 # Edexcel GCE Core Mathematics C3 Advanced January 2010

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C3 Edexcel Core Mathematics January 2010 Question 1

Algebraic Fractions

1. Express
(x + 1)/(3x2 - 3) - 1/(3x + 1)
as a single fraction in its simplest form. C3 Edexcel Core Mathematics January 2010 Question 2

Numerical solutions and iterative methods

2. Given f(x) = x3 + 2x2 - 3x - 11
(a) Show that f(x) = 0 can be rearranged as
2. The equation f(x) = 0 has one positive root α.
The iterative formula is used to find an approximation to α.
(b) Taking x1 = 0, find, to 3 decimal places, the values of x2 , x3 and x4.
2 (c) Show that α = 2.057 correct to 3 decimal places.

C3 Edexcel Core Mathematics January 2010 Question 3

3. (a) Express 5 cos x – 3 sin x in the form R cos(x + α), where R > 0 and 0 < α < 1/2 π.
3 (b) Hence, or otherwise, solve the equation
5 cos x – 3 sin x = 4
for 0 ≤ x < 2π, giving your answers to 2 decimal places.

C3 Edexcel Core Mathematics January 2010 Question 4

4. (i) Given that y = ln(x2 + 1)/x find dy/dx.
4 (ii) Given that x = tan y, show that dy/dx = 1/(1 + x2)

C3 Edexcel Core Mathematics January 2010 Question 5

5. Sketch the graph of y = ln|x|, stating the coordinates of any points of intersection with the axes.

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