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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced January 2012. Try out the Past paper for Edexcel C3 January 2012 and check out the video solutions if you need any help.

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C3 Edexcel Core Mathematics January 2012 Question 6

6. f(x) = x

(a) Show that the equation f (x) = 0 has a solution in the interval 0.8 <x< 0.9

The curve with equation y = f (x) has a minimum point P.

(b) Show that the x-coordinate of P is the solution of the equation

x = [3 + sin(½ x)]/2

(c) Using the iteration formula

x_{n+1} = [3 + sin(½ x_{n})]/2 , x_{0} = 2

find the values of x_{1}, x_{2} and x_{3} , giving your answers to 3 decimal places.

(d) By choosing a suitable interval, show that the x-coordinate of P is 1.9078 correct to 4 decimal places.

6 (a) Roots - Change of sign method.

7. The function f is defined by

(a) Show that f(x) = 1/(2x - 1)

(b) Find f^{-1}(x)

(c) Find the domain of f^{−1}

g(x) = ln(x + 1)

(d) Find the solution of fg(x) = 1/7, giving your answer in terms of e.

7 (a) Simplifying algebraic fractions.7 (c) domain

8. (a) Starting from the formulae for sin ( A + B ) and cos ( A + B ), prove that

tan (A + B) = (tan A + tan B)/(1 - tanA tanB)

(b) Deduce that

(c) Hence, or otherwise, solve, for 0 ≤ θ ≤ π ,

1 + √3 tanθ = (√3 - tanθ)tan(π - θ)

Give your answers as multiples of π

8 (a) Trig. Identities
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