Spm Percubaan 2009 Johor Mathematics

SULIT t449tr Mathematics Paper1 September 2009 lt/o jam

JABATAN PBLAJARAN NEGERI JOHOR

PEPERIKSAANPERCUBAANSPM 2OO9 MATHEMATICS PaperI One hour and fifthteen minutes

JA\GAN I

BUKA KBRTAS SOALAN INI SEHINGGA DIBBRITAHU

,(crlns .soalan ini udalah clalem du,ibql?asa. Soctlendi bahagian qtas adalalt clalqm behasa Inggeris, diikuti oleh bahqsa -\.lelclyu. Calon dikehendekimembecamaklumatdi halaman 2.

Kertas soalanini mengandungi32 halamanbercetak. O FlakCipta JPNJ2009

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INFORMATION FOR CANDIDATES TIUKLUMAT UNTUK CALON

l.

This questionpaper consistsof' 40 questions Kertcts soalan ini mengandungi 10 soqlan.

2.

Ansrver all questions. Juwab sen uo sctulan.

3.

Answer each question by blackeningthe correct spaceon the answer sheet. Jswub dengan menghitamlarn ruangqn yang betul pucla kertasjawapan.

4.

Blackenonly one spacefor eachquestion. Bagi setiap soalan hitqmken salu ruangan sahaja.

5.

If you *'ish to changeyour ans\ver,erasethe blackenedmark that you have made. Sekiranya anda hendqk mentrkarkanjawapan, padamkan tanda yang telah dibuat

6.

'I'henblacken the spacefor the new answer. Ke ruudi an hit amkan.iau'apen yarrg bqru.

7.

The diagrams in the questionsprovided are not drawn to the scaleunless stated. Rajah yang mengiringi seliop soalan lidak diluki,skanmengikul ,gkalakecuali dinyatakan.

8.

A list of formulaeis provided, Satu senarai rumus disecliakan.

9.

is provided. A booklct of four-figuremathematicaltables Sebuah buku sifir matemetik em1tcrtangka disediakun.

10.

You may use a non-programmablescientific calculalor, Andq dibenctrkan menggunakan kcilkulator saintifik yung tidak boleh diprogram.

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MATHEMATICAL FORMULAE RAMUS-RUMUS MATEMATIK thequestions, The symbolsgivenarethe ones The follorvingformulaemay be helpfulin anslvering commonlyused. herikut bolehmembantuanda menjawabsoalan,Simbol-simbolyang diberi adalah Rumus-rurnus ),dngbiasadigunakan. RELATIONS PERKAITAN , I

a

A

m

m

xa

m+n

n :a

n + fI:O

12

Theorem c2= a2+ b2 Py,thagoras TeoremPithagoras

IJ

m= -

1'

m- n

-

l,

xz- xt , m \n =d mn \a )

|

t4 ('l

^^-r--

oa-nl -,

I'U)

= ---

-')

o)

m= -\

/ v - interceDt ) . ---x - tntercept

m---\

I pinlasan - y = .r ) ptwqsan - x

n(e)

n(^s)

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

(x,+x"

v,+v.\

|.,.7 ) Mi d p o i (x,y)=1 n t, Titik tengah Averagespeed=

jarak yang dilalui masayctng,diumbil

Pttrala laju =

l0

Mean

Mitt

lt

Mean

Mitt

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travclled distance --1ime]t[en

=

_ :

sumofdata d"t" ;u*b., "f hqsil --- tambahnilai dats dala bilangan sumof (midpointof intervalx frequency) sumof frequencies hasiltanMerapun) hasiltambahkekerapan t449tl

SULIT SIIAPE AND SPACE BENTUK DAN RUANG Area of trapezium

!

Luas tropezium

L x hqsil tamhqhdua sisiselari x tinggi

2

Circumference of circle = Lilitan bulatan

xd = 2tv nd - 2nj

3

Area of circle = TrrZ Luas hulutan -- rj2

4

Curvedsurfaceareaof cylinder Luaspermukaanmelengkung silinder

5

Surfaceareaofsphere Luaspermukaansfera

6

Volumeof right prism= crosssectional areax length Isipaduprisma tegak : luaskeratanrentas x panjang

7

Volumeof cylinder = *th : nj2t Isipaclusilinder

8

V o l u me o f c o n e

1

Isipadukon

><sum of parallel sides x height

2

=

= 2nrh : 2trjt

= 4rr2 : anjt

l^

-rrth

j', !, J

9

Volumeof sphere = lort 3 = Isipadu.r.fera !rt' J

l0

Volumeofrightpyramid =

1 * basearea x height a J

1

Isipadu piramid tegak

= I

x luas tapak x tinggi

J

ll

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Sumofinterioranglesofapolygon:

(n-2) x 180'

poligon: Hasil tambahsudutpedalaman

(n - 2) x 180'

SI.JLIT

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5 arc lenglh

angle subtended at centre

circumferenceof circle

360'

panjdng lengkok

sudutpusat

lilitan bulaton

13

areaofsector _ areaof circle luas sektor

360.

anglesubtended at centre 360' sudutpusat

luas bulatan

14

Scalefactor,

360'

k= !! PA

Faktorskala, 15

Areaof image= k2 x areaofobject. Luas imej: k2 x luasobjek

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6 Roundoff809430 correctto threesignificantfigures. Bundarkan809430betul kepadatiga angkabererti. A

809

B

8094

C

809000

D

809400

Express0.00000545in standardform. Ungkapkan0.00000545dalambentukpiawai. A

5.45x 10-s

B C

5.45" 10-6 5.45x 10-7

D

5.45" 1fr8

4.7 xl07 +5600000:

A B

1.03" 107 4.76 x 101

C

5.26 " 107

D

6.07x lOi

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Diagram4, showsan emptyperfumecontainerwhich is a right prism, with trapezium is the uniformcrosssectionof theprism. Rajah 4 menunjukkansebuahbekaspewangiyang ko.sangdengankeratanrentss seragamberbentuktr apezium.

50 cm 25 cm Diagram4 Rajah4 A worker fills up half full of the emptycontainerwith a perfume. Calculatethe volume,in cm3,the perfumein thecontainer. sejenispewangike dalam bekastersebutsehingga Seorangpekerja telah memasukkan separuhpenuh. Hitungkanisipadupewangi,dalam cm3,dalam bekasitu.

