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    What did everyone get in question 2 stating the root 3/2 and asking you to find other roots?


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    (Original post by Matt_dragon)
    What did everyone get in question 2 stating the root 3/2 and asking you to find other roots?
    Real Root:

    z = \frac{3}{2}

    Complex roots (conjugate pair):

    z = -3+j
    z = -3-j



    The method I used to get to this solution was to take out the real root first:

    2z^3 + 9z^2 + 2z - 30 = 0

    (2z-3)(z^2 + 6z + 10) = 0

    From there, use the quadratic formula or complete the square to solve:

    z^2 + 6z + 10 = 0

    (z + 3)^2 - 9 + 10 = 0

    (z + 3)^2 = -1

    z + 3 = \pm\sqrt{-1}

    z = - 3 \pm\sqrt{-1}

    z = - 3 \pm j
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    What did everyone get for question 3?
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    (Original post by jonny7bell)
    What did everyone get for question 3?
    For question 3 i), it's important to realise that NN-1 = I

    \begin{pmatrix}-9 & -2 & -4\\ 

3 & 2 & 2\\ 

5 & 1 & 2

\end{pmatrix}\begin{pmatrix}

1 & 0 & 2\\ 

2 & 1 & 3\\ 

-\frac{7}{2} & p & -6

\end{pmatrix} = \begin{pmatrix}1 & 0 & 0\\ 

0 & 1 & 0\\ 

0 & 0 & 1

\end{pmatrix}

    From this, you can choose any of the cell results involving p to find it.
    I chose the lower central column cell, but it's your choice, they all will work.
    So:

    (5\times 0)+(1\times 1)+(2\times p) = 0

    1 + 2p = 0

    2p = -1

    p = -\frac{1}{2}



    For part ii), all you have to do is multiply each side by N-1:

    N\begin{pmatrix}

x\\ 

y\\ 

z

\end{pmatrix}=\begin{pmatrix}

-39\\ 

5\\ 

22

\end{pmatrix}

    N^{-1}N\begin{pmatrix}

x\\ 

y\\ 

z

\end{pmatrix}=N^{-1}\begin{pmatrix}

-39\\ 

5\\ 

22

\end{pmatrix}

    N-1N = I , so these cancel out.
    And then multiply it all out:

    \begin{pmatrix}x\\ 

y\\ 

z

\end{pmatrix}=\begin{pmatrix}

1 & 0 & 2\\ 

2 & 1 & 3\\ 

-\frac{7}{2} & -\frac{1}{2} & -6

\end{pmatrix}\begin{pmatrix}

-39\\ 

5\\ 

22

\end{pmatrix}=\begin{pmatrix}

(1\times -39)+(0\times 5)+(2\times 22)\\ 

(2\times -39)+(1\times 5)+(3\times 22)\\ 

(-\frac{7}{2}\times -39)+(-\frac{1}{2}\times 5)+(-6\times 22)

\end{pmatrix}


    \begin{pmatrix}x\\ 

y\\ 

z

\end{pmatrix}=\begin{pmatrix}

5\\ 

-7\\ 

2

\end{pmatrix}

    So, x=5, y=-7 and z=2.
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    (Original post by Political Cake)
    For question 3 i), it's important to realise that NN-1 = I

    \begin{pmatrix}-9 & -2 & -4\\ 

3 & 2 & 2\\ 

5 & 1 & 2

\end{pmatrix}\begin{pmatrix}

1 & 0 & 2\\ 

2 & 1 & 3\\ 

-\frac{7}{2} & p & -6

\end{pmatrix} = \begin{pmatrix}1 & 0 & 0\\ 

0 & 1 & 0\\ 

0 & 0 & 1

\end{pmatrix}

    From this, you can choose any of the cell results involving p to find it.
    I chose the lower central column cell, but it's your choice, they all will work.
    So:

    (5\times 0)+(1\times 1)+(2\times p) = 0

    1 + 2p = 0

    2p = -1

    p = -\frac{1}{2}



    For part ii), all you have to do is multiply each side by N-1:

