malacca_stpm_trial_maths_t1_2011

8/3/2019 Malacca_STPM_Trial_Maths_T1_2011

1/11

SULIT*CONIIDENTIAL*954/lMathematics I20113 hours

954/l

MAJLIS PENGETUASEKOLAII MALAYSIACAWANGANMELAKAPEPERIKSAANPERCUBAANSIJIL TINGGI PERSEKOLAHANMALAYSIA 2011

MATHEMATICST.#:trJ,Inrtructionr to candidaterDONOTOPENTIIIS BOOKLETUNTIL YOUARETOLD TO DOSO

Answer ll questiow.Answercmq,beu,rittenn eltherEnglishorMalay.AII necessqrylorking houldbeshown learly.

Non-exaclumecql answersmaybegivenc,oftecto three ignilica rtgwes,or onedecimalplace n thecase fanglesn degrees,nlei a different vel o7oi"'il) i, ,p""t?"d in thequestion.Mqthematicalqbles, list ofmathematicalformutaendgraph qperareptovided,

Arahan pada alontJawabsemtl'aoalan.Jawopan olehditulisdalambahasanggeris taubahasaMelarySemuazrjayangperluhendaklahitunjuk*an enganelss.Jawapanerungkak tupatbolehdib,erikanetulhinggqigqangka eterti,qtausafl, empatperpuluhanalauhes udutdaram @jqh, ecuati raskilitwi yanf riin dttentutan aransoalan.

Sitb mqtematihehqraiumus atematikdankettasgrafdibetwlkan.__Thisquestiotraper onsistsf4 p-intedli!6-( eftassoatanni tedbi dafipado halamsnbercetak)@HakciptaMajlisPengetuaekolahMjaysia Cawanganeleri'iielata 2Of1

STPM95411*Kertqssoalqnni SLILIT ehinggaepefiksaanertasni tamat.*Thisquestionapers CONFIDENTIAL ntil theexarninationsover.[Lihat sebelahSULIT


2/11

if A, B and C arearbitrary sets,show hat A - @ w C ) = ( A - B ) - C. [4 marks]

[4marks]

[6 marks]

[4marks][3ma*s]

[3marks]ll markl[4marks]

[5 ma*s]

[3 marks]

f l . t+11,l"z'.,(a)

(b)

(a)(b)(c)

- I + 2xExpressl-- asa series fascendingowersfx up1o le term n xl.' I (l-x)' [6marksjsrPM 95411*This questionpapers CONFIDENTIAL until the oxaminatiotrs over.

Using he rapeziumute,with live ordinales,uluut" [' )- * ." . /5x-3Detenninehe setofvaluesofx satisfting he nequality 2x - ll < ll_;. [5marks]

If v=x+e*-showhat 4 *-:l-= u' dY' (1+e') '

The tunction fis definedby f(x) =r0.

Find lifn- /(x) and liT. /(.r) .HeNrce,etfininewhether is continuousal x = 0.Sketch hegraphof f .

The complexnumbers l andz2 satisry he equ ior^ t - ziz - 5 = O.Express 1aod 22 n the form a+ bi, wherea andb are ealnumbers.Represent l and 22 in an Argand diagam.Foreachof zl and 22 find the modulusand he argumentn radians.

The differencebetween he distanoe fpoint P ftom thepoint (4 , 0) and hedistancof P ftom thepoint (-4 , 0) is zJio units. Show hat the ocus ofP is. . x ' y ' -he hvnentola'^ 10 6

Showalso hat the ine y = x - 2 is a tangeNto this curve.


3/11

10

lBv takinex- i. find anapproximatioDf Jl20O0 intheformof Z wbereLVqp andq arepositive ntegers.. r - . 1 t2 f --LhtxDleSS

-In me lonn ,{ + +

-Mere A" tt. U zrno ,' ( r - lxr ' + l) x -) ) t ' + lareconstants.

Hence. valuate' ^ ^, ' ar.r ) ( r_ lx-r . +l )

Thepolynomial (x)= ax3 8xt+ bx+ 6, wherea a(Idb are ealconstants,sdrvrslDle y x- -zx -J.Find a and b.For thesevaluesof a andb, factorisep(x) completely.Show hat 2 is a zero ofthe polynomial3xa* l4x3+ llx2 + l6x- 12,Hence, olve heequation x4 14x3 11x2 l6x - 12= 0 by using hepolynomial p(x).