A

4.625x fiz

B

5.55x 104

C

7.5006x 104

D

1.11x 105

1100012 -1011'-

l l I 100:

B

1110102

C

1001012

D

1001102

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8 G iv en4 x 5 4 + 3 x 52+ 5p +1 = 40321s,find thevalueofp. Diber i,4 x 5 4 + 3 x 52+ 5p +1 :40321s,cari nilaip.

AI B2 C3 D4

In Diagram7, PQRW is a regularpentagonand RSTIJW is a hexagon. Giventhat IS is parallelto W andO.RSis a straightline. Dalom Rojah 7, PQRII/Vialah sebuahpentogonsekatadan RSTUVWialah sebuah heluagon. TSselari dengan UV dan eRS adalah satu garis lurus

Diagram7 Rajah 7 Find the value of r. Cari nilai n. A

3go

72"

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c

740

D

gg"

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In Diagram8, JK is a tangentto the circleKML at K. JML is a straightline. Dalam Rajah 8, JK ialah tangenkepadabulatanKML di K. JML ialah garis lurus.

Diagram8 Rajah8 GivenJM- MK,fnd the valueofy. Diberi JM : MK, cari nilai y.

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A

4lo

B

49"

c

57"

D

820

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l0

In Diagram9 showstwo flagson a grid. Rajah9 menunjukkanduu huahbenderadi atas kotakbergrid.

v

F

\

o

\

G

Diagram9 Rajah9 FlagG is the imageof flag F undera onetransformation. which of the following correctlydescribethe transformation. BenderaG ialah imagebagi benderaF di buwahsatupenjelmaan.Antara berikut yangmanakohmenghuraikan penjelmaantersebut.

AA

I 'r--^-^t^., ^- f I rranstallonl /l T./ \-

.

(t )

I TANSIdST I

]

\.- 4i

B

Reflection on x-axis Pantulanpada paksi-x

C

Enlargement with scalefactorI aboutcentreO Pembesarundenganfaktorskala 7 berpusatdi O

D

Rotation1B0oclockwiseaboutcentreO Puturun 19ff ikut arahjam berpusatdi O

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il

Diagram 10 shorvsfive trapeziumdrawn on thc squaregrids. Which of the trapezium A, B, C, and D is the image of trapeziumP under an enlargement. Rajoh l0 menuniukkan lima tra1:izium dilukis di atas grid sisiempat ssma. Antora lrapezium A, B, c, dan D yang munakah imej bugi trapezium p di bawah suqtu penfiesoran.

,/;::

A

lS'.l"s'

ffi ls l:i-': ffi*:sffi',; )'i

ffi

;:""{

l-"::"lt$i..l 'ii

A

ffi# !l{

)&

jt N.

{ (.1

€

X x$ *-

i${ iy{

b# .qQ

?:zfg

-N

b.

ff

N

X;

S".v\.t "i-'14

)a'."'l

h,

A

A

':,t:i \

*i*ci

..st N

!

t.i". .^ ' " l

tli

9.t9iri: l+iil1\

I)iagram 10 Rajah 10

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DiagramI I showsa right-angledtrianglePSQandPQR is a straightline and PQ: 15 cm' Rajah ll menunjukkansebuahsegitigabersuduttegakPSQdan PQR ialah garis lurusdan PO: 15 cm 15cm

O

.R

Diagraml1 Rajah1l

{ Giventhatcosro = -i, find thevalueof tan/. 5 a

Diberi kosxo: -i,

cari nilai bagi tanyo.

f

I ;J 3 4 4 5

9 5

t2

Tan0 =-0.5658 and 180"<e < 360".Findthevalueof 0. Tan0 = -0.5658don 180"S 0 < 360'.Cari nilai 0.

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A

2Ag030'

B

24A030'

c

2gg030'

D

330030'

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13

Which of the following graphsrepresents the graphof y: sin xo for 0o S x < 180o. Antara berikutyang manakahmewakiligrafy = sin xo bogi 0o S,r < 180".

C

D

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Diagram14 showsa right prism with the horizontalbase PQRS. Rajah 14 menunjukkansebuahprismategakdengantapakmengfuk PORS

Diagram14 Rajah14

What is the anglebetrveenthe planePQI'|/ andthe plane RSTW? Apolrahsudutdi antarasatahPQll/ dengansatahRSTW?

A B

lstrQ I PTYR

C D

Z T WP

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15

15

Diagraml5 showstwo telecommunication substationson a horizontalplane.PointP andQ arethe fwo tips of the substations. Theheightof the towersare l5 m and20 m. Raiah l5 menuniukknndua buahpenccwangtelekomunikasi di atassatupermukaan mengufuk.Tilik P dan Q beradadi puncakpencawongtersebut.Tinggi l<edua-dua puncakpencewangtersebut ialah 15m dan 20 m.

15

Diagram15 Rajah15

Calculatethe angleof elevationof point Q from point P. Hitung sudutdongakantitik Q dari titik P. A

260 34',

B

63"26',

c 5 3 ' 08 ', D

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360 52'

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Diagram16 showsa flag rRS.ThepointsP, Q, andR lie on a horizontalplane. Rajah 16 menunjukkansebuahbenderaRS.Titik P,8 and R terletakdi qtassatah mengufuk

S

Diagram16 Raiah 16

Theangleofdepressionp from S is 50o. Suduttunduk Q dari titik S ialah 50i Calculatethe distancePR. Kirakanjarak PR.

A

13.43

B

t7.43

C

19.07

D

23.09

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Diagraml7 showsttree pointsP, Q, andR on a horizontalplane. Rajoh 17 menunjukkantiga titik P, Q, dan R pada satahmengufuk

Diagram17 Rajah17 P is a point duewestof p. Find the bearingof R from p. P odalahsuatutitikyang terletaklrebarat Q. Cari bearingR dari Q.

A

020"

B

0600

C

120"

D

200"

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18

In Diagram18, N is the North Pole. S is the SouthPoleand1VO.S is the axisof the earth. Dalam rajah 18,N ialah Kutub {Jtara.s iqlah Kutubseratqndon Nos ialah pat$i bumi. NIU

El30"T

Equator Khatulistiwa

s Diagram18 Rajah18 Find the positionof point p. Cari kedudukantitik Q.

A

(2oo N, fio Ln (2AoU, $o B)

B

(200N, 75'n (2oou,750B)

c

(7ooN,$o rn

D

eoo u, $o B) (700A"75orn Qoori,75oB)

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2(l + 3x)(2- 5x)= A

2+x-15x2

B

4 +2x* 3012

C

8+4x-60x2

D

10- l9x- llxz

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20

19

2(4 - r) Express -+! r3r -r-!

