pra u1 2014 trial.doc
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pra u1 2014 trial.docTRANSCRIPT
,
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