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SULIT
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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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
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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
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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
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q)-r(U)q)a)
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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.
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16 marksl
16 narkchl
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Answeri Jawapan :
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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)
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[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,.
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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 ]
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SULIT Ea)().
(Ua-o
a)c)+
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,\rswer / Jawapan :
(")
l6 1449t2
(h)
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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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Answer / Jau,apqn:
(")
l8
(6) (i)
(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)
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2l
Section BBahagiut B
| 48 marks I
| 48 markah I
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[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
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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
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, 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
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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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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)
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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)
t419t2
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
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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)
1449t2ILihat sebelah
SULIT
Untr*KegunaanPemeriksa
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ForExatniner's
Uv
SULIT
(fi,il,iiii
l:l!!liiliiilil,iliri !'i
tir-- i
l,l4912
II!!!tlii;iiiii:.l.I,'.iiiriii:rit:liiiiii;tr'
t14912SULTT
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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
1449t2ILihat sebelah
SULTT
UntrkKegunao'rPemeriksa
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For lsur,trExaminer's I
Ltv
32
Ansrver /Jawatrtan:
(.r)
1449/2
t449t2STILIT
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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$7g
.f
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ForExaniner's
Llse
SULIT
Answer I Jawapan:
(lr) (i),
34
(ii)
1,149t2
141912SULIT
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SLILIT 35
16 P(50" A, 10" E). Q$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
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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
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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$/o/o/a/bti/t/v
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3m+6n = l5 or 2m+4n
(_-)R
m=5-2n oreqrtrvaLlntl()n = 4(l or 5m = -l -5 or
nt--)n-q
OR
(,r) t (-4["J= []flffi[-rm=-3n=4
3p2-2p=O
e(to- 2)= o
P=(-)
= l0 orequiralent
ecluivalent KI
NINI
K2
NINI
ri:l
:{
a) i IHD or I DHI PI
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(") (i) If -r Ls a uegative nurnber thenr is less than zero.(ii) Tnre
(6) A.\B* B
- 3 0- 3L)f
-=-4 :-(!
PIPI
KI
KI
NI
0=1(+)+cor2'
-x -x _x 3x 3xi -
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& T(,;
,,:,
(--, (,t\Note :
l,;)= {._ rj *,-,.n as final aJrsn€r alvardN'
Nrrre 2n - (3)= fr
Au,arcl P I
(: : \'.r) (- r r1(b I ll I=l r' l.: -a)t,y) (is,(')_ | (-4 -:)i-ti'r[.rJ=
- r,, r-,tlir[-, , ,[. ,* ,l
.\-L
!=-3
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(n,: ) (n,a ) (n.o) (a,:), ie,+ ) (a,o) (ru, 11 (v,+) (ru,0.\ (r,r I (r.a I (r,o)) PI
(o) (e,:)(s,o)l/\ 2 |
Plal= 126
{(e:), (R,4} (n,61 (e,ri (er.:) (r,:)}
r(,,)= **i,
KI
NI
KI
Ni
(")
(6)
rlt;is ii--Jlo, Iiil*' iINI i
(.)
t2
l2-06-0
]*(s-i2)xr or,'i',.-r2ixr -:
95org!1
], [a t (r - o)], 12 or eqrrivalent
l'.,-x[7--(f-6)lxi] =ll3:
KI
K1
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',=s(.a) "
v= -l)
(ht Graph
i\xes clrarvn ur con'ect direction, trttifbrrtt scales in - 4 1 x : 4 and
-i)::.r'--12
All 7 pornts and *2 ptrints correctlr' plcrtted clr cur\,€ passes throtrg;h trll tlrepolnts ii.'r - 4: .r:4 attd - 12'-.v'. 12.
7 or8 points correctl-v'plotted. arvard Kl
Smt'rottr an<t continuotts curve passing through &s -s pohts tbr
-4'--r '.. -l and ihe 4 points for l5.r! 4 anci -i2s )'slz-
(.) i) 3.2s),si.6
ii) - t.8: x '- -1.(>
KIKI
PI
K2
NI
PI
PI
(,t) Identi$ 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:
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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
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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
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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
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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{:
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[]
(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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