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SAINT ANDREW’S JUNIOR COLLEGE
PRELIMINARY EXAMINATION
MATHEMATICS
Higher 2
9740/02
Paper 2
Wednesday
12 Sep 2007
3 hours
Additional materials :
Answer paper
List of Formulae(MF15)
Cover Sheet
READ THESE INSTRUCTIONS FIRST
Write your name, civics group and index number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use a soft pencil for any diagrams or graphs.
Answer
all
the questions.
Give nonexact numerical answers correct to 3 significant figures, or 1 decimal place in the
case of angles in degrees, unless a different level of accuracy is specified in the question.
You are expected to use a graphic calculator.
Unsupported answers from a graphic calculator are allowed unless a question specifically
state otherwise.
Where unsupported answers from a graphic calculator are not allowed in a question, you are
required to present the mathematic steps using mathematical notations and not calculator
commands.
You are reminded of the need for clear presentation in your answers.
The number of marks is given in brackets [ ] at the end of each question or part question.
At the end of the examination, fasten all your work securely together.
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2
Section A (40 marks)
1
Find the three complex numbers,
0
1
2
,
z
z z
that satisfy the equation
0
2
4
2
4
3
i
z
.
Give your answers in the form
θ
i
re
, where θ is in terms of π .
[4]
Hence show that
w
=
6
2
6
1
6
0
z
z
z
is an imaginary number. Find
Im(
w
).
[3]
2
When Mrs Wong retired in 2006, she put a sum of $5000 into a fund that has a constant rate of
return of 5 % per annum.
Starting in 2006, she withdraws $400 each year and gives the money
to her granddaughter as a birthday gift.
Denote the amount of money Mrs Wong has at time
t
years by $
x
.
(i)
The differential equation relating
x
and
t
is in the form
d
dt
x
kx c
. State the values of
k
and
c
.
.
[1]
(ii)
Solve the differential equation and find the amount of money Mrs Wong has after
15 years. Give your answer to the nearest integer.
[4]
(iii)
In which year will the granddaughter receive her last $400?
[2]
Comment on whether the model can be regarded as a good model of the situation in the real
world.
[1]
3
The parametric equations of a curve are given by
secθ
xa
,
tanθ
ya
where
a
is a real
constant.
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 Summer '07
 MOE
 Math, Addition

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