Spm Trial 2009 Addmath Q&a Kelantan

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3472t1

Matematik Tambahan Kertas I September 2009 2 jam

1\ama relalar

:

tinskatan

:

JABATAN PELAJAIL{N KELANTAN DENGAN KERJASAMA PERSIDANGAN KEBANGSAAN PENGETUA.PENGETUA SEKOLAH MBNENGAH MALAYSIA CAWANGANKELANTAN

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2()O9

U n t t t k K egu naa n Pem er i k:;tt

Soalan

Mrrkrh Dioerolehi

3

MATEMATIK TAMBAHAN KERTAS 1

,

3

3 4

4

5

8

3 3 3 3

9

4

t0

3

6

Masa: DuaJam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Arahan: l. Kertassoalanini nrcngandungi 25 soalan. 2. Jawabsemuasoalan. Bagi setiapsoalanberikansatu.jawapan 3. sahaja. 4. .lawapan hendaklah ditulispadaruangyangdiscdiakan dalam kertassoalanini. pentingdalamruangyang Tunjukkanlangkah-langkah 5. disediakan dalamkertassoalan. (r. Jikaandahendakmenukarjawapan, batalkandengankemas jawapanyangtelahdibuat,kemudiantulisjawapanyangbaru. Rajahyangmengiringisoalantidakdilukismengikutskala 7. kecualidinyatakan. Markah yang diperuntukkanbagi setiapsoalanditunjukkan 8. dalamkurungan. 9. S a t u s e n a r a i r u m u s d i s e d i a k a n d i h a l a m a n 2 h 4i ndgagnaj a d u a l taburannormalN(0, l) di halaman5. 10. Andadibenarkan menggunakankalkulatorsaintifikyangtidak bolehdiprogramkan. I l. Kertassoalanini hendaklandiserahkan di akhirpeperiksaan.

Markah Penuh

il l2

l3 t4

7

7

3 3 -t

l5

3

t6

-t

l7 l8

t9 tt) 2.1 )1

23 24 25 TOTAL

4

3 4

3 3 3 4 4 4

80

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3472!r

Thc symbolsgivenare The following formulaemay be helpfulin answeringthequestions' theonescommonlYused. yang diberi Rumus-rumusberiktrtbolehmembantuandamenjav,absoalan.Simbol-simbol adalah yang bia'scrdigunakan' ALGEBRA

-bt , = ---

= a''*n

a^ rTn

= nm-n

: a^'

log;nn

o

log, b Iog,b= lr%,

9

T,=a+(n-l)d

t0

*cn =

tl

Tr: n'n-

12

"n

2;-

a^ xa'

(a^)'

8

= logo m 'r loga n

Ll2a+(n-r)al 2' '

-t) -n(t- r" ) , .\ =* n '(, " l-r

r_l

l o-Ltc , . . L = l o 1 , - m- l o g , , n n

Clrt.

'7

IJ

logo tnn = n log. m

s -_ _ _ , l-r

lrl
CALCULUSI KALKULUS clv

dy L - t r -

y=Ltv

dtt a

cLr

dt

4

v-

OT

Areaundera curvc Luas di ltawah lengkung, b =

.L

- .-_ u-

/

,

Y(LI

du < l y - -dl----dl , \)'

lydx

or \(tt(tu)

tl

dv

b -. J

tx,av a

,l -

dy dy :=:xdu d-r

5

dtr

Volumegeneratcd Isipadujanaan

dr

b

1= flrcv' or (atau) ) ' dr a h -

- l

ItLt-

cly

a

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STATISTICSI STATISTIK

I

lllt, I, r=ffi

-

It

t=T

,p,= tl.

2 x=#

| , } r u- o ) m:L+l=-)r,

itl t, = (n_,f;i

9

n^

t0

r(twn) = r(t)+P(r)- r(tna)

1l

f(x=r)=nC,p'rln

t2

Mean/Mitr,Yt= nP

IJ

o = ^frpq

1A ta

-

, P + c 1= l

X -lt

I:9L"fio Qo GI4OMETRYIGEOMETRI DistancclJaruk

S

--o

I

= ,l(rr- r,)t * (v, - v,)' t,

t

Midpoint I

'l'itik tenguh

6i

-) - ( xt + x2 \/.. x ,.,\ y ) : t ? - ' zLjzr) 1 A pointdividinga scgrrlcntof a line Titik yang mentbethagisuutu lcmbereng garis (x,-v):

( nxl +,nx2 [,;;

try,+ mYr\ ' -..; )

Arca of trianglcI l.uttsscgitiga =

)lt-,rr*.r-2)'3

trr.vr)- ('r.v,t 4v2+ 4y)l

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T R I G O N O M E T R Y / TRIGONOMET'III

sin(,,tt ri) = sin zl cosZl + coslsin Il sin(,,1tr) = sin I kos /l + kos,'lsin /l

Arc length, .s: r 0 Panjang lengkok, s = j0 Area of sector,A =

I. ,

cos(,at r) = c o sI c o s/ l T s i n I s i n B ros(,rtrr) = kos.,1kos 1l T sin Asin R

r" 0

I.

I-uassektor,t= rl'0 : l sinzA+cos2,'1

r0

ltan(tt n) =

ll

tan2l =

t2

ab sin I

t n n , , l+ t a n / I T tan Atan R

sin2l+kos2zl=l sec2A:l+lan2l sck2l : l_l-tan2,,1 c o s e c 2 l= t + c o t 2 u l kosek2l = y.r_kot2.,1 s t n 2 A : 2 s i n/ c o s, 4 sin2l:2sinlkosA cos24 - cos2.4 - sin2A : 2 c o s 2I - | =l -2sin2.'l k o s 2 A= k o s 2 I - s i n 2 l :2kos2A'1 =1 '- 2sirlA

t1 IJ

t4

2tlrn A 1 * tun'I

sin /l

s i nC l

c/ = b2 +c2 - 2bccosA a2 = bz + c2 - 2bc ktts tl Arca of triangleI I'uussegitigo -

I tl]bstnL

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TIIE UPPERTAIL PROBABILITY Q(z)FOR THE NORMAL DISTRIBUTION N(0, l) KEBAMNGKALI. IN HUJUNG ATAS Qfu\ BAGI TABURANNORMA I l

