Page 76 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure
2. The diagram below shows a circle with centre O. 5. The diagram below shows a box being elevated
SPM to the upper level of a building using a pulley with
2018
P diameter of 15 cm. HOTS Applying
3k cm
Q θ rad O

R
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PQ and RQ are the tangents to the circle at points
P and R respectively. Given that the minor arc
length PR is 9 cm and OQ = 5k cm, express in
terms of k Calculate
(a) the angle q, (a) the height, in cm, of the box when the pulley is
(b) the area, A, of the shaded region. rotated by 160°,
(b) the rotating angle, in radian, of the pulley if the
box is elevated 0.35 m.
3. The diagram below shows a sector BCD with [Use π = 3.142]
SPM centre C and radius r cm inscribed in the rhombus
2019
ABCD. 6. The diagram below shows a circle with centre O
B and radius r cm.

A rad C
2
J
D O
2 rad
K
Given the area of sector BCD is 8 cm , express in
2
terms of α,
(a) the radius, r, in cm, If the major arc length JK is 10 cm, express
(b) the perimeter, in cm, of the shaded region. (a) α in terms of r,
(b) the area, in cm , of minor sector JOK in terms of
2
π and r.
4. The diagram below shows a way to treat a broken
femur to reduce pain and bleeding. The angle 7. The diagram below shows the front view of a tent
between the leg and torso is an inclined angle θ at a comping area. DE and FG are the arcs of
whereas the acute angle between the leg and the circles with centres G and D respectively whereas
bed is the reference angle, α. EOF is a sector of a circle with centre O.

HOTS
Analysing

E F Form 5
O

θ
30 30
D 2 m G
If the inclined angle q is 135°, calculate the value of Calculate the area, in m , for the whole diagram.
2
α, in radian. [Use π = 3.142]
[Use π = 3.142]

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