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50/1MathematicsPaper 1July2009

1¼ hours Set 1JABATAN PEAJA!AN PE!A"

PEN#A#AN MENEN$A% !EN&A% 2009

ANS'E! T( S)(!E

2009 PM! *(!E)AST PAPE!

MAT%EMAT#)SPaper 1

1 hour 15 minutes

&( N(T (PEN T%#S +,EST#(N PAPE! ,NT# -(, A!E T(& T( &( S(

1. This question paper consists of .0 questions.

2. Answer all questions

3. Answer each question by blackening the correct space on the answer sheet

4. Blacken only oe space for each question.

5. If you wish to change your answer, erase the blackened mark that you have made.

Then blacken the space for your new answer.

6. The diagrams in the questions provided are not drawn to scale unless stated.

7. You may use a nonprogrammable scientific calculator.

8 A list of formulae is provided.

This uestio paper cosists 20 prite paes3

55



The following formulae may be helpful in answering the questions. The symbols gien are theones !ommonly use".

!EAT#(NS

1.m n m n

a a a +

× =

2. m n m na a a −÷ =

3. # $m n mna a=

4. %istan!e & 2 22 1 2 1# $ # $ ! ! y y− + −

5. 'i"point

# ( $ ! y & +

2

21 ! ! (

+

2

21 y y

6. )erage spee" &"istan!e traelle"

time ta*en

7.sum of "ata

'ean &number of "ata

8. Pythagoras Theorem2 2 2c a b= +

S%APE AN& SPA)E

1. )rea of re!tangle & length×

wi"th

2. )rea of triangle &1

base height2

× ×

3. )rea of parallelogram & base height×

4. )rea of trape+ium &1

sum of parallel si"es height2

× ×

56



5. ,ir!umferen!e of !ir!le & 2d r π π =

6. )rea of !ir!le & 2r π

7. ,ure" surfa!e area of !ylin"er & 2 rhπ

8. -urfa!e area of sphere & 24 r π

. /olume of right prism & !ross se!tional area × length

10. /olume of !uboi" & length × wi"th × height

11. /olume of !ylin"er & 2r hπ

12. /olume of !one & 21

3r hπ

13. /olume of sphere & 343

r π

14. /olume of right pyrami" &1

3× base area × height

15. -um of interior angles of a polygon & # 2$ 180n − × o

16.ar! length angle subten"e" at !entre

!ir!umferen!e of !ir!le 360=

o

17.area of se!tor angle subten"e" at !entre

area of !ir!le 360=

o

18. -!ale fa!tor( k & "A

"A

′

1. )rea of image & 2 area of obe!tk ×

Answer all questions.

57



13 The number 345 678 is written as 350 000 when it is roun"e" off to theA nearest tenB nearest hun"re") nearest thousan"& nearest ten thousan"

23 hi!h of the following fra!tions has alue greater than4

3

A8

7

B3

2

)2

1

&7

5

43 press 33100000

168 as a "e!imal

A 33.168B 33.0168) 33.00168& 33.000168

.3 Table 4 shows the temperature for four towns on a parti!ular "ay.

To Temperature 67)8 2 3 9 8

Table 4

hi!h town was the !ol"est on that "ayA B

) & 9

53 %iagram 5 shows a sequen!e of prime numbers.

17( 1( m( n( 31

%iagram 5

in" the alue of m : n.

A 44

58



B 48

) 52

& 56

3 %iagram 6 shows some fa!tors of 54.

%iagram 6

;"entify three other fa!tors of 54.A 2( 3( 18

B 2( 18( 2

) 3( 4( 8

& 3( 4( 18

:3 Tharma<s Poultry arm pro"u!es 000 eggs a "ay. ;f 1= of the eggs are bro*en( !al!ulatethe number of bro*en eggs pro"u!e" in a wee*.

A 00

B 630

) 180

& 0

;3 -waran ,onstru!tion ,ompany built a roa" from >ampung 'enora to >ampung elam( a"istan!e of 5.54 *m. ;t then built a roa" !onne!ting >ampung elam to >ampung )man( a"istan!e of 6.78 *m. ,al!ulate the total length of the roa" !onstru!te" by the !ompany

A 10 *m 320 m

B 11 *m 320 m

) 12 *m 320 m

& 13 *m 320 m

93 ;n %iagram ( )?, is a straight line.

5

%iagram

1 54 6 27



,al!ulate the alue of !.A 55

B 60

) 70

& 75

103 ;n %iagram 10 ( P@A-T is a pentagon an" -TB is a straight line

%iagram 10in" the alue of p # q # r # s.

A 220

B 400

) 500

& 540

113 %iagram 11 shows a polygon.

%iagram 11

in" the alue of !.A 41

60

T

p°

@

-

A

40°B

P

q°

r

°

s°

%

,

122°

75°

3 !°

?

) 2 !°

3 !°

115°



B 51

) 55

& 61

123 %iagram 12 shows two regular polygons.

%iagram 12in" the alue of m.

A 120

B 132

) 144

& 228

143 ;n %iagram 13( P@A is a rightangle" triangle( A/B is an equilateral triangle an" @A/ is

a square.

%iagram 13,al!ulate the perimeter( in !m( of the whole "iagram.

61

/

m°

C@

T

A

B-

12 !m

5 !m @

/

B

A

P



A 48

B 65

) 66

& 102

1.3 %iagram 14 shows two rightangle" triangles( CDE an" /E.

%iagram 14

in" the area in !mF( of the sha"e" region.A 105

B 75

) 35& 30

153 %iagram 15 shows the plan of an or!har".

%iagram 15

in" the area( in m2

( of the whole "iagram.A 70

62



B 0

) 100

& 130

13 hi!h of the following geometri! soli" is a !one

A

B

)

&

1:3 ;n %iagram 17( the olume of the !ylin"er is equal to the olume of the !one..

%iagram 17,al!ulate the height of the !ylin"er

A 21 !m

B 16 !m

) 14 !m& 7 !m

63



1;3 %iagram 18 shows a soli" pyrami" with a square base P@A- an" height of 4 !m. The areaof the base is 36 !m2.

%iagram 18

in" the total surfa!e area( in !m2( of the soli".A 144B 6) 51

& 48

193 %iagram 1 shows a prism with a right angle" triangle as its uniform !ross se!tion.

%iagram 1,al!ulate the total surfa!e area of the prism.A 120 !mF

64



B 156 !mF) 160 !mF& 180 !mF

203 %iagram 20 shows a re!tangle "$%& an" some !onstru!tion lines ma"e by a stu"ent.

The stu"ent is !onstru!ting the lo!us of C su!h that(A P-C & A-C

B CP & C-) C- & -P& C- is equi"istant from line P@ an" line -A

213 ;n %iagram 21 , ' is the !entre of the !ir!le.

%iagram 21

in" the alue of !.A 115B 110) 80& 50

223 ;n %iagram 22( PTA is a "iameter of the !ir!le an"-T@ is a straight line.