6

1

2 8

4

l

5

7

6

E

9

9

Minus I ToloA

0.i

0.5000

0.4960

0.4602

0.4562

0,4840 0.480t

.4

0.4522

0 . 4 4 8 1 0.4443 0.4404

0.2 0.420't

0,4761 0,412t

0.468t

0.4641

0,J9'14 0 , 3 9 3 6 0 . 3 8 9 7 0 . 3 8 5 9

12 l15 rtl15 illls r0l14 r0 I13 el12

re le 18 t7 16 15

8 | il

14

rl'o tln nlr u|r t u I olu olr ,lo ., lo ,lt

13 t2 r0 e {i 7 6 5 4 4

0.4052

0.40t3

0.3669

0.1632

0.3594 0 . 1 5 5 7 0 . 3 5 2 0 0 . 3 4 8 3

0.4 0.3u6

0.3372 0 . 3] 3 6

0.3300

0.3264

0.3228

0 . 3 1 9< 2 0.lrs6

0.3t21

0.5 0.3085 0.3050 0.3015 0 . 2) 8 1

0.2946

0.29t2

0.2877 0.2843 0.28t0

0.27'76

0 , 6 0.2743

0.2709

0.2676 0.2143 )43 0.2389 0 . 2 3 5 8 0.2\2'l \21

0.261t

0.2578 0,2546 0.2514 0.2483 0.2451

0 . 7 0.2120

0.2296

0.2266

0 . 8 0 . 2 tl 9

0 . 2)31 )33 t62 0 . t t67

0.2005 0.t9't't

0 . 1 9 4 9 0.t922

0 . 1 7 3 6 0 . 1 7|1

0 . 1 6 8 5 0 . 1 6 6 0 0 . 1 6 1 5 0 . r 6 Ir

0 . t; ;t t55 ,.92 0.I t92

0.1492 0.r469

0.1446 0 . t 4 z J 0 . t 4 0 r

0.|]79

0.t2'il

0.125t

0,t230

0 .l 2 t 0

0 .I r 9 0

0 .I | 7 0

0.I 018

0.| 020

0.| 003

0.0985

0.2090

0.2061

0.9 0 . 1 8 4 1 0 . 18 t 4

0.1788

1 . 0 0.I 5t7

0.I 519

0.t562

0.1357 0.1335 0 . l l 1 4

0.2236

0.2206 0.21't1 0.2t48 0,I 894

0.| 867

t . 2 0 . 1l 5I

0 . rI 3r

)93 0,l,)93

0.| 075

0.| 056

l.l

0 . 0 9 5 r 0,0934 0 . 0)1t t88

0.090t

0,0885 0.0869 0.0853 0.0838 0.0821

0.0968

1 . 4 0.0808 0.0793

0.1il2

t64 0.0778 0.0',64

0.0749

0.0735

0.0721 0 0708

r30 0.0618 0.0(i30

0.0606

0.0594 0 . 0 5 8 2 0 . 0 5I7

t . 6 0.0548 0.0537 0.0526 0 . 0; :1;61 6 0.0505

0.0495

0.0485 0..0475 0.0465 0.0455

1 . 5 0.0668 0.0655 0.0643 1 . 7 0.0446 0.0436 0.0427 t . 9 0.0287

, tIl88 0.0,1

0.0694 0.0681 0.0559

0.0409

0.0401

0.0192 0.0t84

.,36 0.0344 0.0:,36 0.0329

0.0322

0.01r4

,,68 0.0281 0.0274 0.0;:68 0.0762

0.0256

0.0250 0.0244 0.0219 0.0213

t . E 0.0359 0.035l

2 0 2 4 28 t2

, r i ' u 2 0 2 4 28

0 . 4 t 6 8 0.4129 0.4190 )90 0.3 0.3821 0.3783 0.3745 0,3707 0.3409

t2lt6

0.4364 0.4325 0.4286 0.424'l

0.0175 0.0367

0.0107 0.0101 0.0294

,rlr:

23 22 22 20 te 18

32

36 )6

2't 3l

l5

26 30

34

25

29

l2

24

21 3l

23

26

29

2t

24

27

16

f9

22

25

15 t4 t2 il r0 8 7 6 5 4

18 20 zJ t6

19 2l

t4

16 t8

f3

t5

t7

ilDt4 l0illl 8 t0 't89

tl

618 566 455

'1,

: : z 2

,1,

|

2

222

13 t2 t e 8 6 5 4 2

15 t4 Il rl e 1 6 4 3

l8

z0

2t

t6

t6

2l

2.6 0.00.166 0.00451 0.00440 0,0i427 0.004 l 5 0.00402 0,0019 r 0.00179 0,00168 0 00357 '1.7 0.00347 0.00336 0_00126 0.0c3 1 7 0.00307 0.00298 0 00289 0.00280 0.002'12 0.00264 / . 8 0.00256 0.00248 0.00240 0.0c233 0 . 0 0 2 2 6 0 . 0 0 2 1 9 0 , 0 0 2 t 2 0 . 0 0 2 0 5 0 . 0 0 t 9 9 0 . 0 0 1 9 1 2 . 9 0.00l 87 0 , 0 0 l E t 0 , 0 0 1 7 5 0.0c1 6 9 0 . 0 0 t 6 4 0 . 0 0 t 5 9 0 . 0 0 t s 4 0 . 0 0 r 4 9 0 . 0 0 t 4 4 0 . 0 0 i 1 9

8lr0 719 ujt n t I tlu l1, ,lo 'l' 'lr

1.0 0.001350.00llt

tlz

2

2

314

2.0 0.0228 0.0222

',:12

0 . 0 2 1 7 0 . 0 " : 1 2 0.0207

2 . 1 0 . 0 1 7 9 0 . 0 1 ? 4 0 . 0 1 7 0 0.0 66 66 2.2 0 . 0 3 t9

0 . 0 1 3 6 0 . 0 1 3 2 0 . 0' 22 ' 99

2 . J 0 . 0 1 0 7 0.0t04

0.0202 0.0t97

0.0192 0,0r88

0 . 0t 8 l

0.0r62 0.0r58 0,01s4 0.0t50 0.0t46 0.0t43 0.0f 25

0.0122

0.0il6

0.0n 9

0.0il1

0.0tt0

0.0t02 990

0.00964 0.00939 0 00914 0.00889 0 . 0 0 8 6 6 0 . 0 0 8 4 2

0.00820 0.00798 0.00776 0.0(/)) 0.00734 0.007| 4

0.00695 0.00676 0.00657 0.00619

2 . 5 0.0062 I 0.00604 0.00587 0.0(5 7 0 0.00554 0.00539 0.00s21 0.00508 0.00494 0.00480

0 . 0 0 r 2 6 0.0ct22

0 . 0 0 l18

0 . 0 0 r14

0 . 0 0|1|

0.00r07 0.001M 0.00r00

f(z\

,1, 2 z

134 231

t5

t7

19

f3

t5

17

ll

l2

14

9 9 '789

l0

566 344

ExamplelContoh:

rfx-N(0, then ,/ikct

maka

t44

1),

x - N(0,l),

Q{z)

Qk) =

!f @a'

P(x> k)= Q$) z'

2.t)

Q Q . t ) =0 . 0 1 7 e

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3472t1 Exuminer's I J.se

Answer all questions. Jawab semu& soalan. Diagram I showsthe relationbetweensetI and set.8. Rajah I menunjukkanhubungan antara set A dan set B. SetB

(-2,

(2.4\

Diagram l Raiah I (a)

State Nyatakan (i) the value of &, nilai h, (ii) the rangeof the relation. julat hubunganitu .

(b) Using the function notation,write a relationbetweensetI and set 8. Denganmenggunakanlatalandafungsi, tulis salu hubungananlara set A dan sel B. [3 marksl 13markahl AnswerlJawapan : (a) (i) h =

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Exaniner's (lst

'. Given the functions .l- : x -+ 3x + m and ./-l x -)

nx+ 1, where m and tlare constants,

13narksl

find the value of ,r1and ol'r.

