# TRIAL MATE SPM Melaka 2011 Paper 1+2+Answer

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• 8/4/2019 TRIAL MATE SPM Melaka 2011 Paper 1+2+Answer

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.,~-:: ....... _ :, .... '

SULIT 1 '449111 4 4 9 / 1MathematicsPaperI20ll1 '1- jam4

MAJLIS PENGETUA SEKOLAH MALAYSIACAWANGAN MELAKA

PEPERIKSAAN PERCUBAANTINGKATAN LIMATAHUN 2011

MATHEMATICSK ertas I

Satujam lima belas minit

JA NGAN BUKA KER TA S SOALAN lN l SEH INGG ~ D IBERITAHUI. K ertas so alan in i ad alah d alam dwib ahasa.2 . S oalan d alam B ahasa In gg eris mendahulu i s oa la n y ang s ep ad an d al am Bah as a Me la yu ,3 . K erta s so ala nin i m en ga ndu ngi 4 0. soalan,4 . law ab sem ua soalan,5 . Jaw ab sem ua so alan d en gan m cn gb ,tam kan ruanganyangbetul pada kertasjawapanobjektif6. Ritamkan satu ruangan sahaja bagi setiapsoalan,7 . R ajah yan g m en girin gi so alan tid ak d iluk ism en gik ut sk ala k ecuali d in yatak an .

8 . Satu sen arai rumus d ised iak an d i halam an 2cffin ,J.9 . A nd a d ib en ark an m en ggun ak an k alk ulato r sain tiflk yan g tid ak b oleh d ipro gram kan .

Ker tas s oal an in i menga ndungi 2 0 h alaman b er ceta k,

i449Jl (12 01 1 U aK C ip l3: M PSM C aw aR giin M elak a [Lihat halaman sebelah. SULIT

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SULIT 2 , 1 4 4 9 1 1MATHEMATICAL FORMULAE

The.following formulae m ay be h e l p f u l i n a n sw e ri ng the questions. The symbolsg~en,~ theon es com m on ly used; , ,R.LATIONS

.;'.

3 (a"'Y'=a-, "',,0

4

"

P(A)= ~~;P (A I) :: r-peA) - '-

. .- '~.-.'r ~ -. .'"'6

'I,:.!. ~, '~ . . :. : .

7 Distance= J(X2 -'Xtl1t ( j j ; 7 Y ; ~ 1 ~ ' . ' _ . ' \ . ;',"r' -,~J;." ";..::~; : . ~ ~ ; ' : : : ' . : . ; : ~ ~ : : , : ; " > i l ~ ? l ~ : ~ '. :. . ~ . : ,. . .. . ' - :-- ...~.- ... ,"""'"

9 Average speed = di~ce tmvel!ed.". ,.t lmetiken . . . . . . ,:... ",/10 sum of data ,Mean = . . . . .nuniberofda~:'

':":,:

12 Pythagoras Theorem .c1 =a1 +b1 '

13 m= Y 2 -YIX1 ....X 1

14 _ y . . . ; interceptm - - ..._ _----......_x - intercept

[Libat halaman sebelab _ , - - : C oSULIT

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'SPLIT 3SHAPES AND SPAC E

2Area o f tr ap ez ium = 1 . x sum of parall el sid es x h eight2 _C irc um fer en ce o f c ir cl e = 7 T d = 21(r

3 Ateaof circle = tr,'4 ';Cu rv ed a re ao f c yl in d er =2 J r r h5 Surface area of sphere - 4trr 26 Volume ofr ig lt tp ri sm = cro ss sectio nal area x len gth

7 Volume ofcYlinder=trr2

h8 , 1 2Vohune of cone = ' 3 tr r h9 4Vo lum e o f sphere = ...,.1l,.3, 310 V olurneofrightpyramid::!x basearea x height3 '11 Sum of in terio r an gles o f a polygon = ( n - 2 ) x I S O C '12 arc length angle subtended at centrec ir cumfe rence o f c ir cl e = 36013 area of sec tor = angle subtended at centrearea of circle 360"14 Sca le fac to r ; k =15 Area of image :: J ? - x ar ea o f o bje ct

1 4 4 9 1 1 e 2011 Hat CipCa MPSM Cawanpn Melaka

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SULIT 4 144911

1 Round off 3.108 correct to three significant figures.Bunda r kan 3. t08 hem! k epa da rig a tm g ka be re ni .A 3.10B 3.11C 3.100D 3.110

"

GIven that 3760 OOO'!::m x 1 0 ' \ where m x Hf is a number in standard form. S ta te th evalue of m and of n ,Diberi bahawa3 760 000 ",,'m x 10" , d J mana m x 1(f lolah satu nambor dalam benfuk piawa i .Nyal i lkan n ila i m da n n ila i n ,A m = 3.76 n = - 6B m =3.76 .n =: 6C m=37.6,n=-6D m= 37.6 ,n= 6

3 93 X 1014 - 45 X 1013 =A 8 85xl014B 4S0xlO'4C g8SxlO'lD 4g0xl013

0.0084 =600000A 1 .4 X to-8B ' , 81 .4 X 10C 1.4 X 10-2D 1 .4 x 102

5 Express 8(82 + 5) as a number in base eightN y a t a J c a n 8(82 + S) se ba ga i sa lu n om bor da Ja m a sa s lapan:A 5010,B SOOtsC 10508D 10058

l449 ft C 201 1 Hak C ip ta MP SM Cawangan Melab [Libat baJaman sebelahSULIT

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SULlT 5

A 10110112B 1 1 01 lObC 11O l11~D 110.11112

7 In Diagram 1 , RST is a s tr aig ht l in e.DaJam Rajah l,RST ioJah Jotu go ri J I ur u s. .

R

T

p Diagram 1R4}ah 1

Find the value of m .C arl n lla i m .A 56B 66C 76D 86

144911 e 20 I J H ak C ip ta MPSM c a w a n p n Mdaka

. :~!

[Libat bala,JD',~sebela., SUL IT

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SULIT 6 1449 /1

8 .In Diagram 2, PQRSI'isa regular pentagon and PQUi s a s tr aig ht lin e.Do /am RDjah 2. PQRS ! ' ialah s eb tm h p en ta g on s ek ala dtm !Q U la/ok mtuga r i s Iunu .

:-...

Dia~2Ro j o h2Find the value of x +y Ca rl n iT a lx +y,A 36B 72C 108D 144

9 In Diagram 3 , PQR isa tan gen t to the circle at po in t Q ..QST i s an iso sce le s mangl e.D ala m R qJa h 3 .PQ R / Q / a h la ng en k epa da bulm an dI lillk Q.QST la la h se gi tlg o lama ka/d.. .,,-.

D iagr am 3Rt{Jah3

Find the value of x,C a rl n ila i s.A 51B 57C 60D 61

1 44 91 1 C 2 01 1 kat Cipca MPSM Cawanpn MdakI [Lihllt baiamaD sebelabSULIT

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SULIT 7

10 In Diagram. 4 , point P undergoes a c lo ckwise Fotation'of9{f;abOut'ceith:e'l;'2;;,ti)~D o /a m R aja h 4,IitikP meta 'u; pUlaran 90D ikUiarizhjanrjJadtijw4C(.,;,2;1).," .v . .

~~.p "-_A '.~. . . ." "..

