Spm Percubaan 2009 Johor Add Maths

SULIT

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NO. KAD PENGENALAN ANGKA GILTRAN

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM 2OA9

3472/l

ADDITIONAL MATIIEMATICS Kertas I Sept. 2 Jam

D ua i am

JANGAN BUKA KBRTAS SOALAN INI SEHTNGGADIBERITAHU 1. Tulis nombor kad pengenalandan angka giliran andapadapetakyangdisediakan.

UntukKegunaan Pemeriksa Soalan I

Markah Penuh

2. Kertassoalanini adalahdalamdwibahasa.

2 3

3. Soalan dalam bahasaInggerismendahului soalanyang sepadandalambahasaMelayu.

4

4 3 3 3 3 3

4. Calon dibenarkan menjawab keseluruhan atau sebahagiansoalan sama ada dalam bahasalnggerisataubahasaMelayu. 5. Calon dikehendakimembacamaklumatdi halamanbelakangkertassoalan.

5 6 7 8 9 10

Markah Dioerolehi

2

3 2 J

2 2 3 4 5 6 7 8 9 20 2l 22 23 24 25 Jumlah

J

2 4 A

A A

, A J A

+ ! A

80

Kertassoalanini mengandungi 20 halarnanbercetak 347211

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giren are lhe ones T'hef|ltov,ing -formulae may be hetpfut in onsw-eringthe qttestions The synbols commonly used. ALGEBRA 1

-b + r lh' - 4ac

x=

l oc.b

l Oe"D= 'l og. a

8

2a

fn:6r(n-l )d

2

r!' x Ll'= Lt "' n

3

t!'+on-

4

(u"')n=a'"'

ll

n-t Tn = a"r

5

log. mn = log am + laga n

t2

S'n=

6

log"

a il' n

10 s"= llzr+(n-l)dl

2'

7

nl'

= log sn - log'n

n log"m':

a(r' -l \ r-l

d S"_= l -r

n lo g o m

u(l -r' ) l -r

=--J,l .r+t)

..

l' " l. r

C AL C ULU S

l=tw,

dv dv -;=t t ; + v ; dx ax

du

du

dv

ax

Area undera curve I

: .v clx

tt

rd yv .

,

=-

dy

tly

du

dx

du

dx

dx

dr 1

or

lY.lr f

=

lx ttV

Votumegenerated

= |tt /w " ctr or oo =

lt l l r {)-

dy

GEOMETRY

1 Distancc =

- -'r,)' + (jr,

2 Midpoint

(x.+xl \,. t r, - + .;r , = { . lr l

(r,r)=

+ -Yr .Y:) ' 1)

5 A pointdividinga segmentof a line ( ra, mr, nv, + .y, ) (r,.v)= i -' i nt+ tt / \ tl r n 6 Areaof triangle

:Jl,,r,r, +,r,-)/3 + r;/', ) - (t,.v,+ r',y,+'t,y',)l

xt+y.l

^

l) 7

V-r-+.Y-

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3472t1 STATISTIC

x

x

= II

7- Zw,I,

N

Lw,

=21 Zr

=,! (n- r)l nl

3o= ,F:,tr ;

'

4-,ry=ffi;

l0

P(Av B) = P(I)+P(B)-P(AnB)

tl

P (X = r) = nC ,p' qn-' ,p+ q:

1)

Meanp- np

[1r-"]

5 m= r+l2-lg

IJ

l'' l

(n - ry.vl

l4

o = J;pq x- u o

6

I =&x100 Qo

TRIGONOMETRY I A r c lengt h ,s = r0 2 A r eaof s e c to r,L = !r' 0 2 3 sinzA + cos 2l : I

9 sin (l t B) : siM cosB t cosl sin.B t0 cos(l t 13)= coM cosB T sinl sin3 1l

4 sec2A=| +tan2A 5 c os ec 2A - l + c o t2 A 6 sinZA:2

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tanA+ tanB lT tanAtanB

o =b =, sin,4 sinB sinC

sinA cosA

7 cos2A = cos2l -sin2 A :2 cos2A- | = |- 2 s i n 2 A g tan2A -

I2

Ian(.{ +

l3 a2= b2+ c2 - 2bc cos"4 I

t4 A reaof tri angl e = :absi n C -2

Ztan4 1-ta n ' A

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For exomrner's use only

Answerall questfbns Diagr a m1 s h o w stn e g ra p ho f th efu n c ti on.f (x) = l x+ i i , forthe domai n - 2< x < 5 . graf f (x) = l.r + | l, untukdomain-2<x<5 ' Raiah1 menuniukkan

S t at e: Nyatakan'. ( a) t he / -' (5 ) ( b) f |Q )

12marksl 12markahl (a) ...... lJawaPan: Answer

I I

(b)

2.

G iv ent h e fu n c ti o ngs :-r+ 7 .v + l Diberfi un g s gi ' .x -+ 7 x + 1 ( a) (b)

a n d h ' . x-+ { -t 3

d a nh :x -+ !* t

fi nO,

C ari ,

g- ' (8 )

14marksl 14ma*ah)

sh(x)

(a) Answer/JawaPan'. .

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(b)

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3.

Giventhefunctions .f(x) =-:; Diberifungsi"f(x) = -:;x-l

and gf(x) = 5x- 4.Find g(.r).

dan gf (x) = 5x* 4 . Carig(x) . [3 marksj 13maftahl

3

| I

l---l 3l

AnswerlJawapan:

4.

Giventhat3 and k aretherootsof thequadratic equation x' +.r = p. Findthevalue of k andp. Diberibahawa3 dank ialahpunca-punca wrsamaankuadratik.cai nilai k dan p . 13marksl [3 markah]

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c Diagram5 showsthe graphof /(x) = a(x - b)2 + c' Statethe value ol a 'b and ' Rajah5 menunjukkangraf f (x) = alx - b)'1+ c'Nyatakannilai a 'b dan c

A

[3 marks] [3 markah] x-b)2 + c

5 Diagram Rajah5 Jawaqan'. Answer/

6.

functionf (x) = 2x' - 7' findtherangeof r if /(x) > I l . Giventhequadratic (x) = 2x' -7, carijulatbagix jika f (x) > l l . Diberifungsikuadratik -f

[3 marks] 13ma*ahl

6 I

I

Answer/Jawapan :

t, 347211

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7.

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Solvethe equation3'*' Se/esaikan persamaan

[3 marks] [3 markah]

1

I I

r--1 lrl

Answer/Jawapan:

Giventhat log3x = loge4, findthe valueof x. Diberi log3x = Iogg4, cari nilai x.

[3 marks] [3 markah]

Answer/Jawapan.

