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1449t2MATHEMATICSKertas 2Ogos2012

z)i"

144912

PE PERTKSAAN PERCUBAAN BE,ITSAMAST.IIL PELAJARAN N,IALAYSIA 2012

ANJURANMAJLIS PENGETTJA SEKOLAH MALAYSTA (MPSIID

CAWANGAN PERLTS

NAMA: .....TINGKATAN:

}IATHENTATTCS

Kertas 2

Dua jarn tiga puluh rninit

J{\Gd\ BLXA KERTAS SOALS

t\.t S EH I\-GGA DIB ERITAHI.;

l. Tulisk,zn narr: t dan tinglcrtanpada ruang yang dtsediakan.

2. Kertas soalan ini adalahdalam dwibahasa.

3. Soalan dalarn bahasa Inggerismendalrufui soalan yang sepadan,lalam bahasa lulelayu

4. Calon dikehendakt membacanctklumat di halarnan belakangkertas soaian ini.

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Kod Pemeriksa

Bahagiau SoalarrMarkahPenuh

MarkahDiperoleh

III

I

I

iI

I!

iii

i

II

I

I;Al

ij

I

I 3

2 4

3 4

.t 3

5 5

6io7 4

B 6

9 6

r0 5

t1 6

B

L2 L2

l3 t'2

t4 t2

15 t2

16 1.2

Junrlah

Kertas soalan ini nrengandungi 36 halarnan bercetak.

1449t2 [Lihat SebelahSULI'T

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SULTT 6

Section ABuhagiutt,4

[52 m"trksl

[52 markahl

I

1149t2,

futsrver all questions in this scctiort.Ja',i,ab serrutu soelcifi ,lalam bahagutn uti.

On ttre graph in the arlswer space .slu<ie tlte region whicit satisties the tltreeirreclualitie.s.y'5 x-i- l, ! . 3xa1dy "' 5.

Pa,ia grrtJ'dt ruattg-lL)wapdrt,lorek ra.ntLuL.yL1t78 fileinu.-iskart ketiga-ri;1ctkctaks,:tmctctft .l ( x t- l, }' ' 3x ,!an;' - 5 .

Artsrr,erdcrwLtpLtn: [3 mctrksl

[3 markahl

1119t2 SULIT



1

' SULIT

t149/2

2 Calculate the value of rz and oIn that satisty the follor.ving simultaneous linearequations.

Hitung nrlai m dan nilai n yang ntemua.tkan perscunttan l.inectr serentctk berikut:

m+Zn-53m-4n--25

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[ 4 marks I

[4 mark<thlAnsr,r,er l./awa.pan:

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3 Solve the following quadratic equation:

Selesaikan persamaqn kuadratik berikut:

p0p+2)=40

Arrsw'er Llawapan .

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14 marksl

f4 markahl

1419t7 SULIT



SULIT t449t2

4 Diagram 4 shows a cuhoid ABCDEFGH rvith a horizontal square base EFGH.Ralah 4 merum.iukkan sebuah kuboid dengan tapctk .segi empat :iamo EFGH di atq.ssatah mengt{uk.

Diagranr 4

Rajah 4

/ is the midpoint of AD. BC:14cm and C-G: 10 cm.I adalah titik tengah AD. BC : l4 cm dctnCG: l0 cm.

a) Name the anqle behveen the plane HIG and dre plane CDHG.NamczJcan sudut di antara satah HIG dengan satah CDHG.

b) Calculate the arrgle behveen the plane HIG and the plane CDIIG.Htnuryl rudut di czrttctrtt satcth f{lc dengan satrth CD\{G.

13 mctrks';

[3 markalt]An*ver'/ Jau,apctn'.

(,-t)

(b)

1449t2ILihat sebelah

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(a) (i)

(i)(a)

i0

Write the converse of ttre following staternent :

Tuliskan akas bagi pernyataan berikut:

If x is lcss than zeyo then x is ir negative nurnber'.Jiknx kurung daripada sifur nruku x iulah nontbor negatif

(ii) State wtrether fhe converse statcment rvritten at tire answer space in5(aXi) is tnte or falsc.N),atakait sama ada itkas bagi pern.yataa,? .t'(vlg drrulis pada ruangjcttt:<zpan soalan 5(a) (l ctd"tlah benaruttctu palsu.

