Epitome Tuition - Free Notes...

24
St]LIT JABATAN PELAJARAN NEGERI SELANGOR AIIGAN KEBANGSAAN PENGETUA SEKOLAH MENENGAH PROGRAM PENINGKATAN PRESTASI AKADEMIK (1) SIJIL PELAJARAN MALAYSIA 2O1O ADDITIONAL MATHEMATICS Kertas 2 Mei 2t/z jam S e6aN\ Dua jam tiga puluh ninit 3472t2 JA}{GAI\ BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU l. Kertas soalan ini adalah dalam &vibahasa. 2. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa Melayu. 3. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini. Kertassoalan ini mengandungi 20 halaman bercetak 347212 @ 2010Hak cipra Jabatdn Pelajaran Selaagor I Lihat halamansebelah STJLIT www.epitomeofsuccess.com

Transcript of Epitome Tuition - Free Notes...

Page 1: Epitome Tuition - Free Notes ...epitomeonlinetuition.com/lessons/wp-content/uploads/2010/09/JPS-AM-F5... · SULIT Section A Bahagian A [40 marks] [40 narluh'l Answer all questions.

St]LIT

JABATAN PELAJARAN NEGERI SELANGORAIIGAN KEBANGSAAN PENGETUA SEKOLAH MENENGAH

PROGRAM PENINGKATAN PRESTASI AKADEMIK (1)

SIJIL PELAJARAN MALAYSIA 2O1OADDITIONAL MATHEMATICSKertas 2Mei2t/z jam S e6aN\ Dua jam tiga puluh ninit

3472t2

JA}{GAI\ BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

l. Kertas soalan ini adalah dalam &vibahasa.

2. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa Melayu.

3. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini.

Kertas soalan ini mengandungi 20 halaman bercetak

347212 @ 2010 Hak cipra Jabatdn Pelajaran SelaagorI Lihat halaman sebelah

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IIlNS ro8lr?las uer€feled u"l"qef eldlJ I?H 0I0Z A ZIZLVE

ENOSO)I NVNYTYH[CY.I >INV'IS

ztzLtt. z JI'INS

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SULIT 3472t2

The following formulae may be helpful in answering the questions. The symbols given arethe ones commonly used

Rumus-rutnus berilail boleh membantu anda menjawab soalan. simbol-simbol yang diberiadalah yang biasa digunakan.

ALGEBRA

2a

a^ xan : a '*n

a'* d ' : a^ 'n

(a^)o: a^ '

Iogo mn: Iog m + lo1* n

,mrogo i

togam - logan

log"m'= n logo m

los.^ brofoD=.-

10g6 a

T,=a+(n- l )d

s"= 1t 2a+tu-11 412-

rn= ar

^ a(rn - l \.). = :

r - l

.s- = a l r l<| - r

-b+I

z

J

4

)

6

7

x=

9

l0

l1

t2

TJ

- 4ac

y:uv,

du dvaY dx dxdx vt

CALCULUSKALKALUS

4 Area under a curveLuas di bawah lengkung

b

: I v dx or (atau\

b

= lx c ly

dy dv du--- = u_+v_dx dx dx

)-u-Y-- t

dv dv du. - - - -=:x_rdxdudx

Voh'me generated / Isi padu janaan

b

= | lry- clx or ( dtaul

b

= l ld- dv

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ST'LIT

l - I ,x=-

,N2 ->, f t

t fL.J

4

STATISTICSSTATISTIK

7 - fvr.I ==!--

>wt8 no = ' l

(n - r)l

9 o^ _ nlvr -

@-i l l

u72t2

4 l0

l l

12

l3

t4

(AwB):r(A)+ 4B)-qA.\B\

P(X:r): oCrp'qn-' , p+ q= |

ManlMin, l t= np

o=,,[rac

. - x- l to

u ,=9x roo%

Lr' -2JV

GEOMETRYGEOMETRI

4 Area of tiangle I Luas segi tiga1,.= 1l{rrl,

+ x"y, + xry r) - (x ry, + xry, + xry )l

3

Midpoint/ Titiktengah 5

/ \( . r . v) : | \+xz

- ! t+ lz I\2 2 ) 6

A point dividing a segment of a lineTitik yang membahagi suan bnhercng garis

,-. -;,, _ ( *, +mx, ny, + tttyr\\L ' . r t - | - r - |

\ m+n m+n )