[3marks]

[5 marks]

[4 marks]

[5 marks][2 marks][2 marks]14marksl

[8 marks]

[5 marks]

[4marks][2ma*s][5marks]

(a)(b)(c)

11 (a) (zt to zz\ (a 7 -13)I fP=14 -8 4l .O=1, -5 c I and Q 72I .vheres he

t t - t t -[4 I t2) (-2 | r t )3 x 3 idqrtity matrix, determine the values ofa, b and c.Hence, uld r _.Using he esult n (a),solvehe system f linearequations

x.-2Y+z=0,x+ 2y+ 32:1080,6x+1Oy+82=4500.12 Thegradientofthe tangent o a curve at anypoint (x , y) is givenby

+ = -j--,- *ho""+ f . P (2 , 9 ) is apont or the curve.dx (2x-1)' 2(a) Find the equationofthe curve(b) Sketchhe cuwe.(c) Find the coordinates fthe mid-point ofQR ifthe normal o the curve atP

meetshey-axisand he x-axis atQ and R rcspectively.STPM 954ll*This questionpaper s CONFIDENTIAL until the exanriqations over.

(b)


4/11

(d) A point (x , y) movesalong he curve n such a way tlat t1lex-coordinateinqeasesat a constantmte of0.03 uaitspersecond.Fiud the rute ofalrangeofthe y-coordinateat the nstantwhen hepoint passesbrcughP. [3 narks]

STPM 954/I*This questionpapers CONFIDENTIAL until the examinations over.


5/11

MARKING SCITEME TRIAL EXAMINATION STFNI VIELAKA 2011MATHEMATICS T/S:PAPEROdestion Answers Rema.rksI LHS=A-(BuC),= A. (BuC)

-An(B'^C')=(AnB')^C'=(A-B)^c'=(A-B)-c

BIB1B1B1

DifferenceD MorganAssociativeDill'ercnceI41z xn: I Yo 0.7071 |x' : l .5 ve0.4114 lxr= 2 lyr=0.3780 _ ]x' :2.5 I vz:0.3244x4=3 ly4=0.2887 I

h=0.5J' J5r_3- ! ro.sro,zortz(o4i 4-o3'7Bo0.3244) .288?}2= 0.836

I)

B1

B1

MIA1 t4l

3 t2x-11


6/11

Question Remarks-dxlaom l ' dy 1+e't l+ex):: '+ - _-:0Jy' ( l+e' ) '

cl"x e- -., ,-+-=uy' (1+e') '

AIA1

t6l5 (a, *tqXrtx)="ll11r+lt *o=lim /(r) = lim e-'z. 1

li l /(x) =1, t(o)zBut 14 (x) + "f(o). . f snotcontinuouslx= 1

'MlAI

MIAI

(b) R1R1RI

Modulusgaphexponential$aphclose ointat(0,2),-1,0).openpointat(0,1).Mustbelabelled

6 (a) 2i t2 ix4.| , 24=2 +i22=*2+r

+40x5) MIAI

AIa)zrcr. t) \

Im axis

,,41e,r)z---->Real axis

D1

(c) lzr l=F+t=./slzrl {5,r.,g"' =,*'' []J= 0.464adiane.eo: o.'l- zl]* 'r- 2.68adian

M1AIBIB1

Apply formulaofmodulus.Forbothans

Uol.noh( t tSt lnt t f , t ) l V" la|a l t l4R^t\ .S.HLML )


7/11

An(wers

'7 Jr. ' r+y ryr \ ' ( "-4) ' -Y' -2 ' / l { )(J( . ' - -4) ' ) / - (2Vlo" ' r ( r -4r ' ' v t7rox +o + rq1"-+1' 1't| ---- lr4x rof= l l totr-+t ' ' l16x28ox+ 1oo: lo( x'?-8x+ 16+ f )3* - 5f =3010 63x'?sl = 30.. . . . . . . . . . . . . . (1)v=x-2. , , , . ' (2)3ubst.2) nto 1) 3* - 5(x-z)2

=30x2*1ox+25=o(x'-5)'? ox= 5,y-3Point f oontact5,3).. y = x - 2 is a angento thecurve

BIMI

M1A1

A1

MI

A1AI t8l

MlA1 J1"3termsI correcl]4,PryI corroclMlAl I As above

MI musthavetrms 10

A1

l--:--I t+ zx

I(1+2t)'z

-1+l(2r)+2'=1+x-] . t '?+2(1 - x)-t

l ,_fvr,r , l , -1, - 1y2r),2. 2"-" , + 2' 2 2. +..-26l "2

r-r\/-1I= l+(-2X-x)+-(-jr)-= I+2x+3x2+4x3+'I(1+2r) t 1 x) '

* (-2X-JX-q)1_ry. ...

= I + 2x+ 3x2+4x3+x+ x2+ xt f,* -11+113+. .

