Page 6 - 1202 Question Bank Additional Mathematics Form 5

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2. The area of a sector KOL with centre O and a radius Given that OA : OP = 1 : 3, ∠POQ = —π rad and
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of 11 cm is 160 cm . OA = 15 cm, find
2
(a) Find ∠KOL, in radians. [2 marks] (a) the perimeter of the area covered by the paper,
(b) If the sector KOL is folded to form a cone, find [3 marks]
the base radius of the cone. [3 marks] (b) the area of the paper used. [2 marks]
Answer: Answer:
(a) (a)

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(b)
(b)

3. Given AOB is a sector of a circle with centre O and a
radius of r cm where ∠AOB = θ rad.
(a) Show that the length of the chord AB is 5. The diagram shows a sector AOB with centre O and a
θ
2r sin —. [2 marks] SPM radius of 15 cm.
2 CLONE
(b) Given r = 5 cm and ∠AOB = 1.2 rad, find the A
difference in length between the arc length AB
and the chord AB. [3 marks] B
15 cm
Answer: C
(a) θ

O
Given that C divides the line OB in the ratio 3 : 2 and
the length of chord AB is 10 cm. Find
(a) the angle θ, in radians, [2 marks]
(b) (b) the perimeter of the shaded region. [3 marks]
Answer:
(a)

4. The diagram shows a paper fan consisting of two
sectors, POQ and AOB. The shaded region is covered
by paper.
P (b)

A

O
B
Q

2 Question 2:
SOS TIP (b) Find the arc length of the sector. When the sector is folded, the arc length of the sector is the circumference of the base of the cone.
Question 5:
2
2
2
Use the cosine rule, a = b + c – 2bc cos θ
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01_1202 QB AMath F5.indd 2 02/12/2021 8:44 PM