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^ Areaofsector. A=!,'g. '2

3 sin2 A + sss2 1:1sn2 )+kosz A:l

4 t""2 A= L+.on2 A

sekz A: | +tan2 A

5 *t""2 A= | + cot2 A

' 3472n

9 cos ( l 1t)=coslcosB +sinlsinB

l0 t^n(AtB): tanA + tatB

l + t,nAtaa B

ll ztrnAtan2A= _______-__;_

| - tan" A

l2abc, sinl sinB sinC

ST'LIT 5

TRIGONOMETRYTRIGONOMETNI

I Arc lengt\ s: r 0 8 sin(,4 tA) = sinT cos, t cosl sin'

Panjang lengkok, s =j 0 rin (z tBy: rin, kosB t kosl sin g

l -LuasseHor,L: i j '$ !os(l t8):koslkosB +sinl sin8

kosek2l =l+kotzA

6 sia2'"/=2sinAcosA 13 a2:b2 +c2 _7bc cnsAsmL4:2 sin I kos I

a2 :b2 +c2 - 2bckos A

\7 cos2A= crlst A-stn2 A 14 Area offriangle I Luas segi tiga

:2 cos2 A- l I: - nb sin-C: l -2sin2 r4 2

koszA= tof z-sin2e .=2kosz A- L= l-2sin2 A

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SULIT

Section ABahagian A

[40 marks][40 narluh'l

Answer all questions.Jawab semua soalan.

Solve the simultaneous equations 2y + x=6andX+ j=6.Give your answers correct to three decimal places.

Selesaikan persamaan serentak 2y + x = A aon ! + j = A.

Bei jawapan anda betul kepada tiga tempat perpuluhan-

Diagram 2 shows the cuwe of a quadratic fi:nc tion f(x) = yz 16 pa _ 5.The curve has a minirnum point at K (3, q) and intersects thefli)_axrs at point Z.Rajah 2 menunjukkan lengkung bagi fungsi kuadratik .f(x) = x, + 6 px _ 5.Lengkung itu mempunyai titik minimum pada K (3, q) dan memotong palui-flx) pada titik L.

Diagra.m 2Rajah 2

(o) State the clordinates ofz.Nyatakan kaordinat L.

3472t2

[5 marks]

[5 narkah]

(b) By using the method of completing the square, find the value ofp and ofq.Dengan mengguna,lan kaedah penyempurnain kuasa dua, can ntilai p'dan nibi j.

(c) Determine the range of values of .r, if f(x)52.Tentul@n julat nilai t, jika f(r) < 2.

[1 mark]I markahl

[4 narks]14 narkahl

[2 marks]p narkahl

K (3, q)

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SI]LIT 3472t2

Diagram 3 shows the number of members in a particular sales team in a dfuect selling company.The team starts with three members and each new member is compulsory to recruit another twonew members in each subsequent week.Rajah 3 menunjukkan bilangan ahli suatu pasukan dalam sebuah syarikat jualan langsung.Pasuknn tersebut bennula dengan tigq ahli dan setiap ahli baru wajib mencari dua ahli baru hgi padas e tiq p minpsu beri kumya.

c' '3Week 1Minggu I

Week 2Minggu 2

Week 3 -------1,Minggu 3

Diagram 3/ Rajqh 3

fu\ CalculateHitung

(i) the number of new members recruited in the 7u week,bilangan ahli baru yang mengqnggotai pasukan in pada minggu ketujuh,

(ii) the total number of members in the team after 12 weeks.jumlah bilangan ahli pasukan itu selepas 12 minggu.

(b) Given the average sales of each member in a week is RM2 500.If the total sales in the nfr week is RM 1 9I2 5OO, find the value of z.Diberi purata jualan bagi setiap ahli dalam satu minggu adalah RM2 500.

