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CHAPTER 8 CIRCULAR MEASURE FORM 4
PAPER 1
1. Diagram 1 shows a secorAOBwih ce!re O.
The "e!gh o# he arcABis $.% cm a!& he 'erimeer o# he
secorAOBis (% cm. Fi!& he
)a"*e o# + i! ra&ia!. , - marks
(. Diagram ( shows a circ"e wih ce!re O.
/i)e! ha he "e!gh o# he ma0or arcRSis 4% cm + #i!& he "e!gh
+ i! cm + o# he ra&i*s.
Use 2 -.14( 3 , - marks
-
O
A
B
DIA/RAM 1
O
R
S
5.-% ra&
DIA/RAM (
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CHAPTER 8 CIRCULAR MEASURE FORM 4
-. Diagram - shows a circ"e wih ce!re O.
The "e!gh o# he mi!or arc is 1% cm a!& he a!g"e o# he ma0or
secorPORis (85o.
Usi!g
2 -.14( + #i!&
a3 he )a"*e o# + i! ra&ia!s.
/i)e 6o*r a!swer correc o #o*r sig!i#ica! #ig*res 373 he "e!gh+
i! cm+ o# he ra&i*s o# he circ"e . , -marks
4. Diagram 4 shows secor OPQwih ce!re Oa!& secorPXYwih
ce!reP.
/i)e! ha OQ 2 (5 cm +PY2 8 cm + XPY2 1.1 ra&ia!s a!& he
"e!gh o# arcPQ2 14cm +
ca"c*"ae
a3 he )a"*e o# + i! ra&ia! +
73 he area+ i! cm(+ o# he sha&e& regio! . , 4 marks
45
O
P
R
DIA/RAM -
P
Y
QO
DIA/RAM 4
X
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CHAPTER 8 CIRCULAR MEASURE FORM 4
%. Diagram % shows a secor QORo# a circ"e wih ce!re O. I is
gi)e! haPS2 15 cm a!& QP2PO2 OS2 SR2 cm.
Fi!&
a3 he "e!gh+ i! cm+ o# he arc QR+ 73 he area+ i! cm(+ o# he
sha&e& regio!.
,4 marks
S
R
P
Q
1.97 rad
0
DIA/RAM %
. Diagram shows a circ"e wih ce!re Oa!& ra&i*s 1( cm.
/i)e! haA+Ba!& Care 'oi!s
s*ch ha OA2ABa!&OAC2 5o+ #i!&
,Use
2 -.14( a3 BOC+ i! ra&ia!s+
73 he area+ i! cm(+ o# he co"o*re& regio!
,4 marks
C
B
A
O
DIA/RAM
41
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CHAPTER 8 CIRCULAR MEASURE FORM 4
PAPER 2
1. Diagram 1 shows he secorsAOB+ ce!re Owih ra&i*s 1% cm.
The 'oi! Co! OAis s*ch
ha OC9 OA2 - 9 % .
Ca"c*"ae
a3 he )a"*e o# + i! ra&ia!+ , - marks
73 he area o# he sha&e& regio!+ i! cm(. , 4 marks
(. Diagram ( shows a circ"ePQRT+ ce!re Oa!& ra&i*s 15
cm.AQBis a a!ge! o he circ"e
a Q. The sraigh "i!es+AOa!&BO+ i!ersec he circ"e
aPa!&Rres'eci)e"6. OPQRis a
rhom7*s.ACBis a! arc o# a circ"e+ ce!re O.
