SPM Trial 2009 Math Q&A (Johor)

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

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SULITt449trMathematicsPaper1September00 9lt/o jam

JABATAN PBLAJARANNEGERI JOHOR

PEPERIKSAAN ERCUBAAN PM2OO9MATHEMATICS

PaperOne hour and fifthteen minutes

IJA\GAN BUKA KBRTAS SOALAN INI SEHINGGA DIBBRITAHU

,(crlns .soalan ni udalah clalemdu,ibql?asa.Soctlendi bahagian qtas adalalt clalqm behasa nggeris, diikuti oleh bahqsa-\.lelclyu.Calon dikehendekimembecamaklumatdi halaman2.

Kertas soalan ni mengandungi 2 halamanbercetak.O FlakCipta JPNJ2009

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SULIT 2INFORMATION FOR CANDIDATES

TIUKLUMAT UNTUK CALON

l. This questionpaperconsistsof ' 40 questionsKertctssoalan ini mengandungi 10 soqlan.2. Ansrver all questions.

Juwab sen uo sctulan.3. Answer eachquestion by blackening he correctspaceon the answer sheet.Jswub dengan menghitamlarn ruangqnyang betulpucla kertas awapan.4. Blackenonly one space or eachquestion.

Bagi setiap soalan hitqmken salu ruangan sahaja.5. If you *'ish to changeyour ans\ver, rase he blackenedmark that you have made.

Sekiranya anda hendqk mentrkarkanawapan, padamkan tanda yang telah dibuat6. 'I'henblacken he space or the new answer.Ke uud an hit amkan.iau'apenyarrg bqru.7. The diagrams n the questionsprovidedarenot drawn to the scaleunlessstated.

Rajahyang mengiringi seliop soalan lidak diluki,skanmengikul ,gkalakecualidinyatakan.

8. A list of formulae s provided,Satusenarai rumus disecliakan.9. A booklct of four-figuremathematicaltabless provided.Sebuah buku sifir matemetik em1tcrt ngka disediakun.10. You may use a non-programmable cientificcalculalor,Andq dibenctrkanmenggunakankcilkulator saintifik yung tidak boleh diprogram.

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SULIT 3MATHEMATICAL FORMULAERAMUS-RUMUS MATEMATIK

The ollorving ormulaemay be helpful n anslveringhequestions,he symbols ivenare heonescommonly sed.Rumus-rurnuserikut bolehmembantu nda menjawab oalan,Simbol-simbol ang diberi adalah),dngbiasadigunakan. RELATIONSPERKAITAN

12 Py,thagorasheorem c2= a2+ b2TeoremPithagoras, m n m+ nI a xa :a

m n m-nA +fI :O

, m\n mn\a ) =d

^-r- | ( ' l - ' )^ - oa-nl- , o)n(e)I'U) = -- -n(^s)

P(A', )=t-P(A)

1' - l,m=- xz- xt/ v - interceDtm=-\ - . - - - -x - tnterceptI pinlasan- ym--- \ =.rptwqsan - x

IJ

t4 ))

(x ,+x" v,+v. \Midpoint,x,y)=1| . , .7)Titik tengah

DistanceJarak

Average peed=

Pttrala laju =

Mean0

distanceravclled--1ime]t[enjarak yangdilaluimasa ctng,iumbil

= su mofdata;u*b., "f d"t"hqsil ambah ilai dats_ ---: bilanganal aitt

l t Mean

Mitt

sumof (midpoint f interval frequency)su mof frequencieshasiltanMerapun)hasil ambah ekerapan

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SIIAPE AND SPACEBENTUK DAN RUANG1 Area of trapezium ! >< um of parallel sides x height2

Luas ropezium L x hqsil amhqhdua sisi elari x tinggi

2 Circumferencef circle = xd = 2tvLilitan bulatan nd - 2nj3 Area of circle = TrrZ

Luashulutan -- rj2

4 Curvedsurface reaof cylinder = 2nrhLuaspermukaanmelengkungilinder : 2trjt5 Surface reaofsphere = 4rr2Luaspermukaan fera : anjt6 Volumeof rightprism= cross ectional reax lengthIsipaduprisma tegak : luaskeratan entasx panjang7 Volume f cylinder = *thIsipaclu ilinder : nj2t

l ^8 Volumeof cone = -rr thIsipadu on !, j',J

9 Volume fsphere = lort3Isipadu.r.fera = !rt'J

l0 Volumeofrightpyramid = 1 * basearea heightaJ1Isipadu piramid tegak = I x luas tapak x tinggiJ

l l Sumofinterioranglesofapolygon (n-2) x 180'Hasil ambah udut edalamanoligon (n - 2) x 180'

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5arc lenglh angle subtendedat centre

circumference f circle 360'panjdng engkok sudutpusatlilitan bulaton 360.

13 areaofsector _ anglesubtendedt centreareaof circle 360'luas sektor sudutpusatluas bulatan 360'

14 Scaleactor, k= !!PAFaktor skala,15 Areaof image k2 x areaof bject.

Luas mej: k2 x luasobjek

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SULIT 6I Roundoff809430 correct o threesignificant igures.

Bundarkan809430betul kepada iga angkabererti.8098094809000809400

Express .00000545n standardorm.Ungkapkan .00000545 alambentuk iawai.A 5.45 10-sB 5.45" 10-6C 5.45x 10-7D 5.45" 1fr84.7xl07 +5600000:

ABCD

ABCD

1.03" 1074.76x 1015.26" 1076.07 lOi

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SULIT 74 Diagram4, showsan emptyperfumecontainerwhich s a right prism,with trapezium

is theuniformcross ection f theprism.Rajah 4 menunjukkan ebuahbekas ewangi ang ko.sang engankeratan entssseragam erbentukrape ium.

50 cm

25 cmDiagramRajah4

A worker ills up half full of the emptycontainerwith a perfume. Calculatehevolume, n cm3, heperfumen thecontainer.Seorang ekerja telahmemasukkanejenis ewangike dalambekas ersebut ehinggaseparuh enuh. Hitungkan sipadu ewangi,dalam cm3, alam bekas tu.