Diberi f : .{ -> 3"r+ m dan ./

A -' '. -) nx * - , dengan keadaan m dan n ialah pemalur' x

J

13markuh)

cari nilai m dannilui n.

AnswerlJawapan '.

The following information refersto the functionsf andg. Maklumatberihtt adalahberkaitandengan./ungsi f dan.fungsig.

.[ :x -+ 3x- k,where k is a constant, tlengankeadaank ialahpemalar, 2x+4 plx-,

"12

(a) Given that./(4): 10, find the valueoffr.

Diberi J(4) : t0, cari niloi k. ( b ) Find g/(r).

14marks)

Cari g/(x).

f4 markthl AnswerlJawapan: (a) k: .... (b)

.

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4

Form the quadraticequationwhich has the roots - 3 and I

4

. Ciu" the answerin the

fbrm ax' + bx + c = 0 wherea. b andc are constants. Bentukkanpersamaan kuadratik dimana punca ialah -3

ax'+bx

12mark:l I

clan - . Beri.iuwapan dalam hentuk 4-

+r'= 0 ,dengan keadaana,b dan c ialah pemalar.

[2 narkohl

AnswerlJawapan: .....

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3 47 2 t l E.tonrner's Use

Diagrarn5 showsthe graph of a quadraticfunctions f (x) = -(x + h)' + k ,

where ft and

k are constants. graf kuadratik -f (x) = -(x + h)'} + k tlengankeadaonh dan k ialah Ra.jah5 menunjukkan Demslar.

Diagram 5 Rujah5 State Nt,ulukun (a) thc value of ft, nilai h, (b) the valueof k, nilai k, (c) the equationof the axis of symmetry. perslmean gr,rris .simetri.

AnswerlJawapan :

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3472 tr (,ite

6

Find the rangeof valuesof :r for x (.r - 5) < 36.

13 rnarksl

Carijulat nilai x bagi -r(x - 5) < -16

13ntarkahl

AnswerlJawapan

7

',

Solvethe cquation: SeIesaikanpersamaan'. a ?.r l.l

I

v9.''

13marks) [3 tnurkuhl

AnswerlJawttptttt

8

Solvethe ecluation: S a I e s u i k u t tp a r s l t u t u n ,

log.(x-l)+3=log.2x

13narLsl 13nturkolt)

A n s w c r l J u w t t p u n '... . .

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Exqni,rcr's Use

9

is 7. The sum of the first six termsis 51. The fourthterm of an arithrreticprogression Find the flrst term and the common ditferenceof the progressiorr. 14markl Sebutanke-empatsuatujctnjangaritnetik iatah 7. Junlah bagi enantsebulattpertamanyqialah 5l tersebut. 14markahl Curi sebutanpertomadan bezasepun.vu.ianjang

A n s w e r l J a w a p a:n . . . . . . . . . .

l0

l/r\"' is given bt I =;[;J The n'r'ternrof a geometricprogression

. Find the sum to infinity 13marksl

of the progression. r / r \"-1

diheri sebttgui f, =+l Sebutartke-n scrtt.t.jnnjtrnggcarnetri

4 \ +l si

Curi hasiltumhuh lcetakterhinggtrttrt [3 narkahl

janjang tersebut.

AnswerlJuwaDan: .

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The threc consecutiveterms of a sequenceare m - 9, 2nt and4m + 5. Find the valuc of m suchthat the sequenceis an arithmeticprogression. f2 mark^s) Tigasebulanberlurut-tutu!sualusiri aduluhm - 9,2m dun 4tn+ 5 . Cari nilui m jiku siri itu sctlu janjang aritmetik. [2 tnurkahl

Answer/Jawapan

t2

Diagram l2 showsa straightline graphof -ry against.r? Rajah12menunjukkan grafgaris lurusxy melawanx2.

xy

x2

Diagraml2 Raiah12

Given that I - u: x

h

find the value of a and of b. , , whcrea andh arc constants. x-

[3 marks]

h

Diberi ! - a = :; , dengan keadaan a dan b ialah pemalar, cttri nilai a dan nilai b. x x'

13 markahl

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3472t1 l:sontinu t,lk'

13

The straightline i.y + 3.r : t passesthroughpoint (0, 2) and is parallelto the straightline j o i n i n gt h ep o i n t s( 3 , | ) a n d( 2 , 5 ) . Garislttrushy + 3x : k ntelaluitilik (0,27 danadalahselari dengangaris lunts vungmenvuntbung titik-titik\3, l) don(2,5). Find Cari (a) the valueofh, nilai h , (b) the valueof k 13 morks)

ttilai k.

13murkuhl AnswerlJawupan: (a) h': (b)ft:

Giventhat the point P (- 3r,2) dividesthe line segmentI (- 4, t) and-B(r, 8) in the ratio AP : PB: | : 4, find the valueofr and ofl. f3 mark';l gurisyangmenghuhung A (-4, r) danB (r,8) dengannishuh Diherititik P (-3r,21 nrembuhugi AP : PR : I '.4 , cari nilai r dannilai t.

AnswerlJawupan : (a) r: ( b )/ :

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472t1

The tbllowing infbrmationrcfersto vector p and vectclrq. Maklumat berikut merujuk kepada vektot' p dan vectot' 8.

p =3t+ m.i , wherel,lris a constants. dengan keadaan nt ialqh pemalcrr. q=2i-4j

Givcn that p and q are parallel,find the value of rn. Diberi buhawa p dan q ialcthsr:lari,cari nilai m. [3 nrurks) 13nutrkahl

AnswerlJctwapqn

'. n1:

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3472t1 Use

l6

Diagranr16 sliows atriangle ABC. Rujoh16menunjukkan sehuuhsegitigaABC

5' D i a g r a n lr6 Ruluhl6

1-lrcpoint S lics on straightlinc,4C'. Ir is givcn that A C TitikS bercrcla tli atusgari; ltrrusrlC. Dil,ati AC -- It

:

ll

,lR

A B: q d a n

: q and z1S:SC:2: I . 4 S: ^ t C:'2 : l .

Expressin telnrsof p andlor q IJngkttpkutt dulqttt scltultttt 7.t dan / o/uu t1 /\:.r .) /

-,q

(b) Bs.

13 narlt.s'l 13nnrkohl

AnswerlJawapan :

(4,)

(b)

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3472t1 E.rominer'.s Use

17

Solvethe equation3 sin x * cos 2r :2

for 0u < x < 360".

persanlaan3 sir -x* kts 2x -- 2 bttgi 0" Sx < 360o. Selesaikan

14murksl [4 markuh]

AnswcrlJawapan '.