.~. .5 4 3 2 U 4 _ ! c ..-,- ,

t-.J. . . , .

x

D iagram 4Rqjah4The co or din ate s o f the im age of point P un der that rotation isK oordin a: ba g; im ej P e li b aw a h p uta ra n (e rS eh ul ia la hA (-2, - 5)B (-5, - 2)C (I; 4)D (4, 1)

11 Diagram .5 shows fiv e pen tagon s < , P, A, B, C and D drawn on square grids.Ra jah 5 menun j u k k a n l ima p en t a g on , P , A. B . C dan D y a n g di lul iJspatio g r i d s eg i e m pa t s om a .

. . . . . . . . ~ . . . . . . . . ~A B. . . . . . . . . . r - ; ; ; . .P

I"""-~ r- . . . . . . . .D (Diagram 5Ra j a hS

( _ 2 4 ) ' ?hich of the pentagon, At B, C or D is the image off under a translationA n/o ra p en ta g on A. B, C a la uD , y an g m an ak a h m e ru po ka n lm e ] ba g l pen tagon P d i bawah SUQ/ulran/asl( _ ~ }

1449 / 1 e 20 1 1 l in k C ipta MPSM Ca.w an ga n M el ak a [Libat halaman sebelabS U L I T

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SUL JT 8 . 1 . 4 4 9 / 112 Diagram 6 show s the graph of y = cosx fo r OO ':sx :s 360 .

Ra j ah 6 m en wY uk ka n g rtJf y :t .koJ;c bogJ 0 0 = = ;c : 5 3 6 < f .y

0 .8660

T he value of P isN lla J P l a J a hA 1500B 210C 3000D 330

. Diagram 6Rojah6

13 In D iagram 7, point P an d point Q lie on th e a rc o f a unit circle w ith centre O.D o /a m R aja h 7 tilJk P da n mit Q terletak ill a im /e ng kg k m a tu b uJa ta nW ilI berpllSat 0 .y

Diagram 7Ra j ah 7.. . ,

F in d the v alu e o f cosxo + sin y O .Carl l ' I i /ai kos~ + sin",'A 0.91B 1 .16C 1.51D 1 .76

[Lihat haiamaa'sebeiahSULIT

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SULIT 9 144911I 4 Diagram 8 show s a c ub oid w ith r ectan gl e PQRS as its h oriz on tal b ase. P oin ts L , Man d N are th e m id po in ts o f PQ , W V an d TU respectively.

R a ja h 8 m en un ju kJu i:n s eb ua h k ub oid d en ga n s eg ie m pa t 12pa1 PQR S s eb ag a i lapaknya . Tlt lk L , M danN lalah l il ik l e n gah bagi PQ. WV dan TV masing- -mas ing .

Diagram 8R ajah 8

Name the angle b etw een th e plane TUL an d the plane TUVW ,Nama k a n sudutamara sa la h iU L denga n salah TUVW ,A LIMNB LLNMC LTLSD LULR

15 In D iag ram 9 , PQRa n d TU are tw o vertical p oles o n a h oriz on tal p lan e.D a la m R aja h 9, PQ R dan TV ada lah duo liang t egak d J a la s sa la h m en gufok .

p1 8mDiagram 9Ra jah 9

The an gle of dep re ss io n o f p oin t T from p oin t P is 35 .Calculate the d istan ce, in m , b etw een the tw o vertical poles.SuduZlUnduk tltlk T da rilitik P ia la h 35.Hi tung j a r a k ; da lam m , d i a m a r a d uo lia ng le ga k ltu.

u R

A 9.77B 11 .43C 12.32D 13.95

1 449 /J C 20 II H alt C ipta M PSM C aW '.m g.anMelaka. [L ihat .ba Ia man 'sebe iabSULIT

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SlILIT 10 1449 / 116 In Diagram 10, JK an d M N are tw o vertical poles on a horizontal land . The angle ofel ev atio n o f K from N is 41' ,

D a la m R aja h )0. JK da n M N la ta h dua baJang liang tegoA ya ng lerleli1k p ad a s ua tu I CUK ihm e n gu ju k.S utiu l dQ nga k K da r i Nialtih 47 "

6mJ 20m

D iagram 1 0Rajah )0

C alculate the height, in m , of po le JK.Hi tung k an l i ngg/ . d a l amm . liangJK.A 19 .64'8 20.63C 24.65D 27.45

17 In Diagram II,M. Nand K are three po in ts o n a ho riz on tal plan e.D a la m R iJ ja h 11 , M , N dan K. i aI a h I lg a lilit pada sua tu Salah mengu f u k .

NorthK

ND iagram 1 1Ra jah 11

T he bearin g of Nfrom XisBea ,.in g N da r; K ia la h

A 024B 134C 204D 244

1449 /1 C 2011 Hak C ipu M PS M Cawanpn M e J a k a [LihBt balamaD sebelabSULIT

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SULIT 11 1 4 4 9 / 118 In Diagram 12, P an d R are tw o points o n the surface o f th e e ar th , N is the N orth Po le, Sis the South Pole and N OS is the ax is o f the earth.

Do /am Ra j ah 12, P dan R a da /a n duo litik di 01(13 permukaan bl lmi . U la /a h K llt uh Utara; S [a /ah KutubSe kua n da n N OS ia lahpalcJ l hi lmi .

,."._..-~~~- , . . .

I

EquatorKhalUl is t iwa

SD iagram 1 2

Ra j a h 1 2

P R is the diam eter of perallel o f l atitu de o f 42 S;P R ia Ja h d iameter b ag ; s ela ria nla litu d 4 t'S.F in d the lo catio n o f po in t P.Ca r l k e d ud u ka n fflJl, P .A ( 4 2 8, 4~W/B)B ( 4 2 8, 4' f1E1T)C ( 4 2 8, 133ElT)D (428 , 13 3W 1 8 )

19 11 m2-(3m-li =A 1-6m-2"rB 1 + 6m-2m2C 2m2-6m+ ID 2m2+6m-l

1449 / 1 eWI j Hak C ip 1a MPSM CaWanpn Melaka [Lihat halamaD sei>elahSULIT

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SULIT 12 1449 /1

20 E pl +3 2 - P . ~ .... 1 ~xpress - - as asiegle traction In itssimp est rorm,3p pp2+3 2-pUngkapk an 3 - -- s e b ag a ; p e ca h a n tunggal d ala m b en tu k l e r endah .p .p

A p 2 +3p-33pB p'1 .- f r .3p-63pC pl + p-6pD p2+3p_2P

"1 0' til 3h h . ft tven . at g =_.-, express In tenns 0 g.2-hDibe r t g = 2!!_ , ung kapk an h do/am s e i n a an g ,2-h .

A h= g2B h=3g2C h = - . 3 . L3+gD h;=2.L2-g

2 2 G 2 3 5(1-4 p)IVen that p + : :: :'- -- - ...: -;, ,7 find the value of p.

AS{1-4p)Dibert hohawa 2p + 3 = 7 ' cQI 'i k an n i la i p.

817.3B

cS

5175D -8 .

