Edexcel Core Mathematics C3 June 2009
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Questions and Video Solutions for C3 Edexcel Core Mathematics June 2009
Edexcel Core Mathematics C3 June 2009 Past Paper
C3 Mathematics Edexcel June 2009 Question 5
Figure 2 shows a sketch of part of the curve with equation y = f(x), x ∈ ℝ.The curve meets the coordinate axes at the points A(0,1–k) and B(½ln k, 0)
where k is a constant and k > 1, as shown in Figure 2.
On separate diagrams, sketch the curve with equation
(a) y = |f(x)|
(b) y = f-1(x)
Show on each sketch the coordinates, in terms of k, of each point at which the curve meets or cuts the axes.
Given that f(x) = e2x - k
(c) state the range of f,
(d) find f-1(x)
(e) write down the domain of f-1.
C3 Mathematics Edexcel June 2009 Question 6
6. (a) Use the identity cos(A + B) = cos A cos B - sin A sin B to show that
cos 2A = 1 - 2 sin2 A
The curves C1 and C2 have equations
C1: y = 3 sin 2x
C2: y = 4 sin2 x - 2 cos 2x
(b) Show that the x-coordinates of the points where C1 and C2
intersect satisfy the equation
4 cos 2x + 3 sin 2x = 2
(c) Express 4cos 2x + 3 sin 2x in the form R cos (2x – α), where R > 0 and 0 < α < 90°,
giving the value of α to 2 decimal places.
(d) Hence find, for 0 ≤ x ≤ 180°, all the solutions of
4 cos 2x + 3 sin 2x = 2
giving your answers to 1 decimal place.
C3 Mathematics Edexcel June 2009 Question 7
7. The function f is defined by Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
f(x) = 1 - 2/(x + 4) + (x - 8)/(x - 2)(x + 4), x ∈ ℝ , x ≠ -4, x ≠ 2
(a) Show that f(x) = (x - 3)/(x - 2)
The function g is defined by
g(x) = (ex - 3)(ex - 2)
(b) Differentiate g(x) to show that g'(x) = ex/(ex - 2)
(c) Find the exact values of x for which g'(x) = 1
8. (a) Write down sin 2x in terms of sin x and cos x
(b) Find, for 0 < x < π, all the solutions of the equation
cosec x - 8cos x = 0
giving your answers to 2 decimal places.
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