18

Diagrarnltl show a semicircleOABC,centreO. Rajah ltl menunjukkun.valusemibulalctnOABC, herpusatdi O

/

n

n v

Diagrarnl8 Iiljah 18 G i v c nt h a tA C : 1 2 c m , Z B O C : 3 5 o , f i n d DiberiAC : 12 cnt , I BOC :35", cari ( U s eI G u n an : 3 . 1 4 2 )

(a) 0, in radian. 0, dolam racliun,

(b) the area, in cm2, of sector OzlB

f3 murksl

lutts,dulam cm2, sektor OAB.

[3 murkuh] AnswerlJawapen | (a)

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4

l9

) ---,., G i v e nt h a tg ( , r ' = , find g'(l). ( 2 . r- l ) '

14murksl

4

= ------; Diberi g(x\ , cari g " ( l ) . (2x - l)'

[4 nwrkalt]

LnswerlJawapan '.

?

20

Two variablesr and ^sarc relatedby the equationr = .r+ -; . Given that r irrcrcaseat a constantrateof 5 unitsper second,find the rateof changeof s when.l'= 2.

[3 marksl

'l

r=s+; Duapentbolelwhahrdans dihubungkanolehpersamaan

.l)iheri rberltunhah

patltt kudur malar sehttnyuk 5 uttilpersaat, cari kaclcrrpertrbahcrns altubilct s :2. [3 ntorkultl

Answer/Jav.,apan

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t-l

2l

.' | , , r-r -r,-- ^r.,, :d u t v e n t n a i l g \ x ) u x = r \ ) , l l n d t h e v a l r . r eo l ' n i f

l,^

,

r

r

/..-

l [ 2 -g- ( . t ) - t r t x ] t l x = 6 m .

J'

13ntark.sl

ll

.ll

Ditteri

|

,

JSGltlx

= l0. cari nilai m iika

f,-

)L2S6l

- mx).lx= 6nt

13markahl

lr

AnswerlJav'apan'. m:

tt

The meanof 5 numbersis 2 Jil . The sum o['the squareo1'thenurnbersis 605 and the

13marks)

varianceis 3,f . Expressir in termsof k

(hta notnbor-nomhor ittrialal't 605 don Min bagi5 nonrbor iatah 2."[i . flasil tttmbah ktLrrsa variansnya ialah 3k2. IJngkttpkan h tlulam :iebutan k.

[3 ntarkuh)

A n s w e r l J a w a p a n '... . . .

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A team of6 studentsis to be chosenfrom 8 boys and 4 girls. Find the number ofdifferent ways the team can be formed if the team consistsof Sekumpulan 6 orongpelaiar akandipilih daripada8 orungpelajar leluki clun4 orangpelaiar perempu.tn.Cari bilangancarupux*an itu duputdibentukjiku pusukanitu terrJiriclaripuda (a)

only boys, han.vapelajar lelaki,,

(b)

the numberof boysand girls areequal. bilungunpelajur Ieluki danperempuanadulahsama. [4 murk.rl 14markahl

Answer/Jawapun : la)

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Diagrarn24 showsthe graphof bonimial distributionfor discretevariableX diskritX. gruJ'taburon binomiulbagipembolehubah Ruiah24menunjuklun P(X : X\

0.3234 tn

0.r 756

Diagram24 Rajah24

Fincl Cori (a) thc value of ru, nilui m , (b) P(.r: I ).

14murksl [4 markahl

AnswerlJau,ttpan

'. (a) (b)

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X is a continuousrandonrvariableof a normaldistributionr.vitha meanof 420 and a standarddeviationof 12. X ialahpembolehubah ruwakselanjarhagi suatutahurannonnal denganmin 120 dan sisihanpiawai 12. Find Cori (a) the z-scorewhenX:.105, skor-zopabilaX=405, ( b ) t h e v a l u eo f k w h e n P ( z > k ) : 0 . 7 8 8 1 . nilai k apttbilaP(z > k) : 0.7881. 14 nturksl 14nrorkoh)

AnswerlJov,apan

: (a)

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SULIT Matematik Tambahan Kertas 2 September 2009 2 lz ja,m

Nama Pelajar : Trngkatan

JABATAN PELAJARAN KELANTAN DENGAN KERIASAMA PERSTDANGANKEBAN GSAAN PENGETUA-PENGETUA SEKOLAH MENENGAI{ MALAYSIA CAWANGANKELANTAN

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2OO9 MATEMATIK TAMBAHAN KERTAS2 Masa: DuaJamTisa PuluhMinit JANGAN BUKA KERTAS SOALAN IN I SEHI NG GA D I BERITAHU Arahan: 1. Kertassoalanini mengandungi3 bahagian: BahagianA, BahagranB dan BahagianC. zJawabsemuasoalandalamBahagianA, empatsoalandanpadaBahagianB dan dua soalandaripadaBahagianC. 3 . Rajahyang mengiringi masalahdalamkertassoalanini dimaksudkanuntuk memberi maklumatyang bergunabagrmenyelesaikanmasalah.Rajahtidak dilukiskan mengikutskalakecualidinyatakan. A Jawapanhendaklahditulispadakeftastulis yangdisediakan. mestiditunjukkandenganjelas.Anda mungkin 5 . Semuakaedahpenyelesaian jika pentingtidak ditunjukkandenganteratur. langkah-langkah kehilanganmarkah 6 . Markah yang diperuntukkanbagi setiapsoalanatauceraiansoalanditunjukkandalam kurungan. 7 . Senarairumusdisediakandi halaman2 hingga4 danjadual taburannormalN(0, 1) di halaman5. 8 . Penggunaankalkulator saintifik yang trdakbolehdiprogramkanadalahdibenarkan. l -

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questions'Thc slmbols givenarethe The following formulaemaybe helpfulin alrsweringthe onescommonlYused. andamenjawtbsoalan'simbol-simbolyang diberi berikutbolehmembantlt Rumus-rumus adalahyang biosa digunakan' ALGEBRA

-ht

8

log. b logob: h% "

o

Tn=a+(n*I)cl

t0

""n

1l

Tr= o"

t2

*. Sn=

l3

s*=

LU

z

,r^ ,an

= Q'*fl

a J

a^

*on

= eil-'

A

(.gm)n = 61'nn

5

l o g om n : l o q a n t* l o g n n

6

m l o-gu-n _ - l o B r n t - l o g n n

7

logo mn : n logn m

= L l z n +( " - t ) , / l 2'

-'

u (t , '

-t\

r_l

'

o(t - ,' ) l-r

q,

t l t-,, ' l''l

CALCULUS KALKULUS y:uv

dy_ 'dr

cly

du

dt

dr

4

Area under a ctlrve Luqs di bawqh leng,kunqi b

[I rv d : r o r ( o t a u )

n z

y. .---u' - - v

dy dv :=Lx-?d x d u d t

dY clr

du ctr

\t-

-

dv d-r

u--

)

b

f-r dv

tt-

Volune of revoluticn Isipadu kisaran

dtt

b f

'),

fn v - d t o r \ a t a u )

b

-

l)

lTLr- d),

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STATISTICS STATISTIK

I

Ft

t

t=T

;--4--

1l

\tv, t, Lw,

fri

8

" P' - = r n l , \n- r)l

g

nc'

Zr l).r"

