paper1 bengkel hotel seri malaysia kulim 2014 (1) 0252 final

8/10/2019 Paper1 Bengkel Hotel Seri Malaysia Kulim 2014 (1) 0252 Final

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PAPER 1ESTIMATE TIME FOR PAPER 13.30 - 6.30


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(a)

5(b){ }3,1,1,3

QUESTION 1


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(a)

1: + xxh(b)

41=+m

3=m

QUESTION 2


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( ) baxxh +=

Comparing with ( ) 35362 = xxh

362 =a

0>a

35=+ bab

babxa ++= 2

( ) ( ) bbaxaxh ++=2

356 =+bb

357 =b

5=b

QUESTION 3

6=a


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(a) 25)( = xxh

625 =x

625 =x

85 =x

58=x

625 =x

45 =x

54=x

QUESTION


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(b) ( ) 25 = xxh

( ) ( ) 2252 =

h

210=

12=

12=


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(a) ( ) 23 = xxfxy = 23

23 += xy

3

2+=

x

y

( )3

21 +=

x

xf

QUESTION 5

( )=xf = )(1 xf3x 2 x 2+3


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(b) ( ) 15

+= x

xg

( ) 551 = xxg

( ) ( ) 65521 += xxhgg

61010 += x410 = x

hg 1

g

)(xh


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853)3( =+=f(a)(b) 5)( += xxf ( ) 51 = xxf

( ) ( )32 1

fkf =Given

( ) 852 =k45 =k

9=k

QUESTION 6


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3

10

3

24 =+=SOR

3

8

3

24 ==POR

( ) ( ) 02 =+ PORxSORx

038

3102 =+ xx

08103 2 =+ xx

QUESTION 7

3

2,4


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pxx =++ 71218 2

071218 2 =++ pxx

pcba === 7,12,18

02 > acb( )( ) 07184122 > p

072504144 >+ p072360 >+ p

36072 >p5>p

QUESTION 8


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( ) ( )( )2142 += xxxx xxxxx 2282 22 +=

0273

2

= xx( ) ( ) ( )( )

( )32

234772

=x

591,2=x 2573.0=xor

QUESTION 9


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042 = pxx

Substitute

( ) ( ) 0141 2 = p1

=

x

041 =+ p5=p

QUESTION 10


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093 2 =++ kxx

3

93 == mSOR

33 =m1=m

mm 2,

223

mk

POR ==

( )2123

=k

6=k

QUESTION 11a

bSOR =

a

cPOR=


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( )121653 2

+ xxxx221653 22 + xxx

01662

xx( )( ) 082 + xx

-2 8

82 x

QUESTION 12


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a) 32

51

=+

3=x

b) 3=x03=x

( ) ( ) 43 2 = xxf

QUESTION 13


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2)(3)( 2 ++= pxxf

(a) 01 =+ p 1=p

(b) 2=q

QUESTION 14


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m=2log5

=9.4log5

5

5

2

525 loglog7log +=( )12 += mp

12 = mp

QUESTION 15

p=7log5

=9.410

49

52

72

=

52

7log

2

5


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122 34

= ++ xx

121216 = xx

[ ] 18162 =x

[ ] 182 =x

322 =x

3=x

QUESTION 16


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9

833 2 =+ xx

( )9

8339 = xx

98)19(3 =x

9

13 =x

233 =x

QUESTION 17

2=x


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0loglog 28 = qpqp 28 loglog =qp 2

3

8 loglog3 =

qp2

3

2

loglog =

qp=33qp=

QUESTION 18


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3loglog24

=x

3log log24

=x

3loglog22

=x

9=x

QUESTION 19


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=y

x3

2log

yx 22 loglog3 =

kh =3

yx 23

2 loglog

QUESTION 20


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QUESTION 21

a) Midpoint of AB

( )

++=

2

37,

2

115

( )5,7=


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(b) Gradient of the straight line AB ( )11537

= 4

1

=

So gradient of the perpendicular bisector of AB 4=

( )5,7,4=m

( )745 = xy 5284 ++= xy334 += xy


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( ) 12 =kpx

2

1

= kp

kp

= 21

QUESTION 22


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QUESTION 23


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QUESTION 24


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4=n mx= 1002 =x k3=

( )

22

xn

x

=

( )24

1003 mk =

mk =259 2

2925 km =

QUESTION 25


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2, 3, 3, 4, 5, 7, 9

1Q Median

3Q

Interquartile range 437 ==

QUESTION 26


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800,60,5 2 === xxN

(a) Mean 12560 ==

(b) Standard deviation

412

5

800 2 ==

QUESTION 27

Nx=

( )2

2

xN

x

=


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5=Median 2=

6 1+ ( ) 156 +=Median 31=

( )26= 12=22 12= 144=

QUESTION 28


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20060=++ rr 1402 =r

70=rrs=

70200=

7

20=

QUESTION 29r

r

60


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rs=6.08=

8.4=

6.0= ROQ542.2=

2

2

1rA=

( ) ( )542.282

1 2=

34.81=

(a)

