Page 16 - 1202 Question Bank Additional Mathematics Form 4

PAPER 2

Time: 2 hours 30 minutes

Section A
[50 marks]
Answer all questions.

1
1. If the line x + 3y = 1 intercepts the curve y – 9 = xy at two points P and Q, find
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2
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(a) the coordinates of P and Q as the x-coordinate of P is positive,
(b) the equation of the line that passes through point Q and is perpendicular to x + 3y = 1.
[7 marks]

1
2. The roots of the equation 3x + bx + c = 0 are m and m .
2
(a) Find the value of c. [1 mark]
1 46
(b) Given m + = , find the possible values of b. [3 marks]
2
m 2 9
(c) Hence, find the possible values of m for b . 0. [3 marks]

3. Diagram 3 shows a piece of land, PQRS drawn on a Cartesian plane. Given the scale 1 unit on the Cartesian plane
represents 5 m on the real ground.

y

Q(5, 10)

R(7, y)
M

x
P(–5, 0) S

Diagram 3
P lies on the x-axis and M divides the line PQ in the ratio 2 : 3. Find
(a) the coordinates of M and R,
[2 marks]
(b) the equation of the line MR,
[3 marks]
(c) the actual area of PQRS, in m .
2
[3 marks]

4. A coil of wire with length t cm is cut into a few parts. Each part is bent into a square. Given that the length of each
side of the square follows an arithmetic progression with the common difference 1.5 cm. The smallest and the largest
squares have sides 1.5 cm and 16.5 cm respectively.
Find the number of squares can be made and the value of t.
[8 marks]

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