Pmr 2009 Mathematics

8/9/2019 Pmr 2009 Mathematics

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Time: t hour 15 minutesThis questionpaperconsistsof 40 questions.Answer all questions.Eachquestion s followedfour choices f answersA, B, C and D. For eachquestion, hoose ne ansueronly. Thediagramsn theroaidedare not drawn to scaleunlessstated.

Which digit has the correct place values inboth numbers?Digit manakah nng mempunyainilai tempatyang betul dalamkedua-dua ombor tu?

DigitDWtPlacevalueNilai tempat

9 348 756 9 754 386aJ

HundredthousandRatus ibuHundredRatus

4 Ten thousandPuluh ribu HundredRatusHundredRatus

HundredthousandRatus ibu5 TenPuluh Ten thousandPuluh ribu

Diagram 1 shows part of a number line.Rajah1-menunjukkan ebahagianaripada uatugnris nombor.

0.309 R 0.313 0.314Diagram LRajah'1,

Find the value of R.Cari nilai R.A 311100B 312100c 3111000D 3121000

3 Diagram 2 shows four number cards, P,Q, Rand S.Rajah2 menunjukkan mpatknd nombor,P, Q,R dan S.

C

D

t r t r t r t r t r

@@@@aDiagram 2Rajah 2

Which card has the smallest value for thedigit 3?Kadmanaknhangmenunjukknnil"ai angpalingkecil bagidigit 3?APB0CRDSDiagram 3 shows a sequenceof numbers.and Q represent wo numbers.Rajah3 menunjukknn uatu urutan nombor.dan Q mewakilidua nombor.

Diagram 3Raiah 3What are the values of P and Q?Apakahnilai P dan Q?A P:1,Q:--2B P:2,Q:-3c P:2,Q:1.D P--3,Q:2

PMR 2009 MATHEMATICS


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An aeroplane ook off from KLIA to Penangat 3.50 p.m. The f l ight normally takes45 minutes. The aeroplane was delayedand landed at Penangat 5.10p.m.How lonB in minutes,was heaeroplane elayed?SebuahknpalerbangberlEasari KLlAkePulauPinangpadapukul3.50 p.m. Padakebiasaannya,penerbangantu mengambilmasa elnma 5 minit.Kapal erbangtu terlewatdanmendarat i PulauPinangpadapukul5.10 p.m.Berapa amaknh, alam minit, knpal erbang tuterlewat?A35 C75840D80The following data showsa sequence f primenumbers in ascending order.Data berikut menunjukknn atu urutan nomborperdnnadalamsusunanmenaik.

In Diagram 4, KLN is an isosceles riangle.DalnmRajah , KLN inlnhsebuahegt igaknkimmn.N

Diagram 4Raiah 4Find the value of x.Cari nilai x.A15 C80B45D85Diagram 5 shows a quadrilateral.Rajah5 menunjukkanebuah isiempat.

Diagram 5Rajah 5Find the value of r.Cari nilni x.A20C45830D50In Diagram 6, HIKLMN is a hexagon. GHJand PML are straight lines.DalamRajah6, HIKLMN ialahsebuah eksagon.GHI dan PML ialahgaris lurus.

^HI

PMLDiagram 6Rajah 6

Find the value of x + y.Car ini la ix+y.A 240 C 245B 242 D 299

10Find the value of m and of n.Cari nilai m dannilai n.A m:9,n:25B m:9,n=2'1,C m:t l .n:27D m:11,n:23The length of a red string is 5 m 20 cm. Thelength of a green string is $ ofthetengthofthe red string. The length of a yellow stringis twice the length of the green string.Calculate the total length, in m, of the greenand the yellow strings.Panjang seutas ali merah alah 5 m 20 cm.Panjangseutas ali hijau adalah daripada4'panjang ali merahtu. Panjang eutasali kuningadalahdua kali panjang ali hijau itu.Hitung jumlah panjang,dalamm, tali hijau dantali kuning itu.A 3.9B 7.8 c 11..7D 1,6.9The mass of box P is 750 g and the mass ofboxQisLkg50g.State the ratio of mass P to mass Q.lisim kotakP ialah750 g daniisim kotakQ ialah1kg50g.Nyataknnnisbnhisim P kepadaisim Q.A 1:2 C 7:10B 5 :7 D 13 :2 '1,

1'1,


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t42 Diagram7 showspart of the sidesof a regularpolygon.Rajah menunjukknnebahagianisisebuaholigonsekntn.