{JngkopkanK A

asa singlefractionin its simplestform.

#

sebagaisarupecahantunggal dqramsebutantermurlah.

14-2r

3r B C tl

2l

14-3r 3r 18-7r

3r 30-7r 3r

Giventhat

Diberi

s , ungkapkanr dalamsebutans dan q.

s2s-3

A

, - -:----i I - .9 -

B

," = -:-------I - s'

C

sq-3 1-s

D

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r interms ofsandq' ' exPress

ffi-

s-3

r ='

a-3 l-s

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20 . 2m+l ' - +l=3m, calculate thevalueof n. Giventhat'-' 3 1m

t7

Diberi +

+1 : 3m, hirungnilai m.

a J

2

A

a J A +

B

3

? D

23

+

;

=61 , find thevalueof p, q, andr.

Giventhat ,[f

s r-: Diberi bahqwa tlp' = 6' , cari nilai p, q, dan r,

A

p=6,Q=3,r=2

B

p:6,q=2,r:3

c

p:6,q=3,r:l

D

P=6,q:1,r=3

.,J

I o ' a -" I

Simplifu

(on')'' /

z

-| I p-s-t\3 Ringkaskan \pq') 6-O

A

p"q-

B

p'q' Rd

C D

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p-q p'oq'

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inequaliti.5 5 +2r< ll and x-l>-2. Listalltheintegersthatsatisfithe ketaksamaqndan 5 + 2.x< 11 Senaraikansemuaintegeryang memuqskqn 1 >_ 1

-

11

-1

01?

B

-i - ?- t

C

-i

? 0 I ? 1

-)

-1

D 26

of savingsdoneby Ahmadfor the first five month Diagram26 showsthe percentage of 1'ear2009. peratussimpananolehAhmaclbagi lima bulanpertomaMei Roiqh26ntenunjukkan dalamtahun2009.

Diagram26 Raiah26 if thetotalsavingfor thatfirst five monthsis RM450, calculatethe savingin RM that represents by the shadedsector. ,likajumlah simpananbagi lima hulantersebutialan RM(50, hitung simpanandalam Rfulyang diwskili oleh kawasanberlorek. A

18.75

B

37.5

c D

67 .5

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Table2Tshowsthe disnibutionscoresof a groupof studentsin a quiz . pelajar dalamsatukuiz. Jadual27 menunjukkantaburanskorsekumpulan

Score Skor Frequency Kekeranan

0

I

1

3

3

5

l0

t2

4

5 a J

Table2T Rajah2T Themeanof thescoreis Min bagiskorialah A

2.17

B

2.50

c

2.60

D

2.67

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Which graphrepresent/:

8 - 5x3?

Grof manakah yang mewakili y = 8 - 5x3?

D

ST]LIT

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Venn Diagram in Diagram29 showsrelationbetweensetX, Y, andZ. hubunganantara setX, Y,dan Z. Gambarrajah Venndalam Rajah29 menunjukkan

Diagram29 Rajah29 The shadedarearepresents Rantauyang berlorekmewakili A

XnZnY'

B

XaYnZ

C

XwZnY'

D

XwYnZ

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25 30

Diagram30 is a Venn diagramshowingthe elementsof the universalsetd, set,{ dan setB. Rajah 30 ialah gambar rajah Yennyang menunjukkanunsur-unsardalam set semesta (, setA dan set B.

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.r o14

Diagram30 Rajah30 List all the elementsof setl' Senaraikansemw unsur bagi setA'.

A

{v}

B

{s,",r}

C

b,r,.,yl

D

lt,r,*,!,q\

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26

Diagram31, showsthe relationbetweenset{ setP, and setQ. Rajah 3],,menunjukkanhubungandi sntaraset (, setP, dan set Q.

Diagram31 Rajah31 = 4, n(Q)=l5 and n(Pu Q)' = 12, calculatethe numbers Given n({) =33, n(P ^Q) of elementin the shadedregion. Diberi n(€) = 33, n(PnQ) =4, n(Q =15 dan n(PvQ)' =72, hitungbilangan elemendalam kawasanberlorek A2 B6 C8 Dl0

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32

In Diagram 32,MNis a straightline with gadient-! 3 Dalam Raiah 32,MN ialah garis lurus clengank r*unon -? 3

Diagram32 Raich 32

Find they-interceptof the straightlineMN. Carikanpintasan-ybagi garis MN.

33

A

8

B

9

c

l0

D

l8

Findthevalueofp if the linejoiningthepoints(4,3) and(2 ,p) is parallelto the line y:2*3x. titik (4 , 3) dan (2 , p) adalahselari Cari nilai p jika garisyang menghubungkan dengangaris lurusy : 2 - 3x .

A

-3

B

-l

c

5

D

9

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In one recent culture show, eachaudienceis given the chanceto pick a ball randomll fiom a bag contains4 red balls, 7 greenballs, and 9 blue balls. A presentis given away to any audiencewho gets a red ball. The ball is return back into the bag before the next audiencedo their picking. Dalam satu petunjukan kebudayaan bsru-bqru ini, setiap penonton diberi peluang memilih secqra rawak sebji bolo daripada sehuah beg yong herisi dengan 4 holq merah, 7 bola hijau, den 9 bola biru. Hadiah akan cliberi kepado penontan )'dng mendapat bola merah. Bola yang dipilih itu dip"ulangscmula ke dalum lseg.;thelum penonton lain membucrtpemilihan berikutnya.

If 240 audiencesattendedthe show, calculaiethe number of presentsthat will probably be given away on that day. Jika 240 penonton menghadiri pertuniukan tersebut, hitung bilangan hadiah yang mungkin diberi pada hari itu. A 12 848

c60 D80

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35

Diagraml9 showsmarblesthatlabelledwith ,R,S, or L RajahI9 menunjukkanguli-guli yang berlabelR, S, QtauT.

e$p^e#S @ *Gfl@ w@w Diagram35 Diagram35 A marbleis chosenat random. Staterheprobabilitythatthe marbleschosenis not labelledwith R or Z. Sebi.iiguli dipilih secarqrav)ak. \jatakan kebarangkalianbahqwapli yang dipilih itu bukan berlabelR atau T. 6 7 B

L

7 l 6 I

Lf

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2

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30 Table36 showsthe valuesfor variablesx andy.