1 4 4 9 1 1 C 2011 HakCipQ MPsM C a w a n g a n Melaka (Libathillam3n sebelahSULIT

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S P L I T23 if-}! =

A m 1B m ;

!D 2'

2 4

A

B

cD

,1 3 l 4 4 9 1 1

~ It is given that 8 +38 < s an d 3r + 1 8 ;:;:r + ~ w here rand sare integers.Find the max imum value of's - r .Diber t bahawa 8 + 3s < s dan 31 '+ 18 ~ r +2, dengan keadoon r da n s Ia la h Integer.Carl n t /a t le rb e sa r bag i s - r . '

A -5B -4C 4D 5

[Liba t ba lamaD"iebe&_sum

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SULIT 1 4 - 1449/1

26 List a ll th e in tege rs x wh ich satis fy bo th th e s imu ltaneou s l in ea r in equa litie s3 x - 4 _ C ! 5 andS - x >~7 .Se na ra ik an se m ua in te ge r x y an g m em ua sk an kedua-dua k e ta k sa m a a n li ne a r s er etu aklx-4:>;SdanS-x>-7.

3,4,5,6,7,8,9,10, IIBCD

-3 1-2. -1,0, 1",2,3,4,5,6, 7 , 7 .9, 10. 11 , 123,4.5 .6, 7.8.9, 10, 11 , 12- ,0- , 1.2,3,4,5,6,67,8,9, 10, 1]

1 .7 Diagram t 3 is a pictogram show ing th e number of shirts sold in a particular sho p o nTuesday and Thursday. The number of shirts sold on W ednesday and Friday are notshown.Ra jah 13 l a lah pilctogram y a n g menun ju k k a n b ila n g an b aju yang t e Jah d i ju aJd i sa lah s ebu ah k ed ai p ad ah a r! S el as a dan K h am ls . B i/a n g a n ba j u yang -d ij u a l pa da h ar t Rabu d on J um a a t lidai. di t l ln juk/wn,

R epresen ts 1 0 shirtsMewak i i i 10 haJu D iagram 1 3

Ra j ah 13

A total of 210 shirts w ere sold overthe four days. The number of shirts sold on Fridayw as tw o third the number of shirts sol d on Thu rsday.H oW man y shirts w ere sold on W ednesday 7 .. l umlah ba juyang d ij ua l d a lam t empoh emp a t har} I tuialah 2 10 h e /til, J um J a h bajll y an g d iju aJ patio ha t ;Ju m aa la da Ja h d uo p e r tig a d ar ip ad aju m la h b ajll d 1j_ ua ipada k ar l K ha m is "Berapakah h ila ng an b aju d lJu af pa da h art R a bu ?A 50B 60C 80D 90

1449/1 e 2 {) 1l H ak C ip ta MPSM Caw anga nMcl uk il [Lihat balamalr sebela-tiSULIT

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SULIT 15 1449 / 1

18 Diagram 14 is a bar chart show in g the n umber o f P ro to n ln spira cars so ld "by a saJesmanfrom July t o Decembe r2010Rq jah l4 k l/a h c ar ta pa la n g yang l 1umunjukkon hi/angan Iwrela Pro to i l / n s pi r a yang dijual o le .h i eorangjtlnl}uol pada OOla n Jl ll aJ h in g g a D i s emb e r 2'010,Number of carsso ld 14Bi /angan k e re ta 1 2d i j u a J 10

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SULIT 16 14491130 W hich graph represents y = x 2 - X - 2 ?

O ro! m a na Aiih y an g m ew a kilf y "" x 2 - X - 2 ?y yA B

~.'l

C y D y-} .t

31 List a n th e su bs ets o f setM;';; fa, P . ' Y } .Se1 ta l'a iJ ca n s emu a s ub set b a gl se t M ; " { a . { : J . 1}.A { C l } . { P}; { y }.B {a}.{p},{y},0.C {a}, { p } .{ ' Y } ,~ a, p } , { a . . , } , { P . ' Y } , { p , c },0 ..D { Cl }, { _ p }I{ ' Y } . { C 1 , ~ } , { C l , " } , { P . '1 }. { a , p . y },0,

32 Given:Universal set ~ = { x: 21 ::::x ::::40, x is in teger } .Set P ::: { x: x is a multiple of 4 }Set Q = { x : x is a multiple of 8 }Which s ta tement is_fal se?Dibert:Set s emena l ';.- { x: 21 :: x : 5 40 , x ia /a h in Teg er }Set P "" { x : x la /o k g a n da a n 4 }s Q= ( x ::r l a l ahgandaan 8 }P en ry ata aa n m 0 1W i.a h y an g po ls u?A Qc PB Pc QC (Pr.Q)=QD (PuQ)=P

- 1 4 4 9 1 1 e 201 1 Hak C ipla M PSM C aw an gan M cIak a [Libat bataman sebelahSULIT

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SULIT 17 1449 / 133 F ind tbe grad ient of the straight line 2y ,.. Sx = 10.

Carl k e c e nma n bag i ga r i s /urus2y - Sol= 10 .5A 225B

cD

34 Diagram 16 shows two straight lines, GH an d HK, o n a C artesian plan e.Ra j ah 1 6 menul! iukkan duo gur fs /urus, GH dan HK. pado suatu s ata h CQ 11 es an .

yK(tO ~8)

D iagram 1 6R q ja J r 1 6

It is given that the grad ien t o f straight lin e aH is 1.an d 2GH;;o HK.. 4Find the y -in te rcep t of the straight line GR .D lb e b a h aw o m : ef'U lla n gwis J U I " i I S G R a da la h _ ! da n 2G H" HK .4Carl pintasan-y bagl gar i s lurw GH.A 3B 4C 6D 8

[Uhat.halamansebelahSPLIT

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SUUT 18 1449 / 135 A bag co ntain s o f 1 20 red and b Jue marb les ..If a m arb le is chosen at random from the

bag. the probability of choosing a blue m arble is ~.8F ind the num ber of red m arbles.Se"uah be g mengandung i 120 biji g uli be rw am a m era h d m J blr J i / u J sebi f i guJi d ip il ih s e co r a Y t lW a kd c ir ip a d a b e g iN i , keborang/ca/ ian r n em i l i h gu/ i be rw a ma biro ~ghi.. - 8Ca r l b i langan gu l l be rwar na me r a h .A 15 '- , > .B 45C 60D 75

36 In a group of 200 students. 44 are from Science stream. 8 Science s t r e a m students werethen tran sfered to an other scho ol,Ifa stud en t is cho sen ran dom ly from the gro up, state the pro bab ility that the stud entcho sen is Dot.from Scie nce s tr eam ..D a /am s ek um pu /a n 200 o ra n g m u ri d. 44 o ra ng a da /a n d a ri a i/r a n SQim . 8 orang tmtI'Jd da r l a li ro n s ain sumudJanny a berpindaJr k e -se lw la h la in . . "Jika se Ol'a ng m urld dJpi/lh se ca ra ra wa k. trya ta ka n k eba ra ng MJ/a n ba ha wa m w id dJpilih bttM If da ria/iran Salm,

A 950

B 316C 39S OD 13-16

1449ne 2 01 Il iil lI .C ip laMP SMCaw an ga n M el ak a [Libat balaman sebelahSULlT

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SULIT 19 _ 1 4 4 9 / 137 Tab le I sho wsso mevaluesofvariab lesP an d Q ,such thatPvariesin verselyasthesquareofQ. .

Find the value of n .JaduaJ Im e nu nju kJu Jn be be ra pa n ila i u ntu k pe m bo le hu ba h P da n Q , de ng an M odoa n P be ruba hse ctirason gsa ng de ng an k ua sa duo Q . - . J , : : . . ;H iru n gk a n n ila i n :

P 3 3. . . .4Q 2 n

Table 1Jadua / l

A 3B 4C 8D 16

'_"._"~_.Y.,.:~_' _.. A:..... . ' ..

