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Edexcel Maths FP1 UNOFFICIAL Mark Scheme 19th May 2017 Watch

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    (Original post by Redcoats)
    I got 8f(k) + 19(3^3k+blah). There are loads of different methods for it.
    Do you remember your working for the question? None of my classmates including me were able to do this question, a few of them are still trying to work it out right now. Any help?
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    For the Area FXD question:
    tangent has equation yq= x+ aq^2
    at directrix, x= -a so yq = -a + aq^2 so y = (-a + aq^2)/q
    F(a,0) X(-0.25a,0) D(-a, (-a + aq^2)/q)
    Area of FXD = 1/2 x base x height = 0.5 x (a+0.25a) x modulus of ((aq^2 - a)/q)

    Lets suppose the y coordinate of D is -5, length is 5, so times y coordinate of D by -1 to give magnitude.

    Area = 0.5 x (1.25a) x ((a - aq^2)/q) = 0.625 x q^-1 x (a^2 - (a^2 x q^2))
    I got it all in terms of q, as q is a parameter and everything in the question is algebra
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    (Original post by Edmar Hadad)
    what question was the p=20 one?
    The equation has an unknown P in it, given the argument it can be proved that P=20
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    (Original post by murat10q7)
    you know the last part of the series question i got 910=sigma k(2^r-1) and couldnt do the rest how many mark do you think that'll get? and how many marks was that last part of the question if any1 knows?
    2 probably thats c2 geometric series btw in an fp1 paper lol
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    (Original post by __Will__)
    Do you remember your working for the question? None of my classmates including me were able to do this question, a few of them are still trying to work it out right now. Any help?
    Hopefully this helps.

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    (Original post by X_IDE_sidf)
    These are my answers, looking for mild confirmation, here also are the marks:

    1) This was a newton r f(x)=\frac{1}{3}x^2+\frac{4}{x^2  }-2x-1

    a) Prove root [6,7] Change of sign (2 marks)
    b) Find first newton approx starting at 6 to 2dp , 6.45 (5 marks)

    2) some matrix question:
    A=\begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix}
    (a) A^-1 = \frac{1}{10}\begin{bmatrix} 3 & 1 \\ -4 & 2 \end{bmatrix} (2 marks)

    P=\begin{bmatrix} 3 & 6 \\ 11 & -8 \end{bmatrix}

    (b) Given AB=P find B B = \begin{bmatrix} 2 & 1 \\ 1 & -4 \end{bmatrix} (3 marks)

    3)
    x=4t , x=\frac{4}{t}
    a) Find a line perpendicular to line between points t=\frac{1}{4} and t=2 that goes through origin. Ans: y=\frac{1}{2}x (3 marks)
    b) cart equation y=\frac{16}{x}

    c) Points of intersection (4\sqrt{2},2\sqrt{2}) and (-4\sqrt{2},-2\sqrt{2}) (3 marks)

    4) Complex Numbers, horra.
    i) w=\frac{p-4i}{2-3i}
    a) a+bi form : \frac{2p+12}{13}+\frac{3p+8}{13}  i (3 marks)
    arg(w) = \frac{\pi}{4}
    b) p=20 (2 marks)
    ii) z=(1-\lambda i)(4+3i) , \mid z \mid = 45

    \lambda = \pm 4\sqrt{5} (2 marks)

    5) i)
    A= \begin{bmatrix} p & 2 \\ 3 & p \end{bmatrix} , B= \begin{bmatrix} -5 & 4 \\ 6 & -5 \end{bmatrix}
    (a) Find AB (2)
    AB + 2A = kI
    find k and p
    (b) p=\frac{3}{2} , \frac{15}{2}

    ii) I forget what the question was but a=\frac{9}{2} (5 marks)

    6 (a) -2-3i (1)
    (x-4)(x+2-3i)(x+2+3i)
    (b) a=2 b=-11 (5 marks)
    7 (a) (4 marks)
    (b) (4 marks)
    (c)  \frac{15}{16}a^2 (2 marks)