Jaduql 36 menunjukkannilqi-nilai bagipembolehubahx dany. x

4

6

r

48

p

Table36 Jadual 36 Given thaty variesdirectly asr2. Calculatethe valueofp. Diberi bahaway berubahsecerelangsungdengan*2. Hitung nilai p. A36 B72

c D 37

108 216

Given rr varies directly as r and varies inverseh' as squareroot ofp when n : g, p : 4 and m:2, find the relation betweenm, n, andp. Diberi m berubah secaro langsung dengan n dan secara songsqng dengan punca kuasa duap apabilan: B,p: 4, dan m = 2, cari hubungan,ntara m, n, rJonp.

A

Bm =

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m = ----:-:--

8 n

,G

C

* =J-nr' 64'

D

.=4p"

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31

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38

Table38 showsthe relationbetweenvariablesW,R, andI . Given that I4/e RT. Calculatethe valueofx. Jadual3S menunjukkanhubungandi antarapembolehubahW,R, dan T. Diberi bahawa llte RT. Hitungkan nilqi x.

W

9

15

R

2

5

T t

J

x

Table38 Jadual 38

A

9 2

B

2 9

C

3

D

2

3e

( 32

/s\ tl

-s)l4 l= t -1 ,

A

B

(ls 8 5)

r"l l8l ls J

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C

(28)

D

(r8)

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40

fo) t'') f'ol

G i venthematrixequation I Z l*l : l= i r l, n n a t n e v a lu epo-q f + r.

[*J [nJ[, J Io.1 f'l ('o\ Diberipersamaqnmatril$ Z t I

l*l -t l=l

I,carikannilaip-q+r.

l-o ) [nJ I r j A

-l

B5 c

ll

D15

END OF QUESTIOIVPAPER KERTAS SOALAN TAMAT

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SULIT 1449/l Mathematics PaperI Ogos/Sept2009

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM TAHUN 2OO9

SKEMA PEMARKAHAN MA T HE MA T I CS

Paper1 One hour and lllthteenmittutcs

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2oo9 G)I{akciptaJPNJ

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SULIT AnswersFor Paperl(MathematicsSPMJulang2009)

I

Answer C

2

B

a J

C

4 5 6 7 8 9

B D B

No

L

C

t)

0

A

I )

B D

J

C

A

D

6

7

B D

t8

C

l9

20

B D

2l

A

22

L.

T

L)

24 25 L t)

27 28 29 30 3l

A D A

C C A A (-

B

)/.

34 35

D B B

Jt)

C

3'l 38 39 40

B D

JJ

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L

B

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Mathematics Paper 2 September2009 2Yzlarn

...;...

T in g k a t a n :

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN

PERCUBAAIT SPM 2AO9

MATHEMATICS Paper 2 Two hours and thirtv minutes

JANGAN BUKA KERTAS SOALAN INI SEHTNGGA DIBERITAHU Untuk Kegunaan P emer il<sa 1 . Tuliskan namo dan tingkatan ruang yang disediakan.

2. Kertas

soalan dwibahasa.

ini

adalah

pada

dalam

3. Soalan bahasa Inggeris dalam mendahului soalan yang sepadon dalam haha.ya Melayu. .a a.

Bahagian Soalan

A

I

a J

2

4

J

A .?

4 5 6

10 1l

t2 5 . Calon dikehendaki membace arahan di

B

13 T4 15 t6

Markah Diperoleh

4 5 5 6 6 6 5

8 9

C al o n di b enarksn me nj ow ab keseI uruhan atau -sebahagian soalan some ada dalam bahctsu 7{elo|,u atau bahasa Inggeris.

halaman 2.

Markah Penuh

4

t2 t2 t2 t2 t2

Jumlah Kertas soalan ini mengandungi 29 halaman bercetak

o llak Cinta JPNJ 2009

1449/2

SULIT

For examiner use

SULIT INFORMATION FOR CANDIDATITS MAKLAMAT

UNTUK CALON

1.

This questionpaperconsists01'twosections:SectionA and SectionB. Kertas soalan ini ntengandungidua bahagian: Bohagian A don Bahogian B.

2.

Answer all questionsin Section A and any four questionson Section B. Jawab semua sonlan dulam Bahogian A dan mana-nlena empat soalemdaripada Baltagian B.

3. Write your answersclearly in the spacesprovidedin the questionpaper. Tulis jawapan anda dengan.ielaspada rulng yang disediakan dctlanr kertassoalan. 4.

Show your working. It may help you to get marks. Tunjukkankerja mengira uncla.Ini boleh membantuandn untuk mendapatkon markah.

5.

If you wish to changeyour answer,crossout the answerthat you havedone.Then write down tlre new answer. Sekiranya anda hendak menukarjawapon, butalkon .icwapan yang telah dihual. Kemudian tulis .iatoapan yttng baru.

6. The diagramsin the questionsprovidedare not drawn to scaleunlessstated. Raiah yang mengiringi ,coctlontidak dilttkiskan mengikut skala kecuali dinyatakan. 7. The marks allocatedlbr eachquestionand sub-par1of a questionare shown in brackets. Markuh 1,ongdiperuntukkan bogi seliup soalan dan ceraicrnsoalan ditunjukkan dulant kurungan. 8.

9.

A list of formulaeis providcd. Satu scnarai rumus clisediakln. A booklet of four-figure mathematicaitablesis provided. Sehwh buku sifir mulemutik empot angka disediakan.

10. You may use a non-programmable scientificcalculator. Anda dibenurkan menggunakrn kalkulator saintifik yang tidak boleh diprogram. I 1. This questionspapermust be handedin at the end of the examination. Kcrtus soalan ini hendaklah diseraltkanpacla akhir peperiksaan.

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SULIT FORMULAB MATHEMATICAL RUMAS MATEMATIK The symbotsgivenaretheones thequestions. Thefollowingformulaemay be helpfulin answering commonlyused. Runtus-rumus berikut boleh membqnlu andq menjawab soalan. Simbol-simbol yang diberi adalqh Yang biasa digunakan' RELATT'NS gERKATTANI) . I

a

m

n xa :a

m+n

t2

Pyhagoras Theorem c' : a'+ b' Teorem Pithagoras

2

a

nt

n + a: c t

m-n

13

m = :---!--:---

a J

( a- ) ' =

y.- v, x r-x ,

A

-

a^'

(d _, | A-' : -----:-----;-l a d -b c \-c

*b) a )

I

14

*: *l *=-(

P(A)

y - intercept x - inlercept

)

pintasan - y pintasan - x

)

n(A)

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

Distance:ffi Jarok

(x,+x, Midpoint, (x, y):

v,+v"\

l'>')l

Titik tengah

distancetravelled -time t a [ e n

Average speed :

jg:slzslg4l!A

Purata laju

l0

mqsa yang diambil sum of data olilrt" ""*b..