ABCD

4.625x fiz5.55 1047.5006 1041.11 105

11000121011'-

BCD

l l I 100:111010210010121001 02

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SULITGiven4 x 54+3 xDiber i ,4 x 54+3 x

852+ 5p +1 = 40321s,ind thevalueofp.52+ 5p+1 40321s,carinilaip.

AIB2C3D4

In Diagram7, PQRW is aregularpentagon ndRSTIJW is a hexagon.Given hatIS is parallel o W andO.RSs a straightine.DalomRojah7, PQRII/V alahsebuah entogon ekatadan RSTUVWalahsebuahheluagon.TS selari denganUVdan eRSadalahsatu garis lurus

Diagram7Rajah7

Findthe valueof r.Cari nilai n.A 3go

c 74 0D gg"

72"

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9In Diagram8,JK is a tangento the circleKML at K. JML is a straight ine.DalamRajah 8, JK ialah tangenkepadabulatan KML di K. JML ialah garis lurus.

Diagram8Rajah8

GivenJM- MK,fnd thevalueofy.Diberi JM : MK, cari nilai y.A 4loB 49"c 57"D 820

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SULIT9 In Diagram9 shows wo flagson a grid.

Rajah9 menunjukkan uu huahbendera i ataskotakbergrid.

DiagramRajah9

FlagG is the mageof flag F undera one ransformation.hich of the ollowingcorrectlydescribehe transformation.BenderaG ialah imagebagi benderaF di buwahsatupenjelmaan.Antaraberikutyangmanakohmenghuraikanenjelmaanersebut.A 'r--^-^t^.,- f I I r ransta l lonl / l

\- T. /

. ( t )I TANSIdST ]\.-4iB Reflection nx-axis

Pantulanpadapaksi-xC Enlargement ith scale actor about entreO

Pembesarun enganfaktorskala7 berpusat i OD Rotation1B0o lockwise bout entreO

Puturun 19ff ikutarahjamberpusat i O

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v

F \

o

\ G

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10 Diagram 10 shorvs ive trapeziumdrawn on thc squaregrids. Which of the trapeziumA, B, C, and D is the imageof trapeziumP underan enlargement.Rajoh l0 menuniukkan lima tra1:izium dilukis di atas grid sisiempat ssma. Antoralrapezium A, B, c, dan D yang munakah imej bugi trapezium p di bawah suqtupenfiesoran.

I)iagram10Rajah 10

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,/;:: lS'.l"s'ffi ls l:i-':ffifi*:sffi',;'iil-"::"lt$i..l' i ;:""{ffiXx$!l{ *-)ff b.jt N. b#.qQ?:zfg NA { (.1 i${iy{ -N X; )a'."'l h,".v\.t "i-'14A

A ' :,t:i\*i*ci..st

! Nt.i"..^ ' " l tl i 9.t9iri:l+iil1\

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SULIT1l Diagram I showsa right-angledrianglePSQandPQR s a straight ine and

PQ: 15cm'Rajah l menunjukkan ebuah egitigabersudut egakPSQdanPQR alahgarislurusdanPO: 15cm

15cm O .R

Diagram1Rajah1l

{Given hatcos o = -i, find thevalueof tan/.5aDiberi kosxo -i, cari nilai bagi tanyo.f

Tan0 =-0.5658 and180" e < 360". ind hevalue f 0.Tan0 = -0.5658don 180"S0 < 360'.Carinilai0.A 2Ag030'B 24A030'c 2gg030'D 3300 0'

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SULIT 13

13 Whichof the following graphsepresentshegraphofAntara berikutyangmanakahmewakiligrafy = sin xo

y: si nxo for 0oS x < 180o.bogi 0o S,r < 180".

C

D

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l4 Diagram14 showsa right prism with thehorizontal asePQRS.Rajah14menunjukkan ebuah risma egakdenganapakmengfuk PORS

Diagram 4Rajah14

What s the anglebetrveenheplanePQI'|/ and heplane RSTWApolrah udutdi antarasatahPQll/ dengan atahRSTW?

A lstrQB I PTYRC ZTWPD tRrvQ

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15 Diagram 5 shows wo telecommunicationubstations n ahorizontalplane.PointPandQ are hefwo tipsof the substations.heheightof the owersare 5 m and20 m.Raiah 5 menuniukknn uabuahpenccwangelekomunikasii atassatupermukaanmengufuk.Tilik P dan Q beradadipuncakpencawongersebut.Tinggi l


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16 Diagram16showsa flag rRS. hepointsP, Q, andR lie on a horizontalplane.Rajah16menunjukkanebuah enderaRS.TitikP,8 and R terletakdi qtassatahmengufuk S

Diagram16Raiah16

Theangle fdepression fromS s 50o.Sudut unduk Q dari titik S ialah 50iCalculatehe distancePR.Kirakanjarak PR.

13.43t7.4319.0723.09

16

ABCD

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020"06001 0"200"

t7

t7 Diagram 7 shows tree pointsP, Q, andR on a horizontalplane.Rajoh 17menunjukkaniga titik P, Q,danRpadasatahmengufuk

Diagram 7Rajah17

P is apointduewestof p. Find hebearing f R from p.P odalahsuatu itikyang terletakrebaratQ. Cari bearingR dari Q.

ABCD

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SULIT 1818 In Diagram18, N is theNorth Pole. S s theSouthPoleand1VO.Ss theaxisof

theearth.Dalamrajah 18,N ialah Kutub {Jtara. iqlah Kutubseratqndon Nos ialahpat$ibumi.

