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SERANGOON JUNIOR COLLEGE
2007 JC2 PRELIMINARY EXAMINATIONS
MATHEMATICS
Higher 2
9740/Paper 2
Tuesday
18 September 2007
Additional materials:
Writing paper
List of Formulae (MF15)
TIME
:
3 hours
READ THESE INSTRUCTIONS FIRST
Write your name and class on the cover page and on all the work you hand in.
Write in dark or black pen on both sides of the paper.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
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 states
otherwise.
Where unsupported answers from a graphic calculator are not allowed in a question, you are
required to present the mathematical 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.
This question paper consists of 8 printed pages and no blank pages.
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Section A: Pure Mathematics [40 marks]
1
The curve
C
is defined parametrically by
sec
xa
and
tan
ya
, where
a
is a fixed
constant.
It is known that the point
P
with coordinates
( sec , tan )
aa
lies on
C
.
Show that the equation of the tangent at
P
is given by
sin
cos
x
y
a
and the
equation normal at
P
is given by
sin
2 tan
x
y
a
.
The tangent and the normal at
P
cut the
x
axis at
T
and
N
respectively.
Prove that
OT ON
= 2
a
2
, where
O
is the origin.
2
(a)
Find the modulus and argument of the complex number
z
, where
2
4
(1
)
3 )
i
z
i
,
giving your answers in exact form.
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 Summer '07
 MOE
 Math, Addition

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