SPM Trial 2009 AddMath Q&A (Johor)

8/14/2019 SPM Trial 2009 AddMath Q&A (Johor)

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SULITNO. KAD PENGENALANANGKA GILTRAN

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JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM 2OA9ADDITIONAL MATIIEMATICSKertas ISept.2 Jam

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Dua amJANGAN BUKA KBRTAS SOALAN1. Tulis nombor ka d pengenalan anangkagiliran andapadapetak angdisediakan.2. Kertassoalanni adalah alamdwibahasa.3. Soalandalam bahasa nggerismendahuluisoalan angsepadan alambahasaMelayu.4. Calon dibenarkanmenjawab keseluruhanatau sebahagian oalan sama ada dalambahasanggerisataubahasaMelayu.5. Calon dikehendakimembacamaklumatdihalaman elakang ertas oalan

INI SEHTNGGA IBERITAHUUntukKegunaanemeriksa

Soalan Markah Penuh Markah DioerolehiI 22 43 34 35 36 37 38 39 210 J2234 J5 26 47 A8 A9 A20 ,2l A22 J23 A+24 !25 A

Jumlah 80Kertas oalanni

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SULIT 3472t1T'he|ltov,ing -formulaemay be hetpfut n onsw-eringheqttestions The synbols giren are lhe onescommonly used.

-b + rlh ' -4ac1 x= 2a2 r! ' x Ll '= Lt" 'n3 t! '+on- ai l 'n4 (u" ')n=a'" '5 log. mn = log am + laga n

nl6 log" ' = lo g sn - log'nn7 log"m' : n logom

ALGEBRA8 loc.blOe"D '-log. a

fn:6r(n- l )d

s"= lzr+(n- l )d l2'Tn = a"r n-t

a(r ' - l \ u( l - r ' ) . .Sn= =--J, l . r+t)' r - l l - rS_ d l ' l .r" l -r "

10l lt2

CALCULUS

. dy tly dudx du dx

dv dv dul=tw, -;=t t ;+v;dx ax ax

du dv.vtt clx dr dx, =- 1rdyv

Areaundera curveI: lY. l r or

f= lx tt VVotumegenerated

tt= |/w" ctroroolt= l l r { - dy)-

GEOMETRY

1 Distancc =

2 Midpoint

5 A pointdividing segment f a l ine( ra,- mr, nv,+.y, )( r , .v)= i- ' i\ t l r n nt+t t /6 Areaof triangle:Jl,,r,r, +,r,-)/3r;/', ) - (t,.v,+r',y,+'t,y',)l

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

^ xt+y. ll) 7V-r-+.Y-

-Yr+ .Y:'1 )

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- -'r, ' + (jr,

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SULIT 34721r

12marksl12markahlAnswerJawaPan:a) . . . . . .

(b)

Answer ll questfbnsDiagram shows negraph f he unct ionf x) =l x+ i i , for thedomain-2


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3. aGivenhe unctionsf(x)=-:; andgf(x)= 5x 4.Findg(.r).-Diberiungsi"f x) = -:; dangf (x) = 5x 4 Carig(x) .x- l

4.

[3 marksj13maftahl

AnswerlJawapan:

Givenhat3 andk are he oots f hequadraticquation' +.r = p. Findhevalueof k andp.Diberibahawa dank ialahpunca-puncawrsamaan uadratik.ai nilaik dan p .13marksl

[3markah]

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A Diagram5 shows he graphof /(x) = a(x - b)2+ c' State he valueol a 'b and c 'Rajah menunjukkan raf f (x) = alx - b)'1 c'Nyatakan ilai a 'b dan c

DiagramRajah

x-b)2 + c

Answer/awaqan'.

[3 marks][3markah]

Forexaminer's

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6. Givenhequadraticunction (x)= 2x' - 7' find he ange f r ifDiberiungsi uadratik-f x) = 2x' -7, cariulatbagi ika f (x)>

Answer/ awapan

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/ (x) > I l .l l .

[3 marks]13ma*ahl

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I r--1I l r l

9

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SULIT7. Solve he equation '*'

Se/esaikanpersamaan

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[3 marks][3 markah]

Answer/ awapan:

Given hat og3 = loge , find hevalueof x.Diberi og3x = Iogg4, cari nilai x.[3marks][3 markah]

Answer/awapan.

Findhesum o nfinig f hegeometriceries1 * I * -!- ..24Carihasiltambahingga etakterhinggaanagisirijanjangeometri*] *1*....), r

12marksl12markah)

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10 . Findhe east umberf ermsn hearithmeticrogressionsumexceeds 00.Caribilanganebufane*ecildalamaniangarithmetic5,tambahsebutanmelebihi00. [3 marks]13markahl

Answer/Jawapan

11 The irst hree onsecutiveositiveerms fa geometricrogressionre2 , y and18.Find hecommonatio f heprogression.Tiga sebutaneftamasuatuanianggeometrialah , y dan18'Carinisbah epunya agi aniang ersebut. 12ma*sl12maftahl

Answer/awapan:....,347211 2oo9HahciptaJPNJ

347211- 5, l, 3, .. so ha t ts

- 1,3, ..supaya asil

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l0| .--lI l r l

l lr-= l2 lt ,

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12.