Ca"c*"ae
a3 he a!g"e + i! erms o# + , ( marks
73 he "e!gh+ i! cm+ o# he arcACB+ , 4 marks
c3 he area+ i! cm(+ o# he sha&e& regio!. , 4 marks
4(
O
C
B
DIA/RAM 1
A
O
ra&
Q
RP
A
C
B
T
DIA/RAM (
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CHAPTER 8 CIRCULAR MEASURE FORM 4
-. Diagram - shows a secorAOBo# a circ"e + ce!re O. The
'oi!P"ies o! OA+ he 'oi! Q
"ies o! OBa!&PQis 'er'e!&ic*"ar o OB. The "e!gh o# OPis
cm a!&AOB2 .rad
I is gi)e! ha OP: OA2 - 9 % . Usi!g 2 -.14( 3
Ca"c*"aea3 he "e!gh+ i! cm+ o#PA+ , 1 mark
73 he 'erimeer+ i! cm+ o# he sha&e& regio!+ , %
marks
c3 he area+ i! cm(+ o# he sha&e& regio!. , 4 marks
4. I! Diagram 4+PBQ is a semicirc"e wih ce!re Oa!& has a
ra&i*so# 15 m.RAQis a secor o# a circ"e wih ce!reAa!& has a
ra&i*s o# 1 m .
I is gi)e! haAB2 15 m a!& BOQ2 1.8$ ra&ia!s. , Use 2
-.14(
4-
O
PA
:Q
rad
DIA/RAM -
P A O Q
R
B
DIA/RAM 4
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CHAPTER 8 CIRCULAR MEASURE FORM 4
Ca"c*"ae
a3 he area + i! m(+ o# secorBOQ , ( marks
73 he 'erimeer+ i! m + o# he sha&e& regio! + , 4
marks
c 3 he area + i! m(+ o# he sha&e& regio! . , 4 marks
%. Diagram % shows a circ"e+ ce!re Oa!& ra&i*s (5 cm
i!scri7e& i! a secorPAQo# a circ"e+
ce!reA. The sraigh "i!es+APa!&AQ+ are a!ge!s o he circ"e a
'oi!Ba!& 'oi! C+
res'eci)e"6.
,Use 2 -.14( Ca"c*"ae
a3 he "e!gh+ i! cm+ o# he arcPQ+ ,% marks
73 he area+ i! cm(+ o# he sha&e& regio!. ,% marks
DIA/RAM %
44
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CHAPTER 8 CIRCULAR MEASURE FORM 4
. Diagram shows wo circ"es. The "arger circ"e has ce!rePa!&
ra&i*s (4 cm. The sma""er circ"e
has ce!re Qa!& ra&i*s 1 cm. The circ"es o*ch a 'oi!R.
The sraigh "i!eXYis a commo!
a!ge! o he circ"es a 'oi!X a!& Y. ,Use 2 -.14(
/i)e! ha XPQ2 ra&ia!s+
a3 show ha 2 1.-$ o wo &ecima"s '"aces3+ ,( mar;s
73 ca"c*"ae he "e!gh+ i! cm+ o# he mi!or arc YR+ ,- mar;s c3
ca"c*"ae he area+ i! cm(+ o# he co"o*re& regio! ,% mar;s
DIA/RAM
4%
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CHAPTER 8 CIRCULAR MEASURE FORM 4
A
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CHAPTER 8 CIRCULAR MEASURE FORM 4
A 1% cos-5o3 > 1% 3
> 4
(%.% 1
-c
PQ2 4.% cm + OQ2 cos -5o
3-5cos3%.4(
1
31%
(
1 ( o
-
41.-8 1
4a 8$.1315
(
1 (1
-.8 1
47151.8$3 > 1 38$.1 > -
4%.51 1
4c 313
(
18$.1315(
138$.131(
1 (( -
-.- 1
4$
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CHAPTER 8 CIRCULAR MEASURE FORM 4
%a
o
OA-5si!
(5 = 1
OA2 45 cm 1
PA2 5 cm 1
arcPQ2 5
-
1
(.84 1
%7
AB2 (( (545 1
(53(545(
1
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(3(5
(
1
8385
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1,( (((( -
-%4.%1- 1
acos 2
45
81
1.-$ ra& 1
7
YQP
2 -.1
1arc YR2 1 -.1 3 1
(8.-$ 1
c
((845 =XY
2 -.1
1
1.-3?31(
13(43-.1
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11.-3(41
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