-^

tI l /-Y I L-r

=z

F ri' l-)

-^

"

["f.ll' /;,,

m:L+

[

\n-r)lrt

l0

r(,rwn) = r'(,t)+P(n)-r(,aan)

ll

f(X = r)= "C, P"l"-'

12

Mean/Min,1t:

LJ

6

'-

, P + q'= |

nP

o = ,frprt t4

x -l.. 7 = o

)

I=9-"100

eo

GEOMBTRY GEOMETRI DistatrceI Jarak

=!G;;t;G)r MiclpointI

't'itik tcngah

6

^

( x 1 + * 2 ) ' r+ - v z ) '

(x,y):t

z

x!+-Yj

?-+

t)

)

tlx- + Y-

2 )

A pointdividinga segmentof a line Titik yang ntcntltoltugi suatu tembereng garis ny+wz) /\ v, r tr , \ : ( n x t + " r x z , m+n ) [ 2l+n 4

Area of trianglc I Ltrctssegitiga

= I I (r,r, + xzlt+ f,:.vr )- (*ry, * 4v2 + *vy)l )1"-

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TIUGONOMETRY TRIGONOMETRI

sin (,4t B) : sin 'zlcosB t cosI sin B

Arc length,s = r0 Panjanglengkok,r =.10

sin (,,tt B) = tin I kos /l t kos Asin B

I

Areaof sector,A :

1rz

cos(,4t B) = coszl cos/l T sin "1sin B tos (,ax B) = kos ,1kos B T sin "l sin /J

g

I

L u a ss e k t o rL, :

,i"0

t0

sin2.{+ cos2A: 1 sinzl+koszl:1 seczA: l +tan2l sekzA:l+tanzA

ll

tanl t tanll , \ tan(l +') = -* o" r-* tt 2tm tl |,dnz'/|-_-_----1 I - titn',,1

(' c o s e c 2 A :i + c o t 2 z l k o s e k 2 l: 1 + k o r z z l s i n 2 A : 2 s i nA c o st l sin2A=2sin,,lkos,'l cos2A -' cosztl - sin2zl :2coszA - | : I - ZsinzA

t)

lJ

sin I

Lt- : /t'

IA la

bz +c2 - 2bccosA lf r- c2 - 2bc kos tl

Areaof triangleI ['utrssegitigu :

kos2A =kos2zI-sin2l = 2kosz4 - | : 1 - ZsinzA

=

sin 1l

sinC

I sinC 1ah

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TIIE UPPERTAIL PROBABILITY Q(z) FOR THE NORIvIAL DISTRIBUTION N(0, l) KEBAMNGKALI,4N HUJUNG ATAS QhI BAGI TABURANNORMAL N I 3

5

'l

6

8

2

()

5

l

o

Minus / Tolak

0 . 0 0.5000

0.4950

0 . 1 0.4602

0.4562

0 . 2 0.4247

t2

1 6 2 0 2 4 28 32

t2

16 20

2 4 28 32

36

t2

15 19 23 27 Jt

35

0.3632 0.3594 0 . 3 5 5 7 0 . 3 5 2 0 0 . 3 4 8 3

n

15 t9

0 . 3 t 9 2{ 0 . 1 t 5 6 0 . 3 1 2 1

tl

t5

A.2776 3

l0

14 t7

3

l0

13 16 t9

0.4840 0.480t

0 . 4 1 6 1 0.472t

0.468 |

0.4M3

0.44M

0.4364 0,4t25

0.4286 0 4241

0 . 4 r 6 8 0.4129 0 . 4190 l,

0.4052

0.4013 0.3914 0 . 3 9 3 6 0 , 3 8 9 7 0 . 3 8 5 9

0.3 0.3821 0.3783 0.3745 0.3lt01 0 . 4 0.3446 0.3409 0 . 3 3 7 2 0 . 3rl 3 6

0.3669 0.3300

0.3264

0 . 5 0.3085 0.3050 0.30rs

0.2946

0.2912 0.?811 0 . 2 8 4 3 0 . 2 8t 0

0.6 0.2743 0_2709 0.2676 0 . 2i4l i

0 . 2 6 1f

0.2578 0,2546 0.25 14

0 . 1 0.2420

0.2389 0.2358 0 . 2tzl t

0.2296

0.2266 0.2236 0 . 2 2 0 6 0 , 2 1 1 7 0 , 2 t 4 8

0 . 8 0 . 2 lt9

0.2090

0.206t

0 .l 8t 4

0.I 788

0 . 2))ll 0 . 1It62

l

0 . 9 0 .I 8 4 1

0.t736 0.l7ll

0 . t 6 8 5 0 . 1 6 6 0 0 , r 6 1 5 0 . r 6 Ir

3

1 . 0 0 .I 5 t 7

0.I 562

0 ,I 5 3 9

0 . 1; t 5

0,14y2 0.t469

0.1446 0.t421

LI

0 .l 1 5 7

0 . 1 3 3 5 0 . r 3 1 4 0 . 1l).92

| 0.t?7

0 .I 2 5|

0 . 1t 5 l

0.llll

0.llt2

0.| 075

0.I 056

0.0968

)18 0.0951 0.0934 0.0,) 0 . 0 7 7 8 0 . 0,64 ''

0.090t

l.l

0.4522

0 . 4181 1

0 . 2) )8 1

0 , l)93 D

0.3228

0 . 2 0 0 5 0 . t 9 1 ' 7 0 .r9 4 9

0.t922

r 0.464

0 . 2 4 8 1 0 . 2 4 r5 0.I 894

0.I 867

4

t8

1 4 1 6 f9

22

t0

t3

7

9t214

6

8

0.| 020

0.0985

2

o

19il

0.0885 0.0869 0.08J3 0.08J8 0.0823

2

0.061E 0.0606

0.0594 0 . 0 5 8 2 0 . 0 5 7 t

1 . 7 0.0446 0.0436 0.0427

29

lt

2

ri30 1 . 5 0.0668 0.065s 0.0643 0.0ii t . 6 0.0548 0.0s37 0.0526 0.0.ij t 6

26

8

2

0.0121 0.0708 0.0694 0.068I

23

8

0 . rt 7 0

0-0749 0.0?15

32

20 24 27 3l 24 27

0 .D 7 9

t . 4 0.0808 0.0793

34

1 5 1 8 2t

0 .t 4 0 t 0.| 001

l0

2 2 25 29

t2

3

0 . 1 2 t 0 0 . rr 9 0 0.I 038

2 2 26

36

t0 8

5

6

4

6't8

1 5 t8

25

20 zJ

16 19 zl t2

t4

t6

f3

15 l'l

t8

il|]t{

t0

t0

lt

t3

0.0559

I

4

561

8

l0

ll

0.0505

0.0495 0.0485 0 . 0 4 7 5 0 . 0 4 6 5 0 . 0 4 5 5

I

3

456

789

0.0409

0.0401 0.0192 0.0184 0.0175 0.0167

l

445

678

0.0329

0.0322 0.01r4

0.0107 0.0301 0.0294

I

2

344

566

0.0262

0.0256 0.0250 0.0244 0.0219 0.0233

I

2

234

455

0.0207

0.0202 0.0197 0 . 0| 9 2

0

I

221

144

0.0r62 0.0t58 0.0r54 0.0t50 0.0r46 0,0143 0

I

222

ll4

0

I

122

231

0

I

llz

222

l

8

r0

0.008890.00866 0.00842 2

1

91214

7

6

8

il

l3

t5

t7

()