(b) Write dorvn Premise 2 to cornplete tlte follorving argumertt :

Tulis Premis 2 untuk nteiengkupkan lttiictl; bcrtkut:

Premise [ :lfsetBisasutrsetof set,4, tlten.4 nB: B.

Premis I : Jtka :;et B i.tl"h subset bctgt -'ie{ .4, ntoka.4 n B : B.

Premise 2l Premrs 2 :

Conclusion : Set B is not a sulrset of set A.Kesimpttlan : Ser B hukan subset bagi set A.

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of numbers [, 6, 12,

nombor l, 6, 12, 20,

(c) \{ake a general cocltrsiott bf irtductiort tbr the sequetlce

20, , .... rvhich follows the follo*'ing pattertt:

Bttat satu kesttnpulan utntttn SeCLtrc aruhan bagi urut"ttt. . ):ang mengtlctit poia bertkur.

I :4(0)--,- 2ta

6 :.1 (!)-11lZ =4(2)- 11

20 = -l (3; * 73

Ansrt'er I Jau, aprttt'.

( ii)

(b) Prerttise 2iPremis

[ 5 marl u,15 markc 8l

c,alLI

TJI-cio/o/o/-c/o,

@l>JL'r/il!/

.aql(u

q)-r(U)q)a)

ar\

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t419t2



SULTT 1449t2

lrr Diagran 6, PQ is parallel to RS and (J is the origin. The equation of straight line PQ is

2y - jx: k and {re equation of ttre straight line PR is .y : _1x + j."4Dalctrn Ralah 6, PQ adalah selari dengan RS dan O ralah asalttn. Persctrnaan garis luru,s

PQ tat<th 2y - jx: k dan persdnlaan garis lur,ts PR ialah.y : -lx + i.4

11

3:

- -_1,4

,a+J

R

Diagram 6

Raiah 6

FindCcU't

(.2) the valtie of l'.nrlat k,

(b) ttreJ: - intercept oIthe straigltt line P*S.

ptntasctn - ), bagi garis 1il'rr.s l?.S.

r449t2

16 marksl

16 narkchl

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Answeri Jawapan :

(")

1.2 t44912

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SULIT 13 1449t?.

7 Diagrarn 7 sltorvs a solid forrtted by joining a half cone and a right prisrn at therectangular plane CDEF. Trapeziunr ABCD is flre uniform cross sectic-rn o[ttrepri.srn.

Ralah 7 ntetrunjukkan sucttu pepelal yang terbentuk daripada cantuman sebttaltseparuh krtn dan sebucth pri.sma tegak pada ,satah segi empd.t tepat CDEF.Trapezitttn ABCD ialah kt,ratan rentas prtsma itu.

D

4 cnr

tlt1

AB : 2CD.

Using 7T -

Diagranr 7Ralah 7

The heieht o[ the half cone is 7 cm.11-' . calctrlate the l,olunre. in crn-t. of the solicl.-7

E

Ats:2CD. Trnggt sepLTruh kon1-)

Menggunctlcctn Ir - 11 . ltrrttng

AnsrYef : .J crv'ctptTt?.

i.tlalt 7 cnt.

t.st padu. tlolctnt crrrt . pepejal itu.

f4 tnarksl

14 mark,ahl


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Ans rver,'.,I.2 u: a p e n :

(a)

(b)

t4 1449/2

[6 rnarks]

f6 mczrkctltl

(z (r\8 (a) It is given that tnatrix K = | ^ l. Find the value of n if the inverse of mah'ix

\3 n)K does not exist.

Diberi baluzwa marnks * : (: 6l a:.,., ttilai n.j*,t .\.()t?gs.angcut hagt1.3 il)

matriks K tidak wujtt<i.

(b) Write tlte foilou,ing sirtrultarteous liueai'ecluations as nratrix ec;uation:

Tttlis persamaan linear serentctk berihtt dctlam persLTtnactn mcttriks:

2x+5;'=-ll3x--1.r.':18

Hettce, by using rnatlix lnethod. calculate the value of x and of.y.