) ,*

Diagram 7Rajah 7How many sides does the complete regularpolygon have?Berapakah ilangansisi poligon sekntatu yanglengkap?A6B8c18D20Diagram 8 shows two squaresand a triangle.Rajah8 menunjukkan us buahsegiempatsamadan sebuah egi iga,

Diagram 8Rajah 8Find theperimeter,n cm, of the whole diagram.Cari perimeter, alamcm, seluruhrnjah tu.A46852c58D66

In Diagram 9, PQRS s a parallelogram andPQT is a straight line.DalamRajah 9, PQRS ialah sebuah egi empatselnridan PQT ialah garis lurus.

Diagram 9Rajah 9GivenSR= 2QT,calculatehe are4 n cm2, f thewhole diagram.DiberiSR 2QT,hitung uas,dalamcm2, eluruhrajah tu.A24830c36D54In Diagram 10, PQRS s a square and PQTSis a quadrant of a circle with centre P.Dalam Rajah 10, PPRS ialah sebuah egiempatsamqdan PQTS nlah sukuansebuah ulatanbernusatP.

Diagram 10Rajah l0Calculate the area" in cm2, of the colouredregion.Hitung luas, dalam cm2,knu)nsan erwarna..,.\lUselGuna L +l/

1.513

A44877c 154D 308

8+ g crn ->


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4cm

7cm

6 Diagram 11 shows a right prism.Raiah 11,menunjukknn ebuah rismategak.

Diagram 11Rajah 1lCalculate he total surfacearea, n cm2,of theright prism.Hitung umlah uaspermuknan,alamcm2, rismategak tu.A58896c 116D 724Diagram 12showsa compositesolid of a rightcircular cylinder and a right circular cone.Rajah12 menunjukknn abungan epejal ebuahsilindermembulategak ansebuahkon embulattegak.

1,.-Diagram 12Rajah 12

The radius of the baseof the rylinder is 3 cmand the height of the cone s 6 cm.Calculate he volume, n cm3,of the compositesolid.lejari tapaksilinder itu ialah 3 cm dankon itu ialah6 cm.Hitung isi padu,dalam cm3,gabunganitu.ABCD

18 Rina drives her car from P to Q at an averagespeed of 90 km/h for 2 hours 40 minutes.She continues her journey for a distance of100 km from Q to R and takes t hour20 minutes.Calculate he averagespeed, n km/h, for thejourney from P to R.Rina memandukeretanya ari P ke Q denganpurata aju 90l


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Calculate the value of x + u + z.Hitungni la ix+y+2. Diagram 17 shows anisosceles riangle QKNand QK = QN.& P and L are the midpointsof QK, QN and K&f respectively.Rajah17 menunjukkan ebuahegi iga knkisama

QKNdanQI(: QN.R,P danLialahtitiktengahbagi QK, QN dan KM masing-masing.o

l+-5 crnlDiagram 17Rajah 77

The area of rectangle t&tSR is 12 cm2.Calculate the area, in cm2, of the colouredregion.Luas segi empat epat IISR ialah12 cm2.Hitung luas,dalamcm2, auasan ang berwarna.

23A L7OB 130 c L20D 110

21 Diagram 15 shows two circles, PQRS andRSTU. PST and QRU are straight lines.Rnjah15 menunjukkan ua buahbulatan,PQRSdan RSTU. PST dan QRU ialahgaris lurus,

Diagram 15Rajah 15Which angle is equal to r?Sudutmanaknh ang samadengan ?CgDhIn Diagram 16, PQST s a quadrilateral andQRS s an soscelesriangle. UTSR s a straightline.DalamRajah L6, PQST alah sebuah isi empatdan QRS nlahsebuah egi igakaki sama.UTSRialahgaris urus.