38 Itis given that t = k Iwhere k is a constant.H 3

Which statement is true?D i be ri b ah aw a "; = 4 : . Oe f f gan keodoan k a da Ja h f) t,;; aw r .HiP e rn y ar ila n m a n a ka h yang benar?

A G varies d irectJY as the cub e 'o f H.G berobob secara/angsung dengan kuasa t iga H.B G varies directly as the cub e roo t o f H.

G beruba h lecara /a ngsung dengan punca kua sa IIga H . . ',"': '."

C G varies in versely as the cub e o f H.G 'berubah seca ra songsang tknga n kuasa liga H .

D G varies inversely as the cube roo t of H.G be ru ha h s ee ar a s on gs an g d en ga n {JU nc akuasa liga H.

1 44 91 1 C ' 2011 Ha k C ip ta MPSM C.wanpn Melalca [Libat h a 1 a ~ ! l n , . e b e t a t i V ~ , ' _ > : ; ? ; SULtr: : :".. I"

.. . .~. . :. ':" ..

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SULlT 20 14491139 Given:

D ibe ri :(2 4 5) - (y - 2 -1) = 3 (2 2 x )

Find the value o f x and of y.Carl n ila i x d on n ila i y.A y= -,.~ ,x=-2B y= -4' .x = 2C v= 4 .x= 6D y= 4 ~x= 2

( 2 - 6 )A -2-37 -1-B [_22 -1

6)

7 -7

C [ ~ = ~ )S 3

END OF QUESTION PAPER

144M 0 2011 H akC ip Ia ~M C a w a n g a n Mclalca S V L I T

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SULITN.-\ME : , , .

1449/21449 /2MathematicsPaper 220112 I .2 " Jam

FORM: ., , , , .

MAJLIS PENGETUA SEKOLAH MALAYSIACAWA. l \ , fGANMELAKA

PEPERIKSAAN PERCUBAAN TINGKA TAN LIMATAHUN2011

MATHElVlA rICSKertas 2

Dua jam tiga puluh rninit,JANGAN BUKA KERTAS SOALAN Ll\,fISEHINGGA DIBERITAHU

1 . Kertas soalan ini adalah dalam dw ibahasa.2. Soalan dalam bahasa Inggeris mendahului soalan

yang sepadan dalarn b ahasa M elayu,3. C alon dibenarkan m enjaw ab keseluruhan atau

sebahagian soalan sarn a ada dalam bahasa In ggerisa ta u b ah asa M elayu .4 . K ertas so alan in i mengandungi dua b ahagia n:

Babagian A dan Sahagian B.5 . Jawab sernua soalan dalam Bahagian A dan

mana - mana ernpat soalan d a rip ad a Bahagia n B6 . Tulisjaw apan anda pada ruang yang d ised iakan

dalam kertas soalan ini.7. R ajah yan g mengiringi soalan tidak dilukis

mengikut skala kecua li d iny atak an.8 . Satu senarai rumus disediakan d i h al aman

2 d an 3.9. Anda dibenarkan menggunakan kalkulator saintifik

y an g tid ak bo leh d ip rog ra rnkan .

Section Q uestion Full Marksmark obtainedI 32 33 44 ., 45 4

A 6 57 68 59 610 511 712 1213 12

B 14 1215 1216 12

Total

K ertas soaJan ini m engand ungi 26 halarn an bercetak1449f2C'ZOl l Hak Cipta MPSM Cawll lIgan ,Vlelaka [L ihat halam an sebelah

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SULIT 144912MATHEMATICAL FORMULAE

The following fo rm ula e m a y be he lpfu l in a nsw er in g the que stion s, T he sy mbols g ive n a re theO n e s c ommon l y usedRELATIONS

1 011 1 x a" = a '" + "2 am + a " ::::a": "

4 A-I = t . ( d -ab),ad "7be +c5 P(A) = n. (A)n ( S )

peA') = 1 - peA)

7

8 Midpoint. (x , y) ::::X l ~ x 2 , YI ~ Y2 )9 distance travelledAverage speed == time taken ;,

10 sum of dataMean==-----. number o f d ata " ,~1 1 Mean = sum o f (classm ark x frequency)

su m of frequency1 2 Pythagoras Theorem

c2 ='a2 +b2

13 m : :: : Yl - Ylx2- XI

14 . y-interceptm =- -=-----=---x - intercept

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SULIT 3

SHAPE S. AND SPACE

1Are a o f tr ap ez ium ;0= 2 " x sum o f parallel sid es x heigh t2 Ci rcumfer ence o f c ir cl e = 7rd = 2n r3 Area o f c ir cl e = 7rr24 Curved s ur fa ce a re a o f cylinder = 2n rh5 Sur fa ce a re a o f s ph er e = 4 ; o r r26 Vo lume o f rig ht p rism = cross sectio nal area x len gth7 Vo lume o f cy lin de r = ;o r ,2h

8

9- 4 3Volume o f spher e = = -7rr. 3

10 1Volume o f r ig ht pyramid = 3" x base area x height1 J Sum o f in ter io r a ng les o f a p ol yg on =(n - 2) x 1800

12 arc length angle subtended at center=c ir cumfe rence o f c ir cl e 3600

I3 area o f secto r = anglesubtended at centrearea of circle 360 0

14 Scale fac to r . k =PAlF A

is Area o f im ag e = K - x are a o f object

1 4 4 9 1 2 0 20 11 H ak C ip ta MPSM Cewanga n Melaka

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SULIT 4 1449/2

Section A[ 5 2 marks ]

Answer all questions in this section.1 On the graph in the answ er space, shade the region w hich satisfy the three inequalities

y+ x ~ 6, y ~ 2x - 4 and x> 1.Pada ruangjawapan yang disedtakan; lorekkan ran/au yang memuaskan riga ketaksamaany + X 5 6, y;::. 2x - 4" dan x > I " [3 ma r k s ]Answer :

yJ~

-, I- ~.o~ l / y 2x -4~ - IIr. I

~/ -,/ I " . .0 / 2 6~V - ,! y-+ X= 1 6V'1

x

144912e2 01 1 H ak C ip ta M PSM C aw an ga n M el ak a [Lihat halaman sebelahSULIT

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SULIT 5 1 4 4 9 1 22 Diagram 2 in the answer space s how s- a c ub oid . The baseABeD is a ho r izon ta l r e ct ang l e.

Rajah 2 di ruang [awapan menunjukkan sebuah kuboid. Tapak A B e l > ia iah segi empo t tepa! yangm en g u fu k : -(a) In Diagram 2 in the answer. space, mark the angle b etw een p lan e ABB and planeABFE .

Pada Rajah 2 di ruang j awapan ; tandakan suilut di antara sarah ABH dan s a t a h ABFE.(b) H en ce, - calcu late th e an gl e b etw e en p lan e ABH an d p lan e ABFE .

S ete ru sn ya ; h itu ng ka n s ud ia di a nta ra sa ta b ABH dan sa l ah ABFE [3 marh]Answer:(a)

8cm

,;'c 15 emDiagram 2

Rajah 2(b)

3 Using facto risatio n , so lve the fo l low ing quadratic equation :M en gg un ak an pem fa kio ra n, s e le s aik an pe r sa m aa n k ua dra tik : berikut:

I( 2/ - 5) + 1 0 1 = 3Answer : [4marhl

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------------ ---__-

SUL.IT 6 1449121IjI!