Seterusnya, ,nenggttn,tkan kcte<lalt tncztriks, littutg ntlai x dttn nil,ti 1,.

t449t2 SLILIT



15 1449t2SULIT

9 Diagram 9 shou,s trvo sectorsOP()Rancl OS7-of hvt'r circles r,vith thesalne centre O. PUO is a semicircle u,ith dianreter P() and PO : 2OT. O.SR isa sh'aight line.

Raiah 9 merutniukkqn dua sektor OPQR dctn OST bagt dua bulatandengan pusat yartg samaO. PUO ialah sebua.h sernihulatan dengctn dtanteterPO dan PO : 2OT. OSR ialah ,satu g<zris lttrtrs.

Diagram 9Rajah 9

14 crn and Z POR : / SOT : 120'14 cnt dan /. POR : / SOT : 120"

Lising ir =22

7calculate

PO:PO:

DenganmenggLlrlakan n : !. ltitttrtg7

(a) the perinteter. in crn. of the r.r'hole diasrarn.perinteter, dalam cm, hagi selunth ralah ttu,

(b) the area, in cm?, of the shacled region.luas dctla,n crr', bagt rantatr berlorek.

[ 6 marks ][ 6 markah ]

1449/2

co

o*6c)

[Lihat sebelah .*P

SULIT Ea)().

(Ua-o

a)c)+

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FuExtvnlner's

U.c

SULIT

,\rswer / Jawapan :

(")

l6 1449t2

(h)

1149t2SULIT



SULIT

l0 Diagram 10. shorvs fivo boxes. A and B. Box A conkrins four carcls labelledwith letters and bor B contains three cards lalrelled rvith nunrbers.

Rajah 10, ntenunjukkan dua kr-ttctk,4 and B.Krttak A mengandungi empat kadberlabel dengan hru/'dcut kotak B menganrlun,qt ttga kad berlabel dengczn

nombor.

l7 1449t2

trtrEE trtr[4Box AKotak A

Box BKorak B

Diagranr l0Raiah l0

A card is picked at randont tionr box A and then a card is picked at random flrombox B.Satu kad dipilih secara rawak daripada kotak,4 dan kemudian satu kad puladipilih secara rawa.k darip<tdra kotak B.

(") List atl sample space. I

Senaraik<t,t ruang sampel. I

I

(b) By listing the sample o[all the possible outcomes of the events. find the I

probabilit-v that I

Dengan tnenvenera.tkan sampel bagt i:esemua kesuiah.in bdgt pertstt\t'd I

yarlg mungktn. cart keharangkaltan b,thcnta I S

(r) a card latrelled n,ith a vorvel and the card labetled uith a nrultiple o[3 are I .gpicked. I 6lsekeping kad herlahel dengan htrru-f't,okal dan sekeprng kad I F/berlabel clengan nontbor gandacui i drptlih. I I

(ii) a card labelled u,ith the letter R or a card lalreled u'ith an odd I Snunrtrer are picked.sekeping kad herlabel dengctn hurtL{'l? ,atau sekeptng kad herlabel I Sldengan nombor ga4iil diptltlt. rE _ , ,l ..,

[5 marksll S[5 markahll s/

se3

ILihat sebela[.8 I

t44gt2 SULI*€oQa"o

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FqExanniner's

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SULTT

Answer / Jau,apqn:

(")

l8

(6) (i)

(it)

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l,{49/2STIL IT



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I I Diagranr I I slrorvs tlte speed-time graphs of the nlovenlertt of hvo particles, P and

Q, for a period of I seconds. The greph ,48 represenls ttre rnovement of P and tltegraph MNB represents the moventent of Q.Rajah rnnunlukkan graf la.1u-masa bctgi pergeralcan tlua zarah, P dan Q dalant

tempoh masa T saat. Graf AB ntenunjukkan pergerakan P dan graf MNBrnerutnjukkttn pe rgerakcut Q.

Speeci (*l'')Laju (ms'')

5

Diagrarn 1lRalah I I

Time (s)Masa (s)

19

(a)

(tr)

State ttre unitbrnt speed. itr ms-r. of particte Q.,\i1'atakatt lrtirt seragaft:. drtlctm ,rrr'' - :arcih ().