El30"T

EquatorKhatulistiwa

sDiagram 8Rajah18

t9

Find hepositionof pointp.Cari kedudukanitik Q.A (2oo , fio Ln

(2AoU, $o B)B (200N,5'n

(2oo ,750 )c (7ooN, o rn

eoou, $o B)D (700A" 5on

Qoo i,75o )2(l + 3x)(2 5x)=A 2+x-15x2B 4 +2x* 3012C 8+4x-60x2D 10- l9x l lxz

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20

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14 2r3r14 3r3r

18 7r3r30 7r

19

Express2(4 r) -+! asa singleractionn its simplestorm.r3r{JngkopkanK -r-! # sebagaisarupecahan unggaldqramsebutan ermurlahA

BCtl 3r

2l Given hat

Diberiffi- '

exPressin ermsfsand's , ungkapkan dalamsebutan dan q.

AB

CD

s2s-3, - -:----iI - .9-s-3,"= -:--------I - s 'sq 31-s

a-3r=' l -s

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20. 2m+lGiven hat'-' ' - +l=3m, calculatehevalue f n.31m t7Diberi + +1 : 3m, hirungnilai m.aJ

2A aJA+B 3

?+;

CD

23 Given hat ,[ f =61 , find thevalueof p, q, andr.r-: sDiberi bahqwa tlp' = 6' , cari nilai p, q, danr,

ABcD

p=6,Q=3,r=2p:6,q=2,r :3p:6,q=3,r : lP=6,q:1,r=3

., JI o 'a-" ISimplifu(on ') ' '/ z -t\3I p-s - |Ringkaskan\pq' )

6- OA p"q-B p'q '

Rd

p-qp'o '

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2l

7< Listal l the ntegersthatsatisf i thenequal i t i .5+2r< l l and x-l>-2.Senaraikan emuanteger ang memuqskqnetaksamaqn an 5 + 2.x< 11- 1>_1

11

BCD

-1 01? ?- i-?-t 0 I ? 1- i -) -1

26 Diagram 6 shows hepercentagef savings oneby Ahmad or the irst ive monthof 1'ear009.Roiqh26ntenunjukkaneratus impanan lehAhmacl agi ima bulanpertomaMeidalam ahun2009.

Diagram 6Raiah26if the otalsaving or that irst five monthss RM450,calculatehesaving n RM thatrepresentsy theshaded ector.,lika umlah simpananbagi ima hulan ersebutalan RM(50, hitung simpanan alamRfulang diwskili oleh kawasan erlorek.A 18.75B 37.5c 67.5D 135

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SULIT27 Table2Tshows he disnibutionscores f a groupof studentsn aquiz .

Jadual27 menunjukkanaburanskorsekumpulanelajar dalamsatukuiz.

Table2TRajah2T

Themean f thescoresMin bagiskor alahA 2.17B 2.50c 2.60D 2.67

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ScoreSkor 0 I 1 3 4 5FrequencyKekeranan 3 5 l0 t2

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Grof manakahyang mewakili y = 8 - 5x3?

SULIT28 Whichgraph epresent: 8 - 5x3

ST]LIT

D

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SULIT29 Venn Diagram in Diagram29 shows elationbetween etX, Y, andZ.

Gambar ajah Venndalam Rajah29 menunjukkanubungan ntara setX, Y,danZ.

Diagram29Rajah29The shaded rea epresentsRantau ang berlorekmewakiliA XnZnY'B XaYnZC XwZnY'D XwYnZ

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2530 Diagram30 is a Venn diagramshowinghe elements f the universalsetd, set { dan

setB.Rajah 30 ialah gambar rajah Yenn ang menunjukkanunsur-unsardalam set semesta(, setA dan setB.

.l ;. r

o1 4

Diagram30Rajah30

List all the elements f setl'Senaraikan emw unsurbagi setA'.A {v}B {s,",r}C b,r,.,ylD lt,r,*,!,q\

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3l Diagram31, shows herelationbetween et setP, and setQ.Rajah 3],,menunjukkan ubungan i sntaraset , setP, dansetQ.

26

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Diagram 1Rajah31Givenn({) =33, n(P^Q) = 4, n(Q)=l5 and n(Pu Q)'= 12, calculate henumbersof elementn theshadedegion.Diberi n()= 33 ,n( PnQ) =4 , n( Q =15 da nn(PvQ)' =72, hitung ilanganelemen alam kawasanberlorekA2B6C8Dl0

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32

,1

In Diagram32,MNis a straightine with gadient ! -3DalamRaiah 32,MN ialahgaris urusclengan r*unon -?3

Diagram32Raich32

Find hey-intercept f thestraightlineMN.Carikanpintasan-ybagigaris MN.ABcD

89l0l8

33 Find hevalueofp if the ine oining hepoints 4,3) and 2 ,p) is parallelo the liney:2*3x.Cari nilai p ika garisyangmenghubungkanitik (4 3) dan (2 , p) adalahselaridengan aris lurusy : 2 - 3x .

-3- l59

ABcD

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SULIT34 In one recent culture show,eachaudiences giventhe chance o pick a ball randomll

fiom a bag contains4 red balls, 7 greenballs, and 9 blue balls. A present s givenaway to any audiencewho getsa red ball. The ball is return back into the bagbefore he next audiencedo their picking.Dalam satu petunjukan kebudayaan bsru-bqru ini, setiappenonton diberi peluangmemilih secqra rawak sebji bolo daripada sehuah begyong herisi dengan 4 holqmerah, 7 bola hijau, den 9 bola biru. Hadiah akan cliberi kepadopenontan )'dngmendapat bola merah. Bola yang dipilih itu dip"ulangscmula ke dalum lseg ;thelumpenonton ain membucrt emilihan berikutnya.

If 240 audiences ttended he show, calculaie he number of presents hat willprobably be given away on that day.Jika 240 penonton menghadiri pertuniukan tersebut,hitung bilangan hadiah yangmungkin diberi pada hari itu.A12848c60D80

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35 Diagram9 showsmarbleshat abelled ith ,R,S,or LRajah 9 menunjukkanuli-guliyangberlabelR, S, QtauT.

e$p^e#S@w@w *Gfl@Diagram 5Diagram35A marbles chosen t random.Stateheprobabilityhat hemarbleshosens not labelledwith R or Z.Sebi.ii uli dipilih secarq av)ak.\jatakan kebarangkalian ahqwa li yangdipilih itu bukan berlabelR atauT.

