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    Hi,
    I am preparing for my exam next week. Unfortunately, I cannot get to the answers for question 11ii/iii/iv on the 2015 June paper. I have put the MS answers below:
    (ii) -2x^2+10x-8 (2 marks)
    (iii) 2.5 (4 marks)
    (iv) 9 (4 marks)

    Here is the question:

    11
    Two curves, S1 and S2 have equations y = x^2 - 4x + 7 and y = 6x - x^2 -1 respectively. The curves meet at A and at B.

    GRAPH

    Points P and Q lie on S2 and S1 between A and B. P and Q have the same x coordinate so that PQ is parallel to the y-axis.

    (ii) Find an expression, in its simplest form, for the length PQ as a function of x. [2]
    (iii) Use calculus to find the greatest length of PQ. [4]
    (iv) Find the area between the two curves. [4]

    Does anyone have any clues???
    Thanks
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    (Original post by EBworkin)
    Hi,
    I am preparing for my exam next week. Unfortunately, I cannot get to the answers for question 11ii/iii/iv on the 2015 June paper. I have put the MS answers below:
    (ii) -2x^2+10x-8 (2 marks)
    (iii) 2.5 (4 marks)
    (iv) 9 (4 marks)

    Here is the question:

    11
    Two curves, S1 and S2 have equations y = x^2 - 4x + 7 and y = 6x - x^2 -1 respectively. The curves meet at A and at B.

    GRAPH

    Points P and Q lie on S2 and S1 between A and B. P and Q have the same x coordinate so that PQ is parallel to the y-axis.

    (ii) Find an expression, in its simplest form, for the length PQ as a function of x. [2]
    (iii) Use calculus to find the greatest length of PQ. [4]
    (iv) Find the area between the two curves. [4]

    Does anyone have any clues???
    Thanks
    What have you tried for both questions?
    • Thread Starter
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    maybe for iii maximum and minimum??? I'm clueless I'll come back to you If I get any answers
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    I know this exam is already over (did it earlier today), but just for my personal peace of mind -

    I don't know ii, but for iii you find the maximum/minimum points of the two curves, then find the distance between these two points. You do this by differentiating the two curves to find their gradient functions, making this equal to 0 and solving the equation to give an x value for each curve. Then substitute this back into the original equation to give the y value of the coordinate. iv is asking you to integrate between A and B, subtracting the smaller from the larger value to find the area encompassed by the two curves.
 
 
 
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