MJC/2007 JC2 Preliminary Examination/9740/01
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2
1
An arithmetic progression
G
has first term
a
and a nonzero common difference
d
. Given
that the sum of the first 10 terms in
G
is twice the 22
nd
term of the series and the 6
th
term
is 37, find the values of
a
and
d
.
[3]
A new series
H
is formed by selecting every third term of
G
. Find the sum of the first 50
terms of
H
.
[3]
2
Express
2
1
f( )
(
1) (
2)
x
xx
in partial fractions.
Hence find the expansion of
x
, in ascending powers of
x
, up to and including the term
in
3
x
, where
1
x
.
[6]
Show that the coefficient of the term in
2
n
x
in the expansion of
x
, where
n
is a
positive integer, is
2
1 4
2
2
3 3
6
n
n
.
[2]
3
A child was blowing bubbles and noticed that if he blows too hard, the bubble would
burst immediately but if he were to blow gently, the bubble increases in size till its
optimal volume and detaches itself off the blowing stick.
At time
t
minutes, the radius of the bubble blown is
r
cm, assuming that all bubbles
blown are spherical in shape. If the child blows gently at a rate of
3
r
cm
3
min
–1
,
where
is a constant, show that
23
d
4
d
r
rr
t
.
[3]
Given that the initial volume of a bubble is negligible and the optimal volume of a bubble
is
6
cm
3
, find the time taken for a bubble to detach itself off the blowing stick.
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 Summer '07
 MOE
 Math, Complex number, key nutritional requirements, Preliminary Examination/9740/01

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