Calculate the rate of change of speed. iu nrs-:.oIparticle Q in ttre tirst6.seconds.Htfiil1g kctdar penrbaha;t laitt, dalant nis-t, .&,,g t zarah Q ,lalatn 6 sartt ):dngpertama.

(c) At f seconds. the total distance travelled trf' P and () is 173 nt. Calcr.tlate the valueof T.

Padn T saat. lumlah jar<tk vang dilaiui r-,leit P dan Q ialah l73rrr. Hittutg nilar T.

16 mrzrksl

16 markahl


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Answer / Jawapan:

(")

2A 1449t2

(6)

(c)

t149t2 SLILTT



2l

Section BBahagiut B

| 48 marks I

| 48 markah I

1449t2

[2 marks I

12 markah I

Ansrver arty four questions frtttn this section.

Jawab mena-mana anpat soalan ciaripade bahagia.n ini.

12 (a) Complete Table 12 in the ansrver space on page 22. forthe equation 1, - - t'

O,

(b)

rvriting dorvn the values of y r.vhen x- -l'5and x=2x

l_2 markslLengkapkctn.Jadual 1,2 di nnng jawapan pczda halaman 22, bagi persamaan

12 . ,. , . .,. ,.,y - -'-a dengan menulis nilai-nilai y apabila x - -l'5 dan x :2 .

-r

f2 markaltlFor flris parl of the question. use the graph paper provided on page 23.You ma-r'

use a flexibte cttrve rule.By using a scale of 2 crn to 1 unit on the x-axis and 2 cm to 2 units on the.v--ais.

drarvtlregraphof -1:=-Efo, -4<x<l and - 1,2at,Sl2. [4marksl-rc

{Jntuk ceraian soalan int, gunaka.n kerras graf ada halaman 23. Anda boleh

menggunakan pem baris /le ks i be l.

Dengan mefiggutTakan skola 2 ctn kepctda I unit ?.ada pal;si-x dan 2 cm l:epada 2

irrzit pacia t:.tkst-1,. lt*ts grdfJ' - - Y 1i1,,1; - 4 < r < -1,lan -12< )' <12.

[1 ntarkaltl(c) Fronr vour graph in l2(6). hnd

Dctri grczf dt l2(b), ca.rt

(i) tlte value of-t, rvhetl x : -3.5.nilai v apahtla.r : --i.i.

(i) the value of x rvltetr )' : 7.

nilai x apabiltz .y - 7.

(d) Drarv a suitable straight line on the graph in

satisfu the eqtration L2 -2x+3 =0 for - 4 <.x

State thcse values of x. f4 marksl

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12(b) to Frnd the

r<4and-12<

values of x

v <12-

rvhich

1449t2

UntrkKegunaattPemenksa



ForExaniner's

IJsc

StiLIT 22 :+4gn

Luki.s .\atu garis lurus yang sesua,i pada gra/'di I2(il Ltntuk melcari lilai-nilcti x

.yang memltaskan persamaan \?-2x+3 = 0 utTtuk - 4 <x < 4 darr

-12< )'<12'Nyc.ttctk,an nilcti-nilat x itu.

fuisrver I Jawctpan :

L2la) y =--

x

14 markahl

Table l2JarJuol ] 2

(b) Refer graph on page 23.Ruluk grc{di hr.Lundn 2-i.

(c) (i) y :

(ii) -r :

(d)

The equation of the straight Iine:Persamaan garts lurus :

x i-n --1 -2 - t.5 I

-l I 1 3 4

v 3 4 6 iL2 -12 -4 -3

t1.l9t2 ST-iLTT



SULTT

, r. : i f I + alii'irii;iil:! iii;iil: i t i *__i_---_-_*,_^.__-._ t-^- ___i i

.t ;iriirli ;iil!:ii iiilI ' ! i | .ili,!.iilr..!,;!lr i1!itiliiij:i,lii: ____i__ i___i-_ i t_ i __1i;:r:ri:.;:'t;l:.i-l:l

1

i'iii;

ti .iiiiI.:.ia:

l-.1 .a:i

23

Grirph for Question 12Graf unlr* Soalan 12

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13 (a)

24

Diagram 13.t shows point A ( l, 3 ) clrawn on a CafiesiauRajah l3.l menuniukkctn titikA ( l, 3 ) dilukis padct suatu

L449t2

plaue.satuh Cartesian.

