May June 12 Paper 32

WORKED SOLUTION

May June 15 Paper 32

WORKED SOLUTION

3) A curve has equation y = cos x cos 2x. Find the x-coordinate of the stationary point on the curve in the interval 0 < x < (pi/2), giving your answer correct to 3 significant figures.

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MAY JUNE 2015 PAPER 31

WORKED SOLUTION

4) The equation of a curve is y = 3 cos 2x + 7 sin x + 2. Find the x-coordinates of the stationary points in the interval 0 ≤ x ≤ pi. Give each answer correct to 3 significant figures.

8) The complex number w is defined by w = (22 + 4i)/(2 − i)^2.

(i) Without using a calculator, show that w = 2 + 4i.

 (ii) It is given that p is a real number such that (pi/4) ≤ arg(w + p) ≤ (3pi/4). Find the set of possible values of p.

(iii) The complex conjugate of w is denoted by w*. The complex numbers w and w* are represented in an Argand diagram by the points S and T respectively. Find, in the form |z-a| = k, the equation of the circle passing through S, T and the origin.