4 Calculate the value of p and of q that satisfy the f ol low ing s imu lt aneou s linearequations:H i tu n g n i la i p d an m la l q y an g m e m ua sk an p er sa m aa n lin ea r s er es ta k b er ik ut :1 . ,-p-2q=132

3p + 4q = -2[4 marks ]Answer:

j11ji

1 4 4 9 1 l 020 11 H al C ipta M PSM Cawangan elab [Libat balamaD'Se~labSULIT " .:

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SULIT 7 1 4 4 9 12

5 Diagram 5 show s a so lid formed by jo in ing a hemisphere and a cone. The diameter of thehemisphere is 14 em. The radius ofthe cone is 5 em .Rajah 5 menunjukkan pepe j a l yang terdiri daripada gabungan sebuah hemisfera dengan sebuah kon:Diameter hemisfora flu lalah 14 em. Jejari kan flu ialah 5 em .

Diagram 5R a jah 5 _ 4Given that the vo lume of the comb ined so lid is 928- cnr',21

4D ib er i b ah aw a is ipa du gabungan pepe j a l i 3 ' J J i a l ah 928 - em1. 21

Using 1t = 22 ,calculate the height, in em, of the cone.7 .22 .Menggunakan 1t =-_, kitung linggi, dalam em. kon ltu.7 ,[4 mark s ]

lU 9!l "201 1 Hak. C ipla M PSM C aw an gan M eJaka [Lihat halamansebelahSULIT_

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SULIT 8 1449/2

6 (a) D eterm in e w hether the fo llo win g sen ten ce is a statem en t o r n on -statem en t.T en su ka n s am a ada a ya : br ik ul a da ia h sa tu p ern ya ta an a ta u bukar : pemya l aan .

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SULIT 9 1449/2

7 In Diagram 7, 0 is the o r ig in . Point R !es o n the x -ax is an d point S Iies o n the y-axi s . STi s pa ra l le l to the x-axis and straight line RS is paral le l to stra ight l ine PQ. The equation ofstraightline RS is x + 3y = - 6 . ".Dalam Rajah 1, a ialak asalan: Titik R terletak di atas paksii-x dan titik Sterletak di atas paksi -y . STa da la h se la ri de ng an pa ks i-x da n g ar is lu rus R S a da la h se ia d de ng an g ar is lu rus P Q. P er sa m aa n g ar lslurusRS i a lah x + 3y = - 6. "

y p

R Q(7,1)

D iagr am 7Ra j ah 7

(a) State the equation of the straight line ST .N ya t a k a n persamaan garis luna ST :

,d

(b) Find the equation of the straight line PQ and hence, state its x-intercept,C a ri pe rsa m a an g a ris lu ru s P Q dan s e te r us n y a n y a ia k a n p in ta s a n -x n y a.[6 marks ]Answer:

(a)

(b)

1 4 4 9 12 e 2 0 I I Hak C ip ta MP SM C aw an ga n M c la ka [L i b.a t b aJaman sebelahSULIT.

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SULlT 10 1449/2

8 ' D iagram 8.1 show s seven cards labelled w ith alphabets and numbers in Box A an dBoxB.Rajah 8 .1 menunJukkan lujuh keping kad yang dilabe! dengan huruf dan nombor di dalam Kotak A danKota k B.

[2J[g]I~I~ III~I~[~]Box AKotakA

BoxBKosa k B

D iagram 8 .1R aja h 8 .1

A card is chosen at random from each box.Sekeping kad dipilih secara rawak dart setiap kalak tersebut,(a) Diagram 8.2 in the answ er space show s the incom plete possib le outcomes of the

event.C om plete the possible outcomes in Diagram 8.2.Rajah 8.2, di ruang jawapan menunjukkan kesudahan yang mungkin yang tidak lengkap bag;peristiwa tersebut.Lcngkapkan kesudahan yang mllngkin dalam Rajah 8.2.

(b) Using the complete possible outcomes in D iagram 8.2, find the probability thatM en gg un ak an k esuda ha n ya ng te la h /en gi.a p da lam Ra j ah 8.2, ca ri k eba ra ng ka lia n ba ha wa(1 ) one of the cards is labelled w ith an alphabet and the other labelled w iththe number 4 .

sam kad dilobe ! deng an huru f dan sa tu denga n n om bor 4 .

(ii) bo th card are labelled w ith alphabets.k edua -dua k ad d lla be l den ga n hun!f[ 5 ma r k s ]

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SULIT 11 144912Answer:(a) Box A BoxB Outcomes

Kotak A KolakB J;e\$udtihtm

3~K 3K4R 3R

Q~K4 Q4R QR

A~K AK4 A4R

(b){i)

o

s~~~R

SK84SR

Diagr am 8 :2R a ja h 8 .2

1 44 'Ile 20 I r H a I r . Cipta MPSM Cawan_ganMelab [L ihat b alam ao sehelah .SULIT

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SULIT 1 .2 1449/2

9 Diagram 9 shows sector,MPQ, sector MSTand semicircle PQR with centre M.Rajah 9 menunjukkan sektor MPQ. sekior MST dan semibulaian PQR yang berpusat di M

14cm M R

Using n : = 22 , calculate7

Diagram 9"-. Rajah.9

22 .>D en g a n m en g g u n a k a n x= r+ , h ilun g7(a) the perimeter, in em, of the whole diagram.

per im ete r, da la m e m, s-e lu ruh r a j a h(b) the area, incm2 , of the shaded region.

lu a s, d o/a m cml, k aw a sa n b er lo re k[ 6 mark r ]

(b )

1 ' 4 4 9 1 2 (12011 Hak Cipta MPSM Cawangan MelW [Lihat balaman sebelahSULIT

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SULIT 13 1449n10 Diagram 1 0 show s the d istance- time graph for the journey of Saidah from her house toth e town ofMalacca.

Ra j a h 10 h l e 1 1 1 J ' l i u J : J : a n g ra jja ra J:- m a sn bag i per jaJanan Sa ida h da ti ru ma JlI1 ya k e Ba nda r Me/aka .Dis tance (m)

Ja rak (mJd - - - -- - - -- ~- - - -. - .- - - -- . -- - - --

600,,

" ,I"'--__ __,'_-J~ -':;...':1> Time (mIn)o 8 11 25 M asa (m i'n )D iagram 1 0R a ja h 1 0

(a) Find the length of time, in minutes, that Saidah stops fo r a rest.Cari tempoh mara, dalam minit, Saidah berhenti reba:(b) Ca lcul ate her speed, inms", in th e fir st 8 minutes,

Hitung / a ju 1 1 ) 'O , dalam n/S-I, dalam g m 1 n i t y a ng p etta m a .(0) If the average speed o f the w ho lejo um ey is 25 I D S - I , find the v alue o f d.