Mean

hasil tambah nilai data bilangan data

Min

sum of (midpoint of class interval x frequency)

Mean Min

SULIT

sum of freqtrencies :

hasil taylah ( nilai titik tengah selang kelas x kekerapant hasil tambah kekeruonn

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For examiner's use

For examtner use

SULIT

4 SIIAPE AND SPACE ( BENTUK DAN RUANG )

1

Area of trapezium

=

1 * ,u* of parallel sidesx height z

Luas trapezium

x hasit tambah dua sisi selari x tinggi

+z

2

Circumferenceof circle : : Liliton bulatan

3

Area of circle Luss bulatan

4

Curved surfaceareaof cylinder Luas permukaan melengktmgsilinder

5

Surface area of sphere : Luas permukaan sfera:

6

Volume of right prism - crosssectionalareax lenglh : luas kerqtqn rentas x panjang Isipadu prisna tegak

7

Volume of cylinder Isipadu silinder

= mzh ry't

8

Volume of cone

=

Isipadukon

:

Volume of sphere

=

9

d = rd :

2m 2nl

= /n2 : 7ti2

:

2mh 27tjt

47y2 4rj'

! *'t

3

I"i', J * *' J

Isipadu sfera

l0

2J "it I - x base area x height

Volume of right pyramid

J

Isipadu pyramid

tegak

=

I ; * Iuas tapak x tinggi J

I1

Sum of interior anglesof a polygon

-

(n - 2) x 180o

Hasil tambah sudut pedalqman poligon

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For examiner's u:te

arc length

:

angle subtended at centre

circumferenceof circle

3600

panjang lengkok

!!4!!2!!!L

lilitan bulatan

13

3600

area ofsector

angle subtendedat centre

area of circle

360" sudutpusat

luas sehor

360'

Iuas bulatan

14

l5

Scalefactor.-PA

k-

Faktor skal,a,

r:

Area of image: Luas imej

SULIT

:

PA' PA' pA

k2 x xeaof object k2 x luas objek

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For euamirer', ute

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6 Section A Bahagian A 152marksj 152markahl Answer all questionsin this section. Jawab semua soalan dalam bahagian ini.

I

On the graph in the answer space, shade the region which satisfies the three inequalitiesr+;l >_5 ,y Sx and x < 4. Pada graf di ruqng jawapan, lorekan rantau yang ketaksamaanx+ y Z 5, y Sx dan x 1 4 .

memuaskon ketiga-tiga

13marks) 13markahf Answer /Jawapan

v \

/

5

v:

/

X /

/

\

y:5 /

0/

\

5

x \

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SULIT 2

For exgmiter's ute

Calculate the value ofx and ofy that satisfy the following simultaneous linear equations: Carikan nilai x dan nilai y yang memuoskanpersamaan linear serentak berikut:

4x+ 3y: 11 3x- Y= 5 [4 marks] 14markahj Answer lJawapan:

3

Solve the following quadratic equation: SeIesai kan pe r samaan kuadr at i k; q* *9x*

13: Z(x-5)

Answer /Jawapan:

SITLIT

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For

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enmirgt',

use

4

A

6cm

B

Diagram 4 Rajoh 4 Diagram 4 shows a combined solid consist of a right prism and a right pyramid, which arejoined at the plane DCGH. zis vertically above the base DCGH. Trapezium ABCD is the unifonn cross sectionof the prism. DC :8 cm. Rajah 4 menuniukkan gabungan sebuahpepejal yang terdiri daripada sebuahprisma tegak dan sebuahpiramid tegakyang tereantumpada satah DCGH. V berada tegak di atas tapak DCGH.Trapezium ABCD ialah keratan rentas seragam prisma itu. DC :8 cm.

Given the volume of the combined solid is 322 cm3. Calculate the heighl i, in cm,of the pyramid. Diberi isipadu gabungon pepejal itu islah 322 cm3. Hitung tinggi, h, dalom cm ,bagi piramid itu.

[4 marks] 14markahl Answer / Jawapan;

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For examircr't use

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

5

make it a true statement. Lengkapkanpernyataan berikut dengan menggunakanpe ngkuantit i " semua " atau "sebllangan" untuk membentuksuatupernyataan benar.

elementsin { 1, 2, 6,9\ areevennumbers. unsurdalam {1,2,6,9} adalah nomborgenap.

(b) Write down Premise 2 to complete the following argument : Tulis Premis 2 untuk melengkapkanhuiah berikut: Prernise1: All regular polygonshave equal sides. Premis I : Semuapoligon sekntamempunyaisi.siyang samo, Premise2: Premis 2: Conclusion: Triangle ABC has an equal sides. Kesimpulan;

Segitiga ABC mempunyai sisiyang ssma.

(c) It is given that the number of subsetswhich has z elements is 2". Write down one ' conclusionby deductionon set A: {u,",i,o,u}. Diberi bilangan subset untuk suatu setyang mempunyai bilongan unsur n ialah 2". Tulis satu kesimpulan secara deduksi,bilangan subset untuk set A : {a,e,i,o,u}. [5 marks] [5 markoh] Answer/Jswapan:

(a)

(b)Premise2:

(c)

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10 Diagram 6 shows a straight line P,Sand a straight line QR drawn on a Cartesianplane. The straight line P,Sis parallel to the straight line QR. p lies on x-axis. Raiah 6 menunjukkongaris lurus PS dan garis lurus QR dilukis pada suatu satah Cartesan. Garis lurus PS selari dengangaris lurus QR.. Q terletok pada paksi-x.

R( 6 , 6 )

Diagram 6 Rajah 6 Find, Cari, (a) the equationof the straightline p.R, persamaan bagi garis lurus QR, ft) the coordinatesof Q. koordinat bagi Q. [5 marks] [5 markahl Answer /Jawapan: (a)

(b)

1119t2

STTLIT

11

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Diagram 7 showsa rectangleABCD. Point D and point B arethe centreof quadrants and sectorof circle with radius 7 cm and 14 cm respectively. Giventhat AE:8 cm andCG: 12 cm. Rajah 7 menunjukknnsegiempatABCD. Titik D dan B adalah pusat bagi sukuan dan sehor bulatan denganjejari 7 cm and 14 cm masing-masingDiheri bahawaAE - 8 cm and CG : 12 cm.

