Page 13 - 1202 Question Bank Additional Mathematics Form 5

PAPER 2

Time: 2 hours 30 minutes

Section A
[50 marks]
Answer all questions.

1. The sum of the digits of three-digit number is 16. The unit digit is 2 more than the sum of the other two digits. The
tens digit is 5 more than the hundreds digit. What is the number?
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[7 marks]

2. (a) Diagram 1 shows the net of an open box.

x cm x cm

(15 – 2x) cm

5 cm
Diagram 1
(i) Show that the volume of the box, in cm , is given by V = 75x – 10x .
3
2
[2 marks]
(ii) Hence, find the value of x, in cm, such that the volume of the box is maximum. State the maximum volume
of the box.
[3 marks]
(b) Find the possible range of values of x if the volume of the box is between 90 cm and 125 cm .
3
3
[2 marks]

3. In Diagram 2, A, B and C are the vertices of a right-angled triangle.

C
D α
F
H
x cm

A
G E B
Diagram 2
Given that ∠ACB = α and BC = x cm.
(a) Express BD and DE in terms of x and α.
[2 marks]
(b) Show that BD, DE and EF form the first three terms of a geometric progression and state the common ratio.
[3 marks]
(c) Find the length of HG in terms of x and α.
[1 mark]
(d) Given that x = 8 cm and α = 60°, find the sum to infinity of the geometric progression.
[2 marks]
90

09_1202 QB AMath F5.indd 90 04/12/2021 9:25 AM