65

%iagram 20



%iagram 22in" the alue of !.A 55

B 40

) 35

& 30

243 %iagram 23 shows a !ir!le with !entre G. PT( @B( A/ an" - are "iameters of the !ir!les.

%iagram 23

hi!h of the following minor ar!s is the longestA TB

B B/

) P

& A-

66



2.3 ;n %iagram 24( G is the !entre of the bigger !ir!le with a ra"ius of 7 !m. The smaller !ir!le passes through G an" tou!hes the bigger !ir!le.

%iagram 24

Bsing H &7

22( !al!ulate the area in !mF( of the sha"e" part.

A 38.5B 77.0

) 115.5

& 154.0

253 ;n %iagram 25( P@A-T is a trape+ium( @-T an" @A- are rightangle" triangles.

%iagram 25in" the length( in !m( of @A.A 12

B 13

) 14

& 15

23 ;n %iagram 26( ),% is the image of )? un"er an enlargement with !entre ).

67

- 5 !m

P@

A T

16 !m

20 !m

6 !m

3 !m

)

%

, ?6 !m



%iagram 26

ien ,% & 6 !m( !al!ulate the length( in !m( of ?.A 3

B 4) 6

&

2:3 ien 3 =+ y ! an" 632 =− y ! ( !al!ulate the alue of . !A 2

B 3

) 4

& 5

2;3 -ole the following inequality.

4

3y : 3 I

4

3

A y I 3B y I 3) y J 3& y J 3

293 ;n %iagram 2( ? is the mi"point of the straight line ),.

%iagram 2

in" the alue of p.

A B 6) 3& 2

68



403 %iagram 30 shows fie points on a ,artesian plane.

%iagram 30hi!h of the following has the same "istan!e as GPA G@B GA ) G-& GT

413 %iagram 31 shows a re!tangle P@A-. PTB is an ar! with !entre @ an" B/ is an ar! with!entre A.

%iagram 31

6



in" the perimeter in !m( of the sha"e"region.

# Bse π &7

22$

A 54

B 61

) 70

& 82

423 Table 32 shows the registration fees for an eamination

?asi! fee A'150ee per written paper A'35ee per oral assessment A'40ee per pra!ti!al assessment A'38

Table 32

'imi registers for 8 written papers( 3 oral assessments an" 3 par!ti!al assessments whereasAoger registers for 7 written papers( 2 oral assessments an" 3 pra!ti!al assessmentsThe "ifferen!e in the total registration fee pai" by 'imi an" Aoger is

A A'75

B A'5

) A'120

& A'150

443 The s!ores obtaine" by )mani an" ?ee Keng in a game are in the ratio of 7 L 4 ( while theratio of s!ores obtaine" by ?ee Keng an" ,eline is 6 L 5. in" the ratio of s!ores obtaine" by)mani( ?ee Keng an" ,eline.

A 7 L 12 L 5

B 7 L 12 L 10

) 21 L 12 L 10

& 21 L 12 L 15

70



4.3%au" "roe from >luang to ;poh. 9is ourney was epe!te" to ta*e 6

2

1 hours. 9e starte"

his ourney at 7.40 a.m. an" arrie" ;poh 20 minutes late. hat time "i" %au" arrie ;poh

A 2.40 p.m.

B 2.30 p.m.

) 2.10 p.m.& 1.50 p.m.

45 %iagram 35 is a pie !hart showing the number of i!e !ream sol" at a stall on a !ertain "ay.

%iagram 35

in" the alue of ! : y.

A 68M

B 135M

) 153M

& 163M

43 ;n %iagram 36( the bar !hart below shows the number of stu"ents in three !lasses.

71



%iagram 36

hi!h of the following statement is trueA The total number of stu"ents in three !lasses is 125

B The total number of girls in ,lass ) an" ,lass ? is the same.

) The number of boys in this s!hool is greater than the number of girls.& The number of girls in !lass , is greater than the number of girls in !lass ?.

4:3 Table 37 shows the number of tea!hers in fie housing estates.

9ousing estates ) ? , % Number of tea!hers 10 13 p 7 5

Table 37The mo"e is ?.in" the possible alue of p.A 12

B 14

) 25

& 35

4;3 Table 38 shows the s!ores in a game

-!ore 0 1 2 3 4 5requen!y 5 7 2 6 4 6

Table 38The me"ian s!ore isA 1

B 2) 3

& 4

493 Table 3 shows the alues of ariables an" y for the fun!tion of y ( )!* + *!

! 2 1 0 1 2 y m 5 0 1 8

Table 3in" the alue of m.

72



A 16

B 8

) 8

& 16

.03 hi!h of the following graphs represents y & ! : 6

A

B

)

&

73



EN& (* +,EST#(N PAPE!

50/1MathematicsPaper 1July20091¼ hours

Set 2

JABATAN PEAJA!AN PE!A"


ANS'E! T( S)(!E2009 PM! *(!E)AST PAPE!

MAT%EMAT#)SPaper 1

1 hour 15 minutes


1. This question paper consists of .0 questions.

2. Answer all questions

3. Answer each question by blackening the correct space on the answer sheet

4. Blacken only oe space for each question.

74



5. If you wish to change your answer, erase the blackened mark that you have made.

Then blacken the space for your new answer.

6. The diagrams in the questions provided are not drawn to scale unless stated.

7. You may use a nonprogrammable scientific calculator.

8. A list of formulae is provided.

This uestio paper cosists 21 prite paes3


!EAT#(NS

1. m n m na a a +× =

2. m n m na a a −÷ =

3. # $m n mna a=

4. %istan!e & 2 22 1 2 1# $ # $ ! ! y y− + −

5. 'i"point

# ( $ ! y & +

2

21 ! ! (

+

2

21 y y

6. )erage spee" &"istan!e traelle"

time ta*en

7. sum of "ata'ean &number of "ata


S%APE AN& SPA)E

1. )rea of re!tangle & length × wi"th75




base height2

× ×



sum of parallel si"es height2 × ×









3r hπ


3r π


3× base area × height


16. ar! length angle subten"e" at !entre!ir!umferen!e of !ir!le 360

=o


area of !ir!le 360=

o

18. -!ale fa!tor( k & "A

"A

′


76



77



Answer all questions.

13 hi!h of the following numbers when roun"e" off to the nearest hun"re" thousan" be!omes8 700 000 A 8 754 321B 8 654 321) 8 643 210& 8 554 321

23 Table 2 shows the types of item that -arah bought from a sun"ry shop.

Types of item Pri!e per *g @uantity;tem ) A'30 4.5 *g;tem ? A'1 2 *g 500 g;tem , A'18 500 g

Table 2

-arah has A'250.009ow mu!h money is left after she has pai" for all the itemsA A'61.75B A'5.85) A'105.50& A'58.50

43 )li ha" 300 "urians. 9e manage" to sell6

5 of the "urians . Kater he gae 20 of the

remaining "urians to his frien"s. ,al!ulate the per!entage of the "urians that he has left.A 50B 16.67) 10& 6.67

.3 %iagram 4 is part of a number line.

