Page 72 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure
9. (a) The diagram below shows a sector POQ
with centre O and sector PMN with centre M.
Given that the radius of sector POQ is 24.2 cm
and ∠POQ is a right angle. M and R are the
midpoints of OP and OQ respectively. 1.8 cm
O 0.8 cm
R
N Q
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M
P Calculate INFO
Calculate the area, in cm , of the shaded region. (a) the rotating distance, in cm, of the small gear,
2
[Use π = 3.142] (b) the rotating angle, in radian, of the big gear,
(b) The diagram below shows sector ABC with (c) the area, in cm , of the sector covered by the big
2
centre B and sector AOD with centre O. Given gear.
that the radius of sector ABC is 9 cm. ∠ABC [Use π = 3.142]
and ∠AOD are 0.87 radian and 1.15 radian
respectively. Solution
A 9 cm 3.142
1
B (a) 300° = 300° × 2 rad
O 180°
= 5.237 rad
Rotating distance of small gear = rq
C
D = 0.8 × 5.237
Calculate the area, in cm , of the shaded region. = 4.19 cm
2
[Use π = 3.142]
10. The diagram below shows a pair of windshield (b) Rotating distance = Rotating distance
wipers of a car that can rotate back and forth at the of large gear of small gear
angle of 1.5 radian. HOTS 1.8 × q = 4.19
Applying 4.19
q =
Wiper blade 1.8
62 cm = 2.328 rad
(c) Area of sector covered = 1 r q
2
2
= 1 (1.8) (2.328)
2
If the windshield wiper blade has a length of 60.9 2
cm and radius of its sector is 62 cm, calculate the = 3.771 cm 2
area of windscreen, in cm , that can be cleaned by
2
the pair of wipers. Try Question 1 in ‘Try This! 1.4’
[Use π = 3.142]
18 Form 5
1.4 Application of Circular Measures The diagram below shows the transition curve on one
side of the road where ∠AOB subtended by the chord
AB at centre O. Given that the length of chord AB is 30
A Solving problems involving circular m and the length of both radii OA and OB are 42 m.
measure

17 A B
The following diagram shows part of the gear network
system in a printer consisting of one small gear and one
large gear with radii 0.8 cm and 1.8 cm respectively. At O
a certain time, the small gear rotates at 300°.

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