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AQA A2 Mathematics MPC4 Core 4 - 9th June 2015 [Discussion & unofficial markscheme] Watch

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    How many marks would I get for 8A if i just left my answer in re-arranged form with X, but forgot to calculate the C (because didn't read question properly) ?
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    Going of this mark scheme, I believe I only made 1 mistake (the angle of the vectors question). I obviously miscopied a number somewhere. So, I believe I will have got 72/73, which should still be 100 UMS.
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    (Original post by student0042)
    Going of this mark scheme, I believe I only made 1 mistake (the angle of the vectors question). I obviously miscopied a number somewhere. So, I believe I will have got 72/73, which should still be 100 UMS.
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    (Original post by Haiych)
    Does anyone think average of 53 on both papers is enough for 140 ums?
    yes it will be, I think
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    (Original post by bthmandem)
    Not really. I just spend my time revising mathematics than posting useless content, which doesn't aid the discussion.
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    (Original post by IAmYourdog)
    How many marks would I get for 8A if i just left my answer in re-arranged form with X, but forgot to calculate the C (because didn't read question properly) ?
    I did the same thing?! It was very sneaky not stating that x=0 and t=0 ..
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    (Original post by CD223)
    Do people think 73/75 on Core 3 and 64 or 65/75 on Core 4 will be enough for 180 on the two?


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    definitely
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    (Original post by CD223)
    *** OFFICIAL AQA CORE 4 MPC4 JUNE 2015 EXAM DISCUSSION THREAD ***
    UNOFFICIAL MARK SCHEME
    1.A) Express f(x)= \dfrac{19x-2}{(5-x)(1+6x)} in the form f(x) = \dfrac{A}{(5-x)} + \dfrac{B}{(1+6x)}

    \Rightarrow A=3, B=-1 (3 marks)

    B) Find \displaystyle\int_0^4 f(x)\ dx in the form p \ln (5).

    = \dfrac{8}{3}\ln (5) (6 marks)

    2.
    A) Express 2\cos x – 5 \sin x in the form R \cos (x+\alpha), R>0, 0<\alpha<\frac{\pi}{2}.

    \Rightarrow\sqrt{29} \cos (x+1.19) (3 Marks)

    B) Find value ofx in interval 0<x<2 \pi where 2 \cos x – 5 \sinx is at a maximum.

    (i) x=5.09(2 Marks)

    (ii) Solve equation 2 \cos x – 5 \sin x + 1 = 0

    x=0.567,3.34 (3 Marks)

    3.
    A) g(x) =8x^3 - 12x^2 - 2x + d. Given when g(x)is divided by (2x+1) the remainder is -2, find d.

    \Rightarrow d=1 (2 Marks)

    B) Given x= - \frac{1}{2} is a solution of g(x)=0, express g(x) as 3 linear factors.

    \Rightarrow g(x) = (2x+1)(2x-1)(2x-3) (3 marks)

    C) h(x)is given by \dfrac{4x^2 – 1}{f(x)} where x>2. Simplify h(x),showing it is a decreasing function.

    h(x) = \dfrac{1}{(2x-3)},

    EITHER

    h'(x) =-2 (2x-3)^{-2}. \rightarrow h’(x) is always negative, therefore it is a decreasing function.

    OR

    Could plot graph of h(x) = \dfrac{1}{2x-3} showing h(x) \rightarrow 0 when x \rightarrow \infty (4 Marks)

    4.
    A) Find the binomial expansion of (1+5x)^{\frac{1}{5}}:

    = 1 + x -2x^2 (2 Marks)

    B)
    (i) Find the binomial expansion of (8 + 3x)^{\frac{-2}{3}}:

    =\dfrac{1}{4} - \dfrac{1}{16} x + \dfrac{5}{256} x^2 (3 Marks)

    (ii) Find an estimate for \sqrt[3]{\dfrac{1}{81}}.

    = 0.2313 (2 Marks)

    5. x = \cos(2t), y = \sin (t).

    A) Find the gradient at t = \dfrac{\pi}{6}.

    \dfrac{dy}{dx}= \dfrac{-1}{2} (3 Marks)

    B) Find the equation of the normal at t=\dfrac{\pi}{6} in the form y = mx + c:

    y=2x - \frac{1}{2} (2 Marks)

    C) Normal cuts curve at Q(\cos (2q), \sin (q)). Set up a quadratic in terms of \sin(q) to find where the normal cuts the curve again. Then find the xco-ordinate of Q.

    \cos (2q)= \dfrac{-1}{8} (5 Marks)

    6. A =(3,2,10), B = (5,-2, 4)
    Line lpasses through A and has the equation r = \begin{bmatrix} 3 \\ 2 \\ 10 \end{bmatrix} + \lambda \begin{bmatrix} 3 \\ 1 \\ -2 \end{bmatrix}.

    A) Find the acute angle between line l and \vec{AB}.

