mmk2pkbs2f2kel2011

5012

Matemat ikKertas 2M e i 2 0 1 1I jam 45 min i t

NO KAD PENGENALAN

Narna Pela.;ar

Tingkatan

N{AJLIS PENGETUA SEKOLAH NTALAYSIA (MPSM)

CAWANGAN KE,LANTAN

MODUL 2TTNGKATAN 2 (20rr )

MATEMATIKKERTAS 2

Masa : Satu Jam Empat Pr"rluh Lirna Minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Arahan:

Tuliskttn nun'tLt dan tingktttrut untlct

purlu ntun g .r'un g disediakan.

Kertus soulctn ini utlulcth dalttrn

clv' ibultusu.Soulun dulum Baltusct Inggeris

menrluhului soulttn .vuttg sepudun dulunt

Bahusct lvleluur.

Calon clibenurkun nteni ctwalt

keselunthun atau sebuhctgitut s ouktn

samo adu clalunt Bultusu Inggeris utcttt

Bahusa Melctvu.

Culon dikehentluki memhucu ttrnhan

cli hulumun belctfumg.

Psr rc r i ksa

S o a l a nMrrkahP c r t u l r

N4 alkah

D i p e r o l c h i

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6 37 l

It) _')l 0 ,4

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. lun i la l i ( ) l i

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Kertas soalan ini mengandr-rngi 20 halarnan bercetak.

I Lihat Sebelah

( 2 )

I\,I A'I' I I I., N,I A'I' I CA I, F'0 ITNT TJ I,r\ IiRUIVUS NTAT'I'NIA'I IK

50 t2

I

2

aJ

4

5

Ttrc t 'o l lorv ing fot ' t t t r t lac r t tay hc [ rc: lpt ' t r l i r l ansr, l 'cr ing thc

arc c()rnnrOnly usccl .

Rttr t t t t .s runtu. \ ' hcr ikut bt t I rh nt t : r r tbuntu rut t lA nu:njuwult

dibc.ri adoloh )'ettg lsittsct dig,ttnakart-

RIiI ,ATIONSPIJRKAITAN

( lL tcs t ions . ' [ ' l i c sy r r lbo ls g ivcn

,soalr t r r . Sintbol -s imbol \ t ( tng

g1 ' ' x t / ' = , r t t t+s1

u ' ' + c t n - ( l n t - n

ktnr) , , = gt t t r t

Distance I Jarok

Midpoint I 7 ' i t ik

( v+ - r ,( . r ,Y )= l - ; -

tengctlr

1'1 * f'"., ), - - l

) l /

Average spccd = diltanc-e ]1"9[4t imc taken

Ptrrttttt laiu = ###::::::#

st t t t t o l ' dat i tv l can ='

t t t tmbc r o f da . t a

hu.s i l turnbuh n i lu i dutuMirt -

h i lu tgurr dutu

Pythagoras ' l ' l t co rcm / ' [ ' ( ( ) rL ' t t t l ' i t l tuqorus

c 2 = d + b t

MODUL SOALAN 2. MATEMATIK KERIAS 2 (TII. . IGKATAN 2) I Lihat Sebelah

( 3 ) 5A l2

SHAPES AND SPACERI . :N 'TUK DAN RUANG

I i \ r ' c i t o f rcc tang lc = l c l rS , th x rv id th

Lrt t t .s . :e,qi er t tytul l (pul = 1tr t t t . iur t14 x lebur

I2 A r c a t t f t r i a n g l c =

; x b a s c x h c i g h t

ILutts segi t i14u = ; x tuPak x t ingg, i

L

3 A r c l o t ' p a r i t l l c l o g r a m = b a s c x h e i g h t

Lt t t t .s ,s 'egi empul 'selar i = tupuk x t inggi

I4 A r . c a t t t ' r r a p e z . i u m =

; x s u m o l ' p a r a l l e l s i d e s x h e i g h t

II . t r t ts t rupezium = ; x husi l tumbah dua sis i selur i x t inggi

5 C i rcu tn fe rcnce o f c i rc le = n t l = 2n r

I . i l i t u r t b u l a l u n = n d = 2 n j

6 Arca t l t ' c i rc lc = f i r )

l .uus bu lu tu r t =n j '