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[3 marks[3 markah]

Th e ariablesand , ar e elatedy heequatioy = +, wherem andn arenconstants. iagram1 snows he straightineobtained y plotting og ryagainst .Pembolehubah da ny dihubungkan lehpersamzotl = 4'0, manam dannn adalahpemalar. Raiah12 menuniukkangaris urusyang diperolehidenganmemplot log, y melawanx .

Diagram 2Rajah12

Find hevalueof m andof n.Cari nilaim dann.

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Answer/ awaoan

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SULIT 3472tLDiagram13 showsa straight ine PMQ.Rajah13 menunjukkangaris urus PMQ.

P1-s ,-4t)

QQ+7,s -21Diagram 3Rajah13

Given hat a pointM(4,4)divideshe in esegmentoining he points (s + t'-4t)an d QQ+7,s - 2) in he ralio2: l Find hevalueof s and .Diberi titikM(4, 4) membahagi emberenggaris yang menyambungkan itikP(s + t,-4t) dan QQ + 7,s - 2) dalamnisbah2:1. Carinilais dan t. [ 4 marks ]14markahl

Answer/JawapSl? s =t-

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14 . Diagram4shows straightineABwhichntersectso hestraightineCDat hepointT(2,3)Raiah14menuniukkanaris urus B bersilangengan arisurusCD pada itikT(2,3)).

*1"*q2Diagram4Rajah 4

Theequationf hestraightl ineBisy=-1r+4 and heequationf hestraight2l ine CD is y=2y-1.Persamaan aris urus AB iatah = *1 , + 4 dan persamaan arisurus CD ialah

LY=2x- lCalculatehe areaof he riangle 7D .Kirakan uas segitiga ATD .

[3 marks]l3 markah

Answer Jawapan

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SULIT l2 347Zt l

15. Diagram 5shows ectors and !. Draw he esul tantector f 2g- b.Rajah15 menunjukkan ektor a dan \. Lukiskan ektorpaduanbagi2a - b.12marks)[2 markah]

Diagram 5Rajah'15Answer Jawapan

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/,/ g

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t6I r-iI l4 lr \

PQ= 2?- 3! and

-) -> ->VeKor PQ dan RS adalah selai. Diberi bahawa PQ =-tqRS= 2-FindCari(a) the valueof /rNilaibagi k(b) the ratioof PQ: RS

Nisbahbagi PQ: RS

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-+ aThe vectorsPQ and Rf areparallel.t is given hat-+onS=(t +Ds-;b..

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16.

2a -3b dan

[4 marks]14ma*ahl

Answer/Jawapan:(a'1(b) . . . . . . . . . . .

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SULIT IAla ['orexaminer'suseonlv17. GivenhatcoS = p and0 is anacute ngle, xpressn erms f p .Diberibahawa kos0 = p, dan0 adalah uatu udut irus,ungkapkan alamsebutan bagi(a) tan d

e(b) s in;z

Answer/Jawapan: a)

.AGiven y = :j , find he approximatealueof y , when ;r changes rom 2 to 2.02.x)4Diberiy =:, , cariperubahanilaibagiy , apabila berubah aripada kepadax2.02.

14marksl14markahl

Answer Jawaoan3472/1 2oo9Hak Cipta PNJ SULIT

t7I r--I l4 l

18.

18

I l4 lr)

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Diagram 8shows seclorOPQwith entreO and adius cm.Rajah18menunjukkaneldorOPQ angberpusatO anejari5 cm.

O Rlcm ODiagram 8Rajah 8

GivenQR =1 cm and IPRO = 900, ind he area n cm2 of the shaded egion.Diberi QR=1 cm dan ./.PRO= 900 kirakan uasdatamcm2 bagi kawasan edorek.

14marksl14matuahl

Answer Jawapan

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t6SULIT 3472t1 Forexaminer'suse only

20 . IFind he coordinates f the turningpointson the curve / = 4x + - and determinehexmaximumDoint.ICari koordinatbagi titik-titikpusingan agi tengkungy = 4x + - dan tentukanx

titik maksimum. 14marksl14markahl

Answer Jawapan' . . . . . .20t--JI l4 l

Given =# andx-!,s@)a'

1- _1Diberi y=2-: dan

Isi)axdy

= 3g(r) where (r) sa functionf x. Findhevalue f

= 3g(x) di mana g(x) ialah ungsibagi x . Carinilai

347211 2oo9HakciptoJPNJAnswer Jawapan

14marks)14markahl

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Table22 shows he marksof a groupof studentsn an examination.Jadual 22 menunjukkanmarkah sekumpulanpelajaryang diperolehidalam suatupeperiksaan.

Marks 1i ?Number f students 4 6 8 7Iable22Jadual22

FindCari(a ) the maximum alueof x if he modemark s 8.nilai markah bagi x jika markahmod ialah8.(b ) the minimum alueof x if he meanof hemarks s greaterha n3nilai minimumbagi x jika markah min ebih daripada3.

[3 marks]13markahJ

Answer Jawapan

Find he number f ways nwhich4 boysan d5 girls an be seated n a row fCari bilangan ara susunan4 budak elakidan 5 budakperempuan olehduduk.(a ) there s no restr ict iontiada syarat dikenakan(b ) the boysand hegir lsar eseated llernatelypelajar elakiduduk berselang selidenganpelajar perempuan. 14marks)14markahl

Answer/Jawapan: a)

317211 2007 lok Ciota JPNJ(b) . , . . .

