1
Form 4
Mathematics
14 June 2007
Paper I
Time allowed: 1 hour 30 minutes
1.
Answer ALL questions.
2.
All working must be clearly shown.
3.
Unless otherwise specified, numerical answers should be either exact or correct to 3
significant figures.
4.
The diagrams in this paper are not necessarily drawn to scale.
5.
This paper carries a total of 98 marks.
1.
Let
k
be a constant.
If the quadratic equation
(2
x
–
1)(
x
+ 1) =
k
has at least one real root,
find the range of values of
k
.
(4 marks)
2.
(a) Simplify
(
2
3)(2 2
3 3)
.
(b)
Hence rationalize
2
(
2
3)(2
2
3 3)
5
.
(5 marks)
3.
Suppose (1, 0) is a solution of the following system of simultaneous equations:
0
1
5
4
2
y
kx
x
x
y
Find the other solution.
(5 marks)
4.
Given that 3
x
2
+ 4
x
–
2
≡
(
Ax
+
B
)(3
x
–
2) +
C
, find the values of
A
,
B
and
C
.
(5 marks)
5.
When a polynomial
f
(
x
) is divided by
x
2
–
x
–
1, the quotient is
x
+ 2 and the remainder is
2
x
–
1.
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 Spring '08
 WOUTERS
 Math, Algebra, Division, Quadratic equation, Elementary algebra

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