Page 73 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure
Calculate Solution
(a) ∠AOB, in radian, (a) 22.5° = 22.5° × 3.142 2 rad
1
(b) the arc length, in m, bounded by the chord AB, 180°
= 0.3928
(c) the area of segment, in m , bounded by the arc and s = rq
2
chord AB. = 12 × 0.3928
[Use π = 3.142] = 4.714 cm

Solution Length of the plastic wrapper = s + 2r
1 1
Minion Pro 10pt = — (a) For ∆AOB, = 4.714 + 2(12)
Minion Pro 10pt = —
2 2 2 2 2 = 28.714 cm
----------------------------------------
---------------------------------------- AB = OA + OB – 2(OA)(OB) cos ∠AOB
2
2
2
Arial
=
8.5pt

Arial 8.5pt = 1 1 30 = 42 + 42 – 2(42)(42) cos ∠AOB (b) Upper surface area of the slice of cake
2 2 42 + 42 – 30 2 1
2
2
2
1 1 cos ∠AOB = = r q
Arial 8pt = 2(42)(42) 2
Arial 8pt =
2 2 3Rights Reserved.
∠AOB = 0.7304 rad = 1 (12) (0.3928)
2
----------------------------------------
---------------------------------------- 2
(b) The arc length = rq = 28.282 cm
2
80
T_Optima 9pt =
A
Cth KB
Cth KBAT_Optima 9pt = 80 = 42 × 0.7304
1.25
1.25
---------------------------------------- (c) Volume of the slice of cake
----------------------------------------
= 30.68 m = Surface area of the slice of cake × Thickness of cake
Penerbitan Pelangi Sdn Bhd. All
----------------------------------------
1
---------------------------------------- (c) Area of segment = r (q – sin q) = 28.282 × 10
2
2 = 282.82 cm
= 1 (42) (0.7304 – sin 0.7304) Try Question 3 in ‘Try This! 1.4’
2
2
= 55.77 m
2
20
Try Question 2 in ‘Try This! 1.4’ The diagram below shows a round picture frame
with centre O and radius of 12.5 cm placed on top
19 of a picture holder. P and R are the midpoints of the
straight lines OA and OB respectively. The height of the
The diagram below shows a slice of cake in the form of picture holder is 8 cm.
sector of a circle VOW with centre O and radius 12 cm. Q
Given that the thickness of the cake is 10 cm.
O
P 100 R
V
8 cm
W A
22.5 B
O 38.2 cm
Calculate
(a) the obtuse angle POR, in radian,
Form 5
(b) the perimeter, in cm, of the whole diagram,
2
A worker needs to wrap the slice of cake with plastic (c) the area, in cm , of the picture holder.
wrapper. Calculate [Use π = 3.142]
(a) the length, in cm, of the plastic wrapper needed Solution
to wrap the entire vertical surface of the slice of (a) 100° = 100° × 3.142 2 rad
1
cake, 180°
(b) the upper surface area, in cm , of the slice of cake, = 1.746 rad
2
(c) the volume, in cm , of the slice of cake. Obtuse angle POR = 2(3.142) – 1.746
3
[Use π = 3.142] = 4.538 rad
234