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22.

22t--_lI r---I l r l

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(a)(b)

23.

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24. f abire 4 shows he numberof colouredmarbles n a bag.Jadual 24 menunjukkanbilanganguli bervvarna i dalam satu beg.

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Colour Number f marblesRed 4Green x+2Purple 2Table24Jadual 4

A marble s drawnat random rom he bag.Given hat he probability f gettingaIgreenmarble s -. Find hevalueof -t .

Sebijigulidikeluarkansscara rawak daripadabeg. Diberi kebarangkalianmendapatIsebiji ul ihi jau alah . Carini laix.J [2 marksl12markahl

AnswerJawaDan . . . . . . . . .347211 2ao9HakciptaJpNJ

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Forexonrineruseonlr-

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Diagram 5 showsa standard ormal istributionraphRajah25 menunjukkangraf taburannormalpiawai.

The probabilityepresentedy he shaded egions 0.7514.Kebarangkalianawasanbedorek alah0.7514.(a ) Find hevalueof &

Carinilaik.(b ) X is a contin uousandom ariables hich s normally istributed it ha mean80 and a variance f 9. Flnd hevalueof X when he z-scores t .

X ialahpembolehubahawakselaniar angbeftabur ecaranormaldenganmin 80 dan varians . CarinilaiX iikaskor'z alah k .14marksl14markahl

Answer/Jawapan: a)th ltv, , . . ' .

END OF QUESTIONPAPER

341211 2oo7Hukc'ipra I'NJ ILihat sebelahSULIT

25 .

1(x)

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L Thisquestion aper onsistsf25 questionsKertassoakn ini mengandungi5 soalan2. Answer ll questions.Jawabsemuasoalan3. Writeyouranswersn thespacesrovidednthequestionaper.Tulisawapanandadalam uangyangdisediakan alsmkertassoalan.4. Showyourworking. t mayhelpyou o getmarks.Tunjukkanangkah-langkahentingdalamkerjamengiraanda. ni bolehmembantu ndauntukmendapatkan arkah.5. If youwish ochangeouranswer,ross ut heanswerhatyouhave one.Thenwritedown henewanswer.Sekiranyaanda hendakmenukarawapan,batalkanawapanyangtelah dibuat.Kemudian ttliscwapanyangbaru.6. Thediagramsn thequestionsrovided renot drawn o scale nless tated.Rajahyangmengiringisoalan fulak ilukis mengihttskalakecualidinyatakan.1. Themarksallocatedor each uestion reshownn brackes.Markahyangdiperuntukkan agi setiapsoalanditunjukkan alamkurungan-8. A listof formulaesprovidednpages to 5.Satusenarai umusdisediakan i halaman3 hingga5.9. A bookletof four-figuremathematicalablessprovided.Sebuah ukusifr matematik mpatangkadisediakan.10.You mayuseanon-prograrnmablecientific alculator.Anda dibenarkanmeng,gunakanalkulatorsaintifk yangtidakbolehdiprogram.I l. Hand n thisquestionapero he nvigilator t heendof theexamination.Serahkan ertassoalan ni kepada engawas eperilcsaani akhirpeperiksaan.

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20INFORMATIONFOR CANDIDATESMAKLUMAT UNTAK CALON

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suLlr3472t1AdditionalMathematicsKertas 1September 0092 Jam

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JABATANPELAJARANNEGERI OHORPEPERIKSAANERCUBAAN PM 2OO9ADDITIONAL ATHEMATICSKertas1

JANGANBTJKA UKUJAWAPANSEHINGGA IBERITAHU

MARKINGSCHEME------J

l(ertas oalanni mengandungihalaman ercetak

[Lihat sebelahSULIT47211 lak CiptaJPNJ 2009

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Submarks Totalmarks

82B1

2B1

.x IJ =* - 9l8(3-) = 227(3 ' ,)g(3.1=23*.33 3*.32 2

I

I f-/ "l--:I '81

I a " : ,l iI i

rog,= os,qlu,g,i i log, =19"sJ-orany aseI I log19i tt-- T-_-I I l tl l "i l^ lI l )oo=-. . - . -i i r li l1t-*-f"---

:i ,o i n=12i tI i ,,' t:*ol_:5rli?_ogi i , , - 2(2)i j ; [ : r -s)+( i?- l )4 j ,2ooi1-I is"200i--]*-i t r 1, .=:I i l , 18t ti i2 vi tf--T-_-i 12 j m=16andn=1.7411i ii l tos,m=4or- loez=-! or logt li I log, ,= logz t_"rlog,l ii lL_t_-

J

82B1

ATlog, n

L__,-.----_-L

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S[b marks T- ; - | Totalmarksl=6ands=-20t=6 or s=--20s+ 3/= -2,2s 4t =16(Solve imultaneousquation)s+l+2t+14

1'l .r ol-l - L-ol2' l ol4l

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821lo 2 o

I-_* ' Ia l i a It l+ r - rA(0,4) rD(0,-1)