%iagram 4

78

P 12 0 @



hat is the alue of P an" @

A P & 18 ( @ & 18

B P & 14 ( @ & 12

) P & 12 ( @ &

& P & 6 ( @ & 18

53 The original pri!e of a Tshirt is A'24.00. The selling pri!e of the Tshirt is12

11 of its

original pri!e. -wee Kan uses2

1of her saings to buy the Tshirt. hat was her

saings before she bought the Tshirt

A A'22.00

B A'28.80) A'44.00

& A'3.60

3 hi!h of the following is the !ommon multiple of 3 an" 5A 8

B

) 25& 45

:3 )li has 5 rolls of rope. a!h roll is2

13 m long. 9e use" 1.6 m of the rope from ea!h roll.

in" the length of the remaining rope.

A .15 m

B .05 m

) .00 m

& 8.05 m

;3 ) bus starte" its ourney from >uala Kumpur an" arrie" at Oohor ?ahru at 4.45 a.m. on the

net "ay. ;f the ourney too*4

15 hours( the bus left >uala Kumpur at

A 1000 hours

B 2200 hours) 2230 hours

7



& 2330 hours

93 ;n %iagram ( )?, is a triangle

in" the alue of !.A 15

B 18

) 20

& 25

103 ;n %iagram 10( pentagon P<@<A<-<T is the image of pentagon P@A-T un"er an enlargement

80-<

T<

P<

A<

@<

P @

TA

-

%iagram



%iagram 10in" the s!ale fa!tor of this enlargement.A 1

B 2

) 3

& 4

113 %iagram 11 shows a regular heagon.

%iagram 11in" the alue of yA 30

B 35

) 40

& 45

123 ;n %iagram 12( P@AT are fie erti!es of a regular polygon.

81

y°

3 !° !°

P

@ A B

-

T



%iagram 12in" the number of si"es of the polygon

A 6

B 8

) 10

& 12

143 The !ost of a metre of fen!ing is A'13.60. The /ision 9ome for the Poor wants to fen!e are!tangular !ompoun" 25 m by 75 m. 9ow mu!h is the !ost of fen!ing the re!tangular!ompoun"

A A'2 520

B A'2 620

) A'2 720

& A'2 820

1.3 ;n %iagram 14( ),% is a rightangle" triangle. The area of triangle )?% is 168 !mF.

in" its height( h in !m.A 11

B 14

) 20

& 24

153 ;n %iagram 15( %9 is a parallelogram an" 9 ia a straight line.

82

h !m

,15!m

14!m) ?

%

%iagram 14



%iagram 15

ien % & 12 !m an" 9 & 15 !m. ;f the areaof triangle is 6 !mF( fin" the area of thewhole "iagram.

A 40

B 54

) 60

& 6

13 %iagram 16 shows the net of a geometri! soli".

%iagram 16

Name the geometri! soli".A Aight prism

B !uboi"

) pyrami"

& !one

83

9

%



1:3 %iagram 17 shows two !ontainers in the shape of a !uboi" an" right prism.

The !uboi" is fully fille" with water. )ll the water in the !uboi" is then poure" into the right prism. The base area of the right prism is 66 !m2 . ,al!ulate the height( in !m of the waterleel in the right prism.

A 13

B 21

) 88

& 66

1;3 )minah is4

34 years ol". ?ala is

12

1 years ol"er than )minah. ,hee 'eng<s age is

2

12

times the sum of the ages of )minah an" ?ala. hat is ,hee 'eng<s age

A8

711

B6

513

)3

116

&24

1146

193 ;n %iagram 1( OGK is a "iameter of the !ir!le O>K' with !entre G. 'KN is a straight line.

84

6 !m

21 !m

11 !m

%iagram 17



%iagram 1in" the alue of !.A 20

B 25

) 30

& 70

203 ;n %iagram 20( % is a !y!li! qua"rilateral.

%iagram 11

in" the alue !.A 50M

B 60M

) 80M& 100M

213 ;n %iagram 21( P@A an" -TB are two !ir!les with a!ommon !entre( G. P-GBA is a straight line.

85



%iagram 21

ien that P- & -G & 4 !m( !al!ulate the area( in !mF( of the sha"e" region.A 8H

B 16H

) 32H

& 64H

223 ;n %iagram 22( G is the !entre of the !ir!le an" PGA is a "iameter of the !ir!le.P@A is a rightangle" triangle.

%iagram 22

in" the area( in !mF( of the !oloure" region.A 25H 24

B 25H 30

) 25H 48

& 100H 48

243 ;n %iagram 23( P@A- is a !y!li! qua"rilateral. NP@ is a straight line an" G is the !entre of the !ir!le.

86



%iagram 23

in" the alue of !.A 50M

B 60M

) 70M

& 120M

2.3 %iagram 24 shows a triangular pattern on a wall.

%iagram 24

) tin of paint is require" to paint an area of 5 mF.9ow many tins of paint if nee"e" to paint the surfa!e of the triangleA 12

B 24

) 25

& 32

253 hi!h of the following "iagram shows line CD nonparallel to line P@

A3

87

C

D

P

@

70G

70G



B3

)3

&3

23 ;t is gien that 1732 −=− y ! an" 4−= ! . ,al!ulate the alue of y.

A 3

88

70G

70G

C

D

P

@

70G

70G

C

D

P

@

110G

110G

C

D

P

@



B 4

) 5

& 6

2:3 %iagram 27 represent two simultaneous linear inequalities on a number line.

%iagram 27

hi!h of the following inequalities is the solution for both of the inequalities on the numberline

A 3 Q Q 2

B 3 I I 2

) 3 Q I 2

& 3 I Q 2

2;3 ;n %iagram 28( , are points on a ,artesian plane.

%iagram 28

% is the mi"point of ,. The !oor"inates of % areA #1( 3$B #2( 3$) #1( 3$& #2( 3$

293 %iagram 2 shows points O( >( K an" ' mar*e" on a gri" of equal squares with si"es of1 unit.

8

<. <4 <2 <1 0 1 2



%iagram 2

hi!h points are equi"istant from point GA ' an" OB ' an" > ) > an" K& > an" O

403 ;n %iagram 30( , is the !entre of the !ir!le an" )?, is a rightangle" triangle.

,al!ulate the perimeter of the whole "iagram.A 60.2 !mB 72.5 !m) 75.2 !m& 75.5 !m

413 -ally( -hirley an" -usan ineste" a sum of money in a boo*store in the ratio 7 L 5 L 6.The total amount ineste" by -ally an" -usan was A'624. fin" the total amount ineste" by-ally an" -hirley.

