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

6. 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.

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C3 Edexcel Core Mathematics January 2010 Question 7

7. (a) By writing sec x as 1/cos x, show that d(sec x)/dx =sec x tan x
   
   Given that y = e^2x sec 3x,
   (b) find dy/dx
   
   The curve with equation y = e^2x 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.

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7. (b)

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7. (c)

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C3 Edexcel Core Mathematics January 2010 Question 8

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

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C3 Edexcel Core Mathematics January 2010 Question 9

9. (i) Find the exact solutions to the equations
   (a) ln (3x – 7) = 5
   
   (b) 3^x e^{7x + 2} = 15
   
   (ii) The functions f and g are defined by
   f (x) = e^2x + 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.

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9. (i)(b)

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9. (ii)(a)

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9. (ii)(b)

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