Page 77 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure
8. The diagram below shows a small circle and a Calculate the area, in m , of the field that cannot be
2
large circle with centres B and C respectively. The grazed by the cow.
radius of the large circle is twice the radius of the [Use π = 3.142]
small circle. Both circles touching each other at
point E. Straight line AD is the common tangent to 11. A cheese cake baked by Reyna has a radius of
both circles at point A and point D. HOTS 11.5 cm and thickness of 8 cm. This cake is divided
Analysing into slices that will be sold at Kedai Kek Istimewa.
B The plastic wrapper used to wrap the vertical
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A
surface of a piece of cake has the measurement of
E 30 cm × 10 cm. Reyna needs to cut the cake with
rad maximum angle, q at the centre of the cake, so that
D C the plastic wrapper is sufficient to wrap the entire
vertical surface of the cake. HOTS
Calculate Creating
(a) q, in degrees, to the nearest integer,
Given the radius of the small circle is r cm, calculate (b) the volume, in cm , of each slice of cake based
3
Arial 8.5pt = 1 (a) α, in radian, on the answer for (a) .
2 (b) the perimeter, in cm, of the shaded region. [Use π = 3.142]
[Use π = 3.142]

9. The diagram below shows sector POQ and PAPER 2
sector OABCD of concentric circle with centre 1. The diagram below shows a circle and a sector
O. Points B and C are the midpoints of the SPM of circle with a common centre O. The radius of
straight lines OP and OQ respectively. Given that 2017 sector AOB is r cm and ∠AOB is q rad.
∠AOB : ∠BOC : ∠COD = 1 : 3 : 1 and the perimeter
of the whole diagram is 32 cm.
D
P A A
B C O
B
O
C
Q D
Given that the arcs length AB and CD are 2 cm
If ∠AOB = θ radian and the radius of sector and 9 cm respectively and BC = 13.5 cm.
OABCD = r cm, express in terms of r,
(a) q, Calculate
(b) the area, in cm , for the whole diagram. (a) the values of r and q,
2
(b) the area, in cm , of the shaded region.
2
10. The diagram below shows a square shaped grass [Use π = 3.142]
field with the length of each side is 8 m. A cow is
tied to a post with a 4 m rope. The post is located 2. The Nature Lovers Club of SMK Setia organised
2 m from the edge of the field as shown in the SPM a competition to design a logo for the club. The
diagram. 2018 diagram below shows a circular logo designed by
HOTS Dahlan. A square is inscribed in the logo.
Form 5
Analysing
8 m
D C A
A
A
8 m A
E 4 m Given that the area of the region marked A is
2 m (32 – 8π) cm . Calculate
2
A B (a) the radius, in cm, of the logo,
2 m
(b) the perimeter, in cm , of the region marked A.
2
[Use π = 3.142]

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