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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) = e^{2x} - 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

### C3 Mathematics Edexcel June 2009 Question 7

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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More videos, activities and worksheets that are suitable for A Level Maths

Edexcel Core Mathematics C3 June 2009 Past Paper

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

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) = e

(c) state the range of f,

(d) find f

(e) write down the domain of f

6. (a) Use the identity cos(A + B) = cos A cos B - sin A sin B to show that

cos 2A = 1 - 2 sin^{2} A

The curves C1 and C_{2} have equations

C_{1}: y = 3 sin 2x

C_{2}: y = 4 sin^{2} x - 2 cos 2x

(b) Show that the x-coordinates of the points where C_{1} and C_{2}
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.

7. The function f is defined by

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) = (e^{x} - 3)(e^{x} - 2)

(b) Differentiate g(x) to show that g'(x) = e^{x}/(e^{x} - 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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