A A'864

B A'576) A'288

0

%iagram 30



& A'48

423 Table 32 shows the pri!e of mangoesteens sol" at four stalls( ( C( D an" E

' =3 mangoesteens for A' 15

5 mangoesteen for A' 20

2 mangoesteens for A' 8

5 mangoesteens for A' 15

- >3 mangoesteens for A' 216 mangoesteens for A' 42

5 mangoesteens for A' 258 mangoesteens for A' 48

Table 32

hi!h stall sells mangoesteens at a pri!e that is proportional to the number ofmangoesteens

A

B C

) D

& E

443 Table 33 shows the number of !omputers sol" by a !ompany from Oanuary to )pril

'onth Oanuary ebruary 'ar!h )pril Number of !omputer sol" 1450 1800 1650 1600

Table 33

?ase" on the "ata in table aboe( whi!h of the following statements is ot true A The "ifferen!e between the highest an" the lowest number of !omputers sol" in a month

is 350B The mean number of !omputers sol" for a month oer this four month perio" is 1625

) The total number of !omputer sol" after ebruary is 3250

& The number of !omputers sol" in )pril is equialent to 30= of the total number of!omputer sol" oer the four month perio"

4.3 %iagram 34 is a bar !hart whi!h shows the number of boo*s sol" by a boo*shop in simonths

1



%iagram 34

;f the number of boo*s

sol" in 'ar!h is 20 000(

fin" the number of boo*s

sol" in ebruary

A 8 000

B 10 000

) 12 000

& 16 000

453 %iagram 21 is a pie !hart showing the types of fruits in a trolley.

%iagram 21There are 252 rambutans.

9ow many mangosteens are in the trolley

A 8B 70

) 42

& 28

43 The line graph in %iagram 36 shows the in!ome of a haw*er in 4 months.

2



%iagram 36,al!ulate the total in!ome in 4 months.A A' 6505

B A' 6500

) A' 6250

& A' 6600

4:3 Table 37 shows the numbers of boo* rea" by Eul*ifli in 5 months.

'onth Oan eb 'a! )pr 'ay Number of boo*s 5 3 2 6 4

Table 37

,al!ulate the mean number of boo*s rea" by Eul*ifli in 5 months.A 3

B 4

) 5

& 6

3



4;3 %iagram 38 shows a graph of a fun!tion on a ,artesian plane.

%iagram 38

The equation that represents the fun!tion isA y & 2

B y &

) y & : 2

& y & : 2

493 Table 3 shows the alues of ariables an" y for the fun!tion of y & 2 !2 : 1

! 2 1 0 1 2 y 7 s 1 1 t

Table 3

,al!ulate the alue of s : t A 1

B 6

) 7

& 8

4

2

2 24



.03 ;n %iagram 40 AB-/012 is a regular o!tagon with si"es 3 !m.

%iagram 40 3 is the lo!us of a point whi!h moes su!h that it is always equi"istant from point B an" . Y is the lo!us of a point whi!h moes su!h that its "istan!e from point 2 is always 3 !m.hi!h of the following points is the interse!tion of lo!us 3 an" lo!us Y

A ,

B

) )

&

EN& (* +,EST#(N PAPE!

5

B -

A

/

0 1

2



50/1MathematicsPaper 2July20091? hours

Set 1

JABATAN PEAJA!AN PE!A"


ANS'E! T( S)(!E

2009 PM! *(!E)AST PAPE!

This uestio paper cosists 1; prite paes3

#N*(!MAT#(N *(! )AN&#&ATES

6

MAT%EMAT#)S

Paper 2

1 hour 45 minutes


4. This question paper consists of 20 questions.

*. Answer all questions. Answer all questions). 5rite your answers clearly in the spaces

provided in the question paper.

6. iagrams are not drawn to scale unless

stated.

7. The marks allocated are shown in brackets.

@uestion )llo!ate"'ar*s 'ar*sGbtaine"

1 2

2 2

3 3

4 3

5 2

6 2

7 3

8 3 3

10 3

11 3

12 3

13 4

14 3

15 2

16 5

17 418 5

1 2

20 3

Total



1. This question paper consists of * questions.

2. Answer all questions.

3. 5rite your answers clearly in the spaces provided in the question paper.

4. &how your working. It may help you to get marks.

5. If you wish to change your answer, neatly cross out the answer that you have done.

Then write down the new answer.

6. The diagrams provided in the questions are not drawn to scale unless stated.

7. The marks allocated for each question are shown in brackets.

8. A list of formulae is provided on pages ) and 6.

. A booklet of fourfigure mathematical tables is provided.

10. -alculators are not allowed.

11. This question paper must be handed in at the end of the e!amination.


7



!EAT#(NS

1. m n m na a a +× =

2. m n m na a a −÷ =

3. # $m n mn

a a=

4. %istan!e & 2 22 1 2 1# $ # $ ! ! y y− + −

5. 'i"point

# ( $ ! y & +

2

21 ! ! (

+

2

21 y y

6. )erage spee" & "istan!e traelle"time ta*en

7.sum of "ata



S%APE AN& SPA)E

1. )rea of re!tangle & length × wi"th


base height2

× ×




× ×



8









3r hπ


3r π


3

× base area × height


16.ar! length angle subten"e" at !entre

!ir!umferen!e of !ir!le 360=

o


area of !ir!le 360=

o

18. -!ale fa!tor( k & "A "A

′


13 ,al!ulate the alue of 42 ÷ 6 10 &

)nswer L



8 * marks9

23 ,al!ulate the alue of4.0

24.06×&

)nswer L

8 * marks9

43 a$ in" the alue of 3

216

1&

b$ ,al!ulate the alue of ( )[ ]23163 +− &

)nswer La$

b$

8 ) marks9

.3 -ole ea!h of the following equations La$ 2 # r 2 $ & 10 5r

b$2

6+ s & 4 s

)nswer La$

100



b$

8 ) marks9

53 %iagram 5 in the answer spa!e shows qua"rilateral AB-. -:< is the image of - un"er a refle!tion in the straight line ;< .Gn %iagram 5 in the answer spa!e( !omplete the image of qua"rilateral AB-.

)nswerL

%iagram 5 8 * marks9

3 %iagram 6 shows two qua"rilaterals( =;<> an" =:;:<:> <( "rawn on a gri" of equalsquares with si"es of 1 unit.

101



%iagram 6 =:;:<:> < is the image of =;<> un"er transformation " .%es!ribe in full transformation ".

)nswerL

R2 marksS

:3 a!torise !ompletely ea!h of the following epressions La$ !8 F !y4−

b$ k 6 F 183 −+ k )nswer La$

b$

102



8 * marks9

;3 -implify ea!h of the followinga$ ( )342 + !

b$ ( ) ( )443 −−−− ! ! )nswer L

a$

b$

8 ) marks 9

93press

−−mn

n

m

2

5

3 as a single fra!tion in its simplest form.

)nswer L

8 ) marks9

103 a$ -ole the inequality 8 : I 14 b$ Kist all the integer alues of whi!h satisfy the inequalities

2 3 I 11 an" 8 3

1 ≥ 7

)nswer La$

103



b$

8 ) marks9

143 The frequen!y table in table 13 shows the number of !ar owners in a housing par*.

Table 13

Aepresent all the "ata by "rawing a hori+ontal "ual bar !hart in the answer spa!e.

