Edexcel GCE Core Mathematics C3 January 2012
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C3 Edexcel Core Mathematics January 2012 Question 6
6. f(x) = x2 - 3x + 2cos(½ x) , 0 ≤ x ≤ π
(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
xn+1 = [3 + sin(½ xn)]/2 , x0 = 2
find the values of x1, x2 and x3 , 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.
C3 Edexcel Core Mathematics January 2012 Question 7
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
C3 Edexcel Core Mathematics January 2012 Question 8
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. Identities8 (c) Trig. equations
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