2B1either aor-b

(a) k=2a' ) * - 2 qk +7=2)@,: =3),"2

g( f t+ )q ::h= l(2q-3[) @ equivalent2-nS = .1.pQ

. - - ]

/,l/\ \

.( l t, \! \

\

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IIIIIIIt_

t. 1r l l - O-(a) v ' -pl r - p '

.e r : ;01 srn--=^l '?\ l )Ll^( g\o: l - 2sin ' l - |' \2)

2.044 cmz1^1: (5) '(0.6435)_ aX3)2' ' 2l11$)' (0.643s) r 1{+X3)Shaded region = Apon AponIPOR = 36.870 or 0.6435 acl

.V 1.44-0.06 -966y=--:x0.02- aa3Z) , ,? = - 4(21)x'5 or -4(24) 5dx

( -t \| -: .4 I\2 )d'y 2 . d2, ,-;* = -; ?r.rd=4 ,=-16dx ' x' ' dx '

, l4-L- ' 2

Q- = q- --1-o equivatentclx x'

4B382

4B382

I

IIB3

82B1

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ZA:i--J 2(--1) 3, - . ]l?r" -11't -" " ll r lIx- l

t Izx-: l; t ? Ir l_ x- I B1(a)7(b) r=1x>0I*:31:J":!l , s25+x

x t-28+x

L2

B1I

B1

Ia

(a) k-0,679 2B1(Z>k;=A.2486

I I (b)r=8203'i lI lo67e=tj lo(b) .r = 82..031

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STJLIT

AdditionalMathematicsKertas2Sept2009^ l- lam2'

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JABATAN PELAJARAN NEGERI JOHORPEPERIKSAANERCUBAAN PM2OO9ADDITIONAL MATHEMATICSKERTAS 2

Du a am tigapuluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertqssoalan ni adalah dalan dt,ihahasa.2. Soalandalam baha,sanggeris mendohului oalunyung, epadundalcnnbahal;a lfelayu.3. Calon dikehendaki nembacemaklumaldi halarnanbelakangkertas soalanni.4. Culon dikehendakimenceraikanwlamctn 9 dan katsehagainukahadapanhersama- ama de, gan atvapan awla..

Kertas oalanni mengandungi9 halaman ercetakan halarnanosongJ+ LLt ,1. SULIT

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sulrT 2 347212The ollowingformulae may behelpful n answering hequestions. Thesymbolsgiven arethe onescommonlywed.

-b+ "[Y 4o;x= 2a2 q^ xan= e^* '3 a^ +t{=a^'n4 (am)"= an n5 logo mn = log um * loga n6 log"m:bggn-logonn7 log attn : n logum

tog,a fo8'blQgc aT,:a+.(n- l )ds^: l tza+(n-r)e l lTn = Qt'n' l

;= a(r" - l ) =a(! - r" ) , r *1" r- l l - rs- = o l r l . t l - r "

ALGEBRA8

t0l lt2IJ

CALCULUSn

" dy d), dudx du dr

dv dv duv=uv. L=u-+v-'&drd\du dv

..uqYdxdr--:_=-._*-;-'vdxu-

Areaundera curyel= lvdx orJ'

b= lxdyJ'Volume generated-- llry' aY orJ-

b-- l|d.- dv

GEOMETRY

'l Distance=2 Midpoint

A pointdividing segment f a l ine( tu, -.*. , rv, mv"\lx, v) = \ frr+n m+n )Areaof trianglel,; l (x,1, + x2y3 x.! , , ) - (xry, + xry, + x,yt) l

(x,+x,(x.y)= l-t2l l f )l r l={ . r -+}-^ xi+vi

17 tVx-+-Y-3412t2

-Y, .Y: )' ) l

SULIT

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

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SULITSTATISTICS

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l_i I ( - r -x)23o=tr t_-= l=' .l ) x-v1/

; zI,'w,Lw,, , _ n!" {n- r1''.n^ nl| =_--r fu* r)!rr 'P(Aw B)--P(A)+P(B) P(Aa B)P(X=r) ='C,P'qn- ' , P+ q = |Mean, p : npo =.[rW__x-po

, - &t/zf,Zr

[ . !"-rlr+l2 lcl f " l

4 o=

5 m=

6 I =9x100O"

l01112

t4

TRIGONOMETRYI Arclength,s=r02 Areaof'sector.e= ! ,'e3 sin2l * "or 'A: |

2

4 sec2A: +tan2A5 cosecz=1+cot2A

6 sinM = 2 siM cosl7 cos2A: cos'A- sin2A=2cos2A-r= l- 2 sin2A

) tqn /8 tan2A: '* " : 'l - Ian'A

3412t2

sin (l + 8) : siM cos8 + cosl sin-Bcos l + B) : cosl cosB F sinl sinB

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

9l0

t2

t314

sinA sinB sinCa2= b2+ c2 2bccoslAreaof triansle = f aDsinC-2

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SULIT )L+ILILSectionABahagianA140marksl140markahl

Answer ll questionsn thissecfion.Jawab emua oalan.1 Solvehe ollowingimultaneousquations:Give ouranswersorreclo three ecimal laces.