1 Curved sur face area o f cy l inder = 2nrh

Ltt t ts permukaan melengkung si l inder = 2nj t

8 Surface area of sPhcrc = 4n rz

I . t tus perrnukctt tn sJeru = 4ni '

g \ /o lume o f r igh t p r ism = c ross sec t iona l a rea x length

Isi padu prismu tegak = luas keratQtt renlas x panjang

l0 Volunre of cuboic l = lcngth x width x height

Lti lxulu kubttitl = ponialtg x lebar x tinggi

I I V o l u m e o f c Y l i n d c r ' = f t r l h

Lsi lsulu . t i l inder = x i ) t

I1 2 V o l u n r e o f c o n e - q n i l t

ILs i pudu kon = 1nj ' r

J

MODUL SOALAN 2. MATEMATIK KERTAS 2 (TINGMTAN 2) ILihat Sebelah

( 4 )

4t3 Vo lume o f sJ lhc rc -

J n r '

,1

lsi pudu s.f'eru = 7 nj'-)

I14 Vo lunre o f r i gh t py runr id =

I x buse a rea x he igh t

IIsi pudu pirumid teguk =

I x luus tapuk x tinggi

15 Sum o l ' i n te r i r . r r ang lcs o f a po lygon = (u -Z ) x 180"

I lusit tumbuh sudut peclulumun pol igon = 0,-Z) x l80o

Arc length Angle subtended at centre

Circumfcrencc 360"

Iyrylg Ir!E!"k * Sudut pu.scttLilitctn bulaten 360"

Area of sector Anglc subtended at centre

Area of circle

I.uas sektor

t 6

= PA'

PA

50 t2

t7360"

Lua.r bulatan

l8 Sca lc fac to r /

_ Sudut pusat

360"

F'aktor skala, k

19 Area of image = kr x arca of object

Lttus imej - k2 x luus ohjek

MODUL SOALAN 2. MATEMATIK KERTAS 2 (TINGKATAN 2) IL ihat Sebelah

Calculate the value of 62 -

I-litungkan nilai hagi 62 -

(s)Answer all questions.Jawab semua soalan.

5 ( 4 5 * 9 )

5 ( 4 5 * 9 )12 mqrks l

12 mqrkahl

50t2

Ansrver I Jawupan:

Calculate the value of

decimal.

Kirakan nilai hugi.

sebagui perpuluhan.

7 . 5 x ( _ 0 . 3 )

7 .5 x (

and express the answer as a

dan ungkapkan i awaPannYa

[3 mark';l

13 markahl

I

Ltr

4) -

5

Answer Llawapan:

2

I r-l

MODUL SOALAN 2 - MATEMATIK KERTAS 2 (TINGKATAN 2) IL ihat Sebelah

3

I t-,1

( 6 )

3 (a) Find the value of :Cari nilai bagi :

i/m3

(b) Calculate the value of:

Hitung nilai hagi:

_ 1 6 _ 3 @

Answer /Jawapan:

(a)

50t2

13 marksl13 mqrkshl

(b)

MODUL SOALAN 2. MATEMATIK KERTAS 2 (TINGKATAN 2) I Lihat Sebelah

( 7 )

' l '11c lgrrv 's. iourne1, f rorrr IJut tenl 'or1lr t t> Kuala l .u l r tpur t tor t la l l l ' takes 4

ficlurs 20 ntinutcs.'fhe krrry leaves Buttcrr,r 'orth at 10.45 a.nr and arrir"es at

Kuala l-unrpur l5 rninr-rtes earlier. At w'hat t ittre. in the 24-hor-rr systcm docs

thc lorry arrive in Kuala Lumpur'/

I'erialunun s'ebutth lori tlari Butlcrv'tvll't kc Kuulu I'umpur hia's'unyu

mengamhil ntusu salamu 1 .jam 20 minit. Lori lcrsehut bertrtlak tluri

Buuervrot'th pudu ltukul 10.45 u.m tlun l ihu di Kuultt Luntpur l5 rninit lebilt

utlctl doriputlu hiasu. I'ttkul herupukuh lori lersehttl tibu cli Kuulct Luntpur,

dul unr .s i.s tam 2 1 -i un.

12 murk,s'l[2 murkull

Ansrver l, luv'ulttut:

David was paid I {M l5 000 conr issior l tbr scl l ing a piccc o1' lanci

l {1\4500 000. Calculate thc pcrccntagc o[- th is comission.

