Page 62 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

Example of HOTS SPM Highlights
HOTS Question
Measat-3b is a Malaysian communications satellite The diagram below shows two sectors KON and LOM
launched into the geostationary orbit, 35 786 km of two circles with a common centre O.
above the Earth. The satellite takes 24 hours to
complete one orbit.
O
Measat-3b L M
satellite
35 786 km K N
The angle subtended at the centre O by the major arc
6 400 km KN is 8θ and the perimeter of the whole diagram is
30 cm. Given ON = r cm, ON = 3OM and ∠LOM = 3q.
Express r in terms of q.
It is given that the approximate radius of the Earth
is 6 400 km. By assuming that the orbit is circular,
calculate the distance, in km, travelled by Measat-3b Solution s = rq

satellite within an hour. KN = r × 8q
[Use π = 3.142] = 8rq
s = rq
Solution LM = r × 3q

q = 1 hour 3
2π 24 hours = rq r 2
2 × 3.142 KL = MN = r – = r
q = 3 3
24
= 0.2618 rad Perimeter of the whole diagram = 30 cm
s + s + KL + MN = 30

s = rq KN LM 2 2
r +
r = 30
rq + rq +

8
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= (35 786 + 6 400) × 0.2618
3
3
= 42 186 × 0.2618 9 rq + 4 r = 30
= 11 044.29 km 3
The distance travelled = 11 044.29 km 27rq + 4r = 30
3
r(27q + 4) = 90
90
Try this HOTS Question r =
27q + 4
Measat-5 is a Malaysian communication
satellite that rotates around the Earth through a
geostationary orbit which is located 35 786 km
from the Earth’s surface. The satellite takes 24 Try This! 1.2
hours to complete one orbit.
1. Calculate the arc length s for each of the following Form 5
By assuming that one orbit is circular, calculate sectors.
the distance, in km, travelled by Measat-5 satellite (a) (b)
within three hours if the approximate radius of the s 2 cm
Earth is 6 400 km. O
[Use π = 3.142]. 0.5 rad 5.28 cm 4.28 rad
Answer: 33 137.10 km O s
(c)
2.89 cm
O
2.3 rad
s

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