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

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Edexcel Core Mathematics C3 June 2011 Past Paper

C3 Mathematics Edexcel June 2011 Question 6

6. (a) Prove that

1/sin 2θ - cos 2θ/sin 2θ = tan θ, θ ≠ 90n°, n ∈ ℤ

(b) Hence, or otherwise,

(i) show that tan 15° = 2 – √3,

(ii) solve, for 0 < x < 360°,

cosec 4x - cot 4x = 1

7. f(x) = (4x - 5)/[(2x + 1)(x - 3)] - 2x/(x

(a) Show that

f(x) = 5/[2x + 1)(x - 3)]

The curve C has equation y= f (x). The point P(-1, 5/2) lies on C.

(b) Find an equation of the normal to C at P.

8. (a) Express 2cos 3x – 3sin 3x in the form R cos (3x + α), where R and α are constants, R > 0, 0 <& alpha; < π/2. Give your answers to 3 significant figures.

f(x) = e^{2x} cos3x

(b) Show that f ′(x) can be written in the form

f'(x) = Re^{2x} cos(3x + α)

where R and α are the constants found in part (a).

(c) Hence, or otherwise, find the smallest positive value of x for which the curve with equation y = f (x) has a turning point.

8 (b)

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