1. Let f (x) = 8x − 2x2. Part of the graph of f is shown below.
(a) Find the x-intercepts of the graph.
- (i) Write down the equation of the axis of symmetry.
- (ii) Find the y-coordinate of the vertex.
3.(a) Expand (2 + x)4 and simplify your result.
(b) Hence, find the term in x2 in (2+x)4(1+1/x2)
4. The straight line with equation y = 3/4x makes an acute angle θ with the x-axis.
(a) Write down the value of tanθ .
(b) Find the value of
(i) sin 2θ ;
(ii) cos2θ .
5.Consider the events A and B, where P(A) = 0.5 , P(B) = 0.7 and P(A∩B) = 0.3 .
The Venn diagram below shows the events A and B, and the probabilities p, q and r.
(a) Write down the value of
(i) p ;
(ii) q ;
(b) Find the value of P(A| B′).
(c) Hence, or otherwise, show that the events A and B are not independent.