Diagram 16Rajah 16Find the value of x.Cari nilai x.A78 C99889D106

In Diagram 18,PQR and PSTare right-angledtriangles. PRS s a straight line.Dalam Rajah t8, PQR dan PST ialah segi_tigabersudut egak.PRS alahgaris lurus.

Diagram L8Raiah 18Find the length, in cm, of ST.Cari pnnjang,dalam crrr.,ST.A7B8c13D14

AeBf A 1.8824 c30D3622 24


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25 In Diagram 19, QTPLI and pSR are straightlines.Dalam Rajah 19, QTPU dan pSR ialah garisIurus.IT

Find the coordinatesof Q.Cari koordinatQ.A (3,3)'B (3, 1) c (2,1)D (2, -1)

Diagram 19Rajah t9It is given that PQ : pp.Find the value of x.Diberi bahaznap : PR.- Cari nilai x.A40c50845D65It is given that A - x2- S.Find the value of y when x : -'1,.Diber ibahawaA:x2-5.Cari nilai y apabila : -L.

Diagram 21 shows three points, p, e and R,on a Cartesianplane.Rajah2L menunjukkaniga titik, p, e dan R,padasuatusatahCartesan.

Diagram 21Rajah 21If P, Q, R and S are vertices of a trapezium,find a possible coordinatesof S.lika P, Q, R dan S ialah bucu-bucusebuahtrapezium, ari koordinstyang mungkinbagi S.A (1,5) c (3,5)B (2,5) D (4,5)In Diagram 22, OFG is a sector of a circlewith centre O.lalam Rajah22, OFG ialahsektorbagi sebuahbulatanberpusatO.

F

Diagram 22Raiah 22

29

o

A-7B-6

A x>-2B x11

C4D-3

C x>2D x


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Table 1 shows the pocket money of a groupof students.ladual1menunjukknn angsakubagisekumpulanmurid.

Pocket money(RM)Wang saku(RM)

1,.002.003.004.005.00

FrequencyKekerapan 7 A+ 6 2 I

Table Llailual I

A total of 850 iles are used for the four rooms.Calculate he differencebetween he number oftiles used in the bedroom and in the kitchen.Sej mlah850ubin digunaknn agiempat ilik tu.Hitung beza ntarabilangnnubinyangdigunaknnuntuk bilik tidur dengandapur.

Which statement s correctbased on this barchart?Pernyataanmanakahangbetulberdassrknnartapalang ni?A The total number of girls is more thanthe total number of boyslumlahbilanganmuridperempuandalahebihdaripadaumlah bilangnnmurid lelakiB Twosportshouseshave mole girls thanboysDua rumah sukan mempunyai ebih ramaimurid perempuan aripadamurid lelakiC Three sports houseshave more boys thangirlsTiga rumnh sukan mempunyai ebih ramaimurid lelaki daripadamurid perempuanD Only one sport househas an equal numberof boys and girlsHanya satu rumah sukan yang bilanganmurid lelaki adalahsama denganbilanganmurid perempuan

The mean age of Encik Ahmad, Puan Fatimahand their three children is 31 years.The meanage of their three children is 19 years.Calculate the mean age of Encik Ahmad andPuan Fatimah.Min umur EncikAhmad,Puan Fatimahdan tigaorang anak merekn alah 3'1. ahun. Min umurbagi tiga orang anak merekaalah 19 tahun.Hitung min umurEncikAhmaddanPuanFatimah.A 44 yeus44 tahunB 49 years49 tahun

C 50 years50 tahunD 68 years68 tahun

A 150B 200

Find the median.Cari median.A RMI.OOB RM2.OO

c 250D 300

c RM2.30D RM3.OO

Lekir Lekiuffi GirlsPerempuan

37

Dagram 26 s a bar chart showing the number ofboys and gtlr ir four sportshouses n a school.Rajah 26 ialah carta palangyang menunjukkanbilanganmurid lelski dan perempuan agiempatrumah sukandi sebuah ekolah.