Jika jumlah jualan dalam minggu ke-n adaloh RM1 912 500, cqri nilai.n.

t

[4 marks]14 markahl

[3 marks]

13 marknhl

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3472n$ruT E

4 A curve heq a gradieot function bf -12, o,ho" fr ir.e constant. The @g€nt to thecurve at the point (1, 5) is parallel to the stalght linc y + 9x + 6 = 0.Suatu lenghng nempnyai fungsi leverunan ld - I 2, dengan kzadaan k ialah parclu.Tangen kcpala lenghug itupada titik (1,5) adalah selti d.engan garls lurlts y + 9x + 6 = O.

FindCari

(a) the value of&,nihi k.

(D) the .r-ooordinates of the tuming points,koo inal-x titik-titih ptrslngan irb

(c) the equation ofthe oruve.percanaot larglamg in.

the coordinates of P nd of Q,koordinat P dat kardlnat Q,

the unit vector in the tlirection of OTvekgr uit dalon arahd,

civen thatrl= (l),r=[i)*^-= [,iJ ,"*

D,beri boha',aFd =tl "

= [l

a,.t = (nu_). *,,

[3 marks][3 narkah]

(a)

(b)

[2 marks][2 n*kah]

[3 marks]P narkahl

[3 narks]13nulahl

[2 narks]Pnukahl

t2 marksl12 narl@hl

@ the value of ft, ifFis parallel to @.nilai h, jika Sselari dengan @.

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sulrT 9 3472t2

6 A set of data consists of 9 mrmbers. It is given flat ) (x - i;'z = 366 -d

the mean of the numbersis 10.

Satu set data mengandungi 9 nombor. Dibei bahawa L (x -7)' = 360 d.an min bagi nombor-nombor ituialah 10.

(") FindCari

(D

(iD

the variance of the 9 numbers,varians bagi 9 nombor itu,

the value of lx2.nilai 2 x2.

(b) When a number &, is removed frorn the set of data, the mean is decreased by 1

and the standard deviation is E." \1 2Find the value of ft.

Apabila satu nombor k dikeluarkan daripada set data itu, min berhtrang sebanyak 1

' . . , , rnaan s$tnan ptawar raran 1l | .

Cari nilai k.

[3 marks]13 markahl

[3 marks]

13 markahl

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ST]LIT l0

Section BBahagian B

[40 marks][40 markah]

Answer any four questions from this section.Jawqb mana-mana emput soalan doripada bahagian ini.

Diagram 7 shows the straight liney =a 4 2;nl"tsecting the crwey = 4 -x2 atthe point ,4 andpoint 3.

Rajah T menunjukka garis lurus y = x + 2 yang menyilang lengkung y = 4 - a2 pada titik A dan titik B.

Diagram 7 IRajah 7

CalculateHitung

(a) the value of /r,nilai k,

(b) the area ofthe shaded region,luas rantau berlorek,

3472t2

[2 marks]12 marknhl

[5 marks]l5 narkahl

[3 marks]

13 markahl

(c) the volume of revolution, in terms of n, when the region bounded by thecurve and the straight line y = 3 is rotated tbrough l80o about the y-axis.isi padu kisaran, dalam sebutan n, apabila rantau yang dibatasi oleh lengkung intdan garis lurus y - 3 dikisarkan melqlui 180'pada pal+si-y.

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SI]LIT 3472t2l l

I

Use graph paper to answer this question.Gunakan krtas graf untuk menjawab soalan ini.

Table I shows the values of two variables,.x and y, obtained from an experiment.Variables r andy are related by the eeuation ay = -rz, u,.[ere a and 6 are constants.Jadual S menunjukkan nilai-nilai btigi dua pemboleh ubah, x dan y, yang diperoleh daipada satu ekspeimen.Pemboleh ubah x dan y dihubungkan oleh persamaan ay = x2t , dengan keadaan a dan b ialah pemalar.

x 1.58 , 5t 3.98 6.92 10.0 t9,9

v 0.95 1.26 1.66 2.88 4.37

Table 8Jadual S

(a) Dased on Table 8, construct a table for the values oflog r and log 1,.Berdasarkan Jadual8, bina satujadual bagi nilai-nilailogx danlogy.