(b)QUESTION 30

8


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(a) 5.555.30 =++ rr 252 =r5.12=r

rs=5.125.30 =

44.2=

QUESTION 31


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(b) 2

2

1

rA=( ) ( )44.25.12

2

1 2=

63.190=

12.5

2.44


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(b)

= 522

78.95

2sin

5

2

2

1 2 =

rr

( ) 78.915.02 =r2.65

2 =r07.8=r

(a)

QUESTION 32

58

( ) sin2

1 2 = rsegment


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(a)

0=dxdyTurning point

( ) 062 =k 62 =k3=k

QUESTION 33


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( )( ) c+= 26

2

231

2

c+= 1261

7=c

76

2

3 2+= x

xy

(b) 63 = xdx

dy

= dxxy 63

cxx

y += 6

2

3 2


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5

31 uy= 16 += xu

( )51631 += xy

( ) ( )61635 4

+= xdx

dy

( )41610 += xdx

dy

QUESTION 34


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xxy 52

=52 = x

dx

dy

152 =x62 =x3=x

QUESTION 35

12+= xy1=m

( )3532 =y 6=( )6,3P

dv


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,3xV=From

23xdx

dv=

Given13 min72.9 = cm

dt

dv

dt

dx

dx

dv

dt

dv=

dtdx= 43272.9

1min0225.0 = cm

QUESTION 36

2)12(3=dx

dv

432=dt

dv

xx

x


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( )213 = xy

( )( )3132 = xdx

dy

( )136 = x

( ) 12136 =x213 =x33 =x1=x

( )( )2

113 =y4=y

( )4,1

QUESTION 37


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( ) ( ) 253 = xxh

( ) ( ) ( )3532 3' = xxh

( ) 3536 = x( ) ( ) ( )35318 4" = xxh

( )45354

=x

( ) ( )( )4"

513

54

1 =h

8

27=

QUESTION 38


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3

3

4rV =

24 rdrdv =

( )264=144=

QUESTION 39

68.5 =r2.0=

rdr

dvv =

( )2.0144 = 8.28=


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(a)

59 =d 4=(b) ,......17,13,9,5 17=a 4=d

( )[ ]dnanSn 122

+=

( ) ( )[ ]41917222020 +=S

1100=

QUESTION 40


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(a) 3824 ==r

(b) ( )11

=

rraSn

n

8744

13

138=

=

n

QUESTION 41


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,...,2,3 pm

QUESTION 42


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1= narTn

163=T

162

=ar

16

82

3 =

ar

ar

2

1=r

843 =+TT

816 4=+T84 =T

83 =ar

162 =ar

16

2

1 2

=

a

164

1=

a

QUESTION 43

64=a


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raS= 1

=

2

11

64

3

128=

(b)


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5=a ( ) 32

53

10

==r

Sum to infinity

=

3

21

5

3

55=

3=

QUESTION 44


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(a) ( )[ ]1532

55 +=S

( )162

5=

40=

QUESTION 45


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(b)455 SST =

( )[ ]14324

40 +=

( )13240 =14=

1= nnn SST

QUESTION 46


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(a) ( )dxxg

1

5

( )dxxg=5

18=

QUESTION 46

( ) 85

1= dxxg

(b) ( )[ ] 105

dk


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108

2

5

1

2

=

kx

182

1

2

25= kk

1812 =k

2

3=k

(b) ( )[ ] 101

= dxxgkx

( ) 101

5

5

1= dxxgkxdx


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QUESTION 47

a b0 x

y

)(xfy =

= b

adxyArea

=b

a dxxf 5)(

a

bdxxf

)(2 = b

adxxf

)(2)5(2 =

10=


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( )xgxxdxd = 32

( )

2

1

2

1 3

2

= xx

dxxg

=

2

3

1

4

14 =

3=

QUESTION 48


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( )xgx

xdxdy = +1

52 ( ) += 152x xdxxg

( ) ( )dxxgdxxg = 3

0

3

0 223

02 1

52

+=

x

x

QUESTION 49

( )

+

= 113

352

2 3=


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QUESTION 50

jiOR 43 +=(a)

22 43 +=OR(b)5=

jiORVectorUnit5

4

5

3+=

QUESTION 51


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( )kjijiba += 713(a)

