stpm 2011 mathematics t2

8/3/2019 STPM 2011 Mathematics T2

1/5

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CONFIDENTIAL*/SULIT*

,;::l:sr954l2''.,,..','*.*,...x;\ 't !:it),ilr:trl{!.i,1,, MATHEMATICS T (MATEMATIK r) lli: lr, ;':',i;:,;r,:;:,;;;,,1,:;;i,iiiili tllllll*;ii*:jiilfi,%tpB2 (KERrAs z).t;:liti,i,ii;ilrri:iilii :li ,i;ifiiit; :i'lj:i'irnii,*iii,,,,r;t{p:,h.eu" (riqa j1m) iij:illlii]illil.:*:irilii;;r:i;

MAJLIS PEPERIKSAAN MALAYSIA(rraravsrnN EXAMTNATToNS couNcrr-)SIJIL TINGGI PERSEKOLAHAN MALAYSTA(nralavsra HTcHER scHool cERTTFTcATE)

Instructions to candidates:DO NOT OPEN THIS QUESTTON pApER UNTIL yOU ARE TOLD TO DO SO.Answer all questions. Answers may be written in either English or Bahasa Malaysia.All necessary working should be shown clearly.l{on-exact numerical enswers may be given correct to three signfficant figures, or onedecimal place in the case of angles in degrees, unless a dffirent level of accuracy is specified inthe question.A list of mathematicalformulae and mothematical tables are provided on pages B to I I of thisquestion paper.

Arahan kepada calon:JANGAN BUKA KERTAS SOALAN INI SEHINGGA ANDA DIBENARKANBERBUAT DEMIKIAN.Jowab semua soctlqn. Jawapan boleh dilulis dalam bcthasa Inggeris qtctu Bahasa Malaysia.Semua kerja yang perlu hendqklah ditunjukkan dengan jelas.Jawapan berangka tak tepat boleh diberikan betul hingga tiga angka bererti, atqu satutempat perpuluhan dalam kes sudut dalam darjah, kecuali aras kejituan yang lain ditentukandalam soctlan.Senaroi rumus matematik dan sffir matematik dibekalkan pada halaman B hingga Il kertassoalan ini.

This question paper consists of 11 printed pages and I blank page.(Kertas soalan ini terdiri daripada 1l halaman bercetak dan t halaman kosong.)O Majlis Peperiksaan Malaysia 2011

STPM 95412 [Turn over (Lihat sebelah)*This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL**Kertas soalan ini SULIT sehingga peperiksaan kerlas ini tamat. SULIT*


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CONFIDENTIAL*1 Prove that (cos 24 - cos 2B)'? + (sinLA - sin2B)2: 4 sin2 (A - B). [4 marl 0 andy > 0, satisfz the differential equationdy _y(y+x).dr x(y - x)

Show that the substitution y : arx transforms the given differential equation into the differentialequation du 2udr x(u - l) 13 markslHence, find the solution of the given differential equation for which y : 2 when , : ;.

16 marksl5 A triangle PQR has median lines PS, QT andRU. The median lines PS and QT meet at a pointG such that PG:G,S : I : h and QG:GT : I : k.

(a) Show that GQ+ d: -2hGF und cF + cF: -ztcQ [3 marksl(b) Deduce that h: k: +. Hence, show that the median lines PS, QT andRUof the triangle

PQR are concurrent at G. l7 marksl6 Theexpressioncosr-y'3 sinrmaybewrittenintheformrcos(x + a)forallvaluesofx,where r is positive and a is acute.

(a) Determine the values of r and ct.(6) State the minimum and maximum values

corresponding values ofx in the interval 0 < x < 2a. 13 marksl[3 markslc) Sketch the curvey: cos x - y'3 sin"r for 0 < x


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CONFIDENTIAL*7 The number of shirts by colour and size in a batch of 100 is shown in the table below.

Small Medium LargeBlue u 20 9White 22 24 l4

Two shirts are selected at random, without replacement.(a) both shirts are of the same colour,(b) at least one shirt is large.

Calculate the probability that

8 A supervisor claims that five in every 1000 compact discs produced by his factory are defective.The compact discs are packed into boxes containing 200 compact discs in each box.

(a) Using a suitable approximate distribution, find the probability that a randomly chosen box

13 marksl13 marksl

12 marksl[2 marhsl

13 marlul

14 marksl13 marksl

(b) Two boxes are chosen randomly. If Xand )zrepresentthe number of defective compactdiscs in the first and second boxes respectively, calculate P(X + I: 2) using a suitable approximate

(i) does not contain any defective compact disc,(ii) contains at least four defective compact discs.distribution.9 The continuous random variable Xhas the probability density functionf-+ r(.r(5.l(x):{ 2l2x- I

lo, otherwise.(a) Show thatE(2X - 1) : ?, and deduce E(.!.(b) Given thatEl(2X - l)'l:24.2, find Var(,$.

95412*This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL*


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CONFIDENTIAL*10 The lifespan, (in hours), of 50 light bulbs are summarised in the table below.

Lifespan (x hours) Number of bulbs1500


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CONFIDENTIAL't 8MATHEMATICAL FORMULAE

pL+ ^br+p'

Trigonometrysin (l + B) : sin A cos B + cosl sin,Bcos (l X B):cosl cosB Tcos A sin B t

tanA + IanBtan (A + B):

-

I T tan AtanBcos 24 : cos'A - sin2 A: 2 cos2 A - | : | - 2 sin2 Asin3A:3 sin A - 4 sin3 Acos 3l :4 cos3 A - 3 cos Asinl + sin B : z srn Lr(A+ B) cos )f,n - nlsinl - sin B: Z cos )@ + B) cos \fa - nlcos I + cos,B : 2 cos \@ + B) "o" !{.t - a)cosl - cos.B : - 2 sin iOq *B) sin )f.a - alIf t:tanlx,thensinx: fiu"Ocosx: #Coordinate geometryThe position vector of the point which divides the line joining the points which have positionvectors a and b in the ratio A: uis

Integration

f ,**:uv- f "*"J#*: mlr1,r;l+c

95412*This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL*

stpm 2011 mathematics t2

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