Trarrsforrnation P

Transtbnnation T

Transforrnation Rpoint (0, 3).

Penlelmactn P i.zlah

Penlelntctctn T ialah

Penjelmaan R ialalt

Diagrarn l3.lR.ycrlr i 3. I

is a retlection the line v' = 2,/- i\

isatranslatiorri - |lr2jis a rr-rtarion of 90" in the anticlockrvise directiou about ttre

satu pantulctn pcttla g<lrts | =2./ -\/-\\sLtlutrLtnr/ds,iI -I

Iz,/sLTtu putctra,t 90"lc7vt()ti arah.Jctttt pctdd pusctt ( 0, -1 )

v

A

_a

At 1, 3,

-r4 2 0 2 4 6 8

-2

-4

t,o/Qlc/at

o*/.=/-S=r'/o/o/

a/gs/

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' ST/LIT 25 1449t2

ILihat sebelahSULIT

State the coordinates of the inrage of point A (1, 3) under the followirrgtransformatiotr:Nyatakan koodinctt ime.j bagt tttrk A (1, 3) dt hrmt,ah penjelntaan berikut:

(i) rP.,(ii) Rr.

Arrsu,er I .Jtmvapan'.

ic) (,

1449t2

(,, )

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ForExaniner'l

Usc

SULIT 26 1i4,4g/2

(b) Diagratn 13.2 strovrs two quadrilateral KLN/IN and EFGH ctrawn on a Cadesianplane.Rajah 13.2 menunjukkan dua sisi etnp(7t KI^MN dqn EF(]H dilukis padLt suatusatah Cartesan.

(i) KL\N is the irnage ol EFGH under the cornbincd transft-rnnatiorl \,ti.Describe, in full. the transtbnnation :

d-L\-/.\' ialah tmel bagt EF(jtl c* hav.'ah 51afutng,tn per.ieimaan I'7-;.

H u ratkan se I e ngkap ny.t pe nj e I m a, m.

(.2) L',(6) |'..

It is given that KLNTN represents an area

EFGH.Dtbert balult'rt KLI/.\i mev,"tktli lt,,':"s 11

EFGH.[8 marks I

| 8 markah I

SLJLT't

(ii ) of -14 unit:. tind the area reprcsented bl'

t t n t i . c L1 r t I ttL) s.uc?/?g rl*t,tl: t I t rt I e lt

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STJLTT

Ansu,er/,Jay)apan :

(b) (i) (n)

t449t2

27 1449/2

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o)

( ii)

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SULTT 28

14 The data in Diagram 14 sllow the attendance ofBahagia during the Teachers Day 201,2.Data dalam Rajah l4 rnenunjukkan kehadiranBahagia pada Hari Guru 201 2.

(a)

students

pelalar

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for 40 classes at SK

untuk 40 kelas dt SK

(c)

Diagranr l4llcz.lrth l1

Based on the data irt Diagrarn l4 and b1, using a class intervaI of 5, cornpleteTable 14 in the ansrver space.

[4 marl:s'lBerdasctt'kan clatu dal"un R<4i"th l5 ,lrtrt menggu,llctkdfi se/ctng kcl"ts 5. lengkerykanJacfuttl l1 dalctm rtrcng j,tw'ctpLtt7.

[1 markahl

Based on Table 15 in (a). calculate the estinrated nlean of'ttre aftendance of rhesf.tdents.

f3 markslBerdasat'kanJadual !5 dalam {a). hr.t min keha,liran bagi nela1,tr.

f3 markaltl

For this par-t of the questiort- use thc graph prc'rr.'ided.

(b)

(d)

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By using a scale of 2 cnr to 5 snrdeuts on the horizontal axis and 2 cnrthe vertical axis, drarv a frequencl' polvgon tbr the data.

Berdas,trkan poltgon kekerapLtn .r:ctt1g dtlukis dt

berkartctrt dengrtn kelrctrltran pe ldlctt' tttt.

to lclass ort

[4 markslUntuk cerctian soctlan ini, gunakan keruts graj'y"tng disedtakan.Dengan menggunakan skala 2 cm kepacla 5 pelrzlctr poda pctkst ntengufi* dan 2

cm kepuda I kelcts pada paksr ftieficc7t1cdng, luki.s saru poligon kekerapan bagidtttct tlu.