Findthesumto infinigof thegeometric series 1 * I * -!-*.. 24 Carihasiltambah hinggaketakterhinggaan bagisirijanjang geometri t *] ) , *1*.... r 12marksl 12markah) 9

[J

I

t2l Answer/Jawapan

r) 347211

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progression - 5, - l, 3,... sothatits of termsinthearithmetic 10. Findtheleastnumber sumexceeds200. Caribilangansebufante*ecil dalamianiangarithmetic-5, - 1,3,...supayahasil tambahsebutanmelebihi200. [3 marks] 13markahl

l0 |

Answer/Jawapan

11,

.--l

I lr l

progression are2 , y and18. positive termsof a geometric Thefirstthreeconsecutive Findthecommonratioof theprogression. Tiga sebutanpeftamasuatuianianggeometriialah2 , y dan 18' Cari nisbahsepunyabagiianiangtersebut.

1 2ma * s l 12maftahl

r-= ll

I

....., Jawapan: Answer/

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l2 l

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12.

n y = +, wherem andn are bytheequatio x and ), arerelated Thevariables n constants.Diagram'12 snowsthe straightlineobtainedby plottinglogr y aga i n s tx .

manam dan y = 4'0, x dany dihubungkanolehpersamzotl Pembolehubah n n adalahpemalar. Raiah 12 menuniukkangarislurus yang diperolehidengan memplot log, y melawan x .

D i a gram12 Rajah12

Findthe valueof m and of n. Cari nilaim dan n.

[3 marks] [3 markah]

t2 lrI l3l Answer/Jawaoan

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Diagram13 showsa straightline PMQ. Rajah 13 menunjukkangaris lurus PMQ.

P1-s+ l,-4t)

QQ + 7,s -21 D i a g ram13 Rajah13

Giventhat a point M(4,4) dividesthe linesegmentjoiningthe pointsP(s + t'-4t) and QQ +7,s - 2) in the ralio 2: l Findthe valueof s and f. Diberi titik M(4, 4) membahagitemberenggaris yang menyambungkantitik P(s + t,-4t) dan QQ + 7,s - 2) dalamnisbah2:1. Cari nilais dan t. [ 4 marks ] 14markahl

l3 I i Answer/JawapSl?i s =

r\

t-

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14. Diagram 14showsa straight lineABwhichintersects to thestraight lineCDat thepoint T(2,3) Raiah14menuniukkan garislurusAB bersilang dengangarislurusCD padatitikT(2,3)).

*1"*q 2 Diagram 14 Rajah14 Theequation of thestraightline ABisy=-1r+4 2

andtheequation of thestraight

line CD is y = 2y - 1.

Persamaangarislurus AB iatahy = *1, + 4 dan persamaangarislurus CD ialah L

Y=2x-l Calculatethe areaof the trianglel7D . Kirakan luas segitiga ATD .

[3 marks] l3 markahI

t4 I I ()

r---1 l3i

Answer/ Jawapan:

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15.

vectorof 2g- b. Diagr am1 5 s h o w sv e c to rs4 a n d !. D ra wthe resul tant Rajah15 menunjukkanvektor a dan \. Lukiskanvektorpaduanbagi 2a - b. 12 marks) [2 markah]

/ g

,/

D i a gram15 R aj ah' 15 Answer/ Jawapan

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16.

-+a

The vectors PQ and Rf are parallel.lt is giventhat PQ= 2?- 3! and -+o

nS = (t +Ds-;b..

-> -> -) VeKor PQ dan RS adalah selai. Diberi bahawa PQ = 2a -3b dan -tq RS = 2Find Cari (a)

the value of /r Nilaibagi k

(b)

the ratioof PQ: RS Nisbahbagi PQ: RS

[4 marks] 14ma*ahl

t6 I

I

r\

r-i

Answer/Jawapan:(a'1

l4l

(b)............. 347211

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Giventhat coSI = p and0 is an acuteangle,expressin termsof p . Diberibahawa kos0 = p, dan 0 adalahsuatusuduttirus,ungkapkandalam sebutanp bagi (a) tan d e (b) sin; z

t7 Answer/Jawapan:(a)

I I

r-l4 l

.A

18.

Given y = :j , find the approximatevalueof y , when ;r changeslrom 2 to 2.02. x )4

Diberiy =:, , cariperubahannilaibagi y , apabilax berubahdaripada2 kepada x 2.02. 14marksl 14markahl

18

I Answer/ Jawaoan. 3472/1

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3472/l Diagram18showsa seclorOPQwithcentreO andradius5 cm. Rajah18menunjukkan seldorOPQyangberpusatOdanjejari5 cm.

O

Rl cm

O

Diagram18 R a jah18 Given QR =1 cm and IPRO = 900,findthe areain cm2 , of the shadedregion. Diberi QR=1 cm dan ./.PRO= 900 , kirakanluasdatamcm2 bagi kawasanbedorek.

14marksl 14matuahl

l9

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Answer/ Jawapan

tt

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I

20.

Findthe coordinatesof the turningpointson the curve / = 4x + - and determinethe x maximumDoint. I

Cari koordinatbagi titik-titikpusinganbagi tengkungy = 4x + i- dan tentukan x titik maksimum. 14marksl 14markahl

20

t--J l4 l

A nsw er/ Jaw apan.'.........

I Giveny =#

x-

= 3g(r) whereg(r) is a function of x. Findthevalueof

and

!,s@)a' 1- _1

Diberi y=2-:

dan

dy

= 3g(x) di mana g(x) ialahfungsibagi x . Cari nilai

Isi)ax' 14marks) 14markahl

2l

I I Answer/ Jawapan : 347211

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Table22 showsthe marksof a groupof studentsin an examination.

22.

Jadual 22 menunjukkanmarkah sekumpulanpelajar yang diperolehidalam suatu peperiksaan. Marks Numberof students

1i?

4

6

7

8

Iable22 Jadual22 F ind Cari (a)

the maximumvalueof x if the modemarkis 8. nilai markah bagi x jika markahmod ialah 8.

(b)

the minimumvalueof x if the meanof the marksis greaterthan 3 nilai minimumbagi x jika markah min lebih daripada3. [3 marks] 13markahJ

22

t--_l I r--I

Answer/ Jawapan (a) (b)

lrl

23.

Findthe numberof waysin which4 boysand 5 girlscan be seatedin a row if Cari bilangancara susunan4 budaklelakidan 5 budakperempuanboleh duduk. (a)

thereis no restriction tiada syarat dikenakan

(b)

the boysand the girlsare seatedallernately pelajar lelaki duduk berselang selidenganpelajar perempuan. 14 marks) 14markahl

)7 tl

I I

r-1 l4l Answer/Jawapan:(a)

\l

(b) . 317211

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24.

For examiner's use only

f abire24 shows the numberof colouredmarblesin a bag. Jadual 24 menunjukkanbilanganguli bervvarnadi dalam satu beg.

