Page 10 - 1202 Question Bank Additional Mathematics Form 5

Section B
13. Ani wants to make a cone-shaped cap for her 16. The diagram shows a rhombus ABCD with sides of
children’s party. The height of the cone is 25 cm and x cm and ∠A = θ rad. HOTS Analysing
the base radius of the cone is 8.5 cm. She takes a
piece of cardboard measuring 27 cm × 35 cm to cut B
out the net of the cone which is a sector of a circle. C
HOTS Analysing
(a) What is the angle, in radians, subtended at the A θ rad x cm
centre of the circle by the arc length of the sector
of the net? [4 marks] D
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x
(b) Based on the calculation in (a), determine Four arcs each with radius — cm are drawn with
whether the cardboard is big enough to make a 3
cone-shaped cap. [6 marks] centres A, B, C and D respectively. Given the shaded
area is half of the area of the rhombus,
2
(a) show that sin θ = —π, [5 marks]
14. The diagram shows a semicircle PORQS with centre 9
O and a radius of 9 cm. HOTS Applying (b) find two possible values of θ. [5 marks]

9 cm O M R
P Q
θ 17. The diagram shows two sectors with centre O.
L
2 cm
M
S
RPS is an inscribed sector in the semicircle with 1.5 rad
centre P. A perpendicular line from S to PQ divides O
the radius of the semicircle into half at M. Find N P
(a) the angle θ, in radians, [3 marks]
(b) the arc length RS, [3 marks]
(c) the area of the shaded region. [4 marks] Given that ∠LOP = 1.5 rad, LM = NP = 2 cm and the
area of the sector LOP is 20.75 cm , find
2
(a) the radius OM, [4 marks]
15. The diagram shows the sector AOB with centre O, a (b) the arc length LP, [2 marks]
SPM π (c) the area of the shaded region. [4 marks]
CLONE radius OB = 8 cm and ∠AOB = — rad.
3
C
18. The diagram shows a sector of a circle with centre A.
A B HOTS Analysing
D E y
P
8 cm
C
π
— rad
3 B
3y + x = 9
O
OC is the bisector of ∠AOB and P is the midpoint of O A(4, 0) D x
OC. An arc DCE of a circle is drawn with centre P to
meet OA and OB at D and E respectively. Find The equation of BD is 3y + x = 9. Find
(a) the angle OPD, in radians, [3 marks] (a) the radius of the sector ABCD, [4 marks]
(b) the area of the shaded region. [7 marks] (b) the angle BAD, in radians, [2 marks]
(c) the area of the shaded region. [4 marks]

10 Question 13:
SOS TIP The radius of the sector of the net is the inclined side of the cone. Sketch the net of the cone as well as the cone before calculating the length and width of the

cardboard.
Question 16:
Area of ABCD = Length of AD × Height of B to AD
1010

01_1202 QB AMath F5.indd 10 02/12/2021 8:44 PM