(b) Plot log y against log;r, using a scale of2 cm to 0.2 unit on the log r-axis and2 cm to 0.2 unit on rhe log /-axis.Hence, draw the line ofbest fit.

Plot log y melawan log x, dengan menggunakan sknla 2 crn kepada 0.2 urLit padapal<stlog x dan 2 cm kepada 0 .2 vrit pada paksi-log y.Seterusnya, lukk garis lurus penyuaian terbaik.

(c) Use the graph in 8(D) to find the value ofGunakan graf di 8(b) untuk mencari nilai

(D a,(ii) b.

[5 marks][5 marknhJ

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[2 marks]12 markahl

[3 marks]

[3 marknhl

I

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3472t2

Diagram 9 shows two circles. The large circle with centre I haq a radius of 8 cm whereas the smallcicle with c€ntre B has a radius of 6 cm.Rajah 9 menunjukikan dua bulatan. Buhtan yang besar berpusot A mempunyaijejari I cm manakala bulatanyang kecil berpusat B mempwryai jejai 6 cm.

12

Diagram 9Rajah 9

It is given that lB : 10 cm.Diberi bahawa AB = l0 qn

[Use / Guna r = 3.142]

CalculateHitung

(a) ZPBQ, inradian,ZPBQ, dalam radian,

(b) the length, in cm, ofthe minor arc Pp ofthe large circle,panjang, dalam cm, lengkok ninor PQ bagi bulatan yang besar,

(c) the area, in cm2, ofthe sbaded region.luas, dalam cm', lawasan bbrlorek.

[2 marks]12 markahl

[3 marks]13 narkahl

[5 marks][5 markah)

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S-IJLIT 13

10 Solution by scale drawing is not accepted"Penlnlesaian secara lukisan bershala tidak diterima.

The stmight line i*4 = I passes through point,{ (- l, - 2) int€rsects the x-axis at point B.-4

Garis tmts 4*4=ty*s netani **11- t,-2) bercilory dengot palci-x poda titik B.4k

(a) FindCari

(i) the value of ft md the coordinarcs of B.

. nilai k dat koordlwt B.

(ii) the equation of the shaight line that passes through the point I andperpendicular to,{.8.persamaan garis lurus yang melalui tit* B dan benereajang dengan AB.

I

I

I

(r)

(c)

The perpendicular line intersec.tsy-axis at point C. Find the area, in unit2,of the niangle lBC.

Garis serenjang itu bersilang dengan pat6t-y Wda titik C. Cari luas, datam ttutl2,bagi segi tiga ABC.

A point P (r, /) moves such that PB - PC. Find fte equation of the locts of P.Suatu titik P (x, yl bagerak dengan kadaat PB : PC. Cari penanaat lohts P.

[2 marks]12 narkaltl

[3 narks]

13 nar.kahT

[3matu]

13 nmkahl

t2rnnlrslt2 nek4hl

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SI,JLIT 3472t2l4

Diagram I 1 shows a trapezfum ABCD. The straight line lC intersects the straight lineBD WIfl.tE.Rojah 11 menunjult:kan sebuah trapium ABCD. Garis lurtts AC bersilang dmgan garis lurusBD di titik E.

Diagram 1 IRajah ll

It is given that IB- = A a,Ed: S y,,lB : DC: 3 : L

Dibei bahawalF= 6 :e, Ed= 5 y, AB : DC = 3 : L

(a) Express in terms of r and / ory :Ungkapkan d.alam sebutan i dan / atau y :

(r) ,{c ,(iD t='..

(D) Given oE:oF m!11:nc,t _Diberi bahawa DE=hDB dan CE= kCA

tsxpress r-r4 m renns or :Ungkapkan DE dahm sebutan

( i ) h,aandy,h, 1dan,y,

(ii) ft, r and y.k, Ldan y.

Hence, find the value of } and of ft.Seterusnya, cai nilai h dan nilai k.

(c) If la l:2 cm and the area of triangle BCD is 60 cm2, findthe length ofthe perpendicular line from B to CD.Jika I x | = ) sra da, luas segi tiga BCD odalah 60 cm2, carijarak garis yang berserenjang clai B ke CD.

