would you have to give the unique solutions to the last question because I think I remember seeing that in one of the previous papers where it asked the exact same thing in the question, but seeing as you had just worked out the inverse of the matrix you could write down the answer much easier. But this question was worth more marks. so?


    Cheers for the answers anyway,
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    (Original post by h2shin)
    i just left the sum as n(n^2+1), thought this would be enough.
    It *might* be but as sum of two squares is part of this specification it might not!
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    Am I also right in solving question 7 simultaneously to see if there are any solutions or not? For part i) I found values for x y and z and so therefore stated there is a unique solution. I think I may have got b) and c) mixed up too and said that b was inconsistent, would I only drop 1 mark?
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    (Original post by tooambitious)
    I didn't do that so drop one mark?
    Probably but not certainly.
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    (Original post by Mr M)
    Mr M's OCR (not OCR MEI) FP1 answers June 2012


    1. (i) 21+11i (2 marks)

    (ii) \frac{26-29i}{41} (3 marks)


    2. (i) \begin{pmatrix} 5 & 2\\13 & 6 \end{pmatrix} (2 marks)

    (ii) \frac{1}{4} \begin{pmatrix} 6 & -2\\-13 & 5 \end{pmatrix} (3 marks)


    3. a=-8 and b=25 (4 marks)


    4. n(n+i)(n-i) (7 marks)


    5. Proof (5 marks)


    6. (i) 5u^2+11u+8=0 (3 marks)

    (ii) \frac{8}{5} (3 marks)


    7. (i) Circle centre 3 + 4i and radius 4 and horizontal line through 0 + 4i (6 marks)

    (ii) -1 + 4i and 7 + 4i (2 marks)

    (iii) Shade top of circle above horizontal line (2 marks)


    8. (i) Show (1 mark)

    (ii) \frac{n(5+3n)}{2(n+1)(n+2)} (6 marks)

    (iii) N = 4 (4 marks)


    9. (i) Shear parallel to x axis taking (0, 1) to (2, 1) (2 marks)

    (ii) \frac{1}{2} \begin{pmatrix} 1 & \sqrt{3}\\ -\sqrt{3} & 1 \end{pmatrix} (5 marks)

    (iii) Rotation clockwise about O by 60 degrees (2 marks)

    10 (i) a^3 - 4a (3 marks)

    (ii) (a) Unique solution

    (b) No unique solution and inconsistent

    (c) No unique solution and consistent (7 marks)
    how many marks would be lost for the following mistakes?
    for Q5 i got to the inductive step but couldn't get it into the correct format (i added the k+1th term to the sum to k)
    Q8.(iii) i had the right method - form a quadratic using (sum to infinity - sum to N) - but i must have made a mistake in forming or solving the quadratic as i got decimal answers
    Q10(ii)(c) i ran out of time so i just said Det = 0 and equations are consistent (i could see by looking at them) but i didn't show any working
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    (Original post by mathsman77)
    Q4 I got the same but factorised, n(n^2 +1), I remember the question asking for it in fully factorised form so i was unsure whether they were looking for n(n+i)(n-i), i wrote both down but was thrown because i didn't they were looking for anything complex in this particular question

    anyone now exactly what format they wanted the answer?
    I considered doing this, but I didn't :/ I don't think the sum formulae work for imaginary numbers though, just natural numbers.
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    (Original post by Mr M)
    Mr M's OCR (not OCR MEI) FP1 answers June 2012


    1. (i) 21+11i (2 marks)

    (ii) \frac{26-29i}{41} (3 marks)


    2. (i) \begin{pmatrix} 5 & 2\\13 & 6 \end{pmatrix} (2 marks)

    (ii) \frac{1}{4} \begin{pmatrix} 6 & -2\\-13 & 5 \end{pmatrix} (3 marks)


    3. a=-8 and b=25 (4 marks)


    4. n(n+i)(n-i) (7 marks)


    5. Proof (5 marks)


    6. (i) 5u^2+11u+8=0 (3 marks)

    (ii) \frac{8}{5} (3 marks)


    7. (i) Circle centre 3 + 4i and radius 4 and horizontal line through 0 + 4i (6 marks)

    (ii) -1 + 4i and 7 + 4i (2 marks)

    (iii) Shade top of circle above horizontal line (2 marks)


    8. (i) Show (1 mark)

    (ii) \frac{n(5+3n)}{2(n+1)(n+2)} (6 marks)

    (iii) N = 4 (4 marks)


    9. (i) Shear parallel to x axis taking (0, 1) to (2, 1) (2 marks)

    (ii) \frac{1}{2} \begin{pmatrix} 1 & \sqrt{3}\\ -\sqrt{3} & 1 \end{pmatrix} (5 marks)

    (iii) Rotation clockwise about O by 60 degrees (2 marks)

    10 (i) a^3 - 4a (3 marks)

    (ii) (a) Unique solution

    (b) No unique solution and inconsistent

    (c) No unique solution and consistent (7 marks)
    Hi Mr M, thanks for these
    For 9.(ii) your answer is 1/2(1, root3, -root3, 1). I halved everything and left it as a decimal so I got (0.5, 0.866, -0.866, 0.5) Would I still get the marks??

    I'm trying to make the brackets look vaguely like a matrix there.
    Also, for the shear question, I put a shear parallel to the x-axis scale factor 2, would that gain any marks?
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    (Original post by Mr M)
    You are absolutely right - I didn't notice the "fully factorised form" bit.

    They want n(n+i)(n-i)
    I just left it as n(n^2 +1) so one mark lost I suppose?
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    (Original post by OrangesAreGreen)
    (9) i) I was under the impression that they wanted the term 'axis invariant'


    Also, are you sure that you could just have x(x^2+1) instead of including imaginary numbers for question 4. I know it says fully factorised but those questions have come up in the past and not once has it requested it to include imaginary numbers.

    Also can you put the method of differences one as the numbers you get after cancelling because that's what I have seen in some of the mark schemes, rather than making it have a common denominator.

    And for the last question how far would you have to go to prove that they are inconsistent? COuld you state that z= 2-x-y and that z=1/2(2-x-y) and would that be enough.

    Would you have to give the unique solutions to the last question because I think I remember seeing that in one of the previous papers where it asked the exact same thing in the question, but seeing as you had just worked out the inverse of the matrix you could write down the answer much easier. But this question was worth more marks. so?


    Cheers for the answers anyway,
    Axis invariant is not compulsory (or even particularly common) language.

    I don't suppose the Chief Examiner has decided whether to give a mark for factorising as the sum of two squares yet. He/she will look at some scripts first. The real product may be fine.

    You don't need a common denominator.

    You showed an inconsistency so that should be fine. I used triangular form.
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    Question 6 (ii) was (1/A - 1)(1/B - 1) where A and B are roots, i think? . I got the answer to this as 3, how did you get 8/5?

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Updated: June 24, 2012
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