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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. The questions are given here.

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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.

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.

8. Solve

cosec

for 0° ≤ x ≤ 180°.

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)

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