Edexcel Core Mathematics C3 January 2011 (II)
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.
C3 Mathematics Edexcel January 2011 Question 7
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.
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.
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