Set 6
Set 6
Set 6
2.
Given that u n ln pq n 1 where p and q are positive constants.
(a) Show that the terms u1 , u 2 , u3 ..., u n form an arithmetic sequence. [3]
(b) Find the expression for S n , the sum to n terms. [3]
(c) Hence, obtain a relationship between p and q if S 3 6 . [2]
(a) Write the augmented matrix for the system of linear equations. [1]
(b) By using elementary row operations, show that the augmented matrix in (a) can be
reduced to
1 2 3 1
0 1 7 2a [4]
0 0 26 k 12 5a
(c) Find the values of a and k if the system of linear equations has many solutions.
Hence, find general form of the solutions. [4]
4.
values.
(a) Express z in polar form. [3]
(b) Hence, by using de Moivre’s theorem, find the values of x and y. [5]
2
5. The parametric equations of an ellipse are x 9t 2 and y 11 1 t 1
(a) Form the standard equation of the ellipse and state its centre. . [3]
(b) Find the foci and vertices. Hence, sketch the ellipse. [4]
2
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