This preview shows pages 1–3. Sign up to view the full content.
H2 MA 9740/S/2006 RJC JC1 Promotion Exam
[Turn Over
2
1
Find
d
d
y
x
for each of the following, simplifying your answers in each case.
(a)
ln
2
x
y
x
=
+
,
0
x
>
.
[2]
(b)
2
cos 2 ,
.
x
t
y
t
=
=
[2]
2
The diagram below shows the graph of
( )
f
y
x
=
. The points
A
,
B
and
C
have coordinates
1
(
,0)
2

, (1, 2) and (3, 1) respectively.
Sketch on separate diagrams, the graphs of
(i)
f
2
x
y
=
,
[1]
(ii)
f
1
2
x
y
=

,
[2]
(iii)
( )
f
'
y
x
=
,
where
( )
d
f
f ( )
d
'
x
x
x
=
.
[2]
State, in each case, the coordinates of the points corresponding to
A
,
B
and
C
, where
appropriate.
3
A curve
C
is given by the equation
2
(
)
2
4
y
x
x

=
+
.
(i)
Find
d
d
y
x
, giving your answer in terms of
x
and
y
.
[2]
(ii)
Find the equation of the normal to the curve
2
(
)
2
4
y
x
x

=
+
at the point (6,2) .
[3]
4
A spherical ice ball melts at a constant rate of
3
1
10cm min

. When the radius of the ball
is 6cm , find
(i)
the rate at which the radius of the ice ball is decreasing,
[3]
(ii)
the rate at which the surface area of the ice ball is decreasing.
[2]
[The formulae for the volume and surface area of a sphere of radius
r
are
3
4
3
V
r
π
=
and
2
4
A
r
=
.]
x
y
( )
f
y
x
=
C
(3,1)
B
(1,2)
1
2
(
,0)
A

0
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document H2 MA 9740/S/2006 RJC JC1 Promotion Exam
[Turn Over
3
5
A sphere of radius 1 m is inscribed in a right circular cone of base radius
r
and height
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/12/2010 for the course C 11 taught by Professor Na during the Spring '10 term at Rappahannock Community College.
 Spring '10
 NA

Click to edit the document details