    N\begin{pmatrix}

x\\ 

y\\ 

z

\end{pmatrix}=\begin{pmatrix}

-39\\ 

5\\ 

22

\end{pmatrix}

    N^{-1}N\begin{pmatrix}

x\\ 

y\\ 

z

\end{pmatrix}=N^{-1}\begin{pmatrix}

-39\\ 

5\\ 

22

\end{pmatrix}

    N-1N = I , so these cancel out.
    And then multiply it all out:

    \begin{pmatrix}x\\ 

y\\ 

z

\end{pmatrix}=\begin{pmatrix}

1 & 0 & 2\\ 

2 & 1 & 3\\ 

-\frac{7}{2} & -\frac{1}{2} & -6

\end{pmatrix}\begin{pmatrix}

-39\\ 

5\\ 

22

\end{pmatrix}=\begin{pmatrix}

(1\times -39)+(0\times 5)+(2\times 22)\\ 

(2\times -39)+(1\times 5)+(3\times 22)\\ 

(-\frac{7}{2}\times -39)+(-\frac{1}{2}\times 5)+(-6\times 22)

\end{pmatrix}


    \begin{pmatrix}x\\ 

y\\ 

z

\end{pmatrix}=\begin{pmatrix}

5\\ 

-7\\ 

2

\end{pmatrix}

    So, x=5, y=-7 and z=2.
    Great, that's what I got. Looks like I have only lost 2 marks so far
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    I did Q3 perfectly, then got z=122 XD Not a clue how, but I checked it about 4 times thinking 'this can't possibly be right'. Also, for Q9 I had no idea how to do the questions, but the answers were really obvious so I just wrote them down. Of course, the mark scheme is going to say 'A1 dep on M1' and I'm going to have lost at least 8 marks just on that
    Didn't have time to finish the very last part either because I spent so long figuring out how to simplify the induction question
    Oh well, might still get an A/B, tho I was hoping for 90%+ to make up for the lovely M2 I have to sit on the 10th. Tho I absolutely refuse to resit.
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    (Original post by CookieInOrange)
    I did Q3 perfectly, then got z=122 XD Not a clue how, but I checked it about 4 times thinking 'this can't possibly be right'. Also, for Q9 I had no idea how to do the questions, but the answers were really obvious so I just wrote them down. Of course, the mark scheme is going to say 'A1 dep on M1' and I'm going to have lost at least 8 marks just on that
    Didn't have time to finish the very last part either because I spent so long figuring out how to simplify the induction question
    Oh well, might still get an A/B, tho I was hoping for 90%+ to make up for the lovely M2 I have to sit on the 10th. Tho I absolutely refuse to resit.
    I really think that this paper was really unfair in terms of the way questions were asked. The first graph question was ridiculous, the induction question was the first one in any of the past papers which when simplified becomes a cubic and so leaves you to wonder whether you are allowed to just factorise with no working out.

    The argand diagram question was easy but I spend 20 minutes for a 4 mark question because the numbers were so awkward.
    All in all the paper wasn't a bad paper, but the confusion from the unusual question types made me run out of time and I'm scared I might have made a stupid mistakes and lose marks in question 1, question 7 and obviously the induction question depends on whether the right answer was to go from a cubic to factorised form.

    In question 1, I rushed it as I was planning to go back and check it but because I kept trying to "fix" the induction question, I completely forgot about it. I'm not sure I done it wrong, but when I solved it at home afterwards, I couldn't remember whether I got the same answers as in the exam.

    I'm hoping the grade boundaries will be low but from the general feedback seen here and in my school, it seems that the paper was not found that difficult. Hopefully it's a small sample though :P
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    (Original post by CookieInOrange)
    I did Q3 perfectly, then got z=122 XD Not a clue how, but I checked it about 4 times thinking 'this can't possibly be right'. Also, for Q9 I had no idea how to do the questions, but the answers were really obvious so I just wrote them down. Of course, the mark scheme is going to say 'A1 dep on M1' and I'm going to have lost at least 8 marks just on that
    Didn't have time to finish the very last part either because I spent so long figuring out how to simplify the induction question
    Oh well, might still get an A/B, tho I was hoping for 90%+ to make up for the lovely M2 I have to sit on the 10th. Tho I absolutely refuse to resit.
    Same ffs. I got z=266 or something I knew I was wrong but I didn't know what else to put. Turns out I missed one of the minus signs. Ah well.
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    Focus on C2 lads
 
 
 
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