1.Let f be a quadratic function. Part of the graph of f is shown below.
The vertex is at P(4, 2) and the y-intercept is at Q(0, 6) .
(a) Write down the equation of the axis of symmetry. [1 mark]
The function f can be written in the form f (x) = a (x − h)2 + k .
(b) Write down the value of h and of k . [2 marks]
(c) Find a .
3.A box contains six red marbles and two blue marbles. Anna selects a marble from the box. She replaces the marble and then selects a second marble.
(a) Write down the probability that the first marble Anna selects is red. [1 mark]
(b) Find the probability that Anna selects two red marbles. [2 marks]
(c) Find the probability that one marble is red and one marble is blue.
4.Let f '(x) = 3x2 + 2 . Given that f (2) = 5 , find f (x) .
5.The random variable X has the following probability distribution.
Given that E(X ) =1.7 , find q .