105

Types o@ )ars Numer o@ 'ome Numer o@ Ma

>an!il 15 5

Persona 18 22

aa 20 28



)nswer L

omen 'en

86 marks9

1.3 The "iagram 14 below shows the number of boo*s borrowe" from a s!hool library by 14stu"ents.

%iagram 14a $ Bsing the "ata( !omplete the frequen!y table below.

b$ -tate the me"ian.

)nswer La$

106

3 2 4 3 5 6 24 2 5 5 3 2 6



Table 17

The ! ais an" the y ais are proi"e" on the graph paper.

a$ ?y using a s!ale of 2!m to 5 units( !omplete an" label the y ais. b$ ?ase" on table 17( plot the points on the graph paper.!$ 9en!e( "raw the graph of the fun!tion.

86 marks9

110



)nswer L

111



!EAT#(NS

1. m n m na a a +× =

2. m n m na a a −÷ =

3. # $m n mn

a a=

4. %istan!e & 2 22 1 2 1# $ # $ ! ! y y− + −

5. 'i"point

# ( $ ! y & +

2

21 ! ! (

+

2

21 y y

6. )erage spee" & "istan!e traelle"time ta*en

7.sum of "ata



S%APE AN& SPA)E

1. )rea of re!tangle & length × wi"th


base height2

× ×




× ×




116



8* marks9

23,al!ulate the alue of 2.6 3.5 ÷

−

5

32 an" epress the answer as a "e!imal.

)nswer L

8) marks9

43 %iagram 3( in the answer spa!e shows two triangles( "$% an" ":$:%<( "rawn on a gri" ofequal squares. ":$:%< is the image of "$% un"er an enlargement.Gn %iagram 3 in the answer spa!e( mar* T as the !entre of enlargement.

)nswerL

118



%iagram 38* marks9

.3 %iagram 4 in the answer spa!e shows qua"rilaterals "$%& an" straight line C "rawn on agri" of equal squares.-tarting from the line 53 ( "raw qua"rilateral 53Y whi!h is !ongruent to qua"rilateral

"$%& .

)nswerL

11



%iagram 48* marks9

53 %iagram 5 in the answer spa!e shows triangle =;< "rawn on a gri" of equal squares. Gnthe "iagram in the answer spa!e( "raw the image of the triangle =;< un"er a rotation of0U !lo!*wise about the point ".

)nswerL

%iagram 5 8* marks9

3 ien that( 53=−

k

p epress p in terms of k

)nswer L

120

P



93 %iagram shows polygon AB-/0 "rawn on a gri" of equal squares.

.

%iagram Gn the gri" in the answer spa!e( re"raw the polygon using the s!ale of 1 L 2.

122

?)

,

%

)nswer L



8) marks9

103 The "iagram 10 in the answer spa!e shows a re!tangle( "$%& whi!h is "rawn on a gri" ofsquares with si"es 1 unit. ' is the mi"point of "$. 3, Y an" are three moing points in the"iagram.#a$ Gn the "iagram "raw

#i$ The lo!us of 3 su!h that it is !onstantly 3 units from line "$.#ii$#iii$

The lo!us of Y su!h that it is always 5 units from line %$.The lo!us of su!h that point from ' is always 5 units.

#b$ 9en!e( mar* with the symbol ⊗ the interse!tion of the lo!us of Y an" the lo!us of .

)nswer L

%iagram 10

86 marks9

113 pan" ea!h of the following epressions L6a8 2− ( )3+ ! : 5 ( )2+ !

68 ( )mn − ( )mn 3−)nswer L

a8

8

123

(

S

+P

!



8) marks9

123press

2

32 +a3

4−− a

as a single fra!tion in its simplest form.

)nswer L

8) marks9

143 ;n %iagram 13( triangles C=> an" C;< are similar.

%iagram 13-tate

#a$ The angle in triangle C;< whi!h !orrespon"s to ∠ C=> .

#b$ in" the length( in !m( of ;< .

)nswer L a$

b$

124

3 !m

2 !m6 !m

O

N

'K

>



8) marks9

1.3 Kist all the integer alues of k whi!h satisfy both the inequalities 2k : 2 ≥ 4 an" 4 k J 0

)nswer L

8) marks9

153 %iagram 15 is an in!omplete line graph whi!h shows the monthly sales of !hi!*ens in amar*et.

%iagram 15

125

'onth



#a$ ;n whi!h month the number of !hi!*ens sol" are the highest #b$ ;f the number of !hi!*ens sol" in Oanuary is half of that in 'a!( how many !hi!*ens

are sol" in Oanuary)nswer L

a$

b$

8) marks9

13 ?se the graph paper provided to answer this question.

Table 16 shows the alues of two ariables( ! an" y of a fun!tion.

! 2 1 0 1 2 3 4 y 4 0 2 2 0 4 10

Table 16

The !ais an" the yais are proi"e" on the graph paper.#a$ ?y using the s!ale of 2 !m to 2 units( !omplete an" label the yais.#b$ ?ase" on table 1( plot the points on the graph paper.

#!$ 9en!e( "raw the graph of the fun!tion.

126



)nswer L

5 marCsD

1:3 ?se of set squares and protractors are not allowed for this question.

127



%iagram 17 shows a qua"rilateral )?,%.

%iagram 17

Bsing only a ruler an" a pair of !ompasses( !onstru!t "iagram 17( beginning from theline )? proi"e" in the answer spa!e.

)nswer L

87 marks9

1;3 -implify #3hm 2 $ 4 #m 2 $ 1− ÷ h 7 m 3− .

)nswer L

8) marks9

193 in" the alue of 3 2

1

54 2

1

2 2

3

.

128

,

?)

%

60U

6 !m3 !m

) ?



)nswer L

8) marks9

203 %iagram 20 shows a right angle" triangle "$A.

%iagram 20

;t is gien that tan V &3

4. !al!ulate the length( in !m( of "%.

)nswer L

8) marks9

12

"

$

%

!V

D cm



ANS'E! T( S)(!EPEN#A#AN MENEN$A% !EN&A% 2009

MAT%EMAT#)S

ANS'E!S *(! PAPE! 1 6SET 18

1. % 21. )2. ) 22. %3. , 23. ?4. % 24. ,5. , 25. ?6. ) 26. ?7. ? 27. %8. , 28. ?

