Questions and Worked Video Solutions for C3 Edexcel Core Mathematics January 2011.

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Edexcel Core Mathematics C3 January 2011 Past Paper

C3 Mathematics Edexcel January 2011 Question 6

6. The function f is defined by

f: x ↦ (3 - 2x)/(x - 5), x ∈ ℝ, x ≠ 5

(a) Find f^{-1}(x)

The function g has domain –1 ≤ x ≤ 8, and is linear from (–1, –9) to (2, 0) and from

(2, 0) to (8, 4). Figure 2 shows a sketch of the graph of y = g(x).

(b) Write down the range of g.

(c) Find gg(2).

(d) Find fg(8).

(e) On separate diagrams, sketch the graph with equation

(i) y = |g(x)| ,

(ii) y = g^{-1}(x)

Show on each sketch the coordinates of each point at which the graph meets or cuts the axes.

(f) State the domain of the inverse function g^{-1}.

6 (a)

7. The curve C has equation

y = (3 + sin 2x)/(2 + cos 2x)

(a) Show that

dy/dx = (6 sin 2x + 4 sin 2x + 2)/(2 + cos 2x)^{2}

(b) Find an equation of the tangent to C at the point on C where x = π/2

Write your answer in the form y = ax + b, where a and b are exact constants.

7(a)C3 Mathematics Edexcel January 2011 Question 8

8. (a) Given that

d(cos x)/dx = -sin x

show that ( ) d d(sec x)/dx = sec x tan x

Given that x = sec 2y

(b) find dy/dx in terms of y.

(c) Hence find dy/dx in terms of x.

8 (a)
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