67B 7 lL 6

ILf 2

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SULIT36 Table36 shows hevalues or variables and .

Jaduql36 menunjukkan ilqi-nilai bagipembolehubah dany.

Table36Jadual36Given haty variesdirectlyas 2. Calculatehe valueofp.Diberi bahawa berubahsecereangsung engan 2.Hitung nilai p.A36B72c 108D 216

37 Given rr variesdirectly as r and varies nverseh'as square oot ofp when n : g,p : 4 andm:2, find the relationbetweenm, n, andp.Diberi m berubah secaro langsung dengan n dan secara songsqng dengan puncakuasaduap apabilan: B,p: 4, dan m = 2, cari hubungan,ntara m, n, rJonp.

,rlim = ----:-:--Bm=C * =J-nr'64'D .=4p"

30

A 8n

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38 Table38 shows he relationbetween ariablesW,R, and . Given that I4/e RT.Calculate hevalueofx.Jadual3Smenunjukkan ubungan i antarapembolehubahW,R, dan T. Diberibahawa lte RT. Hitungkannilqi x.

Table38Jadual 38

ABCD

3e (32

AB

CD

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31

922932 /s\t l-s) l l=t -1 ,( ls 8 5)r"ll8 llsJ(28)(r8)

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fo) t ' ' ) 'ol40 Giventhematr ixequationI Z l*l : l=i r l ,nnatnevalueof-q+r.[*J [nJ ,JIo.1' l ( 'o\

Diberipersamaqnmatri l$I Z l* l - t =l t I ,carikanni laip-q+r.l -o) nJ r jA -lB5c l lD15

END OF QUESTIOIV APERKERTASSOALANTAMAT

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t449ltSULIT1449/lMathematicsPaperOgos/Sept 009

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAANSPM TAHUN 2OO9

SKEMA PEMARKAHANMATHEMATICS

PaperOne hourand l l thteenmittutcs

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SULITAnswersForPaper (Mathematics PMJulang 009)

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No AnswerI C2 BaJ C4 B5 D6 B7 L8 C9 t)0 A

I B) DJ CAT D6 B7 Dt8 Cl9 B20 D

2l A22 L.L) A24 D25 ALt) C27 C28 A29 A30 (-3l B)/ .JJ D34 B35 BJt ) C3' l B38 D39 L40 B

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t449t2MathematicsPaper2September 0092Yz arn

Nama:.Tingkatan: . . . ; . . .


PEPERIKSAAN PERCUBAAIT SPM 2AO9MATHEMATICS

Paper2Two hours and thirtv minutes

JANGAN BUKA KERTAS SOALAN INI SEHTNGGA DIBERITAHU

1.2.

Tuliskan namo dan tingkatan padaruang yang disediakan.Kertas soalan ini adalah dalamdwibahasa.

3. Soalan dalam bahasa Inggerismendahului soalan yang sepadon dalamhaha.yaMelayu.C al o n di b enarksn menj ow ab kese uruhanatau -sebahagian soalan some ada dalambahctsu 7{elo|,u atau bahasa Inggeris.Calon dikehendaki membace arahan dihalaman 2.

Untuk Kegunaan P emer l


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SULITINFORMATION FOR CANDIDATITS

MAKLAMAT UNTUK CALON1. This question aperconsists 1'twosections: ectionA andSectionB.Kertas soalan ini ntengandungidua bahagian: Bohagian A don Bahogian B.2. Answer all questions n SectionA and any four questionson SectionB.Jawab semua sonlan dulam Bahogian A dan mana-nlena empat soalemdaripadaBaltagian B.3. Write your answers learly n the spaces rovided n the questionpaper.Tulis awapan anda dengan.ielaspada rulng yang disediakan dctlanrkertassoalan.4. Showyour working. It may helpyou to get marks.Tunjukkankerja mengirauncla. ni boleh membantuandn untukmendapatkonmarkah.5. If you wish to change our answer, rossout the answer hat you havedone.Thenwrite down tlre new answer.Sekiranyaanda hendakmenukar awapon, butalkon .icwapan yang telah dihual.Kemudian tulis .iatoapanyttng baru.6. The diagrams n the questionsprovidedarenot drawn to scaleunlessstated.Raiahyang mengiringi ,coctlonidak dilttkiskan mengikutskala kecuali dinyatakan.7. The marks allocated br eachquestionand sub-par1 f a questionare shown nbrackets.Markuh 1,ongdiperuntukkan bogi seliup soalan dan ceraicrnsoalan ditunjukkandulant kurungan.8. A list of formulae s providcd.Satu scnarai rumus clisediakln.

9. A booklet of four-figure mathematicaiables s provided.Sehwh buku sifir mulemutik empot angka disediakan.10 . You may usea non-programmablecientific alculator.Anda dibenurkan menggunakrn kalkulator saintifik yang tidak boleh diprogram.I 1. Thisquestions apermust be handedn at the end of the examination.Kcrtus soalan ini hendaklah diseraltkanpacla akhir peperiksaan.

