test

1) (a) State the re al and imaginary parts of each of the following complex numbers. (i) (ii)

1  2 √ 2 3   7

(b) Write each of the following complex numbers in the form  (i) (ii) (iii) (iv) (v)

(2  3 ) ) (52) (2  3 ) ) (52) (2  4)( )(1  2) − +  +   − +

(i) Label and plot on an Argand diagram 

(c)

  .

 =  |33 (ii) Calculate ||  = |

= 3  2.

2| 2|.

2) (a) The coordinates of  (2,2) and  (3, 1) 1) are points on a straight line. Determ ine: i) The gradient of the line joining  . ii)

The equation of the line joining  . If the line segment   is the perpendicular bisector of  , determine

iii) The equation off the line  in the form 

=     .

b) Determine the points of intersection of t he following curve and line by solving the two simultaneous equations.  =    5  3

2 = 3  2 3) (a) Sketch the curve and line in question 2(b) on the grid provided. Clearly labeling their points of intersection, intercepts, roots and turning point. (Show all working). (b) Find the values of x that satisfy the inequalities: i.  4     3 > 0 ii.

|4   |  2 < 0

4) (a) Find the values of   if: (i) 3 = 81 4 = 2 − × 8+ (ii) (iii) (iv)

 (17) 17) = 3      6 = 5

(b) Write the following expression in terms of ln,ln, and   :

   

(c) Given that ℎ( ) =

   2   5  6 factorise ℎ() completely.

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