. , 2. )10. ? 30. ,11. ? 31. ?12. ? 32. )13. , 33. ,14. ? 34. ?15. % 35. ,16. % 36. ?17. % 37. )18. ? 38. ,1. ? 3. )20. ) 40. %

MA!"#N$ S)%EME

13 The number 345(678 is written as 350(000 when it is roun"e" off to theA nearest ten & 345 680B nearest hun"re" & 345 700) nearest thousan" & 346 000& nearest ten thousan" & 350 000 W

130



23 hi!h of the following fra!tions has alue greater than4

3

A 8

7

0.875168

147

8

7 = W

B3

2 0.667 or 168

112

3

2=

) 2

1

0.5 168

84

2

1

=

&7

5 0.714168

120

7

5=

43 33100000

168 & 3 :

100000

168

& 3 : 0.00168

& 3.00168

.3 Town 9 & 8M, #,oolest on a parti!ular "ay$

53 m & 23n & 2m : n & 23 : 2 & 52

3 a!tors of 54 & 1( 2( 3( 6( ( 18( 27( 2)nswerL ) & 2( 3( 18

:3 ?ro*en eggs per"ay & 000100

1

× & 0

Number of bro*en eggs pro"u!e" in a wee* & 7 0

& 630

;3 Total length of roa" !onstru!te" & 5.54 *m : 6.78 *m

& 12.32 *m& 12 *m 320 m

93 ! & 180M 55M #180M 125M$ & 180M 55M 55M & 180M 110M & 70M

103 ∠PT- & 180° 140° & 1.0

p : q : r : s : ∠PT- & #5 2$ C 180°

p : q : r : s : 140° & 540°

p : q : r : s & 540° 140° & .00

131



113 3 ! : 2 ! : 3 ! : 115° : 122° : 75° & #6 2$ C 180°

8 ! : 312° & 720°

! &o720 312

8

− o

& 51°

123 ;nterior angle of pentagon &

( ) o5 2 180

5 & 108°

;nterior angle of heagon & ( ) o6 2 T180

6 & 120°

The alue of m is & 360° 108° 120° & 132°

143 Perimeter is the total length of the boun"aries.& P@:@:/:/B:BA:AP

1. ea!h si"e of square @A/ an" equilateral triangle A/B is 12!m.2. X P@A is a right angle" triangle( therefore

PAF & 5 F : 12 F & 25 : 144

& 16

& 13!m3. Perimeter of the whole "iagram & 5 : 12 : 12 : 12 : 12 : 13 & 66!m

1.31. )rea of X CDE &

2

1 ? 9

& Y 14 15 & 105!mF

2. )rea of X /E &2

1 ? 9

& Y 10 6 & 30!mF

3. )rea of sha"e" reqion & )rea 1 )rea 2 & 105 30 & 75 !mF

153 )rea of whole "iagram& #10 !m 15 !m$ #5 !m 4 !m$& 150 !mF 20 !mF

132



& 130 !mF

13 hi!h of the following geometri! soli" is a !oneA

,ube

B

,ylin"er

)

-phere

&

!one W

1:3/olume of the !one & hr 2

3

1π

& 2143

1 2 ×××π

& 21163

1×××π

& H 16 7 & 112H !mZ

/olume of the !ylin"er & /olume of the !one

9eight of the !ylin"er & H 4F h & 112H

16Hh & 112H

h &π

π

16

112

& 7 !m

1;3 Kength of base & 36

133



& 6 !m

Total surfa!e area of pyrami" & #4 2

1 6 !m 5 !m$ : 36 !mF

& 60 !mF : 36 !mF & 6 !mF

193 P@F & 5F 3F & 25 & 16P@ & 16

& 4 !m

Total surfa!e area of the prism

& 2 #2

1 3 !m 4 !m$ : #3 !m 12 !m$ : #5 !m 12 !m$ : #4 !m 12 !m$

& 12 !mF : 36 !mF : 60 !mF : 48 !mF& 156 !mF

203

P-C & A-C

213 ! &

2

130360 00 −

&2

2300

& 115M

223 ∠ P & 180M #50M : 70M$ & 180M 120M

134



& 60M

! & 180M #0M : 60M$ & 180M 110M & 30M

or

! & 180M #110M : 40M$ & 180M 150M & 30M

or

& 70M 40M & 30M

243 ∠ TGB & 40M∠ BG/ & 60M∠ GP & 50M∠ AG- & 30M

)nswer & ?

2.3)rea of the sha"e" part &

× 27

7

22

× 25.3

7

22

&

× 4

7

22

× 25.127

22

& 154 !mF 38.5 !mF & 115.5 !mF

253 PTF & 20F 16F & 400 256 & 144

PT & 144 & 12 !m

@AF & 12F : 5F & 144 : 25 & 16@A & 16

& 13 !m

23-.

B/

& A-

AB

135



6

B/ &

6

? &

36

& 4 !m

2:3 ! : 3 y & [[.. i 2 ! 3 y & 6 [[.ii

i : ii\ 3 ! & 15

! &3

15

& 5

2;34

3y <

4

3 3

4

3y <

4

123 −

4

3y <

4

−

y < 4

− ×

3

4

y < 3

293 ) #1( 2$ an" , # p( 8$

2

1 p

+− & 4

1 : p & 8 p &

136



403 GP & 22 68 + & 3664 +

& 100

& 10 units

G@ & 22 310 + & 100 +

& 10

G@ ] 10

GA & 22 2 + & 481+

& 85GA ] 10

G- & 22 68 + & 3664 +

& 100

& 10 units

GT & 22 511 + & 25121 + & 146

GT ] 10

∴GP & G-

413 Perimeter of the sha"e" region

137



& # 147

222

4

1 ××× $ : # 77

222

4

1 ××× $ : 7 !m : 21 !m

& 22 !m : 11 !m : 7 !m : 21 !m& 61 !m

423 'imi L A' 150 : # 8 C A' 35 : 3 C A' 40 : 3 C A' 38 $

& A' 664Aoger L A' 150 : # 7 C A' 35 : 2 C A' 40 : 3 C A' 38 $ & A' 58%ifferen!e & A' 664 A' 58

& A' 75

443 ) L ? ? L ,7 #3$ 4 #3$ 6 #2$ 5 #2$

21 L 12 12 L 10) L ? L , & 21 L 12 L 10

4.3 EE -onvert to *62ours system

0740 : 0630 : 0020 & 1430

Time %au" arrie & 2.30 p.m.

453 Total stu"ents & 160

! &160

32 360M & 72M

y &160

36 360M & 81M

153M

138



43

%iagram 24

The bar !hart shows the nmber of stu"ents in three !lasses. hi!h of the following statementis trueA The total number of stu"ents in three !lasses is 125

) & 45( ? & 40( , & 45) : ? : , & 120

B The total number of girls in ,lass ) an" ,lass ? are the same. W

) The number of boys in this s!hool is greater than the number of girls.?oys & 20 : 15 : 20 & 55

irls & 25 : 25 : 15 & 65

The number of boys in this s!hool is less than the number of girls.

& The number of girls in !lass , is greater than the number of girls in !lass ?.The number of girls in !lass ? & 25The number of girls in !lass , & 15∴The number of girls in !lass , is less than the number of girls in !lass ?.