[1 markalt)

Based on ttre frequenc5, poh'gcrn in l4 (c), state one piece of infonttation aboufthe attendance of the srudents.

ll marksll1(c.), n.yamkan satu maklumat

ll markaltl

SULI't

l911L/J

27

J+

/t0

26

30

24

34

37

38

33

32

25

t8

39

39

40

34

25

4L

45

43

t6

L7

4s

43

40

/._1

30

45

39

38

35

29

43

3t

35

37

28



SULIT

Answer I Jawapan.(a)

29 1449t2

Cllss intervirlSelnng kelas

MidpointTitik tensalt

FrequencyKekerapan

t6-20 t8 I2L -25

(b)

(c) Refer to graph on page 30.Rtquk gra,f'di inlctntan 30.

(d)


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l:l!!liiliiilil,iliri !'i

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t14912SULTT



SULIT 1449t2

l5 You are not allowed to use graph paper to ansrver this question.Anda tidok dibenarkart menggun,tkan kertcts grctf untuk menlau,ah soalan tpt.

(a) Diagrant [5.1 shorvs a solid rigtrt prisnr rvith rectangular lrase.4BCD on alrorizorttal plane. Tlte surface ABKGF is the unifonn cross-section of thepristn. Rectangle C|{JK and rectangle ADEF are inclinecl plales. GF and KBare vertical edges. The height of G tiom the miclpoint of AB is 4 cnr.

Raiah 15.! menuniukkan sebuah pepejctl berbentuk prisma tegak deng,:.iiiapak segiempat tepat.4BCD di atas .\(.ltctit mengufuk.Pei.inukczan ABKCFialah keratan rentas seragamn-i:ci. Segietnpat_ tepat GHLK dan segiempat tepatADEF iahzit satah condong. GF dan KB adalah tegak. Tinggi G dari tiiiktengalt AB ialah 4 cm.

8 cnr

3t

Drarv to fi.rll scale. the plan ofLukiskan dengan skctla peruth,

Diagrarn I --s. I

Ralah l5.l

the solid .

pelan pe|)eJctl tht.[3 marks]

[3 markcthl


SULTT

UntrkKegunao'rPemeriksa



For lsur,trExaminer's I

Ltv

32

Ansrver /Jawatrtan:

(.r)

1449/2

t449t2STILIT



SULTT 33

lb) Acuboid is joined to the prism in the Diagram l5.l at tle vert,callrase,4Br?-STCD is ott a horizontal plane. The conrbined st-rlid is as

Diagrartr I 5.2Ralalt 15 2

Drar,v fi.rll scale-Luki.s dengan skala pentth,

(i) the ele'ation of the combinecl solicl on a verticalvier.ved from,k.

1449/2

plane BCJK. Theshorvn in

S

4cm

plane parallel to,4B as

[4 marksl

Unlu*KegunaanPemeriksa

Diagrarn 15.2.

Sebuah kuboid dicitntuntkan kepada prisma tegak d.aktnt rojalt 15. t patla sataltmencQ'tlctzng BCJK. Tapak,4BRSTCD terletctk atcts satah mengt(itk. Gctbttnganpepe.ial ctdalah seperti.yang ditunlukkan dalam Raiah ts.2.

5 cnr

D

,\.

(ii) theelevation of the cotrtbined solicl orr a vertical plane parallel to DA asvierved t}orn I.

dong<tkart gctfurngan pepelrtl itu patla satah n?encancang yang selart deng,an,48 sebctgoirttcutct dilihat dari X, [4 rnarkahl

[5 marksl,longrtkatt gahungan peTtelctl ittt pada satah mencancang yeng sel,eri clenganD,4 sehagdtmana diltlrut dari Y, [5 markah]

[Lihat sebelahSULIT1449/2

N-1-t--

I

2 cn'r

A

"7$7g

.f



ForExaniner's

Llse

SULIT

Answer I Jawapan:

(lr) (i),

34

(ii)

1,149t2

141912SULIT



SLILIT 35

16 P(50" A, 10" E). Q$A" N. 90" W), R and I,' are Four pohts onearth. PR is ttre diatneter of the parallel of latitude of 50" N.P(50" t/, l0'T), QO}'U, 90" B), R dan [/ adalah empat titikPR talah diameter bagi .relarian latitud 50'N.

