(a) Find AB .

(b) Given that X − 2A = B , find X .


2.The following table shows the probability distribution of a discrete random variable X .

(a) Find the value of k .

(b) Find E(X ) .


3.(a) Find ∫104 (x − 4)dx .

(b) Part of the graph of f (x) =√x-4 , for x ≥ 4 , is shown below. The shaded region R is enclosed by the graph of f , the line x =10 , and the x-axis.

The region R is rotated 360° about the x-axis. Find the volume of the solid formed.


4.Part of the graph of f (x) = ax3 − 6x2 is shown below.

The point P lies on the graph of f . At P, x =1.

(a) Find f′(x) .

(b) The graph of f has a gradient of 3 at the point P. Find the value of a .


5.Let sin100°= m. Find expressions for each of the following in terms of m

(a) cos100°;

(b) tan100°;

(c) sin 200° .




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