7

9

tl

ll

15 17

2 , 5 0.0062 I 0.00604 0.00587 0.0r5 7 0 0.00554 0.00519 0.00s21 0.00508 0.00494 0.00480 2

5

689

lt

12 14

2.6 0.00466 0.00453 0.00440 0.0(427

0.004| 5

| 0 . 0 0 3 7 9 0 . 0 0 , 1 6 80 . 0 0 1 5 7 I 0.00402 0.0019

l

567

9

9

?.'l

0.00307 0.00298 0.00289 0.00280 0.00272 0.00264 I

l

456

789

0 . 0 0 2 2 6 0 . 0 0 2 r 9 0 . 0 0 2 1 2 0.00205 0.00| 99

2

144

566

I

22_l

344

I

222

334

LE

,Ll8 0.0,1

:,36 0.0344 0.0., '..68 0 . 0 2 8 r 0.0274 0.0'..

0.0359 0.035 I

1 . 9 0.0287

2.0 0.0228 0.0222 2 . 1 0 . 0 t 7 9 0.0t74

0,0217 0 . 0t'.12 ,: 0 . 0 1 7 0 0 . 0' 6' 6

2.2 0 . 0 1 3 9 0 . 0 1 3 6 0 . 0 1 3 2 0.0 2 9 2 . J 0.0107

0 . 0f 2 5

0.0t22

0 , 0| t 9

0.0t'6

0 . 0| 8 8 0.0||3

0 . 0| 8 l 0.01l0

0 . 0 r 0 4 0.0t02 990

0.00964 0.00919 0 009| 4

0.00820 0.00798 0.00776 0.0(7 5 5 0.00714 I4 0.007

0.00347 0.00316 0.00326 0.0cl t 7

1 . 8 0.00256 0,00248 0.00240 0 , 0 c

2.9 0.001 87 0 . 0 0 1 8 t 0 . 0 0 1 7 5 0.0cr 6 9 0 . 0 0 1 6 4 0 . 0 0l 5 9

0.00695 0 . 0 0 6 7 6 0 . 0 0 6 s 7 0 . 0 0 6 1 9 2

0.00I 9:l

0 . 0 0514 0 . 0 0 r 4 9 0 . 0 0 r 4 4 0 0 0 r . 1 9

3 . 0 0 . 0 0 t 3 5 0 , 0 0 1 3 10 . 0 0 1 2 6 0 . 0 c122 0 . 0 0 t t 8 0 . 0 0 1 1 40 . 0 0 i1l

0.001070.00t04 0.00100

"f (r)

I

1 3 1 5 18 20

2J

16 16 2l t9

I0

ExampleI Contoh:

rf x - N(0, l ) , then , I i k " e X- N ( 0 , mqka

i),

QQ) QQ) =

l re\ a'

J-

P(X>k)= Q&) z>

2.1)

Q Q . r ) =0 , 0 1 7 e

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SectionA BahagianA [40 marksl 140markahl Answerall questions. Jawabsemuasoalan. S o l v e t h e s i m u l t a n e o u s e q u a t i o nns- I *

+ l:0

andm2-9:2n

Give your answers correct to three deciial places.

[5 mailul I

dan m2 - 9 :2n. l:0 i*+ Berijawapan anda betul kepadatiga tempatperpuluhan. ,Selesaikanpersamctanserentak

[5 murkah]

f'unction r-+ A curvewithgradient

x-

has a tuming point at (ft, 6).

Suatu lengkung dcnganJungsi kecerunan x (a)

R , mempunydititik pusingundi \k,6'l

Find the value of ft.

f2 marksf

Cari nilai k.

12murkuhl

(b) Determinewhetherthe turningpoint is a maxilnumor minimumpoint.

f2 murlcsf atautitik tninimum. 12markithl Tentukan samaadatitik pusinganini adolahtitik mctksimum

(c) Find the equationof the curve. Cari persamaanlengkungitu.

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of first five circlesare Diagram3 showsa seriesof circles.The totalcircumference 60r cm.The lengthsof diameterof circlesis 2 cm morethanthe previouscircle. Rajah 3 menunjLrkkansatu .giri bulalan. .htnlah panjang perimeter bagi limtt bulatan yang pertann

ialah 60trcm.

Ponjang dicnneter bulatan-bulalan itu adalah 2 cm lehih berbanding

bululan sebehrmnva.

OOOO Dragram3 Rclcth3

(a)

13marksl

Find the diameterof the smallestcircle.

13marlcah)

Cari diameter htrgi bulatan )'ang terkecil.

(b)

Calculatethe numberof circularringsthatcanbe madeby usinga pieceof wire with lengthof 260n cm. [4 marks] dawai setrtas Hitunghilunganbulatanj,ongbolehdibentukdenganmenggunakan panJangUta 260 r cm. yutlg 14markahl

(a)

Sketchthe graphofy:-l

sinx | + I for 0 < x < 2,r.

Lakarkangra.l'bagiy : -l sinr | + | trntuk0< x < 2l' (b)

Hence,by drawinga suitablestraightline on the sameaxis,find the numberof solutionssatisfyingthe cquation2,r I sin.r I :x for 0 ( x <2tt. Seterusnya, dengan melakar satu gari.s lurus yang sesuai pada paksi ltang sama, Cari bilangan penyelesaian bagi per,samaan 2:t I sin ;r | : x unluk 0 -<x -<21.

[7 marks] l7 narkahl

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Diagram 5 is a histogramwhich representthe distributionof the times takenby a group of45 studentsto travel to school. 45 orang Rajah5 ialah histogramyung mewakilitaburanmasayungdiambilolehsekumpulan pelajar untukpergi kesekolah. Numberof Students BilanganPelajar l5

t2

8 6

9.5

t2.5

15.5

18.5 2t.5

1A <

T i m e t a k e n( r n i n t r t e s ) Masa d i anrhi l (mit :i t .\

Diagram5 Raiah5 Calculate Hitung (a) the valueof k,

ll markl

nilai k,

] morkaltl

(b) the rangeof the timestaken, julat bagi masa diambil,

(c) the standarddeviationof the distribution. sisihan piawai bagi taburan itu.

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347212 (9) Diagram6 showstriangle OPQ . The point S lies on OQ andPR . ThestraightlinePR intersectsthe straightline OQ at the point S' .segitigaOPQ.Titik S terlelakpada OQ danPR ' Garis lunts PR bersilang Raiah6 menunjukkan dengangari.rlunrs OQ di titik S .

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Diagram Rqah 6 (a) Expressin termsof x and v : Ungkapkandalamsebutanx

dan )t'.

