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    (Original post by erawein)
    Ffs, i thought the k series one was kr(2^(r-1)) not k(2^(r-1))
    How did you solve this one, tbh I just added it 12 times
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    (Original post by Charles Omer)
    Hopefully this helps.

    Attachment 648982
    Oh... We weren't taught that you could do multiple f(k) :/
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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 correct too.
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    Can anyone remember the actual question, 5, part ii?
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    (Original post by Charles Omer)
    I believe this is correct too.
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    Yes it is
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    (Original post by __Will__)
    Oh... We weren't taught that you could do multiple f(k) :/
    I think there are different ways to do it, it would have been better if you were taught all the methods... I'm sorry to hear that.
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    (Original post by glad-he-ate-her)
    Am i the only one who forgot the sum for 2 to the power of r-1 from c2 so manually wrote out all 12 terms :clap2:such mathematical elegance
    Fully did the same thing then reverse engineered the 4095 into the sum of a geometric sequence formula to get the marks 😅😂
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    What do you think grade boundaries for 90% will be?
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    (Original post by X_IDE_sidf)
    How did you solve this one, tbh I just added it 12 times
    have to use geometric series formula from c2.
    Also in the determinant question there is another solution, a = -27/2 as well as -9/2 as both of these satisfy mod(detM) = 18. Great job for putting up this mark scheme with the latex and stuff
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    (Original post by k.russell)
    You have to test n=1 and n=2, assume it's true for n = k and n = k + 1 then test if it's true for n = k + 2
    Use the assumption of k with k-1 to get answer and factorise it into 3^k+1((k+1)+1)
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    (Original post by ~K1)
    Use the assumption of k with k-1 to get answer and factorise it into 3^k+1((k+1)+1)
    it's the same damn thing b xxx
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    Must a Cartesian equation be written with y as the subject, as I had written xy=16 and not y=16/x.
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    (Original post by k.russell)
    have to use geometric series formula from c2.
    Also in the determinant question there is another solution, a = -27/2 as well as -9/2 as both of these satisfy mod(detM) = 18. Great job for putting up this mark scheme with the latex and stuff
    ffs, that was a sneaky one. I always seem to forget to consider the negative case.
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    (Original post by X_IDE_sidf)
    ffs, that was a sneaky one. I always seem to forget to consider the negative case.
    yeah I have made that mistake before. luckily I noticed that it was asking for values of a and a wasn't squared so sort of guessed it must be the negative one
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    (Original post by X_IDE_sidf)
    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.
    Shame you couldn't have typeset it properly so that text was a consistent size.
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    (Original post by TBoy11)
    Must a Cartesian equation be written with y as the subject, as I had written xy=16 and not y=16/x.
    Both are correct, btw c=4 and use formula book to get ans directly lol
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    (Original post by TBoy11)
    Must a Cartesian equation be written with y as the subject, as I had written xy=16 and not y=16/x.
    this is fine
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    (Original post by TBoy11)
    Must a Cartesian equation be written with y as the subject, as I had written xy=16 and not y=16/x.
    Either way is fine but xy=16 is probably better.
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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} , k = \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) Proof involving sums:
    (a) (5 marks)
    (b) \frac{2}{9} and \frac{-27}{2} (4 marks)

    9) two proofs questions, each worth 6 marks


    Thanks To:
    - @k.russell for 8 b second answer
    the second answer should be going in 5ii) btw
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    (Original post by Mathsislive)
    Shame you couldn't have typeset it properly so that text was a consistent size.
    If you care so much, feel free to typeset it properly. I'd recommend doing it in latex with the exam document class. Post the PDF after, would be pretty.
 
 
 
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