Dtn,itJ clibul:or ItMl5 000 sebctgcri komisart karana hcrju.,-tt maniuul selc:pu's

rttt:ttittu[ ,sekcpirtg lqnuh .yong hcrhurgu IlM500 000 Kirukun perutus

kontiscn yLttx diterimu oleh Dctvid .

l2 murksl12 rnurkuhl

\rrsr.ver l .luv,ttltcttt:

MODUL SOALAN 2. MATEMATIK KERTAS 2 (TINGKATAN 2)

IiIl

I

l

5012

at

5

f-=i l ' r I

l l " l

http : / /sci:q. b logspot. com

I Lihat Sebelah

(8 ) s0 t2

f)urirrg end of ycar sale , an electric shop oll 'ers a 20 9'o discount fbr all

i tems. Calculate the price of the television set which normally sells for

RM 2000 belbre discount .

Semu,s'a jualan akhir tahun , .s'cbuah kcdai elektrik menuruut'kan polttttgctn

20 % bugi semuu barungun . Kirukan hargu s'ebuah sel televi.\ycn t,ang

selalunya dijual pudu hergu RM 2000 .sebclum potongan.

13 murlcrl13 murkahl

Ansr.ver I Juwupun:

6

l-;ll'l

3Sirrrpl i ly 2 ( ; p

z2 q ) ?(q - p)

2 q ) - 2 ( q - p )3

l'ermuduhkun Z (t p

7

r-=i_r_l

Arrswer lJav,upun:


[2 murks]12 martuhl

http : //sci -q . blogspot.com

I Lihat Sebelah

(e)

l2 marksl

[2 markah]

13 marksl[3 markah]

50t2

List all the llaotors of 70 and state the number of primc f-actors.

Senaraikun semua .f aktor bagi 70 dan nyatakan bilungun./itktor perdctnct

Answ,er Llaw,apan'.

A bird is f lying at a height of 7 m above the sea level. It sees a fish 3 n-r

below the surface of the sea. [t prcpares itsell'to catch the fish by lowering

its position lor 2 m. What is the distance between the bird and thc tish 'l

Seekor burung terbang pada kelinggiun 7 rn di atas pernrukacrn laut. Ia

terlihat seekor ikun pada paras 3 rn di hutvah permukaan laut. [a hersiap

sedia untuk menunglanp ilun tersebut dengan merenduh.kan kedudukannya

kepada 2 m. Berapakah iarak antara burung dan ikan tersebut.

8r-:I l r ll l " l

Answer I . lawapan'.

MODUL SOALAN 2 - MATEMATIK KERTAS 2 (TINGKATAN 2)

9

l-=ll'l

http : / /sci-q . blogspot. com

I Lihat Sebelah

l 0

t_rl

( l 0 ) 50 t2

10 Solve each of the following equations.Sele saiknn t iapt iap pers amoan ber ikut.

( a ) m : - 1 8 - m

(b) 2k= ryl+ ;,;;rfrfrs]

[4 marluh]Answer I Jawapan :

(a)


(b)

http : / /sci:q. b logspot. com

[ l , ihat Sebelah

( i i v e n t h a t u : hDihcri buhuv'u a

: 5 : 8h . : 5

( 1 1 )

irnd b -- u : 60, f ind the value ol h.

.8 clan h u - 60, cqri nilui hugi h-

her,vuma retkctn-6. .liku Ilunttni

13 marksll3 rnurkuh)

5012

Answer Llcrwapan' .

I,lanani bought a computer and she shared the cost witlr her room-tttates,

Aini and Syira in the rat io 5 :4:6. I f I lanani paid RM450. f ind the cost o[

the cotnputer.

l 1

t-;]I l ' i

t2

Hanani membeli ,sebuuh komputer clan kosnyct dikongsi

rukqn sebiliknl'u, Aini dun Sf ivar dolant nisbah 5 : 4 :

ntemhuycrr ,sehctnyclk RM450, cari kos komputeT tersebut.

Answer Ll tnt ,upun:


t 2

r-=I l " l

l l . ' l

[3 marks]

13 merkuhl

http : #sci -q . blogspot.com

I Lihat Selrelah

13

r-_lL_II

Diagram IRaiah 1

In Diagram I , PQR is a straight line. Find the value of x andy.