( )jki ++= 16

kjiji ++= 713kjiji ++= 713

QUESTION 51

(b)


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( ) 641 2 =+ k

81 =+k

7k

18=k

9kor

( ) 1016 22 =++ k

(b) 10= ba

( ) 100136 2 =++ k


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(a)

05=k03=+h

3=h

( ) ( )bkah 53 =+

5=k

QUESTION 52


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QUESTION 53

=

4

6OP

=

5

4PQ

QRPQPR +=

= 4

6

5

4

PR

= 1

10

ji += 10


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QUESTION 54

4

3

2

1=

+ k

644 =+ k

104 =k

2

5=k


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PRPQ :

3

4: =QRPQ

3:4=


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( )xxy = 1022

22 220 xxy =

( )0,pp2200 =

10=p

QUESTION 55

xxy 220

2

=x

y2

x

( )q,3)3(220 =q

14=q

x

y2

x

1qp =


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21

x

q

y

p =p

211pxq

py =

pxp

q

y

111

2+

=

Y-intercept2

1

== p

2

1=p

QUESTION 56p p

05

26

=m

5

4=

5

4=p

q

5

4

5.0=

q5

2=q


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QUESTION 57

QUESTION 58


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p=sin

1p

2

1 p

(a)p

1

sin

1seccos ==

(b) cossin22sin =

212 pp =212 pp =

QUESTION 58

QUESTION 59


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t=tan

(a)t1cot =

t12 +t

1

QUESTION 59


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sin90coscos90sin =

( ) ( ) sin0cos1 =cos=

112 +

=t

( ) BABABA sincoscossinsin =

(b) ( )90sin

t12 +t

1


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02 30sin4sinsin15 += xx

2sinsin15 2 += xx

02sinsin15 2 = xx

( )( ) 01sin32sin5 =+ xx

QUESTION 60


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52sin =x

058.23=x00

42.156,58.23=x

31sin =x

047.19=x00

53.340,47.199=x

0000

53.340,47.199,42.156,58.23=x

122 2QUESTION 61


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5sin82cos3 = xx

1cos22cos 2 = xxx

2sin21=

5sin8sin213 2 = xx

5sin8sin63 2 = xx

08sin8sin6 2

=+ xx

QUESTION 61

xx 22

sincos =

08sin8sin6 2 =+ xx


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08sin8sin6 2 =+ xx

( )( ) 02sin2sin3 =+ xx

3

2

sin =x0

81.41=x00 19.138,81.41=x

2sin =x( )ignore

QUESTION 62


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(a) 7! = 5 040

(b)

QUESTION 62

M M M S S S

4! 3! = 144

QUESTION 63


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(a) Number of four-digits numbers formed360

4

6 == P

QUESTION 63

(b) 3, 5, 6, 7, 8, 9

4

9

543

2404543 =

QUESTION 64


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QUESTION 64

(a) 7925

12 =C

4 monitor2 assistant monitor6 prefect

(b) 1601

2

3

6

1

4 = CCC

QUESTION 65


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(a) Number of ways 35

24 CC =

(b)

QUESTION 65

60=

G G G B B

3! 3! = 36

QUESTION 66


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(a) P(neither of them is chosen)= P(Sarah is not chosen and Aini is not chosen)

12

5

5

2

=

6

1=

QUESTION 66


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(b) P (only one of them is chosen)

= P (SA) or P(SA)

+

= 127

5

2

12

5

5

3

60

29

=

QUESTION 67 5 black


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QUESTION 67

(a) P(Both black) = P(BB)

5 black

15 white

19

4

20

5=

19

1=

(b) P(BW) or P(WB)

+

=

19

5

20

15

19

15

20

53815=

QUESTION 68


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( ) ( ) ( )YYPBBPBBP ++

+ + = 11

2

12

3

11

3

12

4

11

4

12

5

66

19

=

QUESTION 68

QUESTION 69


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10,52 ==

52.1

10

522.67=

=Z

( ) 8849.0=kzP

( ) 1151.02.1 =>zP2.1=k

(a)

(b)

QUESTION 69


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3485.05.0 =k

1515.0=k

(a)

QUESTION 70

QUESTION 71


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(a) 1161

41

41

161 =++++ k

8

51=k

8

3=

(b) ( ) ( )43)3( =+== XPXPXP

16

5

16

1

4

1=+=

QUESTION 71

QUESTION 72


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QUESTION 72

6.0=p 4.0=q 8=n

( ) ( )87)6( =+==> XPXPXP08

8

817

7

8)4.0()6.0()4.0()6.0( CC +=

1064.0=

paper1 bengkel hotel seri malaysia kulim 2014 (1) 0252 final

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