Page 78 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure
3. The diagram below shows a sector AOC with 6. The diagram below shows a circle with centre O
SPM centre O. and radius of 5 cm. The perimeter of circle bounded
2019
A by semicircles APB, BQC, CRD, DSE and ETA with
diameters AB, BC, CD, DE and EA respectively.
O
7.5 cm S
D
E R
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C B
P T O
C
A
Given that ∠AOC is 150° and the arc length BC is B Q
4.83 cm. Calculate P
(a) ∠AOB, in radian, Calculate
2
(b) the area, in cm , of the shaded region. (a) ∠AOB, in radian, correct to three significant
[Use π = 3.142]
figures,
(b) the perimeter, in cm, of the shaded region,
4. The diagram below shows a piece of paper that (c) the area, in cm , of the shaded region.
2
has a shape of equilateral triangle with the side [Use π = 3.142]
length of 10 cm. Teacher Bala gives the papers to
the pupils to make cones. HOTS 7. The diagram below shows the chain drive of
Creating 1
a bicycle. The bicycle chain drive consists of Arial 8.5pt = 2
sprocket with radius 12 cm and hub with radius
3.5 cm located on the rear wheels of the bicycle.

pedal
crank A wheel
arm B
Devyn wants to use the paper as maximum as F C hub
possible to make a cone. Calculate sprocket D
3
(a) the maximum volume, in cm , of the cone made E
by Devyn, chain
(b) the area, in cm , of the paper unused by Devyn.
2
[Use π = 3.142] (a) Given that the radius of the rear wheel of the
bicycle is 35 cm, how far, in cm, can the bicycle
move if the pedals of the sprocket is rotated at
5. The diagram below shows two circles with centres 80°?
M and N overlap with each other. Both circles have (b) If the lengths of both chains AB and DE are
the same radii, which is π cm.
32 cm respectively, calculate the area of the
region ABCDEF, in cm , of the system of the Form 5
2
P
bicycle chain drive.
[Use π = 3.142]
R M N S
8. The following diagram shows the cross section of
Q a tunnel with length of 1.8 km and radius of 12 m
built to reduce the rate of traffic congestion and
(a) Calculate the perimeter of the whole diagram in
terms of π. also solve the problems of flash flood in major
(b) Show that the area of the shaded region is cities. The segment PQ acts as a trench with the
concrete road over it.
3
2
2
1 2π + 3π √3 2 cm .
3

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