    \theta= 60^{o} (4 Marks)

    B) C = (15,6, 2) (4 Marks)

    C) E = (11,0, 0) and (23, 4, -8) (4 Marks)

    7. y^3 +2e^{-3x}y - x = k.

    A) Find kgiven point P \left(\ln (2), \frac{1}{2}\right) lies on the curve.

    k=\dfrac{1}{4}- \ln(2) (1 Mark)

    B) Find the gradient at the point P:

    \dfrac{dy}{dx}= \dfrac{11}{8} (6 Marks)

    8. \dfrac{dx}{dt}= \dfrac{\sqrt{4+5x}}{5 (1+t)^{2}}.

    A) Given t=0when x=0 find x in terms of t.

    x = \dfrac{1}{5}[(\frac{-1}{2} (1+t)^{-1} + \frac{5}{2})^{2} - 4] (7 marks)

    B) Another pond models a circle of radius r. The rate of change of radius ris inversely proportional to pond surface area. Write a differential equationto model this situation.

    (i) \dfrac{dr}{dt}= \dfrac{k}{\pi r^2} (3 Marks)

    (ii) The rate of change of radius r is 4.5 when the radius is 1 metre. Find the radius when the rate is 0.5.

    r=3\ \text{metres} (2 Marks)
    ______________________________

    Date: 9th June 2015
    Time: 09:00am
    Duration: 1h 30m
    ______________________________
    CORE 3 EXAM DISCUSSION THREAD:
    http://www.thestudentroom.co.uk/showthread.php?t=3041463

    MECHANICS 2 EXAM DISCUSSION THREAD:
    http://www.thestudentroom.co.uk/showthread.php?t=3047357

    ______________________________

    RESOURCES:
    Question 8bi - there should be no π in the answer. The question asked for a differential in terms of r, t and a constant of proportionality (e.g. k). While dr/dt = k/πr^2 is technically a correct answer, it is not the simplest form - 1/π is also a constant, and can therefore be included in the constant of proportionality. So the answer should be dr/dt = k/r^2.
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    (Original post by fotevaf)
    definitely
    I'm so worried. I think I lost 10+ marks on that paper due to stupid mistakes


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    (Original post by TimGB)
    Question 8bi - there should be no π in the answer. The question asked for a differential in terms of r, t and a constant of proportionality (e.g. k). While dr/dt = k/πr^2 is technically a correct answer, it is not the simplest form - 1/π is also a constant, and can therefore be included in the constant of proportionality. So the answer should be dr/dt = k/r^2.
    How many do you think you would get if you left the pi in?
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    (Original post by CD223)
    I'm so worried. I think I lost 10+ marks on that paper due to stupid mistakes


    Posted from TSR Mobile


    well if you are correct in your raw marks for C3
    that means you've gotten 100% for that

    so, as long as you get an A (80%)
    you will get an a*

    I reckon an A would be lower than losing 10 marks as it's C4 so.. usually grade boundaries are lower
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    (Original post by student0042)
    How many do you think you would get if you left the pi in?
    I reckon they will only dock 1 mark at most for that. They'll probably just ignore it though, as k/π is still of constant value.
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    Hi, I have created worked solutions of the full paper, I hope they are useful to anyone unsure. The only question I have a different answer to is the second set of coordinates for E in Question 6 part (c) I have (-1,-4,8) rather than (23, 4, 8) as on the Unofficial Mark Scheme.

    Could someone please explain.
    Thanks.

    https://dl.dropboxusercontent.com/u/...204%202015.pdf
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    (Original post by TimGB)
    I reckon they will only dock 1 mark at most for that. They'll probably just ignore it though, as k/π is still of constant value.
    leo ukip got more vote than the libgays
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    Got 65 on Core 3 and 62 on Core 4. Entered these on the AQA UMS converter and for every single year of June Exams (except '10), this has given me an A*!! Thought I'd missed it, but this leaves me feeling better now.

    Also CD223, dude, you've OBVIOUSLY gotten an A*. Look at your results compared to mine, they are way better, and I still could get an A*.

    Anyone think this years boundaries will be particularly higher, and I won't get my A*?
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    how many marks for 8A if you forgot to calculate C but did rest right
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    Think I got about 68 in this paper. Shame I got like 58 in C3 😞. Not getting that A* now
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    what overall grade would it be if I get 57/60 for c3, 48/60 for c4 (made loads of silly mistakes), and 61/75 for s1, considering that I got 240/300 last year?
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    guys, on 7B which is a 6 marker, i forgot to differentiate y in the chain rule, i mean i did right but forgot to write down the y so i got 7/4, how many mark will they take out?
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    (Original post by hamza3256)
    what overall grade would it be if I get 57/60 for c3, 48/60 for c4 (made loads of silly mistakes), and 61/75 for s1, considering that I got 240/300 last year?
    I would say at least a B around 450 ums
 
 
 
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