Page 65 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

Example of HOTS 11
HOTS Question
Calculate the radius, r for each of the following sectors.
At 6 p.m. every day, the lawn sprinkler at Pak Samad’s
farm rotates back and forth automatically in the (a) (b)
angle of 2 radians to water the plants up to 9 m away. 4.52 rad
O 113.8º
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O
1
Minion Pro 10pt = — 9 m Area of sector Area of sector
2
2
---------------------------------------- 2 rad = 133.95 cm = 24.09 cm 2
Arial 8.5pt = 1 Solution
2
1 2A
Arial 8pt = 2 (a) r =
2 Calculate the maximum area, in m , of Pak Samad’s q
farm that the sprinkler could water.
---------------------------------------- 2 × 133.95
=
Cth KBAT_Optima 9pt = 80 Solution 4.52
1.25
---------------------------------------- A = r q = 7.699 cm
1 2
2
1
---------------------------------------- = (9) (2) (b) 113.8° = 113.8° × 3.142 2 rad
1
2
2 180°
= 81 m 2 = 1.986 rad
1 Try this HOTS Question r = 2A
q
XX A water tank truck will do road cleaning work at 2 × 24.09
Penyelesaian 7 p.m. every day. At a certain time, the truck waters = 1.986
the road at a distance of 3.5 m covering a sector
(a) XX
that subtends the angle 1.8 radians at the nozzle = 4.925 cm
of sprinkler.
Try Questions 3 - 4 in ‘Try This! 1.3’

12
Calculate the angle, θ, in radian, for the sectors below.
1.8 rad
3.5 m 17.4 cm O
θ

Calculate the maximum area, in m , of the road Area of sector = 60.8 cm 2
2
Form 5
watered by the water tank truck at that time.
Solution
Answer: 11.025 m 2
q = 2A
r 2
= 2 × 60.8
(17.4) 2
= 0.4016 rad

Try Question 5 in ‘Try This! 1.3’

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