I)alam Rajah I , PQR ialah garis lurus. Cari nilai x dan y.

Answer I Jawapan:

50 t2

[4 marksl

[4 markah)

MODUL SOALAN 2 - MATEMATIK KERTAS 2 (TINGKATAN 2)

( 12 )

l 3

http :/lsci-q . blogspot.com

I Lihat Sebelah

( l 3 )

Diagram 2 shows a cuboid shaped container rvhich is {i l led with 524 cm3

of'water.

Rcriuh 2 menunjukkun sebuah bekus' bcrhentuk kuboitl ),ung leluh diisi

dcngun 524 cmt uir.

l5 cr r r

6 e m

l 0 cnr

[) iagram 2Ruiah 2

Calculate tfte yglume. in cmt, of watcr necdcd to fl l l up thc cclntainer.

Hitung isipudu uir, dalam cm!, yung diperlukan unluk memenuhkun hefutS

ittt.

[3 rnurksl13 murkuhl

Answer I .luw^crpctn'.

i 4


50t2

1 4

r-;l l ' l

l 5

[Hl l l


1 5

( 1 4 )

Solve each of the following equation :Selesaiksn setiap persamaan berikut :

ct ) + :3h

, \ r - 7 2 + rD ) 4 : 5

Answer I Jcwapan :

(a)

5012

[4 mark.s][4 markah]

(b)

( l s )

C

1 5 c m12 cnr

A E T }

Diagram 3Raiah 3

Diagram 3 shows a rectangle ABCD and AE : F,B. Calculatc the area

of the rectangle.

Rujah 3 menun_iukkan segiempal ABCD segiempat tepat dun AE : EB.

Kirakon luas segiempat teput tersebut-[3 marks]

[3 nrtrtuh]

Answerl/av,apan :

D

MODUL SOALAN 2 - MATEMATIK KERTAS 2 (TINGKATAN 2) I Lihat Sebelalt

5012

1 6

r--=I l ' i ll l " l

( 1 6 )

l 5 c m

. f 6 c m L

Diagranr 4Ruiah 4

Diagranr 4 shows a rectangle KLMN and a right angled triangle JLM.Find the area of the shaded region.

Rajah 4 menuniukkan segiempat tepat KLMN tlan ^;egitiga ber.sttclultegak JLM. Cari luas kawasan yung herkrck.

14 murlcll14 markahl

Answer / ,Iawupan:

50t2

t7

t7

I r;l

MODUL SOALAN 2 - MATEMATIK KERTAS 2 (TINGKATAN 2) I Lihat Sebelah

( 17 )

1 8

Diagram 5Ilujah 5

Diagram 5 shows a square ABFG and rectangle BCDE. F is the midpointof BE. Calculate the perimeter of the whole diagram.

Rajah 5 menunjuklun segiempat sama ABFG dan segiempat lepul BCDti.F ialah titik tengah bagi BE. Kirakan perimeter hagi seluruh raiah.

[3 marl<s]

13 murkuhl

Answer I Jawapan:

MODUL SOALAN 2 . MATEMATIK KERTAS 2 (TINGKATAN 2)

http : / lsci-q . blogspot.com

I Lihat Sebelah

50 t2

1 8

i--=L_TJ

l 9

[_;

ll-l


t 9

( 18 ) s0 t2

A stadiunr is built o1 a piecc o{'vacant land in the shape of a trapeziunt

as in Diagram 6. The staciium measures 75 m long and24 m wide'

Sebuuh :;tcuJium dihirut di utu.s .sckeping lctnuh yung bcrhentuk trapczium

seperti clalum Ra.iah 6. StatJium ter.Eebut berukuran 75m puniung dun

24m lebctr.

70m

210m

Diagram 6Raiah 6

Calculate thc arca of the remaining land.

Kira luus kswasun tanuh yung selebihnya-

[4 murks)

14 markahl

Answer Llmvapan:

75 nt

r------l| ,'roo,..," I z+ '"

( l e )

consruct z PQR = 1200

Bina z PQR: l20o

Answer Llawapan :

END OF QUESTION PAPERKERTAS SOALAN TAMAT

[3 marks][3 markah]

MODUL SOALAN 2 . MATEMATIK KERTAS 2 (TINGKATAN 2) [ l,ihat Sebelah

5A l2

20

lri

mmk2pkbs2f2kel2011

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