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SULITMATHEMATICAL FORMULABRUMAS MATEMATIKThe ollowing ormulaemay behelpful n answeringhequestions.hesymbots ivenare heones

commonly sed.Runtus-rumus berikut boleh membqnlu andq menjawab soalan. Simbol-simbol yang diberi adalqhYang biasa digunakan' RELATT'NSgERKATTANI)

. m n m+nI a xa:a t2 PyhagorasTheorem c' : a'+ b'TeoremPithagorasy.-v,m = :---!--:---xr-x,2

aJA-

P(A)

Min

MeanMin

nt n m-na +a:ct

(a-) '= a^'_, | (d *b)A-' : -----:-----;-l Iad -bc\-c a )

n(A)

13

14 *: * l*=-(

y - interceptx - inlerceptpintasan - ypintasan - x

))

l0

P(A') :1*P(A)

Distance:ff iJarokMidpoint, (x, y):Titik tengahAveragespeed :

Purata laju

Mean

(x,+x, v,+v"\l '> ') ldistance ravelled-t imeta[enjg:slzslg4l!Amqsa yang diambil

sum of data""*b.. ol i l r t"

hasil tambah nilai databilangan data

sum of (midpoint of class interval x frequency)sumof freqtrencies: hasil taylah ( nilai titik tengah selang kelas x kekerapanthasil tambah kekeruonn

SULIT 1449t2

Forexaminer'suse

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Forexamtneruse

SULIT 4SIIAPE AND SPACE( BENTUK DAN RUANG )

1 Area of trapezium = 1 * ,u* of parallelsidesx heightzLuas trapezium + x hasit tambah dua sisi selari x tinggiz

2 Circumference f circle : d = 2mLiliton bulatan : rd : 2nl3 Areaof circle = /n 2

Luss bulatan : 7ti24 Curvedsurfaceareaof cylinder : 2mhLuaspermukaan melengktmgsilinder 27tjt5 Surfaceareaof sphere : 47y2

Luas permukaan sfera: 4rj'6 Volume of right prism - crosssectional reax lenglhIsipadu prisna tegak : luas kerqtqn rentas x panjang

7 Volumeof cylinder = mz hIsipadu silinder ry't8 Volume of cone = ! *'t3

Isipadu on : I"i',J9 Volume of sphere = * *'J

Isipadu sfera 2 "itIl0 Volume of right pyramid - x basearea x heightJ

IIsipadu pyramid tegak = ; * Iuas tapak x tinggiJI 1 Sumof interiorangles f a polygon - (n - 2) x 180o

Hasil tambah sudut pedalqman poligon

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SULIT

area of circleluas sehor

360"sudut usat

l2 arc length : angle subtended at centrecircum erenceof circle 3600panjang lengkok !!4!!2!!!L

lilitan bulatan 3600

13 areaofsector anglesubtendedat centre

Iuas bulatan 360'

14 Scale actor k- PA '-PAFaktor skal, PA'a, r: pA

l5 Area of image: k2 x xeaof objectLuas imej : k2 x luas objek

SULIT M49n

Forexaminer'su:te

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Foreuamirer',ute

SULITSection ABahagian A152marksj152markahlAnswer all questions n this section.Jawab semua soalan dalam bahagian ini.

I On the graph in the answer space, shade the region which satisfies the threeinequalities +;l >_ ,y Sx andx < 4.Pada graf di ruqng jawapan, lorekan rantau yang memuaskon ketiga-tigaketaksamaan + y Z 5, y Sx danx 1 4 .

13marks)13markahfAnswer /Jawapan

6

v\ /5

/ v:/X

/ \

/ \y:5

0/ 5\

x

t149t2 SULIT

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SULIT2 Calculate he value ofx and ofy that satisfythe following simultaneous inearequations:

Carikan nilai x dan nilai y yang memuoskan ersamaan linear serentak berikut:4x+ 3y: 113x-Y=5

[4 marks]14markahjAnswer Jawapan:

Forexgmiter's

ute

3 Solve the following quadratic equation:Se esai kanpersamaan kuadrat k;

q* *9x* 13: Z(x-5)

Answer /Jawapan:14marl


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Forenmirgt',use

SULIT4

A 6cm BDiagram 4Rajoh 4

Diagram 4 shows a combined solid consistof a right prism and a right pyramid, whichare oined at the plane DCGH. zis vertically abovethe baseDCGH. TrapeziumABCD is the unifonn cross sectionof theprism. DC :8 cm.Rajah 4 menuniukkangabungan sebuahpepejal yang terdiri daripada sebuahprismategak dan sebuahpiramid tegakyang tereantumpada satah DCGH. V berada tegakdi atas tapak DCGH.Trapezium ABCD ialah keratan rentas seragamprisma itu.DC :8 cm.

Given the volume of the combinedsolid is 322 cm3. Calculate he heighl i, in cm,ofthe pyramid.Diberi isipadu gabungon pepejal itu islah 322 cm3. Hitung tinggi, h, dalom cm,bagipiramid itu.

[4 marks]14markahl

Answer / Jawapan;

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SULIT5 (a) Completethe following statementusing the quantifier o'all" or "some" to

make it a true statement.Lengkapkanpernyataan ber kut denganmenggunakan engkuant t "semua "atau "sebllangan" untuk membentuk uatupernyataan benar.

elementsn { 1, 2, 6,9\ areevennumbers.unsurdalam {1,2,6,9} adalahnomborgenap.

(b) Write down Premise 2 to complete he following argument :Tulis Premis 2 untuk melengkapkanhuiah berikut:Prernise1: All regularpolygonshaveequalsides.Premis I : Semua oligon sekntamempunyaisi.si ang samo,Premise :Premis2:Conclusion: TriangleABC hasan equalsides.Kesimpulan; SegitigaABC mempunyai sisiyang ssma.

(c) It is given that the number of subsetswhich has z elements s 2". Write down oneconclusion y deduction n setA: {u,",i ,o,u}.Diberi bilangan subset untuk suatu setyang mempunyai bilongan unsur n ialah2". Tulis satu kesimpulansecara deduksi,bilangan subset untuk setA: {a,e, i ,o,u}

[5 marks][5 markoh]Answer/Jswapan:

(b)Premise2:

(a)

(c)

Forexamircr'tuse

SULIT 1449t2

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SI]LIT 10Diagram 6 showsa straight line P,Sand a straight ine QR drawn on a Cartesianplane.The straight line P,S s parallel to the straight ine QR. p lies on x-axis.Raiah 6 menunjukkongaris lurus PSdan garis lurus QR dilukis pada suatu satahCartesan. Garis lurus PSselari dengangaris lurus QR.. Q terletokpada paksi-x.