Jika lu ju p ur ata u ntu k le s-e htr uh on p er ja /a n a n i ala h 2.5 "'5-1, carl n ila i b ag i d[5 maru]Answer :

(a)

,(b)

(e)

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SULIT 14 144912

1 1 (a) The inverse matrix of ( 4 -3) is _ ! _ ( n 4 3 ). ) -2 m -1 .M atr ik s song sa ng ba gi ( 4 ' - 3 ) i a l ah _ . ! _ ( n 3 )I -2 m .-1 4F in d the v al ue ofm and of n.C ar i n tia i m dan ni tai ' r :

(b) Wr ite th e fo ll ow in g s imul ta neous l in ear e qu atio ns a s matr ix e qu atio n s.T u lis p er sa m o an lin e ar s er en ta k b er ik ut d a /a m ben tuk : pe rsam a a n m a tr ik s . .4 x -3y = 7

;C - 2y =-2Hen ce, usin g matrix meth od , calcu late the v al ue o f x and of ySe te ru sn y a . den gan m en gg un aka n ka edah m atrtk s, h ilun gk an n ila .i x da n n ila i y. (7 ma r k s ]

(b)

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SULIT -rl..J 1449 /2

Section B(4 8 m a rk s]Answer any four questions from this section,

Jawab mana-mana empat sao/an daripada bahagian i n i .12 (a ) Complete Table 12 in the answer space for the equation y = 6 + 2x - Xl by

writing down the values ofy when x'=' -2 and x =1 .Lengkapkan Jadual 12 di ruang jawapan bag) persamaan y = 6 + 2x - x3 dengan menu/is mlai-n i l a i y a pa blla x =-2 da n x =1, [2 m a rk s]

(b) For this part of th e question, use the graph paper provided on page 17.- You mayuse a flex ib le curve rule.Untuk: ceraian soalan ini, gunakan kertas grqf yang disediakan pada halaman 1 7 . Anda bolehmenggunakan pembaris fleksibel.

Using a scale of 2 em to 1 un it on the x-axis and 2 em to 5 units on the j-axls, drawthe graph of y = 6+ 2x - x3 for - 2.5 \$; x \$; 3.5.Menggunakan skala 2 em kepada 1 unit di paksi-x dan 2 em kepada 5 unit pada paks i -y, lulds grafbag! y =6+2x- Xl untuk: -2.5 ~ x:S: 3.5.

[4 m a rk s](c ) From the graph in 12(b), find

D a ri g ra J 12(b), car l(i) th e v al ue ofy when x =- 1 .5

nilai y apabila x =- 1. 5

(ii) th e values ofx wbeny =-7nllai-nilal x apabila y = - 7 _ '. [2 m a rb ](d) Draw a s uita bl e straight l ine on the graph in 12(b) to find all the values of x which

satisfy the equation xJ - 9x - 3=0 for - 2.5 :;;;x ::;;3.5.S tate these v alu es of x.Lukis sotu garis lurus yang sesuai pada graf di 12(b) un tu k : mencari semua nllal x yang memuaskanpe r s amaan Xl - 9 x - 3 ",,0 un tuk -2.5:; x:; 3.5.N ya la iu :J n n i/a i-n .ila i x itu. [4 m a rk s]

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SULIT 16 1449 /2Answer :/a)

x -2.5 -2 -1 0 1 2 2.5 3 35y 16.6 5 6 2 -4.6 - 1 5 -29.9

Tab le 12Jadua/12 .(b) Refe r g ra ph 0.0 page 1 7.

Ru juk graf pada ha la ma n 1 7.

( 1 ' 1 ' ) x= a '.., ii ~ faII I " ' I

(d) x= . ., ... '." , .... ... It ... ,," .. ...... ..

1 4 4 . 9 1 2 tl2(J I [ Bilk C ipl Ml 'SM Cawang a:n Mel.aka [Libat balaman sebelahSULIT

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SULIT 1449/2

14491l e 2 01 1 F la k C ip ta t- .f PSM Cawan ga n Me la ka [Lihat halaman sebelahSULIT

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SULIT 18 1449/2

13 D iagram 1 3.1 show s poin ts Jan d K d raw n on a C artesian plane.Rajah 13.1 menunjukkan titik Jdan titik K dllukis pada suatu saiah.Cartesan.

v8

bK

4

J2

4 -2 0 .I . '- ~ 1 xD iagram 1 3.1

Rajah 13.1(a) Transform ation P is a reflection in the line y =3.

Penjelmaan P ialah satupantulan pada garls y:= 3.Transfo rm ation R is a clo ck wise ro tation of900 ab out th e cen tre J.Penjelmaan R ialah saiu putaran 90" ikut arahjam pada pusa; J

T ransformation T is a translation ( : 3 ) .Penjeimaan T i~lah satu trans/as! ( _ 2 3 ) .State the coo rd inates of the im age o f po in t K under the f o ll owing t ran sfo rma ti ons :Njalakan koordinat lmej bag! sltik K di bawah penjelmaan berikut:

(i) RT(li) PR[4marh]

(ii)

t44911 e 201 1 Hak C ip ll l.MPSM Cawangan Me la ka [L ib at b alam an se bcla hSULJT

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SULIT 19 1 4 4 9 1 2(b) Diagram 13.2 shows three quadrilaterals, ABC D , JK LM and PQLR drawn on a

Ca rte sia n p la ne .Ra j ah 13.2 m en un ju k ka n tig a s is ; e mpa t ABeD, JK LM dan P QLR dilu ld s pada sua tu sa la h C ar te sa n:

o 4 6 8 10 12 xD iagram 1 3.2R ajah 1 3 .2

(i) PQLR is the image of ABCD under the combined transfo rmation V U.Describe in ful l the tran sfo rm atio n :PQLR ia la h im ej ba g i ABeD d i ba wa h g abun ga n pen je lm aa n VU. H u ra ik a n s eJ en g lr a pT I )' ap e n j e lm aan :(a) U(b) V

(ii) It is given that the area of the shaded region PQKJMR is 1 52 cm 2 Calculatethe area, in crn2, of ABeD.Dibert bahawa luas rantau berlorek PQKJMR t a l ah 152 em2, Hitung fum. dalam emz bog iABeD.

[ 8 ma r k s ]Answer:'(i) (a) U: , , ..

(b) V : , , ..

(ii)

J,l,4111lC ! 2011 Ha k cipta MP5M Caw an gan M eJa ka [Lihat balaman sebelahSULIT

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SULIT 20 144912

14 The data in D iagram 1 4 shows th e masses., to the neares t kg. of a group of students.Da t a dalam Ra j ah 14 menu l l j u kJcan j i \$ i rn .betu! kepada kg terdekat, bag ; sdumpulC1Jf pe / a j a r .

3 6 35 42 2 6 18 33 29 4 33 3 24 31 2 8 41 24 1 7 4720 41 35 29 34 38 4 2 2426 20 2 6 3 6 48 2 1 39 3 43 2 2 4 38 49 40 35 40 28

Diagram 14R a ja h 1 4

(a) Based on the da ta , comple te Tab le 1 4 in th e an sw er sp ace.Berda sa rk an da ta ih l.le n gk ap/w n Ja dua J 14 di r u angan jawapan.

[4 mark s ](b ) Based on Tab le 1 4 in (a) , calculate the mean mass of the students.

B er da sa rk an Ja dua l 14 d i (a ), h itun glca n m in a ng ga ra n be ra t ba g; pe la ja l'-p ela ja r,'[ 2 mark s1

(c) By using a scale o f 2 em to 5 kg on the horizon tal ax is an d 2cm to 1 studen t onthe v ertical ax is, d raw a freq uen cy po ly go n fo r the d ata.Dengan m en gg un ak an sk ala 2 em kepada 5 kg pada pa k s ! m engu juk da n 2 e m k epa da 1 pelojarpada paks) m en een ca ng ; luk isk an sa tu po lig on k ek era pa n bag; d a ta t er s eb u t.