A

[3 marks]13 narkahl

[5 marks]15 markahl

[2 marks]

12 narkahl

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SULIT t5 3472t2

[4 marks]14 narlahl

[6 marks]16 marlcahl

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Section CBahaglaa C

[20 marks]120 narlahl

Answer any two questions from this sectionJawab mana-mana dua soalan daripada bahagian ini.

Diagram 12 shows a niangle ABC wherc ADB and l,CC are straight lines.Rajah 12 menunjuklc<tn sebuah segi tiga ABC di mana ADB d.an AEC adalah garis lurus .

C

Diagram 12Rajah 12

It is given that /D :7.2cm" AE: 4.6cm, BC = l0.7cm, DE:6.3cmandZACB = 46o.Dibqi bahawa AD:7 .2cm, AE : 4.6cm, BC = l0.7cm, DE = 6.3cm dan ZACB = 460.

(a) CalculateHitung

(i) 8Aq

(ii) the lengt\ in cm5 of AC.panjang, dalam cm. bagi AC.

(b) Point I' lies onl C sncbthat AB: A'8. '

Titik A' terletak di atas AC dengan keadaan AB -- A'8.

(i) Sketch A l"C,Laknr AA'BC,

(ii) Calculate the afea, in cm2, of L,A'BC.Hitung luas, dalam cm2, bagi L A'BC.

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SULIT 16

13 Diagrarn l3 shows a quadrilateral lllCD such that ZLBC is obtuse.RaJah 13 merunjuk*an satu sisi empat ABCD dengan freadaan ZABC adalah sudut cakah.

(a) CalculateHitung i

(r) the lengdl in cm, of lC,panjary, dzl@n cn., bagi AC,

(ii) ZABC.

(b) The area of tiangle,4DC is twice the.area of tiangle z{BC.Calculate the shortest dishnce, in cm, from the point B to lC.Luas segi tiga ADC adalah ifua kali tuas segt tlga ABC.Hitung jarak terd.elat dalot cm" dan tuik B ke AC.

(c) Sketch tsiangle B 7'C'which has a different shape fron triangle BIC such thatB'A'= BA, B'C' : BC and, ZB'A'C' = ZBAC.Inktr segi tiga B'A'C' yang nenptryai bena* yang berlainan daripada segi dgaBAC dengan leetdaan B'A'= BA, B'C' = BC dan LB'A'C' = ZBAC.

3472t2

[5 marks]15 tnukahl

[4 marb]

14 narlahl

I mark]

11 nuknhl

-\

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t7SIJLIT

t4

'i- 'v roc - ;

R'-r)

CalculateHitung

(i) the value of -r,nilai x,

'!i! , 91 1 1-r1 -l

I r , : -d '

: ) )

, '+o ' ' l " r r ' - - ,

f ,^ " . f. , - ,?- .

3472t2

[5 marks]l5 narkahl

[5 marks]15 markahl

I Lihat halaman sebelahSULIT

Table 14 shows the price indices and percentage usage of four ingredients, p, 0, and S,in the production ofa tlpe ofbiscuitJadual 14 menunjuklan indeks harga dan peratus penggunaan empat bahan, p, e, R dan S,dalam pmghasilan sejenis bishtt.

IngredientBahon

Price index for the year 2008based on the year 2005Indeks harya tahun 2008berasaskan nhun 2005

Percentage usagePeratus pengganaan

P t25 25o 30R ll0 l0.s 140 35

Table 14Jadual 14

(a) CalculateHitung

(i) the price ofR in the year 2005 if the price in the year 200E is RM 3E.50,harga R pada tahun 2005 jika harganya pada tahun 2008 ialcl, RM 38.50,

(ii) the price index of ,9 in the year 2008 based on the year 2O0Z if its price indexin the year 2005 based on the year 2002 is 125.Indel<s harga S pada tahun 2008 berasaskan tahun 2002 jika indel<s harganyapada tahun 2005 berasasl{an tahun 20Q2 ialah 125 .

(6) The composite index for the cost ofbiscuit pioduction for the year 200g based on theyear 2005 is 130.Indeks gubahan bagi kas penghasilan biskut ini pada tahun 2008 berasaskan tahun 2O05 ialah 130.