Sports housesRumahsukan

38 Table 2 shows the number of plants thatMastura planted in her garden.ladual 2 menunjukkanbilangan pokok yangditanamolehMasturadi tamanrula.

PlantsPokok Number of plantsBilangan pokokChrysanthemumKekwa t4

OrchidOrkid 18RoseMawar t6

CactusKaktus 1,2Table 2ladual 2

Diagram 26Rajah 26


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CachrsKaktusy"

RoseMawarDiagtam 27Rajah 27

All the information in Table 2 is representedby the pie chart inDiagram 27.Calculate the value of y.Semuamaklumat dalnm adual 2 diwakili olehcartapai dalamRajnh27.Hitungknnnilai y.A48880Which of the following is the table of valuesfor the function A : x3?Antara yang berikutl yang manakahadual nilaibagi fungsiA:x3?

In Diagram 28, PQRS s a square and O isthe centre of a circle with radius 7 cm.DalamRajah 28, PQRS alahsebuah egiempatsamadan O inlahpusat sebuah ulatanberjejari7 cm.

oRDiagram 28Rajah 28

X is the locus of a point which moves suchthat its distancefrom O is always 7 cm.Y is the locus of a point which moves suchthat it is always equidistant from point Q andpoint S.Which of the points A, B, C or D, is theintersection of locus X and locus Y?X ialah lokus suatu titik yang bergerak engankeadaanaraknyasentiasa cm dari O.Y ialah lokussuatu titik yang bergerak engankeadaanaraknyasentiasn amadari titik Q daatitik s.Antara titik A, B, C dan D, yang manakahpersilanganokusX dnn lokusY?

40

c96D 108

A

B

C

D

x 1 2 3 4v J 4 5 6x 1 2 J 4v J 6 9 12x 1 2 aJ 4v 1 4 9 t6

L 2 J 4v t 8 27 64


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(60 marks) Time: t hour 45 minutesThis questionpaperconsists f 20 questions. nswer all questions.Write your answers learlythe space roaided.Showyour wo*ings. The diagramsn the questions roaidedare not drawn to scalenlessstated.Theusage f calculators not allowed.

Calculatehe valueof fS + ff + (-16).Hitungnilaibagi S + rf + (-16).Answe{lawapan:

12marksl[2 marknhl

Calculate the value of (6 - 0.24)* { and express he answer correct two decimal places.3 ' 12markslHitung nilai bagi (6 - 0.24)* t aon ungkapknnawapan tu betulkepada ua tempatperpuluhan.[2 markahlAnswerlJawapan:

(a) Find the value of:Cari nilai bagi:/0s1

(b) Calculate the value of:Hitung nilai bagi:

13marksl[3 markahlAnswerllnwapan:(a)

(z* '6) '

PMR 2009 MATHEMATICS


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(b)

4 In Diagram 4, pentagon PQRSTand pentagon KLMN are similar.Dalam Rajah4, pentagonPQRSTdan pentngon KI^AINadalahserupa.

R15cnr

sL3cmM

Diagram 4Rajah 4(a) Name the angle in pentagon PQRSTwhich corresponds o N[(.Namaknn udut dalampentagonPQRST ynng sEadan dengan NJK.(b) Given that MN : /N, calculatethe length, in cm, of PT.Diberi MN : lN, hitung panjang,dalamcm, bagi PT.

Answerllawapan:(a)

13marksl13markahl

(b)


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In Diagram 5, E is the midpoint of the line AC.DalamRajah5, E ialah titik tengahgaris AC.