    8) (a) (5 marks)
    (b) \frac{2}{9} (4 marks)

    9) two proofs questions, each worth 6 marks
    What were proof questions?
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    Shameless Plug: https://www.thestudentroom.co.uk/sho....php?t=4724166
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    (Original post by Elliott M)
    For the Area FXD question:
    tangent has equation yq= x+ aq^2
    at directrix, x= -a so yq = -a + aq^2 so y = (-a + aq^2)/q
    F(a,0) X(-0.25a,0) D(-a, (-a + aq^2)/q)
    Area of FXD = 1/2 x base x height = 0.5 x (a+0.25a) x modulus of ((aq^2 - a)/q)

    Lets suppose the y coordinate of D is -5, length is 5, so times y coordinate of D by -1 to give magnitude.

    Area = 0.5 x (1.25a) x ((a - aq^2)/q) = 0.625 x q^-1 x (a^2 - (a^2 x q^2))
    I got it all in terms of q, as q is a parameter and everything in the question is algebra
    Sorry to say but when x= -1/2a y=0 u can work out what q is which is 1/2
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    (Original post by Isaac_VB)
    I got fisted by the proof but the rest went well
    Exactly the same
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    (Original post by Elliott M)
    For the Area FXD question:
    tangent has equation yq= x+ aq^2
    at directrix, x= -a so yq = -a + aq^2 so y = (-a + aq^2)/q
    F(a,0) X(-0.25a,0) D(-a, (-a + aq^2)/q)
    Area of FXD = 1/2 x base x height = 0.5 x (a+0.25a) x modulus of ((aq^2 - a)/q)

    Lets suppose the y coordinate of D is -5, length is 5, so times y coordinate of D by -1 to give magnitude.

    Area = 0.5 x (1.25a) x ((a - aq^2)/q) = 0.625 x q^-1 x (a^2 - (a^2 x q^2))
    I got it all in terms of q, as q is a parameter and everything in the question is algebra
    I also got this
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    (Original post by Mathsislive)
    What were proof questions?
    one was 19 \mid 3^{3n-2}-2^{3n+1} for all n in natural set
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    (Original post by elliemath)
    How did everyone do the first proof by induction question? Was I wrong to prove true for n=k+1 and n=k+2?
    U have to prove true for n=k+2 by induction and assume true for n=k and n=k+1
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    (Original post by X_IDE_sidf)
    one was 19 \mid 3^{3n-2}-2^{3n+1} for all n in natural set
    I consider this half-answer neither sufficient nor helpful
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    Misread the equation for newton raphson to have be +4/x^2 rather than -. How many marks will I lose
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    (Original post by Faznaz55)
    U have to prove true for n=k+2 by induction and assume true for n=k and n=k+1
    I believe this is also acceptable as a proof.

    Attachment 648992
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    I got k as 3.4892635x10^-14 or something like that!?? help
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    (Original post by arniethepie)
    Also for the matrix question where it was AB +2A= kI, me and my friends got p=3/2, k=15/2
    Correct
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    Ffs, i thought the k series one was kr(2^(r-1)) not k(2^(r-1))
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    (Original post by Mathsislive)
    I consider this half-answer neither sufficient nor helpful
    Sorry, I'll use English,

    The question was to prove that 19 divides 3^{3n-2}-2^{3n+1} where n is a natural number (positive, non zero integer), which I'm sure you can easily do yourself.

    I cannot remember the other one, but it was a sequence of some sort.
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    (Original post by 04MR17)
    Question 5 Matrices
    i.) a.) ((12-5p) (4p-10))
    ..........((6p-15) (12-5p)) [2]
    b.) p=1.5, k=7.5 [4]
    ii.) a=4.5 [5]
    Can you remember what the actual question was, I've forgotten what part ii was?
 
 
 
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