Selesaikanersamaan erentakerikutBerikanawapanandabetulkepada iga itikperpuluhan.P+2q =l

p' -3p+2q' =3[5 marks]15markahl

2 A curve asa gradientunction o.t2x, wherea is a constant.he tangentothe curve t hepoint(1,3)s perpendicularo hestraightine 2y = *x +3 ,Satuengkungmempunyaiungsi ecerunanxt -2x , di mana a adalahpemalar.Tangen epadaengkung ada itik 1,3)adalah ersereniangengan aris urus2Y=-x+3'FindCari(a) thevalue f a, [3 marks]

nilai agi a , 13markah)(b) the equation f he curve. 13markslpersamaanengkung ersebut. 13markah)

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SULIT 347212Ahmadhas 1000 hickensn hispoultryarm.Everyweek, ewillsell40of hischickens.Ahmadmempunyai1000ekor ayamdi ladangayamnya.Setiapminggu, iaakanmenjua! 0 ekorayamnya.(a) Find he otalnumber f chickeneft n hispoultryarmafter 1't week.

Caribilanganayamyang masih inggaldi ladangayamnya e/epasmingguke-21{4 marksl14markahl

(b) Thecostof eedin g ach hick s RM2perweek.Find he otalamount f moneyhathespent n he emaininghickenor he irsttwelveweeks.Perbelanjaan tasmakanan eekor yamadalahRM2seminggu.Kirakanumlah perbelanjaanangdibelanjakan tasumlahayamyangtinggaluntukduabelasminggu angpertama.. [3 marks]13markahl

HeightTinggi(cm) Number fplantsBilangananaman20 -29 430-3940-4950-5960-69 5I ! .J_ IY 1

TableJadual4Table4 shows hedistributionf heheights fplantsn a gardenGivenhemedian s47.5,ind hevalue f aJadual4 menunjukkanaburan inggi anaman i sebuah aman.Diberi medianadalah 7.5,carikan ilai a .Hence,ind hevariance f hedistribution.Seterusnya, ari variansaburaninggi anamanersebut.

13marksl13markahl13marksl13markahl

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SULIT 3472125 Solutions y scaledrawingwillnotbe accepted'Penyelesaian ecara ukisanberskalaidakditerima.

Diagram shows hombus QRS. heequation f PS s 3y +7x = 33 and heequation f PR is .Y -r + I I 'Rajah menunjukkanombus QRS.Persamaanaris urusPS alah3y +7x

=33dan persamaan ais lurusPR ialahy = -'r + I I

DiagramRajah5(a) Find

Cari(i ) the equation f QS ,

persamaangaris urusQS,(i i) th ecoordinatesf S.

koordinatbagiS.

[3marks]13markahl[2marksl

12markahl(b ) A point moves uch hatSf :I Q = 2'.1 Find heequation f he ocus f f,

Satu itikT bergerakdengankeadaanSf :fQ = 2'.1 . CaripersamaanokusT.[3 marks]13markahl

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SULIT 3472/2

6 (a) provethat tos2l = cos 4 sin . t2 markslcosl+s in lBuktikan ahawa kos2A =kosA-sinl t2markahl

kosA+sinA(b) ( i ) Sketchtheraph f /=s in2r+2 for0


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SULIT

SectionBBahagianB140marksl140markahl

Answer ny ou r questionsrom hissection.Jawabmana-mana mpatsoalan aripada ahagianni.

7 Diaoram showshecurve =x2 +2 and hestraightiney=-x+8 '

DiagramRaiah7

FindCari(a) th evalueof k,

nilaibagik,(b) th eareaof heshadedegion,

luas antauberlorek,

3472t2SULIT

34',7212

[3 marks]13markahl14marksl

14markahl(c) th evolume eneratedn erms f a, when he egion ounded y hecurve'

they-axisandy = 6 is revolved60 'abouthey-axis' [3 marks]tsipaduanaan,dalamsebutan , apabilaantau angdibatasi leh engkungitu, paski-ydany = 6 dikisarkan elalui360' padapaksi-y, B markahl

,=x2+2

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SULIT 3472t2

Diagram shows semicircle ADEB, entreO andsector OFC withcentreGiven hatOB= 5 cmand O = 15cm.

Rajah menunjukkanebuah emibulatanADEBberpusat dansebuah ektorTOFCberpusatT. DiberibahawaOB = 5 cm dan O = 15 cm.

10

AOBDragramRajah9

[Use/Guna =3.142)CalculateHitung(a) 4.TCO,

4TCO,

(b) th eperimeter,ncm ,of heshadedegion,perimeter, alamcm,kawasan erlorek.(c ) th earea, n cm2, f heshadedegion.

luas, alamcm2, awasan erlorek.

11markl11markah)

[5 marks]l5 markahl14marksl

14markahl

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l211(a) ln a survey arr ied ut n a school,t s ound hat2 out of 3 students assedtheir Mathematics est.