Diagram 5Rnjah 5(a)

(b)

Find the value of tarru".Cari nilai bagi tan y".Calculate the length, in cm, of AB.Hitung panjang,dalam cm, bngiAB. 13marksl[3 markah]

Answerllawapan:(a)

(b)

Diagram 6 in the ;mswer space shows quadrilateral PQRS drawn on a Cartesianplane.On biagram 6, draw the image of quadrilateral PQRS under a reflection in the y-axis. [2 marks]Rajah6 di ruang awapanmenunjukkan ebuah isi empatPQRS yang dilukis padasatahCartesan.PadaRajah6, lukis imej bagi sisiempatPQRS di bawahpantulanpadapaksi-y. 12markahlAnswe{lawapan:


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Diagram 5Rajah 6


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biugru* 7 shows two triangles, IKL and l'K'L', drawn on a Cartesianplane. 'K'L' is the image of/KL under transformation H.'Rajah7 menunjukkan ua buah segi iga, IKL itan I'K'L', yang dilukis padasatahCartesan''K'L' inlahimej bagi IKL di bawahpenielmaan .

Diagram 7Raiah 7Describe in full transformation H.Huraiknn selengkapnynenielmaanH.Answerllawapan:

13marksl13marknhl

2l t 6l_ j


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Simplify each of the following expressions:Permudahkaniapaiap ungknpan erikut:(a) 2(n +5)-3b) 3@m 3k) - (sk - m)

Answerllawapan:(a)

13marksl[3 markahl

(b)

9 Factorisecompletely;Faktorkan seIen kapnya

Answerllawapan:

5 - 20lc.[2 marks][2 maikah)

10 Diagram L0 n the answer spaceshows an isoscelesriangle PQR drawn on a grid of equal squareswith sides of 1 unit. X and Y are two moving points inside the triangle PQR.Raiah 10 di ruang awapanmenunjukkan ebuah egi tiga samakaki PQRyang ditukis padagrid segiempatsamabersisi1 unit. X dan Y adalahdua titik yang bergerak i dalamsegi iga PQR.(a) On Diagram L0, drawPadaRajah 10, lukis(i) the locus of the point X which moves such that its distance s constantly 6 units from thepoint QIokus bagi titik X yang bergerak engan keadaan itik itu sentiasaberjarak6 unit darititik Q,


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(ii) the locus of the point Y which moves such that its distance s constantly 3 units from theline PQ.lokus bagi titik Y yang bergerak engankeadaan itik itu sentiasaberjarak3 unit darigaris Q.(b) Hence, mark with the symbol @ the intersection of the locus of X and the locus of Y.Seterusnya,andakan engansimbol@ kedudukan agi persilanganokus X dan lokusY itu.

13marksl[3 markahl

Answerllawapan:(a) (i), (ii)(b)

Diagram 10Raiah 1O


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1l (a) Diagram 11.1shows a triangle MNP.Rajah 11,.Lmenunjuklun sebuahsegi tiga MNP.

Diagram 11.1Raiah ll.lMeasure LMNP using a protractor.Ukur LMNP menggunaknn rotraktor.

(b) Diagram 1l..2 n the answer space shows two straight lines, EF and FG.Using only a ruler and a pair of compasses, onstructRnjah 1L.2dalam uang awapanmenunjukknn uagaris lurus, EF dan FG.Menggunaknnpembarisdan angkn lukis sahaja,bina(i) the line FH, the bisector of LEFG,garis FH, yang merupakan embahagi ua samaLEFG,(ii) the quadrilateral EFGH such that EH : 4 cm.sisi empatEFGHdengan eadnanEH: 4 cm.

Answerflawnpan:(a)(b) (i), (ii)

Diagram 11.2Raiah 17.2

[5 marksl15mnrknhl


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a* - #as a single raction n its simplest orm. [3 marksllJngkapkan*- -ffi sebagaiatupecahanunggal alam entuk ermudah. {3 markahlAnswefJawapan:

Given hat k * y = 3 St-, expness in terms of k. 13markslDiberibnhnwaky: +, ungkapknnyalam ebutank. 13markahlAnswerllawapan:

Solve each of the following equations:Selesaiknniap-tiappersamaanerikut:(a) 6ft: -181r) +! =z 13marksl[3 marknhlAnswerllawapan:(a)

(b)


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each of the following:Permudahknniap-tiapyang beiikut/ \z(a) #l\ /

3. 5(b) m'x m2m3

13marksl[3 markah]Answerllawapan:(a) (b)

Nilaikan:132-1 12T x3T

[3 marks]Answeilrawapan:

[3 mar-kahl

all the integervaluesof r which satisfyboth the inequalities + 4 < 13and tr t.Senaraiknnemua ilai integer yangmemuaskanedua-duaetaksamaan+ 4 < 13dan t, U.

