,

1

:

3

-

x

x

g

2

1

Section A [ 45 marks ]

Answer all questions in this section .

1. The function g and h are defined as follows :

0

>

x

,

2

:

x

e

x

h

-

0

>

x

(a) Determine the range of

(i) g

(ii) h [2 marks]

(b) Explain why

h

g

o

exists. Hence, find

h

g

o

and determine its range by sketching the graph

of

h

g

o

. [6 marks]

2. The sum of the first n terms of a series is

),

log(

2

1

2

-

n

b

a

n

show that

(a) the n th term of the series is

).

log(

1

-

n

ab

[3 marks]

(b) this series is an arithmetic series.[2 marks]

3. (a) Use Gaussian Elimination to solve the system of linear equation

x + y z = 0

2x 3y + z = 1

2x + y + 2z = 7[5 marks]

(b) If

-

=

1

3

A

-

1

2

, find the value of m and n such that

.

0

2

=

+

+

nI

mA

A

Hence, find

1

-

A

using the relation above.[5 marks]

4. The complex number

3

1

i

+

is denoted by z.

(a) Express z in form

)

sin

(cos

q

q

i

r

+

where

0

>

r

and

p

q

p