Edexcel Core Mathematics C3 June 2011

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

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6 (b)(i)

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6 (b)(ii)

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C3 Mathematics Edexcel June 2011 Question 7
7. f(x) = (4x - 5)/[(2x + 1)(x - 3)] - 2x/(x² - 9), x ≠ ±3, x ≠ -1/2
(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.

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7(b)

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C3 Mathematics Edexcel June 2011 Question 8
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.

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8 (b)

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8 (c)

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