CAIE Mathematics (9709)

On an Argand diagram, sketch the locus of points representing complex numbers zsatisfying

Find the least value of zfor points on this locus, giving your answer in an exact form.[2] 4Solve the equation 2 cos 5The complex number 2 +yi is denoted bya, whereyis a real number andy<0. It is given thata=a ain terms ofy.

Given that Re 6The equation cot x=3xhas one root in the interval 0<x< π, denoted by!.

Show by calculation that !lies between 0.5 and 1.

Show that, if a sequence of positive values given by the iterative formulan+1 +4 tan converges, then it converges to!.

Use this iterative formula to calculate !correct to 2 decimal places. Give the result of each iteration to 4 decimal places. [3] 7The equation of a curve is 3 +4xy+3y=5.

Show that 3x+2y 2x+3y y+2x=0.

The variables 4+9y 2x+1 It is given that y=0 whenx=1. yin terms ofx.

State what happens to the value of [1] 9Let f

Express f xin partial fractions.

Hence show that fxdx= The diagram shows the curve y=x+5

Find the exact coordinates of M.

Using the substitution the curve and the x-axis. Give your answer in the forma 13, whereais a rational number. [5] 11The points

Show that ldoes not intersect the line passing throughAandB.

Find the position vector of the foot of the perpendicular from Atol. [4] Additional Page If you use the following lined page to complete the answer

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