Colour

Numberof marbles

Red

4

Green Purple

x+2 2 Table24 Jadual24

A marbleis drawnat randomfrom the bag. Giventhat the probabilityof gettinga I

greenmarbleis -. Findthe valueof -t. Sebijigulidikeluarkan sscara rawak daripadabeg. Diberi kebarangkalianmendapat I

sebijiguli hijau ialah;. Cari nilai x. J

[2 marksl 12markahl

24

I r'l A nsw er /Jaw aD an: ......... 347211

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S ULI T For exonriner

25.

graph Diagram25 showsa standardnormaldistribution

useonlr-

Rajah25 menunjukkangraf taburannormalpiawai. 1 (x )

represented by the shadedregionis 0.7514. The probability Kebarangkaliankawasanbedorekialah0.7514. (a)

Findthe valueof & , Carinilaik.

(b)

with a mean whichis normallydistributed X is a continuousrandomvariables 80 and a varianceof 9. Flndthe valueof X whenthe z-scoreis t . X ialahpembolehubahrawakselaniaryang beftabursecaranormaldengan min 80 dan varians9. CarinilaiX iikaskor'z ialah k .

14marksl 14markahl

25

[J I

Answer/Jawapan:(a)

l4 l

thl tv,

,..'.

EN D O F QU ES TIONP A P E R

()

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INFORMATIONFOR CANDIDATES MAKLUMAT UNTAK CALON paperconsists of25 questions L Thisquestion Kertassoakn ini mengandungi25 soalan 2. Answerall questions. Jawabsemuasoalan paper. providedin thequestion in thespaces 3. Writeyouranswers Tulisjawapan andadalamruangyang disediakandalsmkertassoalan. 4. Showyour working.It mayhelpyou to getmarks. pentingdalamkerja mengiraanda.Ini bolehmembantuanda Tunjukkanlangkah-langkah untukmendapatkan markah. youranswer, thatyouhavedone. crossouttheanswer 5. If you wishto change Thenwrite downthenewanswer. Sekiranyaandahendakmenukarjawapan,batalkanjawapanyang telah dibuat. Kemudiantttlisjcwapan yang baru. providedarenot drawnto scaleunlessstated. 6. Thediagramsin thequestions Rajahyang mengiringisoalantfulakdilukis mengihttskalakecualidinyatakan. 1. The marksallocatedfor eachquestionareshownin brackes. Markahyang diperuntukkanbagi setiapsoalanditunjukkandalamkurungan8. A list of formulaels providedon pages3 to 5. Satusenarairumusdisediakandi halaman3 hingga5. 9. A bookletof four-figuremathematical tablesis provided. Sebuahbukusifr matematikempatangkadisediakan. 10. You mayusea non-prograrnmable scientificcalculator. Anda dibenarkanmeng,gunakan kalkulatorsaintifk yang tidak bolehdiprogram. paperto theinvigilator I l. Handin thisquestion at theendof theexamination. Serahkankertassoalanini kepadapengawaspeperilcsaan di akhir peperiksaan.

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suLlr 3472t1 Additional Mathematics Kertas 1 September2009 2 Jam JABATANPELAJARANNEGERIJOHOR PERCUBAANSPM 2OO9 PEPERIKSAAN MATHEMATICS ADDITIONAL Kertas 1

JANGANBTJKABUKUJAWAPANSEHINGGADIBERITAHU

MARKING SCHEMEI ------J

6 halamanbercetak l(ertassoalanini mengandungi

347211tlak CiptaJPNJ 2009

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Submarks

Solution (a) 4 (b) 5

(4 s18)= 1

2

g-'(x) = " =' /

B1

lv

( b)gh(x) = -^ - 6@ equiv a le n t J

qh(x) =z(!-1) + 1 '

'a

(l^

.l

9 l ;-r \J

rJl

^)

\ )

I

1(

g(x) = - TU x

3

11

9(Y) = j5 l

\v

la

) '-l

B2

)

I.

rtl ----1..-*- i= ) \ - 4

)l

\x-r J

i

x- _1 p=12 k=-4

82

3+k=-1 @3k=p@ equiva le n t

B1

J

(a)a=1 (b)b=3 (c) c= -3 6

x<-3 , x>3 \,/ ' t/

*--\ :\--3 \-/

/zi -:+ 3

@equivalent

B1

(x+3)(x-3)"0 @ x=t3

i

'L__

_l

82

'

-L

fotal marks

Submarks

.x

J

=*-

Totalmarks

I

9 l 8 (3 -) = 2

I

2 7 (3 ',)-g (3 .1 = 2

82

3 *.3 3- 3 *.3 2=2

I

f-

I a i" :, li rog,x =los,zqlu,g,+

I

i

i

oranybase i log,x = 19"sJlog19

I

/"

l--:

I

it

t--T-_lt

I I

ll"

i

l^

I

l) o o = -..-.-

B1

I'

l

l81

iirl

: t-*-f"--, o n=12 il1

i

i

I i

t:*ol_:5rli?_og i ,,' 2(2) i,,-

it

j ;[:r-s)+(i?-l)4j,2oo

i

i1-

I is"200 i--]*tr

i

I tt i

1, .=18:

2

i l, i2

B1

v

it f--T-_1 2 j m=1 6a n d n =1 .7 4 1 1 i ii

J

i

-loezr=-! orlog lo g , n ltos,m=4or

i li

I

tl

log,),= logzat_ "rlog,n

82 B1

il

L_t_ _-

A T

-,-.----_-L

L__

S[b marks T Totalmarks -;-| l =6 a n d s=-2 0 t=6 o r s=--2 0 s + 3 / = -2 ,2 s- 4 t =1 6 (Solvesimultaneous equation) s+l+2t+14

? 1 -'l-l 2'l

.r ol L-ol

82

1lo 2 - _ *'

a

I I li

tl+

a

r

ol

o

4l

I

-r

A (0 ,4 o ) r D (0 ,-1 )

/

2

,l /

B1 either2aor

\ \ .(l

-b

t,

\ !

\ \

(a) k=2 ')*-

a

2 q

=3 ), k +7 =2 )@,: "2 g

(ft+ l )q- ::h = l (2 q -3 [) @ equivalent 2nS = .1.pQ

.--]

( a)

1 O'-

t. rvl l-

p

lr- p' (01

.e r:;'

srn--=^l ? \l Ll

)

g\ ^( 2sin'l - | \2)

'o:l-

2.044 cmz 1^ 1

4

- _(aX3) :(5)'(0.6435) 2'' 2 l1

1$)'

(0.643s)or

B3

1{+X3)

82

Shaded region = Apon- Apon IPOR = 36.870 or 0.6435racl

.V= 1 .4 4

4

-0.06

B3

-96 6y=--:x0.02 aa -

82

3Z

),, ? = - 4(21)x'5 dx

( -t

or -4(24)x

\

| -:.4 I

I

I

I

I II I

\2

5

I

4

)

d'y . d2,, -;* = -;2 ?r.rd -=4 ,= -16

dx'

x''

dx'

B3

,l 4-L-'

2 Q- = q- --1-ro equivatent clx

t_

x'

82 B1

I

I

.;4 J

ZA:i--2(--1)- 3 J

,.] l?r"-11' " l

t -" lr l

Ix-l

L

t Izx-:l

;t

?

