F4 AM Circular Measure

8/12/2019 F4 AM Circular Measure

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ADD MATHS CIRCULAR MEASURE

K.Y.LIEW

[email protected]

016-6745 242


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1) Convert each of the following angles into degrees.(a)

rad.

(b) rad.

(c) rad.(d) rad.(e)

rad.


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2)Convert the following into radian in terms of .(a) (b) (c) (d) (e)


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3)Convert the following to radian without stating in terms of ,(a) (b) (c) (d)


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4)Find the length of the minor arc AB of each of the following.(a) (b)

(c) (d)

(e)


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5)Find the length of the minor arc AB of each circle in Q4.


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6)Find the anglex, in radian, for the following diagrams.


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7) The length of an arc of a circle with radius of 18cm is 24cm. Find the anglesubtended by the arc at the centre of the circle, in degrees and minutes.

8)The length of an arc of a circle is twice the length of the radius. Find theangle subtended by the arc at centre of the circle, in radians.


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9)Calculate the perimeter of the shaded region of the followings.(a) (b) (c)

(e) (e)


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10) Find the area of the minor sector of the following diagrams.(a) (b)

(c) (d)


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11)Find the angle , in radian, or radius r,in cm, of each of the followingdiagrams.

(a) (b)

(c) (d)


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12) A sector of a circle with radius 6 cm has an area of 14.4 cm2. Find theangle of the sector of the circle in degrees and minutes.

13) Find the radius of a sector if the angle subtended at centre of the circleis and the area of the sector is 13.1 cm2.


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14) Diagram shows a sector of a circle with centre Oand radius 10 cm. Thelength of the chordABis 16 cm. Find

(a) AOB in radian,(b) The area of the shaded region.


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15) Diagram shows a sector of a circle with centre Oand radius 10 cm. Thelength of chordABis 12 cm. Find

(a) AOB in radian,(b) The area of the shaded region.


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16) Diagram shows a semicircle with centre Oand a diameter of 10 cm.The length of chordBCis 8 cm. Find

(a) AOB in degrees and minutes,(b) The area of the triangle OBC,(c) The area of the shaded region.


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17) Diagram shows a major sectorPABCof a circle with centrePand asemicircle OAPCwith centre Oand radius 4 cm. Find the

(a) Area of the major sectorPABC,(b) Area of triangleAPC,(c) Area of the shaded region.


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18) Diagram below shows two sectors of a circle with centre O. Given thatOD:DC= 3:2, find the area of the shaded region ABCD.


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19) Diagram shows the sector OAB of a circle with centre O. Given thatOM = ON = 5 cm. Find

(a) Angle , in radian,(b) Area of the shaded region.


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20) Diagram shows two circles with centre OandPand with radius 9 cmand 4 cm respectively. Both circles touches atN. A tangent touches both

circles atAandB. Find(a) AON , in radian,(b) BPN , in radian,(c) The area of the shaded region.


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21) Diagram shows a circlePQRTwith centre Oand radius 6 cm.EQFis atangent to the circle at Q. The straight lines,EOandFO, intersect the circle

atPandRrespectively. OPQRis a rhombus.ELFis an arc of a circle withcentre O. Calculate

(a) The angle a, in terms of ,(b) The length, in cm, of the arcELF,(c) The area, in cm2, of the shaded region.


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22) Diagram shows a circle,HPUQKwith centre Oand radius 8 cm.HOKis an arc of a circle with centre U. GivenPQis parallel toHK,PQ= 8 cm and

120HOK = .(a) Find POQ .(b) Calculate the area of the segmentPQU.(c) Show that the perimeter of the shaded region is 88 3 8

3+ + cm.

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F4 AM Circular Measure