+

(i)

(ii)

12 murlc';l

RP

l2 markahf

"o +

_+

_

(b) Using OS : hOQ and P.S- k PR, whereh and k are constants,find the valueof h and of k. +-t+

-- k PR dengan keadqln , OS : h OQ dan PS pemalar, cari nilai h dQn nilai kMenggunakan

h dan k iqlah

15marb) 15nurlrahl

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SectionB Bahagian B 140murlul [40 markah] Answerany four questionsfrom this sectiou. Jav,abmanalnana empat srsalandaripodabnhagianini. : x -2 cutsthe curveat Q(0,-21 Diagram7 showspartof the curve.lr': 4 -,r. The line-y, and P(,r,y). Rajah7menunjukkunsebahogiatttlari lengkung.v: = 4- : .Curis!unt.s t'=x''2 lenghmg pada titik Q(0. -2) dan P(r,.r).

mentttktng

Diagram7 Rajah7 Find Cari [2 rriarks] 12ntat'kuhl

(a) the coordinates of P, koordinat P,

(b) the area ofthe shadedregion, luas kawasen berlorek,

[4 rrarksj 14murkuhl

by the curve (c) the volunregenerated,in tenn of ;r whenthe shadedregionboLrnded [4 rliirks] t-' : 4-x andthe line y : x *2 is revolved360" aboutthe y- axts. isipadu yang diiunakan dalam sebulan rr apabila ronldu ber'lorekyang dibutusi olch lengkttng f4 ttrurltuhl v2= 4 -x dangarislttrus.y: x-2diputarkanmelului 360opadapali.si-.t:

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Use graph paper to answer this question. Gunakankertas graf untuk menjawabsoalan ini. Table 8 shows the values of two variables,,yand-y,ollLarnedliom an experilncnt. V a r i a b l e sx a n d l t a r e r e l a t e d b y t h e e q u a t i o n y = p . l . r + q , w h e r e p a n d q a r c

constants.

Jadttal 8 menuniukkannilai-nilai bagi cluapembolahubah,x dan .v,.t,angdiperoleh duripadu salueksperimen. Pembolehubahxdun.ydihubungkanolehpersamdon y= plx*q, dcngutr keadaanp dan q ialah pemolar.

x

1.0

1.5

2.0

2.5

3.0

3.5

v

5.7

6.5

7.3

8.0

8.7

9.3

Tablc 8 Jadual 8 ( a ) P l o t l 2 a g a i n s t x , u s i n g a s c a l e o2f c m t o l u n i t o n t h e , r - a x i s a n Ic lc m t o l 0 u n i t s on the y-axis. Hence, draw the line of best fit. 15 mtrrksl Plot y2 melawanx , dengan ntengpiunakanskala 2 cn kepada I unil pada pak.six clan I cn'r kepada l0 unit potletpaksi-y. Seterusnya,lukisgari.sluruspenl,uaianterboik. l5 markuhl (b)

Use your graph in 8(a) to find thc valuc of GunakangraJ'di 8(a) untuk mencarinilcti (i) p, (ii) q, (iii) x wheny: 7.0. x apabiloy :7.0.

15murksf 15markuhf

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Diagram9 showsa sectorOMN of a circle,centreO andradiusl0 crn. The pointP ro OM. lt is grventhatZOP= 3PMlieson OM andPN is perpendicular sektorOMN bagi suatubulatanpusot O denganieiari 10 cm. 9 merurnjukkan Ra.iah Titik P beradq di etas OM dan garis PN adalah bersereniangkepaclagaris OM. Diberibahawq2OP:3PM. ( U s e l G u n ax = 3 . 1 4 2 )

Diagram 9 Rujah 9 Calculate Hitung (a) thc length, in cm, of OP, panjemg dolam cm, 0P, (b) the angle, O, in radian, sutlut, 0, daI ant radiu n,

I morkl [1 ntorkah] 12marlLsl f2 ntarkahl

(c) the perimeter, in cm, of the shacledregion,

[4 morks]

perimeler, dalam cnt, kavtasanberlorek,

14murkohf

(d) the area,in cm? , of shadedregion. lna.s,dalenr cmt , ka*usan herlorek'

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10 Solutionby scaledrawingis not accepted. Penyelesaian secarcllukisanberskulutidakditerima. Diagraml0 showsa triangle PQR. PointS lieson Pp. Rajah l0 menunjukkansegitiga PQR. Titik S terletak pada gartsPQ.

Diagraml0 Rajuhl0 lrom pointS is always5 units. (a) A pointMmovessuchthatits distance

f3 murk';l

Find the equationof the locusof M 5 unit. dari titik S aclalahsentiq.sa Suattrtitik M bergerakdengankeatlaan.jarukn.va CaripersamaanlokusM.

13murkuhl

(b) It is giventhatpoint P andQ lie on the locusof M Diberi buhawatitik P dantitik Q terletukpuda lokuslv[. Calculate Hitung (i) thevalueof ft, nilai k. (ii) the coordinates of p. [5 murlu] 15markah)

koc,trdinal Q.

(c) Hence,find the area,in unit2, of trianglePQR cari luas,dalamunit2,bagisegitigaPQR. Seterusnya,

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(a) A studentis consideredpassthe test rvheneversix often questionsare being answeredcorrectly. If 8 studentsare chosenat random, calculatethe probability that Seorongpelaiar dianggap bcrjal;u dalam u.iictn.jikadapat menfav'ab enan dari sepriluhsoulan -r,angtliberi. Jiko 8 orung ltelajar dipilih,secara rawak, hin.tng keburungkulian

pass, (i) exactly2 students tepat2 orartgpelcr.jar ber.ia.y'a, (ii) moretharrI studentpassthetest. lebih daripcrdu scorang het'ftr.t,adalam triian ter.srhut

15murksl 15murkuhl (b) The heights of studentsin School I are nonnally distributedwith a tnean of 1 5 0 c r n a n d a s t a n d a r dd e v i a t i o no l l 0 c m . Ketinggionpelajar tli SeliolahA odalah bertaburanse(ara nonnal denganminttvtr piau,al l0 crn. l50 cm dan .si.sihan (i)

Height exceeds 170 cm are classifiedas tall. It is found that 5'7studentsare tall. Find the total enrolment of the school. Ketinggittnntclebihi 170crn dikatakantinggi di sckolahitu. Didaltati 57 pelaittr aclalqh tinggi. Cari enrolmensekolah itu.