A 5 cm tr

1 4c m DiagrarnT Rajah 7

Using

'>') .| , calculate, .)a

Guna (a)

LL

, kira,

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

(b)

)^ the area, in cm', of the shadedregion. Iuas, dalam cmt, ko*otan berlorek.

[6 marks] 16markahl

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For examtner s u3e

For examtn4r rce

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SULIT AnsweilJswapan: (a) 7

(b)

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13

St]LIT

g

Far examiner's use

(t

(a)

(b)

. (S -l\ . nind the value of rn ,--\ matrix of I ; | ] ir ttt" inverse \z 5) '"-/ 1-2 and value of n' n\iotot matrikssongsangtogi (5" -j'l t Diberibshawomatriks *( r) \z 5) [ -2 Cari nilai m dsn nilai n. *[

Write the following simultaneous linear equations as matrix equation: Tulis persamaan linear serentak berilatt dalam bentuk persamaan matriks: 5 x -Y :

39

? -x + 3 Y : -5 Hence, using matrix method, calculatethe value ofx and ofy. seterusnya, menggunateonkaedoh matriks, hitung nilai x dan nilai y.

[6 marks] 16markahl Answer /Jawapan: (a)

o)

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For ?xaminer use

l4

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Diagram 9 shows the speed-timegraph for the movement of a particle for a period of 16 seconds. Rajah 9 menunjukkangraf laju-masa bagi pergerakan satu zarah dalam tempoh I6 saat.

Time (s) Masa (s\ Diagram9 Rajah 9 (a)

Statethe 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 distancetravelled by the particle in the last 6 secondsis 90 m, find the value of a. Jiko jumlah jarak yang dilalui oleh zarah dalam 6 saat terakhir ialah 9Om, cari nilai bagi u.

(c)

Calculatethe averagespeedof the particle,in ms-I, for the period of l6 seconds. Hitungkan purata laju, dalam ms-l, zarah itu dalam tempoh l6 saat. [6 marks] 16narkahl

Answer I Jcrwapan:

tu)

(b)

(c)

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15

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["or et'omtner'.\ llsc

l0

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

EH MH

ME

Box M Kotak M

Box N Kotak N

m

Diagraml0 Rajah I0 A card is picked at random fronr box M and then a card is picked at random lrom box N. Scttu kad tlipilih secaro ruwsk claripada kotak M dan kemudian sotu kacl dipilih secnra rawak daripatla kotak N. By listing the sample of all the possible outcomes of the event , find the probability that Dengan menyensraikan sampel bagi semuu kesudahan peristiwa yang mungkin, cari keharangfurlian k,

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)

&)

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16

1l

E 8 cm

I I I I ,L

a' D

1 5c m Diagram11 Rajah I I Diagram I l, showsa right prism. TrapeziumABFE is the uniforn crosssectionof the prism.ABCD is the horizontalbaseof the right prism.AE :8 cm, AB = 15 cm, and BC: 5 cm. Rajah I I menunjukkan sebuahprisma tegak. Trapezium ABFE ialah keratan rentas seragamprisma itu. ABCD adalah tapakmengufukbagi prisma itu. AE :8 cm, AB : 15 em,dqn BC :5 cm. Identify and calculatethe anglebetrveenthe line HB and the planeABFE. Kenalpasti dan hitung sudut di entara garis HB dengansatah ABFE.

Ansu,er/ Jawapan:

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[4 marks] [4 nartuh]

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l7

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For emminer's use

SectionB Bahagian B 148 markr) 148markahl Answer any four questionsfrom this section. Jswcrb mana-mona empat ,srtalandttripada bahagian ini.

t2

:2 + 7x - f by 12marksl bagi persam*an y:2 + 7x - xz Lengknpkan.Iadual t 2 rli ruang.ictu'apan *1 dan x :3. 12markahl den.qaimenulisnilai-nilai y apabilax :

(a)

CompleteTable 12 in the answerspacefor the equationy writing down the valuesofy when x: -i and x : 3 .

(b)

For this part of the question,usethe graphpaperprovided on page 19. You may use a flexible cun'e rule. {Jntuk ceraian soalan ini, gunakan kertas graf yang disediakonpada halamsn 19.Anda hoteh menggunakanpemharis boleh lentur" Using a scaleof 2 cm to I unit on the .r-axis and2 cm to 2 units on the y-axis, 14marl<sl drawthegraphof l: 2 + 7 x - * ' f o t -l < x < 7 . Menggunakan skala 2 cm kepada I unit pada paksi-x dan2 cm kepada 2 unit untuk*l <x <7' f4 markah) padapaksi-y,lukisgraf y:2+7x-x'

(c)

From your graPh in l2(b), frnd Dari graf di 12ft), cari (i)

the valueofy whenx:2.5, nilaiyapabi la x : 2 . 5 ,

(ii)

the value of x whenY - - 4Nilaixartabila v : -4 . [2 marks] 12markah)

(d.)

Draw a suitablestraightline on the graphin 12(b) to find the valuesof x which satisfothe equation2 = 6x - x2 for -l < x 5 7. 14marksl Statethesevaluesof x. Lukis satu garis lurus yang.sesuaipada graf 12(b) untuk mencari nilai-nilai x yangmemuaskanpersamaan 2 =6x-x; Nyatakan nilai-nilai x ittt.

bagi -1 <x <J'

14markuhl

Answer lJawapan:

ST'LIT

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18

SULIT For examrfvl use

'J

(a)

x

-1

v

0

I

2

2

8

t2

J

4 l4

t2

6

T

8

2

Table 12 Jadual 12 Refer graph on page 19. Rujuk graf di halaman 19.

(i)

v:

(iD

x:

x:

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19

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Graph ftrr Question l2 Graf untuk soalan I2

{-l

c nr

I

i, i

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For examiner use

For examinel use

20

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l3

(a)

rs )

Transfornation M is a translation [\/2 l. jn Transformation N is a refleclion the line y : 3.

Penielmaan M iuluhtrrrr,rtori Il]. \.2) PenjelmaonN ialah pantulan pada guris lurts y:

j"

Find the coordinates of the inrage of point (-3,1) uncierthe foilowing combined transformations : Cari koordinat ime.i bagi titik (*3,I) cli hav,uh g,abungan penjelrnuan berikut:

(b)

(i)

M2

(ii)

MN

[4 marks] f4 narkahl

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

Diagram l3 Ra.iuh l-)

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21

SULIT (i)

(ii)

For examltEr u:te

ZPS is the image of ABC under a combined transformation VW. TPS ialah imej bagi ABC di bawah gabunganpenjelmaonYW. Describe in full transformation Hur ai kan seIengkapnyop enj eImaan (a)

\il,

(b)

v.