Dalam satu injauanyang dijalankan e atasmurid-muriddi sebuah sekolahdidapati2 daripada3 orangmurid lulusdalam ujian Matematik.(i ) If 7 students rom hat schoolare chosenat random, alculate he probability

thatexactly studentsassedheirMathematicses t [3 marks]JikaT orangmuriddaripada ekolahtudipilih ecara awak,hitungkebarangkalianahawa epat6 orangmurid ulusdalamujianMatematik.13markahl( i i ) f here re600 tudentsn heschool,ind henumber f students ho ai ledthe Mathematicsest. 12marksl

Jika terdapat60A orangmurid dalam sekolah tu, cari bilangan orang murrdyang gagal dalam ujian Matematik 12markahl(b) A surveyon body-masss doneon a groupof eachers. he massof he eachershas a normal ist r ibut loni tha meanof 45 kg andstandard eviat ion f 10 kg

Satu kajian terhadapberat badan sekumpulanguru telah drlakukan.Berat Badanguru- guru adalah mengikut aburannormaldenganntrn45 kg dan sisihanpiawai10 kg.( i ) A teacher s chosen t random rom hegroupFind he probabi l i tyhat he body-mass f he eacher s ess han42.5kg.

Seorangguru dipilihsecara awak darrpada umpulan ersebut.Cari kebarangkalian ahawaguru tersebut nentpunyai erat badan kurangdari 42 5 kg.( i i ) l l 12.3% f the eachers avea body-mass f more hank kg, ind hevalueof k.

Jika12.3% uru ersebulmempunyaieratbadan ebihdarik kg, carinilaibagik. [5 marks]15markahl

SULI ' I '

3172/2SULI'T

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t3SectionC

BahagianC[20marksll2AmarkahJ

Answerwo questionsrom hissection.Jawabdua soalan aripada ahagianni.

12 A particle moves long straightineandpasseshrough fixedpointO.l tsveloci ty,ms-t ,sgiven y r'= 6t ' -4t-2, where is he ime, n seconds,afterpassing hroughO.Suatu arahbergerakdi sepanjang uatugaris urusdan melaluisatu titik etapOHalajunya, ms-t diberi leh t '=6t2-4t-2,dengankeaclaan ialahmasa,dalamsaaf,selepasmelaluiO.(a) Find

Cari(i) th e nitial elocity f heparticle ,halaju walzarah ,(ii) it svelocity t he nstant hen heaccelerations zero,

halajunya adaketikapecutan dalah ifar,(iii) he ime nterval uring hich hepafticle ovesowardshe eft,

Julatmasaapabila arah tu bergerak rahke kiri,the distance,n m, travelled y heparticleuringhe irst hree econds,[3 marks]jarak,dalam m,yangdilalui lehzarahdalam iga saatpertama, 13markahlSketchhevelocitytime raph f hemotion f heparticleor0 < I < 3 12marks)Lakargrafhalajumelawanmasa agipergerakanarah tu untuk0 < I < 3.[2 markah]

I Lihat setrelah

sut_t'f

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3412t2

11markl11markahJ12marks)

12ma*ahl

12marksJ12markahl(b)

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SULIT14 Diagram 4 shows trianglePQR.

Rajah 4menuniukkanebuah egiigaPQR

Diagram 4Rajah 4

(a) Calculate.PQR,Krakan {PQR,

3472t2SULIT

15 3472/2

[2 marksl12markahl

12marksl

(c)

(b) Sketchand abela trianglePQ'Rwhichhasa different hape rom rianglePQRsuch ha t ength fPQ,PR and PR Q remain nchanged.State Pp'R,Lakardan labetkan ebuahsegitigaPQ'RyangberlainandaripadasegttlgaPQRdalam rajahdi atas,dengankeadaan anjangPQ, PR dan PRQ dikekalkan'Nyatakan .PQ'R,Hence, alculateSeferusnya, irakan(i) the ength f Q'Q, n cm,panjangQ'Q, dalamcm,(i i) th eareaof he riangle RQ',ncm2.luassegitigaPRQ', alam cm'.

12markahl

[6 marks]16 markahl

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SLTLIT l( ) 34'.12t215 Usegraph aperoanswerhis uestion.Gunakan erlas rafuntukmeniawaboalanni .

Afactory roducestwoypes ffurni ture, and B.Each urniture eeds typesof ra wmaterialsP andQ and he number f each awmaterials eededor each urniturerepresentedn heTable 1 below.Sebttah ilangmengeluarkanua enisperabott aituA danB.Setiap erabotmemerlukan ahanmentahP danQ dan bilangan ahanmentahyangdiperlukanbagi setiap erabotditunjukkanalamadual15 di bawah.

Table 5Jadual 5Thenumber f rawmaterials left n he actorys30and thenumber f rawmaterials left s 24.It sgiven hat henumber f urni ture producedsatmost wice henumber ffurniture producednd he actory roduces unlts Turniture and units ffurniture .Bekalan ahanmentahP yang inggal alam ilangadalah30 manakala ekalanbahanmentahQ yang inggal alam ilang dalah 4. Diberibahawa ilanganperabotA adalah elebih-lebihnyauakali bilangan erabotB dankilangtumengeluarkan unit perabotA dany unitperabotB.(a ) Write hree nequalities,ther hanx > 0 andy > 0, which atisfy l l he constraintsaoove. 13marksj

Tulis igaketaksamaan,elain > A dany > 0, yangmemenuhisemuakekangan i atas. l3 markah)(b ) By using hescale f 2 cm o 2 units n hex-axisan d2 cm o I uniton hey-axis,constructndshadehe egion which atisf iesheabove onstraints.[3 marks]

Denganmenggunakan kala cm kepada unitpada paksi-xdan2 cm kepada1 unit pada paksi-y, inadan orek antauR yangmemenuhi emLtaekangandi atas. 13markahl

3472t2ST]I,IT

Number f rawmaterialsBilanqan ahanMentah

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SLILIT

3472t2SUI,IT

t7(c) Useyourgraphn 15(b),o in dGunakan rafandadi 15(b), ntukmencari

(i ) th emaximum umber f units f urniture,Broducedf 4 units f urnitureareproducedBitanganmaksimum nitperabotByangdihasilkanika bilanganunitperabotAyangdihasilkan adalah 4.