'm:rr3x+:t ' - t j . 'r'**=rMalhemtict Tl/sl 20ll bial - Meldlia " MAPKNG SCIIEaE 3


8/11

RemarksF;,1,rlr 'l \1ol 12000 {'?9sq8lJ'?t00*r , r , I r -ar l l 11,1, ,

l l l l0 2lo 2 lo= 4032000

....h2000- 2189432000

B1

IvI

AI

Subst : 1l0

tel9 x' -2x- l

( '- l)('z

+1)-r-r)().-+ ,- B . Cx+D(.x-lX.Y'+1)' x-| x2 +1

x2 2x -l = B ( x, +1)+ (Cx+D) x-Whenx=1,8=-1Whenx=0,D=0.Compareoeffof x'', C=2

l )

.12xx-l r" +1,)(x '?+1)T dx(x- l )(r '?+1)

=1'11-1+f; . rx4 -r- l .x- t l= [x - ln (x - 1)+ ln(x'+1)]], , 10= (J -2) - ln(:)+ ln(;)

BI

BI

MI

AI

M1A1M1A1

(Longdivisior)

l0 (a)

(b)

p(x)= (x' - 2x 3)Q(x)= (x-3X + 1)Q(x)l i i l i r to- t=o 11qt l v L9a+b= 22.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( i )p(-1)= oa-8-b+6=0a+b =-2.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( i i )a=3 b=-5p(x):3x3-8x2-5)(+6=(x,-2x-3)(3x-2)=(x-3Xx+1X3x-2)

BIM1A1MIA1M1AI

FactorizeForm2 eqn aa&bBoth corect

Solving heqnForbothanswe$Findthe linearfactor(cAo)

Mokenot:B Tl/S1 20IIftiol Melokr -- MARKINGSCHEME


9/11

Rsmarks

(c) Let(x)-3xa- 14xrr . 1x2+ 6x- 12t(2)= 2(2)4 14(2)1 11{2)2 16x - 12=0..2 isazerooff(x)3x4- 14x3+lx2 + l6x- 12:o(x - 2)(3xr 8x'z-5x1 6)= 0( x-2) (x-3Xx+ 1X3x-2)- 0. ' .x:2,x=3,x= 1,x= 2i3

MIAI

MlAIM1AILongdivide oobtain (x),Factorize[13]

l l (4,

(b)

PQ=72r(24 40 32)(a z -r:l]4 -8 4l i b 5 c l=72t\4 8 12)\-2 | t I )(2aa a,b 64. 168-200+32| 4a-8b-B 28+40+I qa+8b-2c 28-40+12(72 o oll0 72 0l[0 0 12)4a+ 8b 24= 0.. . . , , . . . . , . . . . . ( i )4a 8b 8= 0 . . . . . . , . . , ( iD-312+40c+352=0 c=-1. . .a=4 b= 1c=-1PQ=72rl-po =t'72 -

l^P-t=iu

- 312+ 0c 3521-s2-Bc+441=-5r+R.+1l t I

(LL18 72I I -s=l i il l a\36 '72f' -, rlf/)l1 2 3 ly l[e ro s.J['J(24 40 32\(la -r al ll4 s rz][

iti ),01080.4500t;

II)000120

M1

AIAIMlAI

MI

AIMIAI

B1

Solving or a,b&c

Transform oreq. form

Matheha .tTI/Sl 20ll tml Melala MA?rJ:tC SaFEMa


10/11

Ouestion ,Answers Rsrnarkst"'l1l, r l(22a| 1e0u60220^

'llJt'lt'li'j

8000.l0lt320)'18000

04320(4 7 - r3lf rsoou)l ' -5 - ' l l 0 l\-2 r rt ) \ 4320.)I

;),y= 190,2 160

M1

AI

Multiply(his)inverse

l2 (a)

(c,

(b)

dv6d.x (2t -t)'zn= [--i- a,- t 12x r).6' -2(2x-t)3

, . -1

ArP(2.9).9= i rc' 2(2)-1..c=10Theequation f thecu*" i, u = - J- n19

YI l ,x=r /2| / l") / :_i l , i . . ._____._l i / ' -l r /---*-**nffi

| : /I t ll i lGmdientoftangentat P= -Gradient fnormalat P : -i 2Ecn f normal tP s v- g : -],*- Z,"2

v: -1x + 12-2

AIRI

MIA1M1

B1B1MI

R1

For 2 brarlchesof ourve

All corett

MathematicsTlSl 2All Tial- Melaka , MAP,XINGSCHEME 6


11/11

Answers

(d)

Q:(0, 12),R=(8,0)Mid-pointofQR = (4 , 6): = 0.03dt:a = : x(0.01)dt3

- 0.02 unit per second

AIAI

MIAl

ilatrmqtics TlA j 2011Trial- Mehkt - MARtuNGSC.{EME 'l

malacca_stpm_trial_maths_t1_2011

Documents