I

rl_ x-

I

(a)7

B1

(b ) .r=1 x>0

I*:31:J":!l 2 5 +x

,s 2 B1 I

B1

x t-2 8+x

I a

(a) k-0,679

2

P(Z>k;=A.2486

= 82..031 (b) .r .r=8203' I I(b) il I lo67e=tjlo

L _i__

I

II

I

__i_

B1

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Additional Mathematics Kertas 2 Sept2009 ^l /-lam 2'

JABATAN PELAJARAN NEGERI JOHOR PERCUBAAN SPM2OO9 PEPERIKSAAN ADDITIONAL MATHEMATICS KERTAS 2 Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1.

Kertqs soalan ini adalah dalan dt,ihahasa.

2.

Soalan dalam baha,saInggeris mendohuluisoalun yung,sepadundalcnnbahal;allfelayu.

3.

Calon dikehendakirnembacemaklumaldi halarnanbelakangkertas,soalanini.

4.

Culon dikehendakimenceraikanlwlamctn I9 dan ikat sehagaitnukahadapan hersama-sama de,nganj atvapan awla..

Kertassoalanini mengandungi t9 halamanbercetak dan I halarnan kosong J+ L L t,1 .

SULIT

347212

2

sulrT

Thefollowingformulae may be helpful in answeringthe questions. Thesymbolsgiven are the onescommonlywed. ALGEBRA

-b+ "[Y 4o; x=

8

2a

: fo8'b tog,a l Qgc a T,:a+ .(n-l )d

2

q ^ xa n=

3

a ^ +t{= a^' n

t0 s^:

4

(am)"= ann

ll

5

logo mn = log um * loga n

t2 ;="

6

lo g"m:bggn- logon n lo g a ttn : nlogum

7

e^* '

ltza+ ( n- r ) ell

T n = Q t'n'l

a(r"-l) =a(!-r") , r *1 r-l l-r o s-" = lrl.t " l-r

IJ

CALCULUS dv dv uvd\. L = u -+ v 'v&=dr

du

n

Areaundera curye =

du

dy dx

d), du

l vdx

dv

. . uqY dx--:_=-._*-;-' dr v dx u "

l

J'

or

b

=

lxdy

J'

Volume generated

du dr

-- llry' aY or Jb

--

l|d.- dv

GEOMETRY

'l Distance=

- r, )t + (.Y,- Y,)'

2 Midpoint (x.y)=

( x ,+ x , l-

t2 lrl={.r-+}ll

f

)

') -Y,+.Y:

')l

A pointdividinga segmentof a line ( tu, ,rv,, mv" \ -.* . lx, v) = frr+ m+ n ) n \ Areaof triangle= l,

;l (x,1,

^

+ x2y3+ x.!,,) - (xry, + xry, + x,yt)l

xi+ vi 17t

Vx- + -Y3412t2

SULIT

3472/2

SULIT STATISTICS

,-

&t/

; zI,'w,

zf,

,, _ n! " {n - r1''.

Lw,

Zr l_

n^ |

-r

l= ' .

i I(-r-x )2 l) x3o=trt_-= v 1/

4

o=

l0

P(A w B) --P (A) + P (B)- P (A a B)

11

P (X = r) = ' C ,P ' qn-' , P + q = |

12

Mean, p : np

[.!"-rl

5 m= r+l2

o =.[rW

lc

l f" l 6

nl

= _fu* r)!rr'

t4

I =9x100

__x-p o

O"

TRIGONOMETRY I A r c length ,s = r0 Areaof'sector. ,e = ! ,'e 2 2l | 3 s in * " o r' A : 2

9 sin (l + 8) : siM cos8 + cosl sin-B l 0 cos(l + B) : cosl cosB F sinl sinB fl

tnn l *1911$ tan(A +B ) = ' * " ' I + tanltan B

4 sec2A: | +tan2A 5 c os ecAz =1 + c o t2 A

t2

abc

sinA sinB sinC

6 s inM = 2 s i M c o s l 7 cos2A: cos'A - sin2A = 2c o s 2 A -r = l- 2 sin2A )tqn

8 t an2A :

3412t2

t3 a2= b2+ c2 - 2bc cosl 14 Areaof triansle = f aDsinC -2

/

' * " :' l- Ia n ' A

I Lihat sebelah SULIT

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)L+ILIL

SectionA BahagianA 140marksl 140markahl Answerall questionsln thissecfion. Jawabsemuasoalan. equations: simultaneous 1 Solvethe following Giveyouranswerscorreclto threedecimalplaces. persamaanserentakberikut: Selesaikan Berikanjawapanandabetulkepada tiga titikperpuluhan. P+2q =l p' -3p+2q' =3 [5 marks] 15markahl The tangentto 2 A curvehas a gradientfunctionco.t-2x, wherea is a constant. to thestraightline 2y = *x +3 , the curveat the point (1,3)is perpendicular axt -2x , di mana a adalah pemalar. Satulengkungmempunyaifungsikecerunan (1,3) dengangarislurus pada adalah bersereniang titik Tangenkepadalengkung 2Y=-x+3' Find Cari (a) the valueof a, nilaibagi a , (b) the equationof the curve. persamaan lengkungtersebut.

3472t2 SULIT

[3 marks] 13markah) 13marksl 13markah)

347212

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Ahmadhas 1000chickensin his poultryfarm.Everyweek,he willsell40of his chickens. Ahmadmempunyai1000ekor ayamdi ladangayamnya. Setiapminggu,dia akanmenjua!40 ekorayamnya. (a) Findthe totalnumberof chickenleftin hispoultryfarmafter21't week. Cari bilanganayamyang masihtinggaldi ladangayamnyase/epasmingguke-21. {4 marksl 14markahl (b) The costof feedingeachchickis RM2perweek. chickenfor thefirst Findthe totalamountof moneythathe spenton the remaining twelveweeks. PerbelanjaanatasmakananseekorayamadalahRM2seminggu. Kirakanjumlah perbelanjaanyang dibelanjakanatasjumlah ayamyang tinggal untukduabelasmingguyangpertama.. [3 marks] 13markahl

Height Tinggi(cm)

Numberof plants Bilangantanaman

20 -29

4

30-39 40-49 50-59 5

6 0 -6 9 I!.J_

1

IY

Table4 Jadual4 Table4 showsthe distribution of the heightsof plantsin a garden Giventhe medianis 47.5,find thevalueof a Jadual4 menunjukkantaburantinggitanamandi sebuahtaman. Diberi medianadalah47.5,carikannilai a . Hence,findthe varianceof thedistribution. Seterusnya,cari varianstaburantinggitanamantersebut.

