Page 9 - 1202 Question Bank Additional Mathematics Form 5

PAPER 2

Section A

1. The diagram shows a circle with centre O and a radius 4. The diagram shows a trapezium ABCD where AB is
SPM of 25 cm. parallel to DC. HOTS Applying
CLONE
A 5 cm B
A
α 6 cm
25 cm E
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θ
O D π π C
B — rad 12 cm — rad
6 3
π
Given AB = 5 cm, DC = 12 cm, ∠ADC = — rad,
6
π
A sector with angle θ = 1.2 rad at the centre is ∠BCD = — rad and E is the midpoint of BC.
3
removed. Then, the end A is joined to B to form a Calculate
cone. Calculate (a) the perimeter of the shaded region, [4 marks]
(a) the base radius, in cm, of the cone, [3 marks] (b) the area of the shaded region. [4 marks]
(b) the angle α, in degrees. [4 marks]
5. The diagram shows a circle with centre O and a radius
of 6 cm and a rectangle ABCO with an area of 48 cm .
2
2. Point A is a fixed point on the circumference of a
circle with centre O and a radius of 10 cm. Point A
P moves along the circumference of the circle at a B
speed of 3 cm per second. Given the angle AOP is 6 cm E
θ rad, find
(a) the rate of change of θ, in radians per second, O D C
[3 marks]
(b) the rate of change of the area of sector AOP.
[3 marks]
Calculate
(a) ∠AOB, in radians, [3 marks]
3. The diagram shows one of the pattern of a mural (b) the area of the sector EOD. [4 marks]
SPM drawn by a pupil on the wall of a school canteen.
CLONE
C 6. A ball is floating on the surface of water such that the
highest point of the ball from the surface of the water
D is half of the radius, r cm, of the ball. HOTS Applying

O P Q
r cm
A B
10 cm O
Given AB = 10 cm is a chord of the major sector ACB
with centre O and a radius of 15 cm. AB is also the
diameter of a semicircle ADB. A small circle with
centre O inscribed in the semicircle. Calculate (a) Find the length of the chord PQ, in terms of r.
(a) the arc length ACB, [4 marks] [3 marks]
(b) the area of the shaded region. [4 marks] (b) Find the area, in cm , of the cross-section of the
2
ball below the water if r = 25 cm. [4 marks]

8 Question 3:
SOS TIP The diameter of the small circle is the same as the radius of the semicircle and AB is the tangent to the small circle.

Question 6:
(b) Cross-sectional area in the water = Cross-sectional area of a circle – Area of segment above the surface of water
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01_1202 QB AMath F5.indd 8 02/12/2021 8:44 PM