13marksl[3 marknh]


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Answerllawapnn:

Table L8 shows the number of geometrical setssold over four days.ladual lS menunjukknn ilanganset geometri ang dijual dalam empohempathari.

DayHari MondayIsnin TuesdaySelasa WednesdayRabu ThursdayKhamisNumber of geometrical sets

Bilangan set geometri J 8 + 9Table 18Rajah 18

On.Diagram L8 in the answer space, he information for Monday is shown in the bar chart.Complete the bar chart to representall the information in Table 1,8. [3 markslDalam Rajah 18 di ruang atnapan,maklumatbagihari Isnin ditunjukkandalamcartapalang.Lengkapknnartapalang tu untuk mewnkilisemuamaklumatdalam adual 18. 13markahlAnswerllawapan:

ThursdayKhamis

WednesdayRabu

MondayIsnin

Diagram 18Rajah 18

Number of geometrical setsBilangansetgeometri

DayHari

TuesdaySelasa


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19 is a pie chart showing the number of rambutans eaten by 4 students.Rajah19 ialahcarta pai yang menunjukkan ilanganbunh rambutanyang dimakanoleh 4 orangmurid.

Diagram19Rajah79CalculateHitung(a) the mean number of rambutans eatenby a studen!min bilanganbuah rambutanyang dimaknnolehseorangmurid,(b) the angle of the sector representingDavid.sudut sektoryang mewakiliDaaid.

Answerllawapan:(a)

14marksl14markahl

(b)

David18


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the graph paper on page 126 to answer this question.Gunaknn ertasgraf di hnlaman126 untuk meniawnb oalanni.Table 20 shows the values of two variables,x and A, of a function.ladual 20 menunjukkan ilni-nilai dua pembolehubah,dan y, bagi suatu ungsi.

Table 20lailual20

The r-axis and the y-axis are provided on the graph PaPeron page 126.Paksi-xdan paksi-y elnhdisediaknn ada certas raf di halamanL26.(a) By using a scaleof 2 cm to 2 units, complete and label the y-axis.Dengan menggunakan kala2 cm kepada2 urit, lengknpdan labelkanpaksi-y.(b) Basedon Table 20, plot all the points on the graph paper.' Berdasarlunadual 20,plot semun itik padakertasgraf itu.(c) Hencq draw the graph of the function.Seterusnya,ukiskangraffungsi itu. [4 marksl[4 marknhl

x -5 4 -3 + -1 0 1v -1,4 -6 0 4 6 6 4


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(b) (2rx 39+: 2-"*1 3u'i- t-1v22

1=: X 9z=22

20 Given cos y" : 5IJ48_s_13

.l ,

2#o.3oeI n I o.srso.er+t t l!/ !/ \Yo31omo3i2311u.Ju = 1000Atsunr: Ct.Q)r46 e.-t4(3Y 0.94s2 4.74}:9

Place Tenths Tens {undredt}rThus, the smallest value for thedigit 3 is 0.003 .e. card QAnstaer:B

ltl |Il ffi] l;^'-] r;r,.,.:...-l L..:J L.:...-.i L]sI f:l\----^ \---r' \-_--.. \---,-3 -3 -3 -3P:4+ (-3)= 1

Q:1+(-3)=-2Answer:ADeparhle time :3.50 p.m.: 1550hourstI|24husrt"'"]Arrival time = 5.10p.m.= I/IU noursTime taken to fly from KLIA toPenang:

hr min77 10-15 50'1, 20-'{ hr 20 mirs= 80 minutesThe aeroplanewas delayed by = 80- 45: 35 minutesAnswer:A