3412t2 SULIT

13marksl 13markahl 13marksl 13markahl

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SULIT 5 Solutionsby scaledrawingwill not be accepted' Penyelesaiansecaralukisanberskalatidakditerima.

Diagram5 showsrhombusPQRS.Theequationof PS is 3y +7 x = 33 andthe equationof PR is .Y= -r + I I ' garislurusPS ialah 3y +7x =33 Rajah5 menunjukkanrombusPQRS.Persamaan dan persamaangais lurus PR ialah y = -'r + I I

Diagram5 Rajah5 (a) Find Cari (i) the equationof QS, persamaangaris/urusQS, (ii) the coordinates of S. koordinatbagi S.

[3 marks] 13markahl [2 marksl 12markahl

(b) A pointf movessuchthatSf :IQ = 2'.1. Findtheequationof the locusof f, lokus T. SatutitikT bergerakdengankeadaan Sf :fQ = 2'.1 . Cari persamaan [3 marks] 13markahl

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6 (a) provethat

tos 2l = cos,4- sinI . cosl+sinl

t2 marksl

kos2A =kosA-sinl Buktikanbahawa kosA+sinA

t2markahl

(b) (i) Sketchthegraphof /=sin2r+2 for 0<x
untuky<x
[6marks] 16markahl

I Lihat sebelah 3472t2 SULTT

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SectionB BahagianB 140marksl 140markahl fromthissection. Answeranyfour questions Jawabmana-manaempat soalandaripadabahagianini.

liney=-x+8 ' 7 showsthecurvey=x2 +2 andthestraight 7 Diaoram

,=x2+2

Diagram7 Raiah7 Find Cari (a) the valueof k, nilaibagik, (b) the areaof the shadedregion, luasrantauberlorek,

[3 marks] 13markahl 14 marksl 14markahl

Intermsof a, whenthe regionboundedby the curve' (c) the volumegenerated 360' aboutthey-axis' [3 marks] the y-axis andy = 6 is revolved janaan,dalam sebutann , apabilarantauyangdibatasiolehlengkung tsipadu itu, paski-ydany = 6 dikisarkanmelalui360' padapaksi-y, B markahl

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SUI,IT

froman experiment. x and y , obtained 8 TableB showsthe valuesof twovariables, = Variables.rand y are relatedby theequation.y 2ox) + bx, whereaand b are constants. satu x dan y didapatidaripada nilaiduapembolehubah, Jadual 8 menunjukan denganpersamaany =2qx2 + bx, x dan y dihubungkan Pembolehubah eksperimen. dengankeadaana dan b adalahpemalar. A t

v

1 4 .5

1

q

o

7

25

39

tr A

Table 8 J a d u a lI

(a) Plot i

v

against.r, usinga scaleof 2 cm to 1 uniton bothaxes.

Hence,drawthe lineof bestfit.

14marksi

skala2 cm kepada'1unitpada graf ! lawanx , denganmenggunakan Ptotkan kedua-duapaksi. Seterusnya,lukiskangarisluruspenyuatanterbaik.

14markahJ

(b) Useyourgraphin 8(a),to findthevalueof Gunakangrafandadi 8(a), untukmencariniilai (i) a, (ii) b, (iii) y when x= 1.2. ), apab1ax = 1.2.

[6 marks] 16markahl

f Lihat sebelah

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OADEB,centreO andsectorfOFC withcentreL DiagramI showsa semicircle GiventhatOB = 5 cm and fO = 15cm. AADEBberpusata dan sebuahsektor Rajah9 menunjukkan sebuahsemibulatan TOFCberpusatT. DiberibahawaOB = 5 cm dan fO = 15 cm.

AOB 9 Dragram Rajah9 r =3.142) [Use/Guna Calculate Hitung (a) 4.TCO,

11markl

4TCO,

11markah)

(b) the perimeter, in cm,of theshadedregion, perimeter,dalamcm,kawasanberlorek. (c) the area,in cm2,of the shadedregion. luas,dalam cm2,kawasanberlorek.

3472/2 SULIT

[5 marks] l5 markahl 14marksl 14markahl

SULIT

ll

3472/2

10 Diagram10 showstriangleoPQ.Thepointr lieson QP andthe points lieson op The straightlineOf intersects thestraightlineQS at the pointR. Rajah 10 menunjukkansegitigaOPQ.Titik T tertetakpada eP dan titik S tertetak pada OP. Garislurus OT bersilangdengangarislurus eS dl t/tk R.

Diagram 10 Rajah10 1r It is giventhatO"S=-OP, Qf =:QP, OP= p andOQ= q t.

= lrlr , gr =\e, , oF = p danOg= q Diberi bahawaos z) (a) Expressin termsof p and (1. Ungkapkandalamsebutanpdan q"

(r or, (il) gJ ,

(iii) .5.

14 marks) 14markah)

(b) GiventhatOn =n(fi andQF.=16 ,whererr and n are constants,findthe valueof m andof n . [6 marks] DiberiOR=rrOT aan QR=nQS , dengankeadaanm dann adatah pemalar, cari nilai m dan nilai rt. 16markahl

34',72t2 STILIT

I Li hat sebel ah

S ULI ' I '

l2

) + I :t./"

11( a) ln a su rv e yc a rri e do u t i n a s c h o o l ,i t i s foundthat 2 out of 3 studentspassed their MathematicsTest. Dalam satu tinjauanyang dijalankanke atasmurid-muriddi sebuah sekolah didapati 2 daripada 3 orang murid lulusdalam ujian Matematik. (i) If 7 studentsfrom that schoolare chosenat random,calculatethe probability

passedtheirMathematics Test thatexactly6 students

[3 marks]

JikaT orangmuriddaripadasekolahitu dipilihsecararawak,hitung bahawatepat6 orangmuridlulusdalamujianMatematik. kebarangkalian 13markahl (ii) lf thereare600students findthenumberof students whofailed in theschool, th e M a th e m a ti cTs e s t. 12marksl Jika terdapat 60A orang murid dalam sekolah itu, cari bilangan orang murrd yang gagal dalam ujian Matematik 12markahl ( b) A s ur v e yo n b o d y -m a s si s d o n e o n a groupof teachers.The mass of the teachers has a n o rma ld i s tri b u tl ow n i tha me anof 45 kg and standarddevi ati onof 10 kg Satu kajian terhadapberat badan sekumpulanguru telah drlakukan.Berat Badan guru- guru adalah mengikuttaburannormal dengan ntrn45 kg dan sisihan piawai 10 kg. ( i) A te a c h e ri s c h o s e na t ra n d o mfromthe group th a tth e b o dy-massof the teacheri s l essthan 42.5 kg. F i n dth e p ro b a b i l i ty Seorang guru dipilih secara rawak darrpadakumpulan tersebut. Cari kebarangkalianbahawa guru tersebutrnentpunyaiberat badan kurang dari 42 5 kg. ( ii) l l 1 2 .3 %o f th e te a c h e rsh a v ea body-massof morethan k kg, fi nd the v a l u eo f k .

