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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced January 2010.

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

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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

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

Given that y = e

(b) find dy/dx

The curve with equation y = e

(c) Find the values of the constants a and b, giving your answers to 3 significant figures.

7 (b) 7 (c)

8. Solve

cosec

for 0° ≤ x ≤ 180°. C3 Edexcel Core Mathematics January 2010 Question 9

9. (i) Find the exact solutions to the equations

(a) ln (3x – 7) = 5

(b) 3

(ii) The functions f and g are defined by

f (x) = e

g(x) = ln (x – 1), x ∈ ℜ, x > 1

(a) Find f

(b) Find fg and state its range. 9 (i)(b) 9 (ii)(a) 9 (ii)(b)

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