(ii) the maximum rofit btained y he actory f he profitrom hesaleof a unitof urniture /'sRM 20 0and heprofitrom hesaleof a unitof furniture isRM2s0.Keuntunganmaksimumyangdiperolehika keuntungan aripadaualanseunitperabotA adalahRM 200dankeuntungan aripadaualan seunitoerabotB adalah RM254. 14marksl14markahl

END OF QUESTTON APERI Lihat sebelah

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Jq/Zl!9Nama:Kelas:ArahanKepadaCalon

I Tulisnamadankelas nda ada uang angdisediakan.2 Tandakan { ) untuk soalan angdijawab,3 Ceraikan eiaianni dan katsebagai ukahadapanersama-samaengan ukujawapan.

I Lihat sebelah3472t2SULIT

Bahagian Soalan SoalanDijawab MarkahPenuh MarkahDiperolehi(UntukKegunaanPemeriksa)A 5

2 6J 74 65 86 I

B 7 108 109 l0t0 t01i 10

L 12 1013 t0T4 10l5 10

Jumlah

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SULIT 3472/2

INFORMATION FOR CANDIDATESMAKLUMAT UNTUK CALON

l. This questionpaperconsistsof threesections:Section A, Section B and Section C.Kertas soalan ini mengandungi iga bahagian: Bahagian A, Bahagian B danBahagian C.

2. Answer al l questionsn SectionA, four queslions rom SectionB and two qucstionsfrom Secfion C.Jala,absemua soalqn dalam Bahagian A, empot soalan daripada Bahagian B dandua 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 membantuanda untuk mendapatkanmarkah .

4. The diagrams n the questions rovidedare uot drawn to scaleunlessstated.Rajah yang mengiringi soalan tidak dilukis mengikutskala kecuali dinyatakan.

5. The marksallocated or eachquestionand sub-partof a questionareshown nbrackets.Markah yang diperuntukkan bagi setiap soolctndttn kraian soalan ditunjukkandalam kurungan.

6. A list of formulae s providedon pages2 to 3.Satu senarei rttmus disediakandi halarnan2 hinggo 3 .

7. Graphpapersareprovided.Ke rt as gr af di sedi akan.

8. You may use a non - progralnmable cientificcalculator.Anda dihenarkan menggunakankalkulutor saintifk yang, idak boleh diprogram.

20

3472t2SULIT

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SULIT3472t2AdditionalMathematicsKertas2September 0092'h Jam

3472t2

JABATANPELAJARANNEGERI OHORPEPERIKSAAN ERCUBAAN PM 2OO9

ADDITIONALMATHEMATICSKertas 2

JANGANBUKA KERTASSOALAN N!SEHINGGADIBERITAHU

RKINGSCHEUIE

Kertas oalan nimengandungi7halaman ercetak

[Lihat sebelahSULIT347212 Ha kCiptaJPNJ 2009

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SULlT

[ ]"*_

2BAHAGIAN

Solution

3472t2

Submarks roGimarks1- np=1-2q Orq=-- ' . lP l I2 l l

Eliminate or q"(1 2q) ' - 3.(1*2q) + 2q2- 3 = OOrp2-3p +2"(\P )2-3*-0?_or eouivalent

6q'+2q-5=03p'-8p-5=0

Solve lrequadraticequation y using hefactorization@quadraticormula@completinqhe sq-z r J+ "(oX-sj2(6)ri i&4:ll3&t2(3)

q=0.761,-1.095orp=-0.523,3.189

Ip: - 0.523,.189(9q = 0.761, 1.095

if the workingcl fsolvingquadratic quations not shown

ILihat sebelahSULIT

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t_

Jt*+"' 2x)rtx

a=4

Solution

SULIT 347212

2a)

i, ,"/ - axt -zxdx

2y=-y+JIIfl'ln = - -2

*1r=2E]substitute= 1 n o axo2x = 2a (1) ' 2(1) '=

Submarks

[Lihat sebelahSULIT

Totalmarks

PFIIntegrate =

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

Substitute= 1,y=3 into4xa 2x2y = :.i + c, to find he

valueof c.y=x4-x2+3.

Nqte:.y: J(*4x'' - Zx)h must have at least1 ter"m ith power ncreased yAt.

