Form 4ABCDEF
Mathematics
14th June, 2006
Paper I
Time allowed: 1 hour 30 minutes
Answer ALL questions.
This paper carries a total of 94 marks.
1.
Rationalize
5
2
3
1
.
(3 marks)
2.
Solve the simultaneous equations:
0
12
4
4
0
2
2
y
x
x
y
x
.
(6 marks)
3.
(a)
Solve the equation
18
45
y
y
.
(b)
Hence, or otherwise, solve the equation
18
)
5
3
(
5
3
45
2
2
x
x
x
x
.
(8 marks)
4.
Consider the quadratic equation
0
)
2
(
)
3
(
2
2
k
x
k
kx
, where
k
is a nonzero
number.
(a)
Find the discriminant of the above equation. Simplify your answer.
(b)
Prove that the equation always has two distinct real roots.
(5 marks)
5.
When
a
x
x
ax
x
7
2
2
3
4
is divided by
3
2
x
, the quotient is
1
4
2
x
x
and the
remainder is
c
x
5
, where
a
and
c
are constants.
(a)
Expand the product
1
4
3
2
2
x
x
x
.
(b)
Using (a), or otherwise, find
a
and
c
.
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 Spring '08
 WOUTERS
 Math, Algebra, Equations, Quadratic equation, Elementary algebra

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