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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 (Part 2).

**Related Pages**

Edexcel GCE Core Mathematics C3 Advanced June 2011

More Lessons for A Level Maths

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

C3 Edexcel Core Mathematics January 2010 Question 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.

C3 Edexcel Core Mathematics January 2010 Question 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.

- (b)

- (c)

C3 Edexcel Core Mathematics January 2010 Question 8

- Solve

cosec^{2}2x – cot 2x = 1

for 0° ≤ x ≤ 180°.

C3 Edexcel Core Mathematics January 2010 Question 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.

- (i)(b)

- (ii)(a)

- (ii)(b)

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