[ 5 mar k s ](d ) Based on the frequency po lygon in 1 4(c) , state the number o f studen ts w hosem ass is m ore than 30 kg.

Berdasarkan pa lig all k ek era pa n d i 14{c), nyatokan bilangan pelajaryang berj i s im lebih dar lpadaJOkg.

[1 ma r k s ]

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SULIT

(e)

(d)

21 144912

Class interval Frequency Midpoint16-20

(b)

R efe r g ra ph on page 21.RujuA: graf di halaman 21 .

T ab le 1 4JaduaJ 14

...... : 11 .' ,.. , " " " , , ' O ,

.,~ " " ~ , . '" " ~ ,. : " " 1 1 ; t I 01 ~ .. 1 1 , . ~ 1 1 1 ' . ' " 1"" ' M t

144911e2011 . H a I c C ip ta MPSM Cawangal l Mdab [Lihat h .a laman sebe lahSULIT

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SULIT 2 2 1449 /2Graph for Question 14

. .: .. r + ~ , r I ; , H-H t I + i - H - - *HH+ + " i ;-1+ "r, ; , ~: rf+i ,.: ' : . I ; ; ." '1 - - I ,- r r : t ! : - - L ~ . t : ~ -ti"t"1Tt4. -j- 1: = q : : - + + r . : J I-i++H-i-t- .j+ .i ., i ;~I . 1 : i ' " - - - 1 + . . - ' - H - - - l - . - l"+'I .L __ _, !i 1 I' lin." , I i ~::itr - r , . . J . IU ....._- ' 11_. ' I ,~. l .; .. fr - t :Ttl :i - !+- . __ .t:L .. . 1 t . ! r,:; ;; j 1 I I ~. Ii., , J ! __ ! ._.. 1.J.!"T""n r,. . I j t1: t I l-1T r" I' ~T'H -l - r - + - - - . - . I' ~+ + + + + - -4tH-+..-+H- -i-'++i-~~+ : p . . ." : ; : ' L + - i - - -+1+ H.. .H+:1f . . + 1 = +H- I ++ . .. J . ' - . l '......H-+ TJ-;-~+++i-L ..+tt-i'"ti+~+ ..- - i" '''H - . .. : .. .d- : : ; : : f + ' " ';-"-'-+-- _,__,_-..,. -1+ '~'-~.l---!--- L I - + 1- - -- -!-!-. Hi+t1 - I I: j i ; ~ ~ r ~-1 . :! ; I I . ! 1 ! :. I -! ~ I ..f+ H - ' + ' + + - l+l+l- . ~ ~~!H~H-- I ' + t m . t '" " ~ . ! - ~- F ': T J"-tTi-d-++ . T-!-tH~"-, ..f - , , _ t ' + + + + " f " - - - . . - - + +I-H- ,-:; ,i-I- -_. ' - - - i - - - i + H - - t - -+

. . 1 " " 1 ' " ' +, '+H-

144912 e 2011 F l a k ' C ip taM l>SM Cawan ga n Me la ka [Lihat halaman sebelahSULIT

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SULIT 23, 1 4 4 9 12

15 You are no t allow ed to use graph paper to an swe r th is q ue stio n .Am / a tidak d lbe na rk an m en gg un ak an k er ta s grqf u ntu k m e n ja w a b soa lan tni.(a) Diagram 15(i) shows a solid right prism with rectangular base ABCD on a

horizontal table. BCFGJ is its uniform cross section. The rectangle GH I J isinclined and the rectangle GFEH is horizontal. Al, BJ, C F and D E are verticaledges.R aja h 1 5(1 ) m e nlin juk ka n se bu ah pe pe ja l pr ism a te ga k de ng an ta pa k se gi e m pa t te pa t AB CD d ia l a s m eja ya ng m en gu fu k . BC FGJ ada la h k e r m a n r en ta s s e ra g a m n y a: Se gle mpa t tep at GHIJia lah s a l a h condong da n s eg iem pa t te pa t GFE H i a l ah sa ta h m en gu fu t AI . B J . CF dan D Ea da la h s is i-s is i le ga l

E

A

F

,. . "'~D~~" ',_ .~. _ 6cm2cm

B

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SULIT 24 1 4 4 9 1 2

(b ) A cuboid is removed from the so lid in Diagram 15(i) as show n in D iagram15(ii).Sebua h k ubo id d ik elua rk an da rt pepe jaJ d ala m R aja h 15{i) s ep er ti y an g di tunj l lk fcan da /a m R aja hlS(ii). .

E

I2emA

T

6em/ BDiagram 15(ii)Ra j ah 15(ii)

Draw to fun scale,L u ki s d e ng a n s ic a /a p e n uh ,(i) the plan of the remaining solid,

pe la n ba gi pepe ja l itu , . [4 ma r k s ](ii) the elevation of the remaining solid on a vertical plane parallel to BA asviewed from Y.d on g d lc a n p e pe ja l t tu poria sa l ah t e ga ! y a ng s ela ri d en g an B A s eba g aim a n a d ilih tiJ

dari.[ 5 ma r k s ]

1 449 11 C 20 1 , Hak Cipta MPSM Cawangan Melaka [Llhat halamansebelahSULIT

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SULIT 2 5 1449/2Answer:(b) (i) (ii)

1 4 4 9 1 l C2011 H a l : : Ciptl~ Cawanian MeJak il [Libafhit laman sebelah-'SULIT

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SULIT 26 1 4 4 9 12

16 D (50 oS. 35 W). F(500S , 5 E), G and H are four po in ts on the surface of the earth. D G isthe diameter of the parallel of latitude.D(SffS. 35 B). F(500j~ 5 ti G da n R ialah empat titik pada permukaan bumi. DO ialah diameterselarian Ian tud .(a) State the longitude of G. [2 marks ]

N y a t a k a n Jo ng itu d b ag i a .(b) Ca lc ul ate th e d is ta nc e. in n au tic al m il es , fr om D to F measu red alo ng th e p arallelof latitude. [3 marks]

Hihingjarak, da lam batu TILll/IJka, dor i Dk e F. diukur 1epanjang s e l a r i an kui tud:(c) H l ie s n o rth ofF and the d istance of /IF m easured along the surface of the earthis 51 00 nautical m iles.C alcu late th e latitu de o f H. [4 ma r k s ]if ter leta i : ke u ta ra F da n ja Ta lr . H F d iu ku r s epa ry an g pe rm u ka an bum ; i a la l l 5I 0 0 batu naut ika:

HUl lng la titud H .(d) An aeroplane took off from D and flew due east to F and then flew due north to

H. T he average speed fo r the w ho le flight w as 5 10 k no ts.C alculate the to tal tim e, in hours, tak en for the w hole flight. [3 ma r k s }Sebua h k apa lle rba ng be rle pa s dar; Dd an te rb an g ke a ra h lim ur ke F da n k em ud ia n k e a r ahs aa ra m e nu ju ke H. P lU 'a l a J a j- u k apaJ terbang b a g i /c es e lu ru h an p en e rb a n ga n jill ia/oil 510 bJol .H illln gjum la h m a sa , da la m ja m . ya ng d ia mbi f ba gi l;e se lu ruh an pen erba ng an i1ll.