It is given that the areaof the shadedregion is 165 cm2. Calculate the area,in cm2,of triangle PQR. Diberi bahawa luas lvrwasanyang berlorek ialah 165 cmz, Hitung luas, dalam cm', segitiga PQR. l8 marksJ 18markahl

Answer I Jawapan: 13

(a)

(i)

(ii)

(b)

(i)

(a)

(i)

o)

(ii)

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For examitv/ utte

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14

Table 14(a) shows the frequencydistributionof the age,in years,of 40 visitors at a book exhibition. Jadual l4(a) menunjukkan tahuran umur, dalam tqhun, bagi 40 pelswat ke satu pameran buku.

Age (Years) Umur ( T'ahun\ 5-9 t4 l0 t9 15

Frequency Kekerapan 0 1 a J

6

2 0 -2 4 2 5 -2 9 3 0 -3 4 3 5 *3 9

10 1t

40-44

2 Table 14(a) Jaduol l4(a\

(a)

(b)

Calculate the estimated mean of the age of the visitors.

[5 marks]

Hitung min anggaran umur bagi pelcrwat-pelawal itu.

15markahl

Basedon Table l4(a), complete Table 14(b) in the answerspaceto show the cumulative frequencydistributionof the massess. fl mark:sl Berdasarkqn Jadual U(a), lengkapkanJadual14ft) pada ruang juwapan untuk menunjukkan kekerapanlonggoknnjisim itu. ll markahl

(c)

For this part of the question,usethe graphpaperon page24. Untuk ceraiqn soalan ini, guna kertas grcf yang disediakan pada halaman24 By using the scale of 2 crn to 5 years on the horizontal axis and 2 cm to 5

visitors on the vertical axis, draw an ogive for the data.

[4 marksl

Dengan menggunakanskala 2 cm kepada 5 tahunpada paksi mengufukdan 2 cm kepada 5 pelawat pada paksi mencancang,lukis satu ogif bagi data tersebut. 14markahJ (d)

Basedon your ogive, find the total numberof the visitors whose age are more than 33 yearsold. 12marksl Berdasarkan daripada ogif'anda, cari bilongan pelawat yang berumur melebihi 33 tahun l2 markahl

1 {J9 2

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23

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For exominer use

Answer /Jatuapan: 14

(a)

Mean: Min

(b) Upper Boundary Sempadan atas

Cumulative frequency KekerapanLonggokan

9.5 t4.5

Table l4(b) Jadual 14(h)

SLILIT

(c)

Refer to graph graph on page 24. Rujuk graf pada muka surat 24.

(d)

Ase : Umur

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24

SUL for erdtnlner use

Graph for Question 14(c) Grof untuk Soalan 14 (c)

2 cm --)

i

I

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25

SULIT l5

For examinl use

You are not allowed to use graphpaperto answerthis question . Andcttidsk dibenarkunmenggunakankertasgraf untuk menjatt,absoctlanini. ta)

Diagram 15(i) showsa solid right prism with a rectangularbascABCD on a horizontal plane. RectangleADEF is an inclined plane and the rectangle GHJK is a horizontalplane. The edgesCJ, BK, FG and EH are verticals. A B - DC : 6 cm, B K = CJ : 6 c m, E H: F G : 2 c m,J K : HG : E F : D A : cB = 4 cm an
X Diagram15 (i) Rajah 15 (i) Draw to full scale, the elevationof the solid on a vertical plane parallel to D.-1as viewed from X. 13marksf Lukis dengan skqla penuh, dongukanpepejal itu pcda satah nzenconcatlg)'ang selari denganDA sebagaimanadilihat dari X. 13marknhl

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For exatntnel u3e

26

SULIT (b)

A half-cylinder is cut and removedfrom the solid in Diagram 15(i). The remainingsolid is shown in Diagram 1s(ii). Semi-circleLQM andPltN is the uniform cross-sectionof the half- cvlinder.The radiusof the semi circle is 2 cm. ,4L : MB = DP :NC:1cm.

c--____f

Diagram 15 (ii) Diagram 15 (ii) Draw to full scale, Lukis dengan skala penuh, (i) the elevationof the remainingsolid on a vertical plane parallel to AB as viewed from I [4 marks] dongaknn pepejal yang tinggal itu pada satah mencancangyang selari dengan AB sebagaimanadilihat dari Y. [4 markah] (ii) the plan of the remainingsolid. pelan pepejal yang tinggal itu.

i 4-r92

[5 marks] 15marlrahl

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27

T emn, t

Answer /Jawapan: ls (a)

(r) (i)

(ii)

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For examther ' use

SULIT 16

G(35o N , 70o D, H and J are three points on the surface of the earth. G,,/ is 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 adalah diameter bumi. GH ctdalah diameter selarian latitttd 35o (J.

(a)

Statethe longitudeof -{ Nyatokan longitud bagi J.

(b)

[2 marks] [2 markah]

Calculatethe shortestdistance,in nauticalmiles, from G to ll measuredalong the surfaceof the earth.

[3marks]

Hitung iarak terdekat, dalam batu nautike, dari G ke H diukur sepuniang permukaan bumi.

(c)

[3 marknhl

An aeroplanetook off from G and flew due west to Fl along the common parallel of latitude and then flew due southto I Sebuah kapul terbang berlepas dari G dan terbang ke arah barat ke H sepanjang selarian latitud sepunyadqn kentudian terbang ke arah selatan ke J. Calculate Kira (i)

the distance, in nautical miles, from G to H measuredalons the common parallel of latitude. iarak, dalam batu nautika, dari G ke tI diukur sepanjang selarian latitud sepunya.

(ii)

the time taken for the whole flight if the averagespeedof the whole flight is 710 knots. masa yang diambil, untuk keseluruhanpenerhanganjika purata laju keseluruhanpenerbanganialah 710 knot . 17marks) l7 markahf

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29

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F. exomt t/li

Answer /Jawapan: 16

(a)

(b)

(c) (i)

(ii)

END OF QUESTIONPAPER KERTASSOAI-ANTAMAT SULIT

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1449t2

1449/2 Mathematics Paper 2 September2009

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM TAHUN 2OO9

SKEMA PEMARKAHAN MATHEMATICS

Paper2 Trvoho u rsa n dt h irrymin u t e s

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No

Answers

Marks PI (f o rlin e x = 4 dotted/solid line)

X:4 I I

i

Y:X

I

I

I I

5

P2

0 +y:5

(areashaded a n dx : 4 mus tb e dottedline) Note : AwardPl forx :4 solid lin e .

