Edexcel Core Mathematics C1 June 2010

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Question Paper (pdf)

Core 1 Mathematics Edexcel June 2010 Question 6

1. Figure 1 shows a sketch of the curve with equation y = f (x). The curve has a maximum point A at (–2, 3) and a minimum point B at (3, – 5).
   On separate diagrams sketch the curve with equation
   (a) y = f (x + 3)
   (b) y = 2 f(x)
   On each diagram show clearly the coordinates of the maximum and minimum points.
   The graph of y = f (x) + a has a minimum at (3, 0), where a is a constant.
   (c) Write down the value of a.

Core 1 Mathematics Edexcel June 2010 Question 7
7. Given that y = 8x³ - 4√x + (3x² + 2)/x, x > 0, find dy/dx.

Core 1 Mathematics Edexcel June 2010 Question 8

8. (a) Find an equation of the line joining A (7, 4) and B (2, 0), giving your answer in the form ax+by+c=0, where a, b and c are integers.
   (b) Find the length of AB, leaving your answer in surd form.
   The point C has coordinates (2, t), where t > 0, and AC = AB.
   (c) Find the value of t.
   (d) Find the area of triangle ABC.

Core 1 Mathematics Edexcel June 2010 Question 9

9. A farmer has a pay scheme to keep fruit pickers working throughout the 30 day season. He pays £a for their first day, £(a + d ) for their second day, £(a + 2d ) for their third day, and so on, thus increasing the daily payment by £d for each extra day they work.
   A picker who works for all 30 days will earn £40.75 on the final day.
   (a) Use this information to form an equation in a and d.
   
   A picker who works for all 30 days will earn a total of £1005
   (b) Show that 15(a + 40.75) = 1005
   
   (c) Hence find the value of a and the value of d.

Core 1 Mathematics Edexcel June 2010 Question 10

10. (a) On the axes below sketch the graphs of
    (i) y = x (4 – x)
    (ii) y = x²(7 – x)
    showing clearly the coordinates of the points where the curves cross the coordinate axes.
    (b) Show that the x-coordinates of the points of intersection of
    y = x (4 – x) and y = x²(7 – x)
    are given by the solutions to the equation x(x ² – 8x+ 4) = 0
    The point A lies on both of the curves and the x and y coordinates of A are both positive.
    (c) Find the exact coordinates of A, leaving your answer in the form (p + q√3, r + s√3), where p, q, r and s are integers.

Core 1 Mathematics Edexcel June 2010 Question 11

11. The curve C has equation y = f(x), x > 0, where dy/dx = 3x - 5/√x - 2
    Given that the point P (4, 5) lies on C, find
    (a) f(x),
    (b) an equation of the tangent to C at the point P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

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