beratbadanlebihdarik kg, carinilai Jika 12.3%gurutersebulmempunyai bagik. [5 marks] 15markahl

3172/2 SULI'T

t3

sut_t'f

3412t2

SectionC BahagianC [20 marksl l2AmarkahJ fromthissection. Answertwo questions Jawabdua soalandaripadabahagianini. 12 A particleP movesalonga straightlineandpassesthrougha fixedpointO. vms-t,is givenby r'= 6t' -4t-2, wherer is thetime,in seconds, lts velocity, afterpassingthroughO. Suatuzarahbergerakdi sepanjangsuatugarisIurus dan melaluisatu titiktetapO t ialahmasa, Halajunya, u ms-t,diberioleh t'=6t2-4t-2,dengankeaclaan dalamsaaf,selepasmelalui O. (a) Find Cari

11markl 11markahJ

(i) the initialvelocityof the particleP, halajuawalzarahP,

12marks) 12ma*ahl

is zero, (ii) its velocityat the instantwhenthe acceleration halajunyapadaketika pecutanadalahsifar, (iii) the timeintervalduringwhichthe pafticlemovestowardsthe left, Julat masaapabilazarahitu bergerakarahke kiri,

12marksJ 12markahl

duringthefirstthreeseconds, ( b) the distance, in m, travelledby the particle jarak, dalam m, yang dilaluiolehzarahdalamtiga saatpertama, graphof the motionof the particlefor 0 < I < 3 Sketchthevelocitytime

[3 marks] 13markahl 12marks)

Lakargrafhalajumelawanmasabagipergerakanzarahitu untuk0 < I < 3. [2 markah]

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3172/2 SULIT

14

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13 Table13 showsthe priceindicesintheyear2009 basedon theyear 2007of of a cake. fouritems,A, B, C, andD, usedin theproduction tahun2007 Jaclual13 menunjukkanindeksharga bagitahun 2009 berasaskan bagi empatitemA, B, C dan D, yangdigunakanuntukmembuatkek Item

PriceIndexin theyear2009 weightage basedon the year2007 130

B

144

(,

115

U

120

1

2n

Table13 Jadual13 its pricein2007. ( a) Giventhe priceof A is RM2.60in theyear2009,calculate

[2 marks] Diberiharga untukA adalahRM 2.60dalamtahun 2009,kirakanharganya 12markahl dalamtahun2Q07,

indexfor theyear2009basedon the year2007is (b) Giventhatthe composite

13marksl Diberi indeksgubahanbagi tahun2009berasaskantahun 2007 ialah 13markahl 125, carikan nilain 125, findthe valueof n.

pricein the Find the priceof the cakein theyear2007rt its corresponding year2009is RM46. 00. l2 marksl Cari hargakek dalam tahun 2007lika hargayangsepadandalamtahun 12markah) 20A9 iatahRM46. 00. (d)

10% fromthe Giventhat the priceofitem D is estimatedtoincreaseby year2009to 2010,whiletheotheritemsremainunchanged. calculatethe compositeindexof thecakefor the year2010basedon the t3 marksl year2007. Diberi harga item D diiangkameningkatsebanyak10ok dari tahun 2009ke 2010, manakalaitem-itemlain tidak berubah. tahun2007. Kirakannomborindeksgubahanpada tahun2010berasaskan 13markahl

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14 Diagram14 showsa trianglePQR. Rajah14 menuniukkansebuahsegiigaPQR

14 Diagram Rajah14

(a) Calculate/.PQR, Krakan {PQR,

[2 marksl 12markahl

(b) Sketchand labela trianglePQ'Rwhichhas a differentshapefromtrianglePQR suchthat lengthof PQ,PR and IPRQ remainunchanged. 12marksl State lPp'R, Lakardan labetkansebuahsegitigaPQ'Ryang berlainandaripadasegttlgaPQR dalam rajahdi atas,dengankeadaanpanjangPQ , PR danIPRQ dikekalkan' 12markahl Nyatakan /.PQ'R, (c) Hence,calculate Seferusnya,kirakan (i) the lengthof Q'Q,in cm, panjangQ'Q, dalamcm, (ii) the areaof thetrianglePRQ',in cm2. luassegitigaPRQ',dalam cm'.

[6 marks] 16 markahl

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15 Usegraphpaperto answerthisquestion. Gunakankerlasgrafuntukmeniawabsoalanini. A and B. typesoffurniture, Afactoryproducestwo Eachfurnitureneeds2 typesof rawmaterials , P and Q andthe numberof eachraw arepresentedin theTable'15 below. materials neededfor eachfurniture dua ienisperabottiaituA dan B. Sebttahkilangmengeluarkan Setiapperabotmemerlukanbahanmentah P dan Q dan bilanganbahanmentah dalamjadual 15 di bawah. yang diperlukanbagi setiapperabot ditunjukkan Numberof rawmaterials BilanqanBahanMentah

Table15 Jadual15 P leftin thefactoryrs30 and thenumberof raw Thenumberof rawmaterials materials Q leftis 24. is at mosttwicethe numberof A produced It is giventhatthe numberof furniture A andy unitsof x unltsoTfurniture furnitureI producedandthefactoryproduces furnitureB. BekalanbahanmentahP yangtinggaldalamkilangadalah 30 manakalabekalan bahanmentahQ yang tinggaldalamkilangadalah24. Diberibahawabilangan perabotA adalahselebih-lebihnya dua kali bilanganperabotB dan kilangitu x unit perabotA dany unitperabotB. mengeluarkan (a) Writethreeinequalities, otherthanx > 0 andy > 0, whichsatisfyall the constraints aoove. 13marksj selainx > A dan y > 0, yangmemenuhisemua Tulistiga ketaksamaan, kekangandi atas. l3 markah) (b) By usingthe scaleof 2 cm to 2 unitson thex-axisand2 cm to I uniton they-axis, theaboveconstraints. andshadetheregionRwhichsatisfies construct [3 marks] Denganmenggunakanskala2 cm kepada2 unitpada paksi-xdan 2 cm kepada 1 unit pada paksi-y,binadan lorekrantauR yangmemenuhisemLtakekangan di atas. 13markahl

3472t2 ST]I,IT

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t7

J+tztz

(c) Useyourgraphin '15(b), to find Gunakangrafandadi 15(b),untukmencari produced (i) the maximumnumberof unitsof furniture,B if 4 unitsof furnitureA are produced BitanganmaksimumunitperabotB yang dihasilkanjika bilanganunitperabotA yang dihasilkan adalah 4. (ii) the maximumprofitobtainedby thefactoryif the profitfromthe saleof a unit A /'sRM 200andthe profitfromthe saleof a unitof furnitureI is of furniture RM 2s0. Keuntunganmaksimumyang diperolehjika keuntungandaripadajualan seunitperabotA adalahRM 200 dankeuntungandaripadajualan seunit oerabotB adalah RM 254. 14marksl 14markahl

END OF QUESTTONPAPER

3472t2 SUI,IT

I Lihat sebelah

l9

J q/Z l !