Subtotal z

9 x- 3 y: 15 or y:3x-5 1 3 x:2 6 or equivalent x:2

o re q r. riv a le n t

,, y -- |r

3

K K N N ,,|

Subtotal 4x'-llx*3:0 (4x + l)(x - 3 ):0

KI KI NI NI

X :-l ,X :3 A

Subtotal 4

I

'x(6

4

KI

+8)x5x6

2

KI

1 " 6 x8 xh a J

1

'x(6

+8)x5x6

2 h:7

Subtotal

+

I x6x8xh=322

KI

J

NI

4

5

(a) Some

P1

(b) Premise2

Triangle ABC is a regularpolygon.

(c) 2 -

P2 K1 N1

)z

( note: withoutworkingaward KlNl) Subtotal 6

(a)

5

l T l p s :tT l e R :

6:2(6)+c

8 -0

2-e2t orequivale n t

KI KI NI

Y :2x-6 (b) 0: 2x - 6 or equivalent (3,0)

KI NI

Subtotal

7

(a)

1^22 47 1^22_ -x /.x 47

72 * 2 x 4 x l4 360 7 72 * * 2 r 4 x 1 4 + 14+15+12+8+ 5 360 7

/ o,

-x zx_x

411 '^- or

82

"1

or 82.6cm.

KI KI N1

(b)

!*Lrf o , 7 2 , ? r 1 4 , o r 1 9 x1 5 47 3607 - 7 2 r 4 r t4 ' rexrs - 1*2*f 47 3607

KI K1

1 2 3 3o r n 3 ! o r 1 2 3.3cm2 l0 l0

NI

Subtotal

6

8

(a)

m: n:

(b)

1 17 I

P1 P1

(s -r)(') f3 0)

[z t )lr)=[-rJ

P1

3

KI

/x\ tt-

')|,3o) \v) s(3)-(-1X2)l-2sr[-s] tt-

v :-5

N1 N1

Subtotal 6

6 P1

!* r,* 6 =90 2

KI

x:5

9

(a) (b)

u:30 (c)

NI

Itzo*30)4+(6x30)+eo

2

K2

t6 Z3l or 23J25 8 Subtotal

L i sti n gS : { (A ,7 ),( A ,9) ,( A,l0) (R ,7 ),(R,9) ,( R,10) (t,7 ),(t,9) ,( t,10) ( F ,9)(, F,10)) (F ,7 ),

l0

(a)

(b)

NI 6 P1

{(A ,10),(t,l 0)} 2l t26

KI

{(A,7),( A,9),(R,7) ( R,9),(t,7),( 1,9), (F,7),( F,g), (R,10),( F,l0))

KI

N1

10 5 '-or 126

N II

Subtotal

5

ll

ZHBE

P1

B E : 1 7cm

P1 KI

T a nI H B E : 5 t7 Z 16.39"or 16 23' Subtotal

I2

4

(a) 1 -l

-6 b)

(c)

a J

t4

Graph ( Re-ferto the g'aph I The axesdrawn in the right directionwith a uniformscalefor -l<x<7 7 points and*2 pointsplottedcorrectlyor the curvepassesthroughthe 9 pointsin the rangeof - I < x < 7 Note: If 7 pointsare plottedcorrectly, award Kl if 6 pointsor lessareplottedconectly,award K0 Smoothand continuousculve that passes throughall the 8 points correctlywithout any straightsegmentin the rangeof -1 < x < 7, Ignorethat areout ofthe range. (i) y: t3.2 +0.2 (ii) x= -0.8*0.1

(d) y:x+

4 The straightline y = x * 4 drawn correctly. ( Judgment: straightline that'spasses 2 pointsrnarkscorrectly) Valuesofx= 0.4 +0.I x= 5.6*0.1

l3

NI

(a)

K1Kl KI K2

N1 N1 NI Kt KI NI NI

Subtotal

t2

i )( 7,s )

P2

Note: (2 ,3 ) getP l ii) (2,7 ) Note: ( -3 , 5) get Pl

P2

(b) i) W - Rotation 90ocloc k r, v isaeb o u t(l , -2 ) ( Note : (i) Rotation90oclockwise/ Rotationabout ( | , -2) awardP2) (ii) Rotation Award P1. V - Enlargementat centre( - l, l) with scalefactor4 (Note: (i) Enlargement at centre( -l,l) or Enlargement with scalefactor 4 awardP2) (ii) EniargementawarciPi . ii) 4' x PQR- PQR= 165 A reaof P QR: llunit t r Subtotal

P3

P3

KI NI

t2

(a)

UpperBoundary

CumulativeFrequency

Tablel4 Jadual ll UpperBoundary Cumulativefrequency

MeanAge:

(12X l )+ (t7X 3) + (22 ) ( 6 )+ ( 2 7) ( 1 0 )+ ( 3 2 ) ( 1 1+) (b) (37)(1)+ (42)(2) 40 29 (c) Ogive ( Refer to the graph ) Correctlabelingof the horizontalaxis. All pointscorrectlyplotted. Point is plottedcorrectlyandthe ogive passes throughit. Smoothcurvethat passesthroughall the points Note:If 6 pointsareplottedcorrectly,entitle Kl If 5 pointsor lessareplottedcorrectly,assign K0

(d)

40 -28 t2

KI Correct shape KI DH:AG>DA:H G > EH:FG NI Accurate measurement ( + 0.2cm)

KI Coruectshape * Accept sketching of semi circle KI BK>GK>FG>AL :MB * Acceptonly drarvingof semi circle

A/D

LIP

HiEiR

JIC

N2 ( Accurate measurement) KI (correctshape) Ignoredottedline LP andMN KI ( BothDottedline LP andMN)

G/F/Q

K/B

l /l I\I

DJ>AK>AD=CH= KJ > AG:GK =DH _ III

- nJ

N2(Accurate measurement)

t6

(a)

I 10"W

P1P1

(b)

180-35-3s ll0x60 6600n.m

KI K1 NI

(c) (i) 180x 60 x cos35o n.m 8846.84 (ii) 70 x 60 70 x 60 + 8846.84 710 18.38hoursor l8H 23 Min . Subtotal

K I K1 N1 PI K2 NI

t2

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

cm->

Q 14(b) & (d)

_Age=33.0

t