(b)

(c)

(d)

END OF QUESTION PAPER1 44M C 201 1 H.ak C iPta M PSM C aw an pn M .elak a SULIT

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MAJLIS PENGETUA SEKOLAH MALAYSIACA\VANGAN MELAKA

PEPERIKSAAN PERCUBAAN TINGKATAN 5TAHUN2011

PERATURAN PEMARKAHANMATEMATIKKERTAS 1 1449/1

1 B 1 1 C 21 C 3 1 02 B 1 2 0 2 2 A 32 B3 A 13 0 23 C 33 04 A 1 4 B 24 C , 3 4 . A5 C 1 5 B 2 5 0 3 5 B6 B 16 D 26 A 36 D7 A 17 C 2 7 C 37 B8 C 18 0 28 C 3 8 B9 A 1 9 D 29 C 39 ' B'.10 C 20 A 30 B 40 C

Peraturan in i adalah u ntu k p an du an g uru sah aja. Jika terdapat k esil ap an , sila semak sern ul a d anbetulkan sendiri .

Terima Kasih

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....~

MAJLIS PENGETUA SEKOLAH MALAYSIACAWANGAN MELAKA

PEPERIKSAAN PERCUBAAN TINGKATAN 5TAHUN2011

PERATURAN PEMARKAHANM.ATEMATIK'KERTAS 2 1449/2

Nota:JUMLAH MARKAH (100%) :

K ERTA S 1 (4 0% ) + KERTA S 2 (1 00%). I h M k h (kertasl +kertas2) 100Kese uru an ar a = x

140Peraturan iniadalah untuk panduanguru sahaja. Jika terdapat kesilapan, sila semak semula danbetulkan sendiri

Terima Kasih

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. ,. :~.' MARKAH MAKS IMUM :sAG I KERTAS,INI : . f O O M A R K A HPeraturanPernarkahan Markah

_ "" .

'~ .,... .,-:~

. ~ 1

(~. ~ j:_" X, "' y+x=6

j

y

v'7

~Da5hed linefo r x =1

R . ~ g i ( ) ncorrectlyshaded

1

2

3

a (a)

: 2

1

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, ,

No

(b) 1 _m=--311= --(7) + c3 1 10 'y = --x+-3 31 10O=--x+-3 3

x = 10

1- - 1

111 rr

. 'PeratUran'Pem arkahan . , ftliarkah

1.- 1r- 1

" 1, rr

..

4 p - 4 q =26 @ equivalen t4p = 24 @ eq uivalen tp= 6q= -5

5 , 1 22V c O O e = -x- x 5x 5x h .3 71 4 22 -3 'Vhemisphcre = - x - x - x 72 3 7

, '._,

h=8

6 (a) Statement(b) 2 is a prime number and al l m ultiples o f 5 are m ultip les o f 1 0.(c) If p is a fac to r o f 24, then p is a facto r o f 8~

False.. (c) The exterior angle o f a reg ular p e n u ' : g o r t : w ith 5 sides is

3600 = 720 --5

7 (a) y = -2

1111 4I11

1

1

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~~:~ "

, 2156 or 7182 or 718.67 13 3 .. rr"

'1 0 (a) 3 m in s .~.~;~~' ' ' ' ' -;: ' - .,' .. . ,', 1600 1(b) 8x 60 ' .

5 1 11.25 or - o r 1-4 '4d t(c) = 2.52S'x60 -

", td =3750 ~

60 22 120. 2214+28+14+-x2x-x14+-.x2x-x28 1360 7 360 7388 or 129lor129.33 13 3

8

(b) 120 x 2~ x 142or . u o xz,~ x 28?~r 6 0 x ' 22 X 142360 7 360 7 360 7120 22 120 22 2 60 22 2- x - X 282 - - X - x 14 + - x - x 14360 7 360 7 360 7

Peraturan' PI " ,u l ri

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, -No - P e r a t t l ' r a h - Pemi;~kahan1 1 (a) m = -5, n =-2

(b) G ~ a : ) = ( : 2 )( x ) 1 ( - 2 : 1 : 2 )= -5 -1 ~-/- i= G ) - _ - - -x = = 4, 'Y = 3 ,-

- ( ; ) = ( : ) a s a nswer , d e d u c t 1 mark.ote:12 (a)

13

(b) (i) (a) U: Rotation, 180, about centre (8, 3)Note: (1) Rotation only award 1 mark

(2) Rotation 180, award 2 marks(3) Rotation., centre (8,3), award 2 marks _

I ; 1 ~ ~ I~(I Refer to graph

Uniform scale and axes incorrectdirectionsPlot all points correctly, .Smooth curve _

"Note: lor 2 po in ts w r ongly-p la tt ed , award Lroark,_,andO-ttiark.for graph-.-(c):(i)

(ii)--6 ~ y s,72 . 6 \$x \$ 2 . 7

(d) Line y = = 3 - 7xDraw l i n e . . }/= 3 - 7 xx ~0.45 ~, 3.15 O.!- ~ - v - " ' - ,

(a) (i) (3, 4)Note: (1,2) seen o r marked ,award 1 mark

(ii) (6.0)Note: (6, 6) seen or marked, award 1 mark

'5

__Markah1, 1

2

1, 1

121

111 , 1 _tr22

3

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-v'" ,

.~

I,

No PeratUr.n Pemarkahan H Markah(b) V: Enlargement with scale factor =3. centre L 3

Note: I. Enlargement with scale factor = 3 only @ Enlargement atcentre! award 2marks2. Enlargement only award 1 mark(ii) 32 (area of ABeD) - area of ABeD = 152 orequivalent 1

area of ABeD = 19 1 U(a)

14 Class interval Frequency Midpoint.16-20 4 18".)1':""25 5 23

..' 2 p - - c , 3 0 7 28.31-35 9 3336-40 7 3841-45 5 4346-50 3 .48 1. 2. 1(b) 4(18)+5(23)+ 7(28) +9(33)+ 7(38)+5(43) +3(48) 140 _ .32.625 1_ .(c) Refer to graph

Uniform scale (from 0 to 9 for y- axis and correct axes (from 13 1to 52 for x-axis), using midpoints or boundaries (with or withouth is to g ram )

. All ~iritscorrectly plotted 2Straight lines pass throlighall correct points. 1(13,0) and (52,0) seen. t. (d) 24 1 12

15 (a) 4 Correct shape 1Correct dimensions 1 ,6 Accuracy _ ( 2 mm, 1~ 1 ,2 18

"~

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......._-_.~_---,,-_.-._ - - . _ - _ , ~o... _-' -. -r-- --:0. _._" . , . : \r ; . . , ._ , ~ . ; . . ,. _ _ . . . . .. . . .. _ _ , . - ,~ _ .= < \ ; . _ , . ' .-- Markaf io Peratuean Pemarkahan

2 ,\.IS (b) I Correct shape 1 i ) 4 Cor rect measu remen t s" I ~4 Accuracy ( 2 rom, 1) 22r-,

4,i I-~ 6~, J(ii) 2 4 Correct shape. 1I -Correct.dasbed line 1I Correct dimensions 14 I Accuracy ( 2 mm, 1) 2II

I Ndte ,: . ;I2 I DaShe

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v ~ jGraph for Question '1 2

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'-.'1'

G_rap~ fo r Ques ti on 14