R( 6,6 )

Diagram 6Rajah 6

Find,Cari,

(a) theequationof the straight ine p.R,persamaan bagi garis lurus QR,

ft) the coordinates f Q.koordinat bagi Q.

Answer /Jawapan:(a)

[5 marks][5 markahl

(b)

1119t2 STTLIT

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SULIT

UsingGuna(a)

11

Diagram7 showsa rectangleABCD. PointD andpoint B are he centreof quadrantsand sectorof circle with radius7 cm and 14 cm respectively.Given hatAE:8 cm andCG: 12cm.Rajah 7 menunjukknnsegiempatABCD. Titik D dan B adalah pusat bagi sukuandan sehor bulatan denganejari 7 cmand 14 cm masing-masing-Diheri bahawaAE - 8 cm and CG : 12cm.

A 5cm tr 14cmDiagrarnTRajah 7

'>').|

.)aLL

, calculate,, kira,

the perimeter, in cm, of the shaded egion.perimeter, dalam cm, katvasan berlorek.

)^the area, n cm', of th e shaded egion.Iuas, dalam cmt, ko*otan berlorek.

(b)

[6 marks]16markahl

SULIT u49n

Forexamtner su3 e

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Forexamtn4rrce

SULITAnsweilJswapan:7 (a)

t2

(b)

r119t2 SULIT

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St]LIT( t -- \ . (S - l \g (a) *[ , ] ir ttt" inversematrix of I ; "- |. nind the value of

rn1-2 5) \z ' /and value of n'

Diberibshawomatriks *( t n\iotot matrikssongsangtogi (5 " -j'l[ -2 5) \z r)Cari nilai m dsn nilai n.(b) Write the following simultaneous linear equationsasmatrix equation:

Tulis persamaan linear serentakberilatt dalam bentukpersamaan matriks:5x Y: 39?-x+3Y:-5

Hence,using matrix method, calculate he value ofx and ofy.seterusnya, menggunateonaedohmatriks, hitung nilai x dan nilai y.

13

Answer/Jawapan:(a)

[6 marks]16markahl

o)

SI]LIT M49n

Farexaminer'suse

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For?xamineruse

SULIT9 Diagram 9 shows the speed-timegraphfor the movement of a particle for a period of16 seconds.Rajah 9 menunjukkangraf laju-masa bagipergerakan satu zarah dalam tempoh

I6 saat.

Time (s)Masa (s\Diagram9Rajah 9

(a) State he length of time, in s, that the particle moves with uniform speed.Nyatakan tempoh masa,dalam s,zarah itu bergerak dengan laju seragam.(b) If the total distance ravelled by theparticle in the last 6 seconds s 90 m, findthe value of a.Jiko jumlah jarak yang dilalui oleh zarah dalam 6 saat terakhir ialah 9Om,cari nilai bagi u.(c) Calculate he average peedof theparticle, n ms-I, or the period of l6seconds.Hitungkan purata laju, dalam ms-l, zarah tu dalam tempoh l6 saat.

[6 marks]16narkahlAnswer Jcrwapan:tu)

l4

(b)

u49n(c)

SI.]LIT

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SULIT

l0 Diagram 10 shows four cards labelled with lettcrs in box M ancl hree numbered cardsin box i/.Rajah 10, menunjukkan empat kad berlubel dengan huruf di dalunt kotuk M dan tigakad herlabel nombor di dalam kotak N.

15

EHMHBox MKotak M Box NKotak N

Diagram 0Rajah 0A card is picked at random fronr box M and then a card is picked at random lrom boxN.Scttu kad tlipilih secaro ruwsk claripada kotak M dan kemudian sotu kacl dipilihsecnra rawak daripatla kotak N.By l isting the sample of all the possibleoutcomesof the event , find the probabil i tythatDengan menyensraikan sampel bagi semuu kesudahan peristiwa yang mungkin, carikeharangfurliank, a card with a vocal and a card with a two-digit numbers are picked,satu kad huruJ-vokal dan satu kad nombor dua digit dipilih,(b) a card with a consonant or a card with an odd number are picked.solu kud huruf konsonon fltausatu kad nombor ganiil dipilih.

[5 marks][5 markah]

Answer I Jdv'opun:(o)

MEm

SULIT

&)

1449t2

["oret'omtner'.\

llsc

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Forexamtneruse

SULIT 16

1l

E8cm

15cmDiagram11Rajah I I

Diagram I l, showsa right prism.TrapeziumABFE is the uniforn crosssectionof theprism.ABCD is the horizontalbaseof the right prism.AE :8 cm, AB = 15 cm, andBC: 5 cm.Rajah I I menunjukkansebuahprisma tegak. TrapeziumABFE ialah keratan rentasseragam risma itu. ABCD adalah apakmengufuk agiprisma itu. AE :8 cm,AB : 15 em,dqn BC :5 cm.Identify andcalculate he anglebetrveenhe ine HB and he planeABFE.Kenalpasti dan hitung sudut di entara garis HB dengansatahABFE.

[4 marks][4 nartuh]Ansu,er Jawapan:

IIII

,La'D

1449t2 SULIT

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(a)2

(b)

SULIT l7SectionBBahagian B

148markr)148markahlAnswer any four questions rom this section.Jswcrbmana-monaempat ,srtalan ttripada bahagian ini.

CompleteTable 12 n the answerspace or the equationy :2 + 7x - f bywriting down the valuesofy whenx: -i andx : 3 . 12markslLengknpkan Iadual t 2 rli ruang.ictu'apanagipersam*any:2 + 7x - xzden.qaimenulisnilai-nilaiy apabilax : *1 dan x :3. 12markahlFor this part of thequestion,use he graphpaperprovidedon page 19.You may usea flexible cun'e rule.{Jntukceraian soalan ini, gunakan kertasgraf yang disediakonpada halamsn19.Anda hotehmenggunakanemharisboleh entur"Using a scaleof 2 cm to I unit on the r-axisand2 cm to 2 units on they-axis,drawthegraph f l :2 +7x- * ' fot l < x


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SULIT 19Graph ftrr Question l2Graf untuk soalan I2 {- l cnr

I

i ,i

Forexamineruse

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l3

SULIT

(a)

20rs)Transfornation M is a translat ion[ 2 l .\ /Transformation N is a refleclion jn the line y : 3.