(ii) If 30% of the stLrdents are categorizedas shoft. What is the height which is still short'/ Jika 30ohdaripada pelajar itu dikategorikan rendah. Berollakah ukurun ketinggian ),ang masih clikotakctnrcndalt'l 15 marksl 15maduhl

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120marksl 120mctrkcrhl Answerany two questions from this section. Jawab mana-manqdua soqlandaripadabahug;ttnini. 12 A parliclenlovesalonga straightline andpasses througha flxed point O. lts vclocity, , m r - ' , i s g i v e n b y v : 2 t 2 - 7 t + 3 , w h e r e t i s t h e t i m e i n s e c o n d s a tlteear v i n g p o i n t s O . Satuzarah hergertrkdi ,scpanjangsuolu€lari:;lunrs dun melalui .sttttrlilik letap O. H u l u j u n v ur,m s - ' , t l i b e r io l e h v : 2 i ' - 7 t + 3 , < l e n g u n / i u l u h m u . : u a l u l u n t s a u. ls c l a p u s mclaluititik O. Find Curi (a)

(i)

the tirne intcrval during which thc particlc movcs towards thc lcfi, julal ma.saapabila zarah itu bergerctkarult ke kiri,

(ii)

t h e a c c e l e r a t i o no f t h e p a r t i c l ew h e n t : 2

seconds,

pecutanzarah itu aptrbila| :2 saat, (iii)

the time when the velocity is constant. ntasa apabilo haloiunya malar. l5 mttrks) 15nutrkuhl

(b)

Sketch the velocity-time graph of thc motion of thc particle for O < t < 3. Lakurkangra/'haluiu-nrusabugi pergenrkonzurah ilu untttkO < t < 3. 12 norlcsl 12nrrrliull

(c)

Calculatethe total distance,in m, traveled during the first 3 secondsafter leaving pornt O. IIinng.juntlah jarak, tlalam m, yang dilului dulum 3 suut ydng pcrtumtt sc!epttsmelului titik o. 13 murks) [3 ntarkuhl

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Table 13 shows the prices, the price indices and percentageof usageof tbur items A, B, C andD, which are the main ingredientsin the manuf'acturingof a types of biscuits. Jadual 13 menunjukkanharga, indek horga dunperatus penggunaanernpat barangan A, B, C dan D, yang mentpakan bahan utama dalam penghasilunsejenisbiskut.

Item Item n

,|

2007

Price index for the year 2007 basedon the year 2005 Indekshargnpadatqhun 2007 berasas tahun2005

45

125

7m

Price per unit (RM) Hargaper unit (RtuI)

2005 n

Percentageof usage(7o) Peratus penggunaan

B

55

q

t20

8m

L

40

/1")

105

2B

D

50

47

r

(oh)

9m

Tablel3 Juduul13 (a) Find the value ofp, of rTand of r'.

13rnorksl

Cari nilai p, nilai q clannilai r.

13marliuh)

( b ) Statcthc valueof rr. I'lence,calculatcthc colnpositcindextbr the costof

the biscuitsin the year2007basedon the year2005. manufacturing

13marks)

N.vatakannilai m. Sctet'usrt1,4,hitttng notnbor indelcsgubahan bugi kos penghosilan 13 markuhl biskut itu patlu tahun 2007 berasaskan tahun 2005. (c)

thc priccof a box of biscgitsin thc ycar2005if thc corresponding Calculate pricein the year2007is RM 25.70 12murks) paclu tulrun hurganya patla 2005 tuhun .veputlun hiskut Hittrnghargasekotak lika .vang 2oo'7iolohRM 25 70 [2 tnut'kttlt)

the biscuitsis expcctedto increascby 20% Il'ornthc ( d ) The coastof manulacturing ycar 2007to the year2009.Findthc expcctedcompositcindcx fbr thc year2009 basedon theyear2005. l2 nurksl Kospenghasilan hisktil ini dijangktt neningkat sebanyah20uh dari tahun2007 lic tuhun2009. Cari nontbor inde.k.tgubahan yong dijangkalran pada tahun2009 heru.stt,tkrtntahttn2005. 12 markahl

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14 Diagram14 showstwo triangleABC andACD. I ABC is obtuseand sin I ABC =

3

Giventhat AB - 7 cm,BC - 5 cm and CD:9 cm. Raiuh I4 menunjttkkan dua ,segitiguABC dan ACD Diberi bahawa AB : J cm, BC : 5 cnr und CD:

LlBC

atlulah cakah dan sin I ABC

:i 5

9 cm.

Diagram14 Rojuh 14

Caiculate Itlitung

(a)

the length, in cm, ol- AC, punjung,duluntcrn.bugi AC,

14nrurksl 14murkuhl

(b)

t ADC,

12murks) l2 marliuhl

(c)

the area,in cm2, of theABCD. luas,clulamcm'.ABCD.

14 nturksl 14ntarkaltl

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Gunakankertasgraf untukmeniaw'uh,soalut itti. The English Languagesociety sells.r packetsof snackA and;r packetsof snack B at a school funfair. Persatucrn Bahasa Inggeris ntenjual x bungkus snek .4 dan v bungku,t snek B pada hari pasoria sekolalt. Thc numbcr of packcts of snacksis bascdon thc fbllowing constraints: Bilongon bungkus ,snekherdo,sarkanpada kekctngonberikut '. I :

T h e n u m b e r o f p a c k e t s o f s n a c k A i s a Ll e a s t 15 0 . 150. Bilungun btrnghr.ssnckA sekurung-kurangn.t,u

Il

:

T h c n u m b c r o 1 ' p a c k c t so f s n a c k , 9i s a t l c a s t2 5 0 250. B sekurung-kurungn.t'u Bilungun httngkr.;,snek

III :

The total nurnberof snacksA and Il is at least500 but not ntore than U00. 500 tetopi tidok lebilt Juntlahhiltttrgun.strckA tlun B .sckurttng-k:trengn.vu dttri 800.

(a) Write three inequalitics,other than x := 0 and y > 0 , whiclr satisly all thc 13 ntorhs)

above constraints selainduri -r ", 0 und t, Tuli.sliga ketttlLyttmuun

--> 0 ,.vangtnctnctttrlti.tL'tnttd 13ntttrliah)

kekongantli cttus. ( b ) B y u s i n g a s c a l eo f 4 c n r t o 2 0 0 p a c k e t so f a s n a c k so n b o t h a x e s , constructand shadcthc rcgion R rvhich satisficsall thc abc'rvcconstraints.

[3 rnarks]

,skoltt4 cn kcprclu20{'lbungkussnakpada kedua-duopak,ri, Dangunmenggtrntrkotr santuukakunguntli u/tt.t. hinu dun lorck runtuttR vungntcntcnuhi

[3 nurkuh]

( c ) T h e p r o f i t o f a p a c k c t o f s n a c k , 4i s R M 0 . l 5 a n c i t h c p r o l r t o sf n a c k B i s R M 0 . 4 0 by using the graph fionr (b), find snckA iuluh ltM0.l5 clunkeuntungutlrugisnckB iuluh Kauntttngurt bugi .sabungltus RM0.40, dengonmanggunakangrtd dari (b), c'ari ( i ) t h c m a x i m u m p r o f i t f r o m t h c s a l c o f s n a c k sA a n d B , keuntungan ntoksimumiuulon snek A don B, (ii) thc minimum profit fiom thc salc of snacksA and B. keuntungttn minimumittalan snek A dan B [4 nrarks] [4 nnrkah)

END OF QUESl'lON PAPER KERTAS SOALAN TAMAT TAMBAHANKERTAS2 SP[,4(2009).N,'IATEMATIK PERCUBAAN

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