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Mass of box P : 750 IMassof boxQ:1kg50g= 1050gThus, ratio of massP to mass Q= 750: 1050Answer B

LNKL : 180'- (50"x: 180" 100"= 80"tnUS,.x:6U-JC=45Answer:B

60"+xo+2x"+3x"60" + 6x"6x"

Answer:D

llHN:180"-160"- tn oreflex angle N = 360'- 80": 280'tNML = 180"-120':60'

LKLM = 180"-65'- 11(o

x+y+20+280+60+115: 720 (sumof nterioranglesofhexagon)) t+y+475=720x+y=720-4V5:245Anstuer;C

: 360= 360: 360'- 60"_ 3006=50

\2

Interior angle of = 360o _ 200othe regurar Porygon

13

Number ofsides

15s14 cm

= 160"360"- 180'- interiorangle_ 360"180' 160'= 360'20": 18sidesAnstuer:C

7:,[19-@=BcmPerimeter:(3xgcm)+(3x6cm)+10 cm=24cm+18cm+10 cm:52cm

Answer:B

sR:2QT=2x3cm:6cm1Areaof AQRT: I x 3 x +2:6cm2

Area of parallelogram PQRS=6x4= 24 cn:fThus, area of the whole diagram=6+24= 30 cm2Answer:B

t6

Angle subtended at _ 90'- nU"centre 2Area of the coloured regiontf l )) . . -. -. ". 2:5X-Xl4+Al4u350" ,r': // Cm'Answet: B

4c m 4c m C\cm5cm

A B E FD)/

Total surfacearea of the Prisrn=Areaof(A+B+C+D+E+F)11 \: (4x4)+(4x4) +| \2 x11 x4J

11 \+l;x11 x4l +(7x4)+\z I(sx4)=76+16+22+22+28+20= 124 cmzAnswer:D

l---\f---.--4 t .I l l4cmt - - -------- . t lr l*1Volumeof=*XnX3X3X6Jcone = t6fi

Volumeot= nY.3X3X4cylinder = 36n cm3Thus, volume of = Ign + 36nthe composite solid -: 54n cm3Answer:C

18 Distance from P to Q: Average speed X time):90x2+Jp It r---- ----------- 90 x { t ---t,2 hrs 40 mins l3 i--^.---*-J: 240 km

Averagespeed rofl-$j,si5cefor the iournev = jt?","::""lotal ttmelrom l'to K taken

4c m

17

7cm


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20

240 + Lf:,O2 hrs 40 mins + t hr 20 mins3404: 85 km/hAnnter: B

ITcrnl IThe height of water needed tofill up the container=15-7=8cmHence, the volume of water neededto fill up the container:L5xL5x8= 1800 cm3Answer: B

U = M+2:20A = x= ZOQR:20"(anglesn the same egment)z:9{J-ZOQR(anglen a semicircle): n-n:70:.x+y+z--20+20+70: 110Anguer: D

lx is the exter ior angle ofquadrilateralZe is the interior opposite angleof lx..'.r = e (exterior angleof the cyclicquadrilateral is equal to theinterior opposite angle)Answer:A

ZRSQ = 74"^QST = 1.80-74.= 106.

2l

22

25

23

IPTS = 180'- 115"= 65or+90+106+65:360(sum of angles n a quadrilateral)x+26L :360x = 360 -261=99Anstuer:C

^L M ocm NGiven QK: QNArea of rectangle LMSR = 12 cm2LM=6cm+2:3cmSM:S8:12+3:4cm

1Area of LaSP =; x SP x 5Q1: ix3x4

:6cm2Area f AQKN+ x KNx eM

:l*rzts2' --: 48 cm2Thus area of the coloured region: Area of AQIO{-Areaof AQSP

- Area of rectangle LMSR:48-6-12: 30 crn3Answer;

pp: {122a s,: L3cmsr: ,{w=89: '{Et=E= ,/49:7cmAnswer:A

Given PQ = PRLQPR:180o-130o=50oZPQR: (180'- 50') + 2: 130'+ 2: 650ZSQR = ITSQ = 20" (alternateZS)