Penielmaan iuluh rrrr,rtoril] .\ .2PenjelmaonN ialah pantulan pada guris lurts y: j"Find the coordinatesof the inrageof point (-3,1) uncier he foilowingcombined transformations :Cari koordinat ime.i bagi titik (*3,I) cli hav,uh g,abunganpenjelrnuan berikut:( i ) M2

(ii) MN[4 marks]f4 narkahl

Diagram 13 shows three triangle, ABC, PQR and PZl9, drawn on a Cartesianplane.Rajah l3 menunjukkqn tiga segitiga ABC, PQR dun I'7'5. diluki.; pado suatu,sa(0hCartesun.

Diagram l3Ra.iuh -)

(b )

r149/2 STILIT

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SULIT

Answer Jawapan:13 (a) (i)

(b) (i) (a)

(i) o)

21(i) ZPS s the image of ABC undera combined transformation VW.TPS alah imej bagi ABC di bawahgabunganpenjelmaonYW.Describe n full transformation

Hur ai kan se engkapnyopenje maan(a) \il,(b) v.

(ii) It is given that theareaof the shaded egion s 165cm2.Calculate the area, n cm2,of triangle PQR.Diberi bahawa luas lvrwasan ang berlorek ialah 165 cmz,Hitung luas, dalam cm', segitiga PQR.l8 marksJ18markahl

(ii)

(ii)

SULIT L449D

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Forexamitv/utte

SULIT

14 Table 14(a)shows he frequencydistributionof theage, n years,of 40 visitors at abook exhibition.Jadual l4(a) menunjukkan ahuran umur, dalam tqhun, bagi 40pelswat ke satupameran buku.

Age (Years)Umur ( T'ahun\ FrequencyKekerapan5-9 0l0 t4 115 t9 aJ20-24 625-29 1030-34 1t35*3940-44 2

t7

(a)

Table 14(a)Jaduol l4(a\

Calculate the estimated mean of the age of the visitors.Hitung min anggaran umur bagi pelcrwat-pelawal itu.

[5 marks]15markahl

(b) Basedon Table l4(a), complete Table14(b) n the answerspace o show hecumulative requencydistributionof the massess. fl mark:slBerdasarkqn Jadual U(a), lengkapkanJadual14ft) pada ruang uwapanuntuk menunjukkan kekerapan onggoknnisim itu. ll markahl

(c) For this part of the question,use hegraphpaperon page24.Untuk ceraiqn soalan ini, guna kertas grcf yang disediakan pada halaman24By using the scale of 2 crn to 5 years on the horizontal axis and 2 cm to 5visitors on the vertical axis, draw anogive for the data. [4 markslDengan menggunakanskala 2 cm kepada5 tahunpada paksi mengufukdan 2cm kepada5 pelawat pada paksi mencancang,ukis satu ogif bagi datatersebut. 14markahJ

(d) Basedon your ogive, find the otal numberof the visitors whose agearemorethan 33 yearsold. 12markslBerdasarkan daripada ogif'anda, cari bilongan pelawat yang berumurmelebihi33 tahun l2 markahl

1{J9 2 SULIT

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SULIT

Answer /Jatuapan:14 (a) Mean:

Min

Table 4(b)Jadual 14(h)(c) Refer to graph graph on page24.Rujuk graf pada mukasurat 24.

23

(b)

(d) Ase :Umur

Upper BoundarySempadan atas Cumulative frequencyKekerapanLonggokan9.5t4.5

SLILIT u49n

Forexomineruse

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fo rerdtnlner

us e

SUL 24Graph for Question14(c)Grof untuk Soalan 14 (c)cm --)

i

Il

t449t2 SULIT

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SULIT 25l5 You arenot allowed to usegraphpaper o answer his questionAndct idsk dibenarkunmenggunakan ertasgraf untukmenjatt,ab octlan ni.

ta) Diagram 15(i) showsa solid rightprismwith a rectangular ascABCD on ahorizontalplane.RectangleADEF is an nclinedplaneand the rectangleGHJK is a horizontalplane. The edgesCJ, BK, FG andEH are verticals.AB - DC : 6 cm, BK= CJ: 6 cm, EH: FG : 2 cm,JK: HG : EF: DA: cB = 4 cm an


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Forexatntnelu3e

SULIT(b) A half-cylinder s cut and removed rom thesolid n Diagram 15(i).Theremainingsolid is shown n Diagram1s(ii). Semi-circleLQM andPltN is theuniform cross-section f the half- cvlinder.The radiusof the semicircle is 2 cm.

,4L: MB= DP:NC:1cm.

c--____f

Diagram 15(ii)Diagram 15 (ii)Draw to full scale,Lukis dengan skalapenuh,(i) the elevationof the remainingsolid on a verticalplaneparallel o ABasviewed from I [4 marks]

dongaknn pepejal yang tinggal itu pada satah mencancangyang selari

26

denganAB sebagaimanadilihat dari Y.(ii) the plan of the remainingsolid.pelan pepejal yang tinggal itu.

[4 markah][5 marks15marlrahl

i 4-r92 SULIT

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SULITAnswer Jawapan:ls (a)

(r) (i)

27

(ii)

SULIT M49n

emnt

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Forexamtheruse

SULIT16 G(35o N , 70o D, H and J are three points on the surface of the earth. G,,/ s the

diameter of the earth. GH is the diameter of the parallel of latitude 35"N.G(35' U , 70" T), H, dan J cdalah tiga titik di atas permukaan bumi. GJ adalahdiameter bumi. GH ctdalah diameter selarian latitttd 35o (J.