, ! ' ,on L . . \ j , . . !L l i )

r,-rr. " - ' '-r\J

A' \ t )4)o-t . '1. ,o o)''DL 'ji.

' r :c l(ii) the price ofa packet ofbiscuit in the year 2008 if the corresponding price

in the year 2005 is RM45.00.harga sebungkus biskut ini pada tahun 2008 jika harganya sepadan pada tahun 2005ialahRM45.00.

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3472n

Diagram 15 shows abar chart representing the montbly cost offour oomponents used in buildinga mathematical model in the year 2fi)6.Table 15 shows the prices and price indices for the componeDts.Fajah 15 nntmjukkan cana palang bagi perbelanjaan untuk empat komponen yang digunakan unnkmembina suotu model natenatih pado talnm. 2006,Jad al 15 mernmjul,kn, harya dan lndele hugd bagi konpoaen-konponar tasefut.

Monthly Cost (RM). PerbelanJaan Bulanan @M)

iljI

li

1!1Il

j

R

Diagram 15Rojah 15

Table 15Jadual 15

ComponentKompnnen

ComponentKomponen

Hce ( RM ) for the yearIIaryr (RM) podt tshun

Price index for the yesr 2007based on tle year 2005

Irul*s hargopada tahun 2Wber.alsaafunthun20052006 2007

P RM 2.00 RM 3.00 150o RM4.00 RM5.00R RM2.50 v t20s Z RM 0.70 r75

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SIJLIT

(a) Find the value ofCqi nilai

(i) a(ii) y,(111) z.

END OF QTIESTION PAPERKERTAS SOALAN TAMAT

347212 A 201ro Hak Cipta Jabatan Pelajaran Selangor

t9 3472t2

[3 marks]13 markahl

(b) Calculate the composite index for the cost of these models in the year 2007based on the year 2006. [3 marks]

Hitung indel$ gubahan bagi kos mernbina model ini pada tahun 2007 berasaskan tahun 2006.13 marknhl

(") The composite index for the cost of making these models increases by 30olo fiom the year2007 to the year 2009.

Indela gubahan bagi kos membina model ini meningkat 30o/o dari tahun 2007 ke tahun 2009.

CalculateHitung

(i) the composite index for the cost ofmaking these models in the year 2009based on the year 2006.

indelcs gubahan bagi kos membina model-model ini pada tahun 2009 berdasarkan nhun 2006.

(ii) the cost of building these models in the year 2009 if its conesponding cost in theyear 2006 is RM45.

kos membina model-model ini pada tohun 2009 jika kosnya sepadan pada tahun 2006 iaitu RM45.

[a marks][4 markah]

sul,fr

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ST'LIT 20

INTORMATION FOR CAI\DIDATESMAKLUMAT UNTAK CALON

3472t2

1. This question paper consists of three sections: Section A, Section B and Section C.Kertas soalan ini mengandungi tiga bahagian: Rahagian A,BahtgiznB dan Bahsgian C.

2. Answer all questions in Section A, four questions from Section B and two questions fromSection C.

Jawab semta soalan dalam Bfizgiat A, emp t soalan daipada Bahegian B dan dtua soalandaripada Bahzgirn C.

3. Show your working. It may help you to get marks.

Tunjul*an hngknh-langkah penting dalam kerja mengira anda. Ini boleh membanht qnda untuk mendapatknnmarknh.

4, The diagrams in the questions are not drawn to scale unless stated.Rajah yang uengiringi soalan tidak dilukis mengihlt skala kecuali dinyankan.

5. The marks allocated for each question aDd sub-part ofa question are shown in brackets.Marknh yang diperuntukkan bagi setiap soolan atau ceraian soalat ditunjukkan dalam kurungan.

6. A list of formulae is provided on pages 3 to 5.Satu senarai rumus disediakan di halaman 3 hingga 5 .

7. Four-figure mathematical tables are allowed.Sifr matematik enpat angka dibenarkan.

t. You may use a non-progammable scientific calculator.Anda dibenarkan menggunakan ktlhrlator saintifik yang tidak boleh diprogram.

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