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 .