Page 75 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

Try This! 1.4 3. The diagram below shows the cross section of a
slice of cake in the form of a sector of circle AOB
1. The diagram below shows two gears rotating with centre O and radius of 10 cm.
simultaneously in a model. The diameters of small B
gear and large gear are 5 cm and 12 cm respectively. A
At a certain time, the large gear rotates at 140°. 36 O

12 cm

Minion Pro 10pt = —
Minion Pro 10pt = — 1 1 If the thickness of the slice of cake is 8 cm, calculate
2 2
----------------------------------------
---------------------------------------- 5 cm (a) the length, in cm, of the plastic wrapper
wrapping the entire vertical surface of the slice
Arial 8.5pt =
Arial 8.5pt = 1 1 of cake,
2 2 2
1 1 Calculate (b) the upper surface area, in cm , of the slice of
8pt

Arial 8pt = (a) the rotating distance, in cm, of the large gear, cake,
Arial

=
2 2
(b) the rotating angle, in radian, of the small gear, (c) the volume, dalam cm , of the slice of cake.
3
----------------------------------------
---------------------------------------- (c) the area, in cm , of the sector covered by the [Use π = 3.142]
2
small gear.
80
Cth KB A T_Optima 9pt = 80 [Use π = 3.142] 4. The diagram below shows a round shaped souvenir
Cth KBAT_Optima 9pt =
MKN with centre O and radius of 20 cm placed
1.25
1.25
----------------------------------------
---------------------------------------- 2. The diagram below shows a transition curve on one above a souvenir holder. The straight lines OJ and
section of rail track where ∠POQ subtended by the OL passing through points M and N respectively.
---------------------------------------- chord PQ at centre O. Given that the length of chord The straight line JL is the tangent to the circle MKN
----------------------------------------
PQ is 45 m and the length of both radii OP and OQ at point K.
are 50 m respectively.
1 1 P Q O 20 cm O
XX Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
XX
125
N
M
Penyelesaian J K L
Penyelesaian

(a) XX
(a)
X
X
Calculate
Calculate (a) the obtuse angle MON, in radian,
(a) ∠POQ, in radian, (b) the perimeter, in cm, of the whole souvenir
(b) the arc length, in m, bounded by the chord PQ, including its holder,
(c) the area of segment, in m , bounded by the arc (c) the area, in cm , of the souvenir holder.
2
2
and chord PQ. [Use π = 3.142]
[Use π = 3.142]
SPM Practice 1
SPM Practice
Form 5
PAPER 1
1. The diagram below shows two sectors AOD and The angle subtended at centre O by the major arc
SPM BOC with a common centre O. AD is 15t radian and the perimeter of the whole
2017
C diagram is 96 cm. Given OA = j cm, OB = 3OA and
B ∠BOC = 3t radian, express j in terms of t.
D
A
O
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