-11 cmo

28

Hence,r=65-20=45Anster: By:f-sWhenr:- l ,y= (-1) ' -5= 1-5

_AAnswer:C

2-x13r+L0-x-3x


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,4\xt Y, / h\'ffi*P

32

16 cmLengthofbaseQ:2 a 16:32 cmHeight of Q: Fase !Height of P Baseof PHeightof0: 322.5 872 x 2.5Hence, height of Q = ":-=-d:10cm

Answer:CGiventhatk:.m:n=3:5:4m-k:72m+n 5+4'=--K 5-Jm+n 9122 9xt2m+n-- ^-- 54Answer:CTotalnumberof prefects nthe school:40+20+15+5:80Number of boy prefects:80-22=58Thus, fraction of boy _ 58prefects in the group - 802940Answer:DTotal number of tiles used for fourrooms : 850 tilesNumber of tilesused orthekitchen: 850 (13 x 50)= 8s0 - 650= 200 tilesTherefore, the difference betweenthe number of tiles used in thebedroom and in the kitchen=(7xs0)-200= 350 - 200= 150 tilesAnswer:ATotal number of data=7+4+6+2+l: 2g.-Ev.munberlThe two middle values are the 10thterm and 11therm, that is RM2.00and RM2.00.

33

37

.'. Median = RM2.00 RM2.00= RM2.00Answer; B

Sports house febat has an equalnumber of boys and girls.Answer:DThe mean age of the three children: 19 yearsThus, he total ageof the 3 children:19x3: 57 yearsLet the ageofEn. Ahmad and PuanFatimah be .r and y respectively.x - ]t + 57 _ y, FfmealrEAlq = rr*---lof en .nhmia, Ix+i+57=lss l r t*q{* ltnef J cruldren Ix + y = 1,55 57 li , :r y"*r. Ix+y=Y6Thu+ the mean age of En Ahmadand Pn Fatimah982: 49 yearsAnswer:BTotal number of plants that Masturaplanted = 14 + 18 + 1,6+ 12 = 60Number of roseplants :16u =!9xs6o"60

-96Answer:CGiven y : fwhenr=l,y=t3=twhenr:2,y:23=8whenr=3,y=33=27whenr=4,y=43=64Thus, thetableof values or functionv: f

38

I 2 3 4v I 8 27 64

Paper 215+11+(-16)A\= 15+: + (-16)4=15x4+(-16)5= 12+ (-1,6)= t2-L6=46-0.24\*L=S.Ze*L

JJ-- 5.76x L

I= 1-.44 3: 4.32(a) /-ost : o.s(b) (7+31-+F : (7+ (-2))'z:(7-2) ' ,

:J --7 4

(a) .TPQ(b) Given MN = /NPT-RSMN LMPT_1573 1,5 , -'l = - /3:35cm

(a) Length of EC : ,{R') - 17:5cmNFtan V" : ";iIL_125(b) Lengthof AC = 2 x 5= 10cmLengthof AB = {G=e= 6cm


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8 (a) 2(n +5)-3:2n+10-Z. =2n+7(b) 3(am 3k)- (5k - m):12m-9k-5k+m:12m+m-9k-Sk= 13m-7&

e s-20tc=5(r_4F)= 5U1)'-@d'l= 5(1+ zk)(r x)(ii)

:.,...1I

,1-.i/

..t.if- '

1-t. .". . i . .' i-.

11 (a)(b) (i) ( ii)

, , 3 _ k+15_'- 5m IOmk 3x',2k _k+155mx2k 10mkOK K+1570mk 10mk6k-k-1570mk

)K-I510*ks(k 3)

1!71x122x32 | 3= 2rx(4x3) ix3;= T1x(Z\3) ' \3 ' "= 2r x Y"ix 3ix gi20

IJ: Zr+1 X 3, +i= Tx3a= 1X32

17 r+4 < 13 and !l>32r

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Pmr 2009 Mathematics