(a) State the location o[R.ltr.y ct t czka rt ke d u du k a n R.

(b) Catculate the shortest distance. in nautical mile, f]-orn Psurface oi tlie earih.

t449t2

the strrface of the

di perntukaan bumi.

[! itung jarak terpendek, do.!ampermukactn Bunti.

[3 marksl

[3 markah]

to R measured along the

f2 marl:slbaht. nautika, ciari P ke R, drukur sepanjang

[2 mark<th]

(c) Calculate the distance. in rtautical mile. from P due west to Q measured along ttrecomnlon parallel latitude. [3 markslHitung jarak, dalam batu nautika, dari P arah ke harat ke Q cliukur sepanjangselarian latitrtd sepunva- 13 rnarkahl

(d) An aeroplane tcok off fiorn Q and tlerv due south to l/. The average speed of theflight rvas 800 knots and tinre taken rvas 6 lrours.Sebuah kapal terbang berlepas dari O ,trith ke selutan ke I,'. Purtzta lct_jtt

penerbangctn ittr ialcth 800 knot dctn masa .yang diantbil ttntuk penerbctrTgan ttuialah 61am.

CalcutateI{irung

(i) the distance- irt nautical nrile. ttorrr (i to I nleasured along the rueridian.

larctk. dctldnt hat.u tttttttikct, dctrt Q i:a it rJnthrr scLl(tnlarlg mertdtan.

(ii) the latitucle of l.lctttntde bttgt [''.

f4 markslf4 markahl

1449t2ILihat sebelirh

SULTT

UntukI{cgunaanPemeriksa



FuExanniner'.t

Us

STJLIT

Ansrver I J,.twttpctn'.

(")

(./) (,)

END OF QtiESTIOf,i PAPERK ERTAS SO,{I"{T 7.4 T T AT

36 t449/2

(b)

(c)

(u)

1449t2STILIT



PEPERIKSAAN PERCUBAAN BERSAIUA SPM 2012MATHEMATTCS I44912

PERLIS

Scraight ime r- = -3x correctlv drarr:rRegron cor;€th'shadedNote,Arr.arC Pi ttr shaded regr'.n bounded b)'an)'n..!1 .rrrrccl iiflcs

A

B7a/

=E$/o/o/a/bti/t/v



3m+6n = l5 or 2m+4n

(_-)R

m=5-2n oreqrtrvaLlntl()n = 4(l or 5m = -l -5 or

nt--)n-q

OR

(,r) t (-4["J= []flffi[-rm=-3n=4

3p2-2p=O

e(to- 2)= o

P=(-)

= l0 orequiralent

ecluivalent KI

NINI

K2

NINI

ri:l

:{

a) i IHD or I DHI PI



(") (i) If -r Ls a uegative nurnber thenr is less than zero.(ii) Tnre

(6) A.\B* B

- 3 0- 3L)f

-=-4 :-(!

PIPI

KI

KI

NI

0=1(+)+cor2'

-x -x _x 3x 3xi -



& T(,;

,,:,

(--, (,t\Note :

l,;)= {._ rj *,-,.n as final aJrsn€r alvardN'

Nrrre 2n - (3)= fr

Au,arcl P I

(: : \'.r) (- r r1(b I ll I=l r' l.: -a)t,y) (is,(')_ | (-4 -:)i-ti'r[.rJ=

- r,, r-,tlir[-, , ,[. ,* ,l

.\-L

!=-3



(n,: ) (n,a ) (n.o) (a,:), ie,+ ) (a,o) (ru, 11 (v,+) (ru,0.\ (r,r I (r.a I (r,o)) PI

(o) (e,:)(s,o)l/\ 2 |

Plal= 126

{(e:), (R,4} (n,61 (e,ri (er.:) (r,:)}

r(,,)= **i,

KI

NI

KI

Ni

(")

(6)

rlt;is ii--Jlo, Iiil*' iINI i

(.)

t2

l2-06-0

]*(s-i2)xr or,'i',.-r2ixr -:

95org!1

], [a t (r - o)], 12 or eqrrivalent

l'.,-x[7--(f-6)lxi] =ll3:

KI

K1



',=s(.a) "

v= -l)

(ht Graph

i\xes clrarvn ur con'ect direction, trttifbrrtt scales in - 4 1 x : 4 and

-i)::.r'--12

All 7 pornts and *2 ptrints correctlr' plcrtted clr cur\,€ passes throtrg;h trll tlrepolnts ii.'r - 4: .r:4 attd - 12'-.v'. 12.

