Question-1: A linear recurrence sequence is given by :
(a) Obtain the parameters r and d and write down a recurrence relation for the sequence. [4marks]






(b) Find the closed form for the sequence . [4marks]




(c) Using (b): (i) compute the 5th and 10th terms . [2marks]



(ii) deduce the long term behaviour of the sequence. [2marks]


(d) Use Mathcad to list and plot the first 10 terms of the sequence. Compare with (c). [3marks]








Question-2: The circle S has equation : .
(a) Show that are ends of a diameter. [4marks]







(b) Show that lies on S and determine angle ACB. [4marks]





(c) Find the distance from to the nearest point E on S. [3marks]





(d) Find the the x-coordinates of the points of intersection of S with the line joining D and F(0,2). [4marks]












Question-3:
(a) Show that the function : is 1-1 and find its inverse.
[4marks]







(b) Evaluate (i) (ii)
[4marks]







(c) Obtain parametric equations for the circle S with equation: [4marks]








(d) Show that the center of the circle S lies on the line with parametric equations : . [3marks]



Question-4: In this question and .

(a) Describe a sequence of scalings and translations that would transform the graph of f(x) into the graph of g(x). [4 marks]






(b) Obtain the domain and range of . [4marks]





(c) Solve the equation: [4marks]







(d) Use Mathcad to solve the equation : [3marks]