Nama: Kelas: ArahanKepadaCalon I 2 3

Tulis namadankelasandapadaruangyangdisediakan. Tandakan( { ) untuk soalanyangdijawab, Ceraikanheiaianini danikat sebagai mukahadapan bersama-sama denganbuku jawapan.

Bahagian

Soalan

L

MarkahPenuh

MarkahDiperolehi (UntukKegunaanPemeriksa)

5

A

B

Soalan Dijawab

2

6

J

7

4

6

5

8

6

I

7

10

8

10

9

l0

t0

t0

1i

10

12

10

13

t0

T4

10

l5

10

Jumlah

3472t2 SULIT

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3472/2

INFORMATION FOR CANDIDATES MAKLUMAT UNTUK CALON

l.

This questionpaperconsistsof three sections:Section A, Section B and Section C. Kertas soalan ini mengandungi tiga bahagian: Bahagian A, Bahagian B dan Bahagian C.

2. Answer all questionsin Section A, four queslionsfrom Section B and two qucstions from Secfion C. Jala,absemua soalqn dalam Bahagian A, empot soalan daripada Bahagian B dan dua soalan daripada Bahogian C.

3. Show your working. It may help you to get narks. Tttnjukkan langkah-langknh penting dalam kerja mengiro anda. Ini boleh membantu anda untuk mendapatkan markah .

4. The diagramsin the questionsprovided are uot drawn to scaleunlessstated. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

5. The marks allocatedfor eachquestionand sub-partof a questionare shown in brackets. Markah yang diperuntukkan bagi setiap soolctndttn kraian soalan ditunjukkan dalam kurungan.

6. A list of formulae is provided on pages2 to 3. Satu senarei rttmus disediakan di halarnan 2 hinggo 3 .

7. Graph papersare provided. Ke r t as gr af di sedi akan.

8. You may use a non - progralnmablescientific calculator. Anda dihenarkan menggunakankalkulutor saintifk yang, tidak boleh diprogram.

3472t2 SULIT

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3472t2 Additional Mathematics Kertas2 September2009 2'h Jam JABATAN PELAJARANNEGERIJOHOR PEPERIKSAANPERCUBAANSPM 2OO9

ADDITIONALMATHEMATICS Kertas 2

JANGAN BUKA KERTASSOALAN IN! SEHINGGADIBERITAHU

RKINGSCHEUIE

Kertassoalanini mengandungi17 halamanbercetak

347212 Hak CiptaJPNJ 2009

[Lihat sebelah SULI T

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3472t2

2 A BAHAGIAN Solution

p = 1 -2 q

Sub marks

roGi marks

1- n

Orq =--'. 2ll

l Pl I

Eliminatep or q "( 1 - 2q)' - 3.(1 *2q) + 2q2- 3 = O

Or p2 - 3p +2"(\P )2-3*-0 ?_ or eouivalent Solvetlre quadratic equationby usingthe factorization@

6q '+2q-5=0 3p '-8p-5=0

quadratic formula@ completinq the sq

-z r J+-"(oX-sj 2(6)

ri i&4:ll3&t 2( 3)

q = 0 .7 6 1 ,-1 .0 9 5 or p = - 0 .5 2 3 ,3 .1 8 9

p: - 0.523, 3.189 (9

I

q = 0.761,- 1.095

if the workingclfsolvingquadraticequationis not shown [

]"*_

347212 llak CiptaJPNJ 2009

ILihat sebelah SULI T

347212

SULIT

Sub marks

Solution

2

Total marks

i ,,

"/ - axt -zx dx

a) 2y=-y+J fl'ln = - -

I I

2

*1r=2 E] substitute x = 1 in to axo-2x = 2 a ( 1)'- 2 (1 )'=2

a=4

Integratey=

P FI

Jt*+"'- 2x)rtx

4 xo 2 x' {-c v'A .)- -----.-+L

x = 1, y= 3 into Substitute 4xa y = :.i

2x2

+ c, to find the

valueof c. y=x4-x2+3.

N qte: .y: J(*4x'' - Zx)h

must have at least 1 ter"mwith powerincreasedby

A

t.

t_ 347212 t{ak CiptaJPNJ 2009

[Lihat sebelah SULIT

A "t

- -Solulion

347212

Sutr marks

Total marks

tr_l U se T n -a +(n_1) d 7 2 1 =4 0 +20"( 40)

1 0 00- *840=160 OR othervalidmethod

b)

l.JseSn= !; tz^ + (n - 1 )dl

+(11x40)l I rrrooo)

3472t2 Hak Cipta.JPNJ2009

l ,l

fl-ihat sebelah

rUILI

{

SULIT

---

- --olution

* L=3 9.5or*F=7or

"fr=d

lP l

347212

Sub marks

I

Use medianformula al' \

47 .5 =.39.5 + (

,^

I r'-Y --1l-* (7 \ 2\ '

1

*a

to "L With "f, and F corresponding

or Zl*Zf*= 1425

72917sm

/+ Ffr, 'Zf -- |t-J --- - "1 ' tGt"

f

4

st- t-

,1425,2 *72917.5 -30--'-30-''

y= x+ 1 ii)

3 y + 7 x=3 3 y=x+1

ST = 2TQ Can be impliedas formula. I Pl

s (3,4) I

Usingthe formuiadistance /

,,n7 tr t

Jtr-:)' +(y-4)' = 2JG-7)'+(r'-8)' \:_l

\

- - - - .-

\-_,

l?7--q --]=Y PPvJ 9r1rqv1-qql_347212 Hak Cipta JPNJ 2009

[Lihat sebelah S ULI T

347212

9UUr

m

[_i-Solution

Use identity C os2A -S in2A =Cos2A

L HS = RHS Ns mistake allowed

b ) i)

Fr*l

GraphSin l p e ri o C i n0 sxs 1 Amplitude

n

tir*l E]

Drawingof the straightlinefrom the equationinvolving ( X and y, eithergradientOR y interceptof straight l-ine must be correct.

