9709/MayJune/2006/3/Q9

(i) Express 10/(2-x)(1+x^2) in partial fractions. [5]

(ii) Hence, given that |x| < 1, obtain the expansion of 10/(2-x)(1+x^2) in ascending powers of x, up to and including the term in x^3, simplifying the coefficients. [5]

Solution:

Reference: PYQ - May/June 2006 Paper 3 Q9

9709/MayJune/1/2007/Q8

The function f is defined by f(x) = a + b cos 2x, for 0 ≤ x ≤ π. It is given that f(0) = −1 and f(1/2π) = 7.

i) Find the values of a and b.

ii) Find the x-coordinates of the points where the curve y = f(x) intersects the x-axis.

iii) Sketch the graph of y = f(x).

Solution:

i)

ii)

iii)

Reference: PYQ - May/June 2007 Paper 1 Q8