Edexcel GCE Core Mathematics C3 Advanced January 2010


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Questions for the Edexcel GCE Core Mathematics C3 Advanced January 2010 {PDF}.

C3 Edexcel Core Mathematics January 2010 Question 6

  1. Figure 1 shows a sketch of the graph of y = f (x).
    The graph intersects the y-axis at the point (0, 1) and the point A(2, 3) is the maximum turning point.

    Sketch, on separate axes, the graphs of
    (i) y = f(–x) + 1,
    (ii) y = f(x + 2) + 3,
    (iii) y = 2f(2x).

    On each sketch, show the coordinates of the point at which your graph intersects the y-axis and the coordinates of the point to which A is transformed.

C3 Edexcel Core Mathematics January 2010 Question 7

  1. (a) By writing sec x as 1/cos x, show that d(sec x)/dx =sec x tan x

    Given that y = e2x sec 3x,
    (b) find dy/dx

    The curve with equation y = e2x sec 3x, -π/6 < x < π/6, has a minimum turning point at (a, b).
    (c) Find the values of the constants a and b, giving your answers to 3 significant figures.
  1. (b)
  1. (c)



C3 Edexcel Core Mathematics January 2010 Question 8

  1. Solve
    cosec2 2x – cot 2x = 1
    for 0° ≤ x ≤ 180°.

C3 Edexcel Core Mathematics January 2010 Question 9

  1. (i) Find the exact solutions to the equations
    (a) ln (3x – 7) = 5

    (b) 3x e7x + 2 = 15

    (ii) The functions f and g are defined by
    f (x) = e2x + 3, x ∈ ℜ
    g(x) = ln (x – 1), x ∈ ℜ, x > 1
    (a) Find f –1 and state its domain.
    (b) Find fg and state its range.
  1. (i)(b)
  1. (ii)(a)
  1. (ii)(b)


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