Maths T STPM 2014 Sem 1 Trial King George
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Transcript of Maths T STPM 2014 Sem 1 Trial King George
2014
-1-N
S-K
ING
GE
OR
GE
Sec
tion
A [4
5 m
arks]
An
swer a
llqu
estions in
this sectio
n.
1.
Th
e fun
ction f is d
efined
by
�:���,�
�0
(a) S
tate the ran
ge o
f f.
[1
mark
s]
(b)
Fin
d �
�.
[2
mark
s]
(c) S
ketch
the g
raph
of f an
d �
�.
[3
mark
s]
2.
Fin
d th
e exp
ansio
n o
f 9����� as far as term
in �
�an
d state th
e range o
f valu
es of x
for
wh
ich th
e exp
ansio
n is v
alid. H
ence, o
btain
the v
alue o
f √9.05
correct to
fou
r decim
al
p
laces.
[6
mark
s]
3.
Fin
d th
e inv
erse of m
atrix A
by u
sing elem
entary
row
operatio
ns
A =
29
8
61
3
20
1
[4 m
arks]
Hen
ce, solv
e the sim
ultan
eou
s equ
ation
s
x +
2z =
1
3x
+ y
+6
z = 2
8x
+9
y +
2z =
-1
[4
mark
s]
4.
Fin
d th
e roo
ts, den
oted
by �
and �
, of th
e equ
ation
��� 2�
�4�0
in p
olar fo
rm.
Usin
g d
e Mo
ivre’s th
eorem
, sho
w th
at ��� �
�.
[1
0 m
arks]
5.
Th
e equatio
n o
f an ellip
se is 4������8�
�12
�0.
(a) O
btain
the stan
dard
form
of th
e equ
ation
of th
e ellipse.
[2
mark
s]
(b)
Fin
d th
e centre, fo
ci and
vertices o
f the ellip
se.
[4
mark
s]
(c) S
ketch
the ellip
se.
[2
mark
s]
6.
Th
e vecto
r v =
ai + b
j + c
k is p
erpen
dicu
lar to th
e vecto
rs i – 2
k an
d 2
i + j –
k.
(a) F
ind a an
d b
in term
s of c.
[4
mark
s]
(b)
Giv
en th
at |# | = √56
, and
that c is p
ositiv
e, find
c.
[3
mark
s]
Sec
tion
B [1
5 m
arks]
An
swer a
ny o
ne q
uestio
n in
this sectio
n.
7.
Giv
en th
at ,
)(
f2
3q
xp
xx
x+
++
=w
here
pan
d q
are con
stants, is d
ivisib
le by
).1
(−
x
Wh
en d
ivid
ed b
y),
2(
−x
the rem
aind
er is 17
. Fin
d th
e valu
es of %
and
&.
[4 m
arks]
(a)Sho
w th
at 0
)(
f=
xh
as on
ly o
ne real ro
ot. F
ind
the set o
f valu
es of �
such
that
0)
(f
>x
.
[6
mark
s]
(b)E
xp
ress )
(f
91
1
x
x+
in p
artial fraction
s.
[5
mark
s]
8.
Th
e straigh
t line y
= m
x –
2 in
tersects the cu
rve �
��4�
at two
differen
t poin
ts, P(�
�, , ��)
and Q
(��, , �
� �. Sh
ow
that
(a) m '
0 an
d m
>���
(b) �
�����
( )
*��
)�
(c) ������
()
If the p
oin
t O is th
e orig
in an
d p
oin
t T is a p
oin
t such
that O
PT
Q is a p
arallelogram
, pro
ve
that w
hen
m ch
anges, th
e equ
ation
of th
e locu
s of T
is ���4�
�4�
. [1
5 m
arks]