7 or8 points correctl-v'plotted. arvard Kl

Smt'rottr an<t continuotts curve passing through &s -s pohts tbr

-4'--r '.. -l and ihe 4 points for l5.r! 4 anci -i2s )'slz-

(.) i) 3.2s),si.6

ii) - t.8: x '- -1.(>

KIKI

PI

K2

NI

PI

PI

(,t) Identi$ equabon - 12

=-\'

Straightlutev=-2-r+3

-2-r + 3or 1'; : -la + l

con'ectly drarvn

KI

KI

NINI

rr)

(-4.31Note ,.-4 . 3 j marked on the iiraeratnar(l . i) or (f - i) markedtrn tLe ciiaeiam arvarC Pi

( -:- -t)Ncrt€ ( -: , -i) ntarkeci c1n the aragain

or (--l- 5 ) or (-a-5) markt'd on tlie drasraln arvard P I

P:

www,mysch0olchildren.com www.myschoolchildren.com



b) V: Eo,laryenrent at K / ( -4 , I ) with scalc t'acror ol'2Note : Enlargentent scale factor 2 or

Enlargetnent cenfc K(-1 , l) arv:rrd p2Enlargement, arvard PI

I



Class lnterral

t6 - 2()

-iqs

._ Miclpoint I Ftcquetrc]'

ls:.1--2r _.---l---

5

26 30 28 6

3l -35 33 E

35-40 38 l04t-45 43 7

Class interval .

Midpoini :

Frequency :

I.lote : Ts'o mistakes tbr tire vatues of ti'equency, as,ard P I

rs(a)+ 23(5) r zt(e)+ 33(.s)+ rs(to)+ a{z)

32.5

(c) Frequenc!, PolygonAxes drawn in correct directions rvith unifonn scales for13s-r<48and 0<.1,!10Horizontal axis is labelted rvith upper boundaries i class interval r

midpointsand vertical axis labelled rvith values of fre<1uenc1,.

Note , 8 pourts correctly plotted6 or 7 porns conectlv plc':fted. arvard Kl

Correct ltequenc;- poll'gc''n passmq through all S

Correct point-s usrng the siven scales

(,d) The tugtrest altendance is i(t classes orThe hrqhest frequencv is l(i trrThe modal class ts 36 - {(i trrThe li\l'esl allen,Cance ls -1 cia.sses

40

PiotP?

K2

K2

NI

PI

NI

PI

12



Correct shape uith recrangle DAKJ and DAGHJD>DA>-{G=GK

,\{easuremens correct to (= 0 2cz)and all angles at vertices 90o; l.

(6X,)

AII solid lines K1K1

NI

il



il-l_Con'ect shape with pentagon ABKGF and rectangleAll solid lnes

AS>BK.;'PS -- CK - BS >AF >FC

lvleastremenls correct to lrt 0 2oz)z B, ZS, Z P and iQ = 90or lo.

(6) ii)

Correct shaJ:e rvith rectangles ADjK, ARQL and EFGH.All sotid tines (lgnore ML)

\,{ - L is joined rvit}r a dashed line to fomr rectangle JKLN{

jD = DR > DA = (rft;-1..1 - AR > O, = ,O ', ,"O

N{easurements correct ttr (: 0.2crr)Ail anqles at reftices 9t)o - 1o

Kt

KI

KI

KI

KI

j{:



[]

(o)

(b)

(s0"ru fio"w)

80x 604800

(.") (t O + SO)x 6(1,: cos 5Ol

3856.73

(d) (r) 4800

.{800(tt,l

- or 80

6B0 - -50

= 30o5'

PIP2

KINI

K2

NI

KI

KI

KI

NI

I

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