(a) [2 marks][2 markah]

(b) Calculate he shortest istance,n nauticalmiles, from G to ll measured longthe surfaceof the earth. [3marks]Hitung iarak terdekat, dalam batu nautike, dari G ke H diukur sepuniangpermukaanbumi. [3 marknhl

(c) An aeroplaneook off from G and lew due west o Fl along thecommonparallelof latitudeand hen lew duesouth o ISebuah kapul terbang berlepas dari G dan terbang ke arah barat ke Hsepanjangselarian latitud sepunyadqn kentudian terbang ke arah selatankeJ.CalculateKira(i) the distance, n nautical miles, from G to H measuredalons the

common parallelof latitude.iarak, dalam batu nautika, dari G ke tI diukur sepanjang selarianlatitud sepunya.

(ii) the time taken for the whole flight if the averagespeedof the wholefl ight s 710knots.masayang diambil, untuk keseluruhanpenerhangan ika purata lajukeseluruhan enerbanganalah 710 knot .

17marks)l7 markahf

State he longitudeof -{Nyatokan ongitud bagi J.

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SULIT

Answer /Jawapan:16 (a )

(c) (i)

END OF QUESTIONPAPERKERTASSOAI-ANTAMAT

29

(b)

(ii)

SULIT 1449t2

F.exomtt/li

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SULIT1449/2MathematicsPaper 2September2009

1449t2


PEPERIKSAAN PERCUBAANSPM TAHUN 2OO9

SKEMA PEMARKAHANMATHEMATICS

Paper2Trvohours nd hirryminutes

1449/2 SULIT

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No Answers Marks

5

0

X:4II

iII

II

Y:X

+y:5

PI(for l inex=4dotted/solidine)

P2(area hadedand : 4 must edotted ine)Note AwardPlforx :4 sol idl ine.Subtotalz 9x 3y:13x:26x:2, , - |y- r

15 or y:3x-5 oreqr.r ivalentor equivalent KKNNSubtotal ,,|3 4x'- l lx*3:0(4x+ l)(x - 3 ):0X:- l ,X:3A

KIKINI NI

Subtotal 44 I'x(6 +8)x5x621"6x8xhaJ1'x(6 +8)x5x62h:7

I+J

x6x8xh=322

KIKIKI

NI

Subtotal 4

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5 (a)(b)(c)

SomePremise TriangleABC is a regular olygon.2-)z( note withoutworkingaward KlNl)

P1P2K1N1

Subtotal 56 (a)

(b)

lT lps: tTleR: 8-02-e2t6:2(6)+c orequivalentY:2x-60: 2x- 6 or equivalent(3,0)

KI

KINIKINI

Subtotal7 (a)

(b )

1^22-x zx_x /471^22_-x /.x47411 1'^ - or 82 "

o, 72 *2x4xl4360 7* 72 *2r4x14 +360 7or 82.6 m.

14+15+12+8+5

!*Lr f o, 72,?r14, or 19x1547 3607rexrs - 1*2*f - 72r4rt4 '47 36071233or n3! or 123.3 m2l0 l0

KI

KIN1

KIK1

NI

Subtotal 6

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8 (a)

(b)

m: 117n: I(s -r)( ' ) f30)[z t ) l r)=[-rJ/x\t t -t t -\v)x:5v:-5

3 ' ) | ,3o)sr[- ](3)-(-1X2)l-2

P1P1

P1

KIN1N1

Subtotal 69 (a)

(b)

(c)

6!*r ,*6 =902

u:30I tzo*30)4+(6x30)+eo2 t6Z3 l or 23J258

P1

KI

NI

K2

NISubtotal 6l0

(a)

(b )

List ingS: { (A,7), A,9), A, l0)(R,7),(R,9),(R,10)(t ,7),( t ,9),( t ,10)(F,7),F,9), F,10){ (A,10),( t , l0)}2 lt26{(A,7), A,9), R,7)(R,10), F,l0))10 5'-or -126

( R,9),t,7), 1,9)(F,7), F,g),

P1

KIN1KINI I

Subtotal 5

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l l ZHBEBE: 17 mTan HBE: 5t7Z 16.39" r 16 23'

P1P1KINI

Subtotal 4I2 (a)

b)

(c )

(d)

Graph ( Re-fero theg'aph IThe axesdrawn n the right directionwith a uniformscale or- l


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(a )

(b )

(c )

(d)

Table 4Jadual lUpperBoundaryCumulativerequencyMeanAge:(12Xl) ( t7X3)+ (22)(6) (27 (10) (32)(11)(37)(1) (42)(2)

4029Ogive( Refer to thegraph )Correctabeling f thehorizontalxis.Al l points orrectly lotted.Point is plottedcorrectlyand he ogivepasseshrough t.Smooth urve hatpasseshroughall thepointsNote: f 6 pointsar eplotted orrectly, ntitleKlIf 5 pointsor lessareplottedcorrectly, ssignK0

40-28t2

UpperBoundary Cumulative requency

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A/D LIP

KICorrectshapeKIDH:AG>DA:HG > EH:FGNIAccuratemeasurement( + 0.2cm)

KICoruect hape* Acceptsketchingf semicircleKIBK>GK>FG>AL:MB* Accept nlydrarving f semicircleN2( Accuratemeasurement)KI(correct hapeIgnore otted ineLP andMNKI( BothDotted ineLPandMN)l/ lI\I

DJ>AK>AD=CH=KJ > AG:GK =DH_I I I-n JN2(Accuratemeasurement)

HiEiR

G/F/Q K/B

JIC

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t6 (a)

(b)

(c )

I 10"W

180-35-3sl l0x606600n.m

(i) 180 60x cos35o8846.84.m(i i ) 70x 6070 x 60 + 8846 84

71018.38 ours r l8H 23Min.

P1P1

KIK1NI

KIN1PIK2NI

K1

Subtotal t2

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Q l2 (b),(c)and d)+-2 cm->

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Q 14 b)& (d)

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SPM Trial 2009 Math Q&A (Johor)

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