347212 |'lak Cipta JPNJ 2009

rr

[Lihat sebelah gUL[

SULIT

3472t2

7 BAHAGIANB

Sub marks

Total

marks

Solvethe simultaneous x?'+2= * x + 8 x 2 + x -6 x=2,x = -3

-n

lntegratex2+2 Uselim it

F2

I'

u

'1

in to .[\x) - + 2xJ J

Or findthe areatriangle % (6)(6)

lntegrate (x'+2) + areaoftriangie

T +rc 3

(24.667)

c) lntegratez x2

n t tt'- 2),1t,

Uselimit /\ \ Kl \*__r/

in ., r Q) | - 2 yl

/

\

I \

I

i

L 3472t? Hak Cipta JPNJ 2009

[Lihat sebelah S ULI T

SULIT

3472t2

Sub marks

Solution

Total marks

8 a)

M Note: lf tableis notshownawardF,lmarkif all the pointsare plottedcorrecily. b)

v lJlotj- agatnstx x \K] (Correctaxes and uniformscales)

/

-r

l--r r'ir )

6 *pointsplottedcorrectly

\

-r

(xr

Line of bestfit

\

\*-"

c)

//Il

! =zax"oLl]_l

x Or implied. i)

Use*m = t"

ii)

8-2

i

I I

Frcm graplr ): againtx

i

/-)

\5!,

(*'

)

a="tL ( 0.7<---),0.8)

ii)

b=-

2.45

[ -2 . S 0 < ---+ -2 . 3 0 ]

t- = -0 .6 x

= -0 .6

1/

y=-0 .7 2

\

Nl

,/

Note:

ss-1if, Part of the scale is not uniformat the x-axisand/0rthe I -axis.

x OR not using the given scales. OR not using graph paper. 347212 Hak CintaJPN.| 2009

10 [Lihat sebelah

$uur

_i

3472t2

v x I

7

6

5

4

3

2

:i

r^"r ,t' I

.4 ii

r{

ri ..^ t ;!

1i

,l

7212"Hak" ei$t5J]rNru''20f.rs

347212

10

SULIT

Total marks 9 a)

b)

< TCO = 45" OR 0.7855rad OR

v 4

Use S = r 0 la find the lengthof arc BE

or ODFC

1s(?-) or 5(i)

KI Use Pytho.Teoremto find CO

16.2132 Perimeterof the shadedregion "23.565+ *16.2132+ *3.9275 + 5

4azasr// 48706//

aazt

Use Y, f g to find the area of sectorTODFC Or sectorOEB

Area of shadedregion ( 176.7375 - 112.5)+ I 8188)

'/roaua//74.06

347212 Hak Cipta JPI'IJ 2009

ILihat sebelah

sULlr

SULIT

3472t2

lt

Solution

10 a) i) ii) iii)

Usethetrianglelaw for Of or g..t or .V

or =

1)

I

lo. io

;0

t2

--p+;Q OJ

N1

2

f f i = 6 q 1 p * ;q ) J I

QR =n1-c +1n) Use the trianglelaw to find

oQ=on*nO 1 71 j tP o

Jn,q-ntp*nq=q

Comparethe coefficient ,.-*\ / Kt ) of p andq. \*-/ l^1rn .

n=0

JL J

m= --n

2

2 - m+n;1 _) af

-(-n )+ n = 1 J 11a

rJ

n=---.m=-1A .4-

a

{Both are correctl

347212 Hak CiptaJPNJ 2009

[Lihat sebelah LULlT

SULIT

t2

347212

Solution 11 a) i)

Sub marks

Total marks

2 ----1 lpr I

I

0.2048 Usenq I

/^\

6 0 0."). (:) \ J

Kr )

-\-____,

zooI !!1 | b) i)

UseZ

P(2.*#",

r-\ \Kr/ -\

oaorsl_rur I P( Xtk)=0.123

p '(z> L:45 )=0.123 i0 k -4 5 l0

347212 Hak CiptaJPNJ 2009

= 1.16

[Lihat sebelah SULII

SULIT

13

3472t2

BAHAGIAN C $olution

Sub

rng$s

Total marks

12 a) i) ii)

,1 ,,

Use al = 0. to findt dt 1

t= l

a I

- |,,)y=tr(J

1

*4 G) -2 a I

_)

6

=.---

J

ii i )

v< 0 ( t- .lx3t+l)<0

G) \--

0
lntegratet = -2) (tt Jlott 1t 2t3-2.t2-2t K1

S u b s t it u t e t =l o rt = 3 FindSr or 53.

Ditancetraveled * 2 + 2 + 3 0 =34 c)

Forshapeofthesraph L{ Ip r

| "'

347212 Hak CiptaJPNJ 2009

I

andx-intercept I y- intercept

[Lihat sebelah S ULI T

sur=rT

14

347212

Solution 13 a)

(l) User=9- xloo n rvv \ - K{

eo

2'6 0

x I00 = 130

\_,

X

Ll!]_] x = RM2.0o

+ (140)3 + ( 1 1 5 ) 2+n ( 1 2 0 ) n Zt w = ( 1 3 0 ) 1 t- t, I

-

Use,=

\ tw

T,

= 125 r--r \.KIJ t\

1_Nln=2

,,=-13,:ttl 100 t32

I :{tl r!$;) +'l:():!_?g) l0

347212 Hak Cipra JPNJ 2009

[Lihat sebelah

suLlI

t5

SULIT

3472t2

Sub marks

SinQ

\rct )

Sin45"

\\

62.12'il 62' zl xrrI

r__--.1

L NI I < e , o b t u s e


a

_ Qg' _ ____6 __ Sin55.76Sin62.12" Q Q' = 5.6115 f;-

.-fll

30---=---_-7-lc, t

Si n l T .1 2 ,S uI r1 7 ^8 y

-f

RQ'= 2.4977

Area of trianglePRQ' = % (V.5)(2.4977)sin45"

6.6230

347212 Hak Cipta JPNJ 2009

[Lihat sebelah SULIT

t6

SULIT

347212

Sub marks 15 (a)

2x + 5y < 30

or equivalent

3x + 2y s 24 or equivalent x < 2,!

or equivalent

at leastonestraightlinefronithe Drawcorrectly *inequalities x andy. whichinvoves Drawcorrectlyallthree"straightlines Note: Acceptdottedlines. The correctregionR shaded A =4 Furniture ( f r omx=4 i n th e re g i o n ) c) i)

pointat (5,4) Maximum

@ trr:l

Use200x+ 250y for pointin the *regionR RM2000

ss-1i f

In (a) the symboi" - " is not used at ali or morethanthree are given. Inequalities In (b) does not use the scalegiven or does not use graph paperOr interchangebetweenthe x-axisand the y-axis'

347212 Hak Cipta JPNJ 2009

[Lihat sebelah SULIT

SULIT

t7

-t t

Y'1

i

t

$t i i

l:

,: !l

i{ il

3472t2