4:3 'o"e & ? & 13,hoose the answer whi!h is less than 13.-uitable answer is ) & 12

4;3 Total frequen!y & 30

'e"ian &2

1615 datadata thth +

13



&2

33 +

&2

6

& 3

493 y & 32 2-ubstitute & 2Then( y & 32 2 y & 3#2$2 2#2$ y & 3 #4$ : 4 y & 12 : 4 y & 16

.03 y & ! : 6The graph interse!t yais at 6.#6( 0$ an" #0( 6$ !ertify the fun!tion y & ! : 6

140



ANS'E! T( S)(!EPEN#A#AN MENEN$A% !EN&A% 2009

MAT%EMAT#)S

ANS'E!S *(! PAPE! 1 6SET 28

1. ? 21. ,2. % 22. )

3. , 23. ?4. ) 24. )5. , 25. ?6. % 26. )7. ? 27. ,8. % 28. ,. % 2. %

10. ? 30. ,11. ) 31. ?12. ? 32. ,13. , 33. %14. % 34. ,15. ? 35. ?16. ) 36. ,17. ? 37. ?18. % 38. ,1. , 3. %20. ) 40. ?

MA!"#N$ S)%EME13 hi!h of the following numbers when roun"e" off to the nearest hun"re" thousan" be!omes

141



8700000 A 8754321 & 8800000B 8654321 & 8700000 W) 8643210 & 8600000& 8554321 & 8600000

23 250 #4.5 30$ #2.5 1$ #0.5 18$ & 58.50

43#6

1 300$ 20 & 30. Per!entage "urians left &

300

30 100= & 10=

.3 P & 12 6 & 18

@ & 18

53 Griginal pri!e & A' 24.00

-elling pri!e & 11 2412

%< ×

& 22 %<

-wee Kan uses2

1of her saings.

∴9er saings was 222 %< ×

& 44 %<

3 ) 238 =÷ remain"er 2 158 =÷ remain"er 3

? 33 =÷

15 =÷ remain"er 4

, 8325 =÷ remain"er 1

5525 =÷

% 15345 =÷

545 =÷

∴,ommon multiple of 3 an" 5 is 45

:35 rolls of rope

13

2m & 17.5 m

5 rolls of rope 1.6m & 8.45mKength of remaining rope & 17.5m 8.45m & 9305m

;3 2400 : 0445 05152330

93 !^ : !^ : 35^ : 62^ : #180^ 147^$ & 180^

142



2 !^ : 130^ & 180^2 !^ & 180^ 130^2 !^ & 50^ !^ & 25

103 -!ale fa!tor( k &PQ

Q'P'

k & 224 =

113;nterior angle of regular heagon &

6

180)26( ×−

&

1206

720 =

The alue of y &2

120180 −

&

302

60 =

123 3 ! : ! & 180°

! &4

180

& 45°

Number of si"es &

45

360

& 8 si"es

143 1 m & A' 13.60

The Perimeter of Ae!tangular ,ompoun"& 2 #25m$ : 2 #75m$

& 50m : 150m

& 200m

,ost of fen!ing

& 200 A' 13.60

& A' 2720

1.32

1 14 h & 168

143



7h & 168

h &7

168

& 24 !m

153

2

1 3 & 6

& 6 3

2

& 4 !m

)rea of the whole "iagram

& 6 !m 2 : #12 !m 4 !m$

& 6 !m 2 : 48 !m 2

& 54 !m 2

13 Aight prism

1:3 /olume of !uboi"L /olume of right prism & base area height& 21 6 11 66 h & 1386

& 1386 h &66

1386

h & 21

1;3)minah age<s &

4

34

?ala age<s &12

1013

12

1

12

4

12

1

4

34 =+=+

,hee 'eng age<s &24

1146

24

1115

12

223

2

5

12

718

2

5

12

1013

12

4

2

5

12

1013

4

34

2

12 ==

=

=

+=

+

193 ∠ O & ∠ > & 70M

∠ ' & 0M

∠ OK' & 180M #0M : 70M$

& 180M 160M & 20M

144



203 ∠ & 100M

& 180M #100M : 30M$

& 180M 130M

& 50M

213 )rea of the sha"e" region

&21 H 8F

&2

1 H 64

& 32H

223 P@F & 10F 8F & 100 64 & 36P@ & 36

& 6 !m

)rea of the !oloure" region

& #5F H$ #2

1 8 !m 6 !m$

& 25H 24

243 ! & 180M 120M & 60M

or

! &2

120°

& 60M

2.3 9eight of triangle & 22 1517 − & 22528 −

& 64 & 8 m

)rea of triangle &2

1 15 m 8 m

& 60 mF

Number of paint tins & 60 mF _ 5 mF & 12

145



253

180M 70M & 110M

Kine CD nonparallel to line P@.

23 2 3y & 17

2 #4$ 3y & 17

8 3y & 17

3y & 17 8

&

y &3

& 3

2:3 ` 3 [ #a$ I 2 [. #b$∴ 3 Q I 2

2;3 , #7( 8$ an" #5( 2$

Ket the !!oor"inate of % be ! L2

57 +− & !

2

2− & !

Thus( ! & 1

Ket the y!oor"inate of % be y L2

$2#8 −+& y

2

6

& y Thus( y & 3

Then( the !oor"inate of % is # 1( 3 $

293 GO & 5 units G' & 6 units

G>F & 3F : 4F GKF & 8F : 6F& 25 & 100

G> & 5 units GK & 10 units

9en!e( "istan!e of GO & "istan!e of G>

146



403 ),F & 12F : F& 225

), & 15 & ra"ius

Kength of ar! )% & )ngle at the !entre × !ir!umferen!e360

& 150° × 2λr

360 & 150° × 2 ×

7

22 × 15

360 & 3.2 !m

Thus( the perimeter & 3.2 + 15 + + 12 & 75.2 !m.

413 L 624 & 12 L 13

624 ! & 13

12

C & 1213 624

& A' 576

4236

3 &

42

21

443 30 = of the total number of !omputer sol" oer the four month perio" is 150

4.3 10 square gri"s & 20 000 1 square gri" & 2 000

-o ( for ebruary( 6 square gri"s & 12 000

453 2y : 5y & 140

7y & 140

y &7

140

y & 20

'angosteens & 5y

5y & 5 20

& 100M

Number of mangosteens

& 252360100 ×°°

147



& 70

43 Total in!ome & A'1 400 : A'1 800 : A'1 350 : A'1 700 & A'6 250

4:3'in &

5

46235 ++++

&5

20

& 4

4;3 y & : 2 be!ause #0( 2$ an" #2( 0$ satisfy the equation an" the graph interse!t yais at 2.

493 y & 2 !2 : 1

-ubstitute & 1Then( y & 22 : 1 y & 2#1$2 : 1 y & 2 #1$ : 1 y & 2 : 1 y & 1 so s & 1

-ubstitute & 2Then( y & 22 : 1 y & 2#2$2 : 1 y & 2 #4$ : 1 y & 8 : 1 y & 7 so t & 7

s : t & #1 $ : # 7$ & 1 7 & 8

148



.03 ? #interse!t at point $

2009 *(!E)AST PAPE! 2SET 1

Aser Scheme

13 42 ÷ 6 10 & 7 10 W & 17 W

R 2 mar*sS

23

&4.0

44.1

10

10 GA &

4

4.26× F

&4

4.14 F & 3.6 F

& 3.6 F

14

B -

A

/

0 1

2



R 2 mar*sS

43a$

3

33

6

1

216

1

=

&6

1 F

b$ & ( ) 21327 +− F

& ( ) 214−

& 16 F R 3 mar*sS

.3 a$ 2 # r − 2 $ & 10 − 5r

2r − 4 & 10 − 5r 7r & 14 r & 2 F

b$ s + 6 & 4 s 2 s + 6 = 8 s F s − 8 s & −6 −7s & −6

s = 7

6 F

R 3 mar*sS

53

150



;mage !orre!tly"rawn 2 mar*s

R 2 mar*sS

3Transformation " is a translation

6

8.

