1. The first three terms of an infinite geometric sequence are 32, 16 and 8.

(a) Write down the value of r .

(b) Find u6

(c) Find the sum to infinity of this sequence.


2. Let g (x) = 2x sin x .

(a) Find g′(x) .

(b) Find the gradient of the graph of g at x = π .


3.The diagram shows two concentric circles with centre O.

Points A, B and C are on the circumference of the larger circle such that AOB is π/3 radians.

(a) Find the length of the arc ACB .

(b) Find the area of the shaded region.


4.The diagram below shows the probabilities for events A and B , with P(A′) = p .

(a) Write down the value of p .

(b) Find P(B) .

(c) Find P(A′|B) .


5.(a) Show that 4 − cos 2θ + 5sinθ = 2sin2θ + 5sinθ + 3 .

(b) Hence, solve the equation 4 − cos 2θ + 5sinθ = 0 for 0 ≤θ ≤ 2π .




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