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A"t

- -Solulion347212

tr_lUseTn-a+(n_1)d721=40+20"(40)

1000-*840=160

b)

OR otherval idmethod

l.JseSn= !; tz^+ (n- 1 )dlI rrrooo) 11x-0)l

l , lfl-ihat sebelahrUILI

Sutrmarks Totalmarks

3472t2 HakCipta.JPNJ 009

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*L=39.5or*F=7or "fr=d lPl IUse median ormula47.5=.39.5 + (

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

Zf*= 1425rZl*- 72917smFfr, 'tGt" f 4- | ---st - t -

Submarks

Using he formuiadistance ,,n7- - - - . -

/ t r t \Jtr- : ) ' +(y-4) '=2JG-7) ' r ' -8) ' \ :_l\-_,9r1rqv1-qql_-PvJ?7--q--]=Y

SULIT {- --olution ---

347212

[Lihat sebelahSULIT

*aWith "f , and F correspondingo "L

/+-"1Zf - t-J

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

i i ) 3y+7x=33y=x+1y=x+1

s (3,4)ST = 2TQCan be implied s ormula. Pl I

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9UUr[_i-- m347212Solution

Use dentityCos2A-Sin2A=Cos2A

LHS= RHSNs mistake allowed

b) i )

Graph inl per ioCin sxs nAmplitude

Drawing f thestraightine rom he equationnvolvingX and y, eithergradientOR y intercept f straightl-inemust be correct.

Fr*ltir*lE]

[Lihat sebelahgUL[

( rr

347212 |'lak Cipta JPNJ 2009

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SULIT 7BAHAGIAN

3472t2

Submarks

[Lihat sebelahSULIT

Totalmarks

c)

Solvehesimultaneous

lntegrate2+2

lntegratex'+2)+ areaof riangieT +rc3

lntegratez x2n t tt'- 2),1t,

x?'+2=*x+8x2+x-6x=2,x=-3

F2 u '1Use imit I ' in o [ \x) - +2xJJOr find he area riangle% (6)(6)

in . , rQ)| -2yl

IiL

-n

(24.667)

l imi tse/ \\ Kl /\*__r/

\I\

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SULIT

Frcmgraplr ): againtb=- 2.45[-2.S0


54/62

3472t2vxI

7

6

5

4

3

2

:ir^"r,t 'I.4

iir{r i. .^t; !1i,l

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

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SULIT 3472t2t

Solution

10a)i )i i )i i i )

Use he riangleawfor Of or g..t or .V

1)or =lo. io

2;q)J

I;0

t2- -p+;QOJ N1

f f i=6q1p*IQR=n1-c+1n)

Use he triangle aw o findoQ=on*nO171j tPo Jn,q-ntp*nq=q

1arJn=--- .m=--1A.4- a{Both arecorrectl

,.-*\ Comparehecoefficient/ Kt )\*-/ of p andq.l 1rn. n=0JL

2-m+n;1_)af-(-n)+n=1J1 -

Jm= --n2

[Lihat sebelahLULlT

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SULIT t2 347212

[Lihat sebelahSULII

Solution11a)i) 2 ----1I lpr I

0.2048UsenqI600(: )") .

J

/^\\ Kr )

b)i) r-\\Kr/- \ oaorsl_rurI

k-45 = 1.16l0

Submarks Totalmarks

-\-____,zoo !!1 |

UseZP(2.#",P(Xtk)=0.123p(z> L:45 )=0.123 i0

347212 Ha kCiptaJPNJ 2009

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SULIT 13BAHAGIAN

3472t2

[Lihat sebelahSULIT

Totalmarks$olution Subrng$s12a) )i i ) ,1, ,Useal = 0. o finddt

1t= laI- | , ,y=tr( - ) -J

6=.---J

1I*4G) -2a_)

i i )

b)

v


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Ztw = (130)1 (140)3 (115)2n (120)nt-t , I- \ tw r--rUse = T, = 125 \.KIJ

t\1_Nln=2

,,=-13,:t l100t32I {tl r!$;) +'l:():!_?g)l0

sur=rT

2'60 x I00= 130X \_,Ll!]_] x=RM2.0o

347212

[Lihat sebelahsuLlI

14

Solution13a) User 9- x loo ( l )

eon rvv

\-K{

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3472t2

[Lihat sebelahSULIT

t5ULIT

\ rc t )\- \zlxrr

SinQ Sin45"

62.12' l 62'

Submarks

r__--.1LNI I


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SULIT t6 347212

Submarks15(a) 2x+ 5y< 30 orequivalent3x +2y s 24 or equivalent

x < 2, ! or equivalentDraw orrectlyt eastonestraightine roni he*inequalitieswhichnvoves andy.

Draw orrectly ll hree straightinesNote Accept ottedines.ThecorrectegionR shadedFurniture = 4(fromx=4intheregion)Maximumoint t (5,4)

Use200x+ 250y*regionR for point n the

ss-1i f

c) i)@trr:l

RM2000

In (a) he symboi - " is notusedat al ior more han hreeInequali t iesregiven.In (b )doesno tuse he scalegivenor doesno t usegraphpaperOr interchange etween he x-axisand he y-axis'

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SULIT t7 3472t2

ii{il

Y'1

l:!l

t

t ,:

-tt$ii

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SPM Trial 2009 AddMath Q&A (Johor)

Text of SPM Trial 2009 AddMath Q&A (Johor)

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Dapatkan Skema di ...Soalan Pendidikan Islam Kertas 1 Percubaan SPM Johor 2011; soalan percubaan spm johor 2011; skema johor spm 2011; skema pemarkahan jokor 2011; trial johor 2011

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SPM Trial 2009 AddMath Q&A (Johor)

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