R2 marksS

:3 a$ !8 F !y4− & $2#4 y ! ! − F

b$ k 6 F 183 −+ k

& 3 #2k F : k 6$ W & 3 #2k 3$ #k : 2$ FR 2 mar*sS

;3 a$ 8 ! : 6 F

b$ ( ) ( )443 −−−− ! !

164

4123

+−+−+−

!

! !

R 3 mar*sS

93 #3$ 5#2 $5

n n

mn

− −=

151

F

F

F

F

FF FF

WW



3 10 55

n n

mn

− +=

8 105

n

mn

−=

8 ) marks9

103 a$ ! I 14 8 ! I 6

b$ 3 ! I 11 2 an" 3

1 ! ≥ 7 8

3 ! I 3

1 ! ≥ 1

! I 3 ! ≥ 3 ! J 3 ! ≤ 3

! & 2( 1( 0( 1( 2( 38 ) marks9

113 k m 452 =+

542 −= k m

54 −= k m

8 ) marks9

123 a$ 2412 −− ÷ q pq p

& 2142 +−− q p W

& 36q p −

& 6

3

p

q W

b$ & 3 2

& W8 ) marks9

152

FF

F



Number of !ars

143

>ey L'omeMa

Bniform s!ale 1 mar* a!h set of bars 1 mar*

8 6 marks9

1.3 a$

Numer *reuecy

2 43 34 25 36 2

)ll the frequen!y !orre!t 2 mar*s3 or 4 !orre!t 1 mar*

b$ 5.32

43=

+

R3 mar*sS

153& 634

2

1 ×

×× W

& 36 !mF W R2 mar*sS

13 a$ PA # 2 mar*s $

153

Ko!us C

Ko!us y

⊗

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

>an!il

Persona

aa

Types of !ars

F

F

;nterse!tion point

@

-



b$ i. lo!us !orre!tly "rawn F ii. lo!us y !orre!tly "rawn F!$ interse!tion point !orre!tly mar*e" F

R5 mar*sS

154

GP A



1:3

a$ uniform !orre!t s!ale on yais 1 mar* b$ points !orre!tly mar*e" 2 mar*s!$ graph !orre!tly "rawn 1 mar*

R4 mar*sS

1;3

155

@ A

y45

40

25

20

15

10

5

0

G5

G10

G15

G4 G2 G1 1 2 4 . H

-



@

T

,onstru!tion of point - 1 mar* ,onstru!tion of re!tangle P@A- 1 mar*

,onstru!tion of perpen"i!ular line 1 mar* -traight line "rawn from A 1 mar* Kabel T !orre!tly mar*e" 1 mar*

R5 mar*sS

193

;mage !orre!tly "rawn 2 mar*sR2 mar*sS

203a$ tan o &

6

8

156

P

@<

P

P<

A

A<

G



&3

4 F

b$ length of <"$ & 8: F & 17 !m F

R3 mar*sS

Set 2 Paper 2 6 *orecast +uestio 8Aser Scheme

157



13&2

3

−

15

10

15

21

&2

3

15

11 W

&1011 or 1

101 F

R2 mar*sS

23& .1 _

−

5

13 F

& .1

−

13

5 F

& 3.5 F

R3 mar*sS

43

%iagram 3

T !orre!tly mar*e" FR2 mar*sS

158



.3

%iagram 4

@ua"rilateral 53Y !orre!tly "rawn FR2 mar*sS

53

%iagram 5

;mage !orre!tly "rawn F R2 mar*sS

3 k p 53 =− F35 += k p F

R2 mar*sS

:3 a$ −4 − 6 ! & 14

15



−6 ! = 18 F ! & −3 F

b$ 3m − 10 & 8m F 3m −8m & 10 −5m = 10

m & −2 FR4 mar*sS

;3 & abbbab 8104736 +−−+− F& 14ab 7b 3 F

R2 mar*sS

93

)ny 2 lines !orre!tly "rawn 1 mar* )ny 3 lines !orre!tly "rawn 2 mar*s)ll the line !orre!tly "rawn 3 mar*s

R3 mar*sS

160



G

- A

@P

103

⊗ interse!tion of lo!us y an" +

%iagram 10

Ko!us !orre!tly "rawn 1 mar* Ko!us y !orre!tly "rawn 1 mar*

Ko!us + !orre!tly "rawn 1 mar* ;nterse!tion point !orre!tly mar*e" 1 mar*

R4 mar*sS113 a8 & 2 ! 6 : 5 ! : 10 !

& 3 ! : 4 F

8 I nF mmnmn 33 +−− F F ( nF mmn 34 +− F F

R3 mar*sS

123&

2

32 +a3

4−− a

&6

$4#2$32#3 −−+ aa F

&6

826 +−+ aa F

&6

174 +a F

R3 mar*sS

143 a$ ∠OK' F

161

Ko!us y

Ko!us +

Ko!us



b$ =>

;< &

C>

C<

6

;< &

3

5 F

;< &3

5 6 F

& 10!m F R3 mar*sS

1.3 2* : 2 ≥ 4 2* ≥ 6 * ≥ 3 F 4 * J 0 * J 4 * I 4 F

* & 3( 2( 1( 0( 1( 2( 3 F

R3 mar*sS

153 a$ 'ay F

#b$1

3502

× F

175= F3 mar*sD

162



13)nswer L

G2 G1 0 1 2 4 . H

y ais !orre!tly mar*e" 1 mar* 7 points !orre!tly mar*e" 2 mar*s # 6 points 1 mar* $ )ll the 7 points oine" 1 mar* -mooth !ure 1 mar*

R5 mar*sS

1:3163

-

10

;

.

2

G2

?

,

)

6 !m

3 !m

%

60U



0U !orre!tly !onstru!te" at ? 1 mar* ?, !orre!tly !onstru!te" 1 mar* 60U !orre!tly !onstru!te" at ) 1 mar* )% !orre!tly !onstru!te" 1 mar* ,% !orre!tly oine" 1 mar* R5 mar*sS

1;3 & ÷× −2844

3 mmh 37 −mh F

&328744

3 +−−

mh F & 381 mh −

&3

81

h

m F

R3 mar*sS

193 & 2

3

2

3

2

1

2

1

2323 ××× F

& 22 23 × F&

× 4

& 36F

R3 mar*sS

203tan o I

3

4

164



tan V &

$%

$%&3

4

@A &3

4

& 12 F

PA & 2 : 122 F

& 225

& 15!m FR3 mar*sS

kertasmodelpepsebenar(pmr)_01

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