SULTT954t2Mathematics TPaper 23 hours

954n

STVIJK JIT SINTAMAN SRI RAMBAI

TRAIL EXAMINATIOru 2OOgUPPER SIX

:1MATHEII,IATICS T

Paper 23 houns

DO NOT OPEN UNTTL YOU ARE TOLD TO DO SO

1. This paper contains l2questions.2. Do all and show your steps clearly .3. Non-exact numerical answers may be given correct to

three significant figures, or one decimai place in caseof angles in degrees, unless a different level of accuracvis specified in the question.

This paper has 3 printed pages95412SULIT

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4, 123Given that sin A= 3, where A is an acute angle and cos B=-;

13 )where B is an obtuse angle, find the value ofU ""r t

n;ei -:

.6l- "- ii) tan (A - B) - -s6-' / - - - \ 6 33 t6I

cn50

aVelrvBl

0=?=

slunf

w>l

N>(

2. AErmer flas an adjustable electric fence that is 100m long. Heuses this fence to enclose a rectangular grazing area on threesides, the fourth side being a fixed hedge. Find the maximumarea he can enclose. iZ50 rt"

t7l

3. rino ihe scalar product of a=2i-3j+5k and b=i-3j+k and hencefind the cosine of the angle between a and b.

141

4. mhrp n rnoves with a uniform velocity of (4i+3j)kmh'' a1d a. -nsecond ship B moves with a uniform velocity of (12i +1Bj)kmh-.' 'where the unit vectors i and j are in the directions due east andnorth respectively. Calculate the magnitude and direction of the.vetocity ot snip A relative to that of ship B. At a particular instant,tne poiition oi B relative to A is -24ikm- Calculate the closestdistance between the two ships in their subsequent motion'At the time when B lies exactly to the south of A, the ship A

changes its course but increases its speed to 1@ kmh-l in

order to meet the ship B. Find the course that the ship A has tobe steered and the time taken for it to reach B'

112l

5. Solve cosec g cot0 =Tr,tor 0'SeS180" B = (F,53t,os I = -2.*19?-elA

t5lt.(sn"A

6. ffilate cerea! is distributednormally with a mean of 100 g and a standard deviation of 2g. Calculate the ProbabilitY that- (a) three boxes of chocolate cereal, chosen at random'

each has a mass less than 98 g. o. o3cq?(b) three boxes of chocolate gereal, chosen at random,

have a total mass exceeding 305 g. o' 0l+t

{c} out of three boxes of chocolate cereal chosen atrandom, exactly two have a mass greater than 98 g

while the mass of the remaining box is greater than105g. f (2 botes '18g ond I

bsx

c

In the diagram, O is the centre of the smaller circle ABG isa straight line . Show that the triangle ADC is an isoscelestr iangle.lf AD=DB, prove that AD is a tangent to the larger circlecircle at D. 13l

l4lB. By using substitution z=x+y , for the differential equation

dl ='* y * 1., when x=1 and y=3, prove that the

dr x+ v -4 '

differential equation x+y = {5 U-i*'lr-r . l5l

L Water flows from a hole to a cylinder with the differentialdh . r

equation -i = -k.'!h where k is a constant and h is thedt

depth of the water in cylinder at time t. The depth of waterfalls from 10000 mm to 8100 mm in one minute. Determinetime taken to make the cylinder empty.

1 mlauter t4I

4ntv. The following table shows the lifespan of 100 of car tyres

produced by a company,

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(a)

(b)

(c)

frequency@

Hence, estimate the median and semi-interquartileqnge_for the lifespan of the tyres.Galculate the mean and standard deviation for thel i fespan ofthetyres. i : gl gSu tf i

' g= 553+.2lct '^

t3I

t3I

I5I

3067s8

Afairdiceistosffias follows:.A : The surn of the scores i"?OO number.B : The sum of scores is i3.AC : The number 6 appeare in the third throw.

(a) Find p(A) and p(AlC), and state if A and G areindependent events. :L. r ruEPcu(rei l l evenls, i l -(b) Find F{B} and p(Btc), anA statdh and B are

A continuous random variable

1'(a) Show that a=+ and find the value of b. b. -+

6I

(b) Find P(X>1+). Z ' .+r ,

-3-o'2 '8(c) Find the value of rn such that p(X

S.M.J.K. JIT SINBukit Mertajam.

Soalan Markah

Jumlah

Nombor Pusat / Nama

Perkara Angka Giliran

Juttgun tulis.tpu-upu dtruang ult

,t, Va' eu t 3 j i nVs' Vn- Va M,TVB= t l i + r&j i ei = Vt- ( t : . ; + l t l

Va= ( l

AVg= Vn - Vg= trr*3j - ( tU +tej)

= - pd - 15 j tttq +

^vsl = p"* 3! f - s l :o(- &)- + [- tl)'= f tkq{"- t A,

I

V4= l ) i+ l? j

vo-

, eyl/ ll,r.e d1yu*foyr tl"af ft n

'Yr = tanJ (#)akl : EY t1 t' fi t,,."]-t vulo r ; 4r

6

tan &= $&=-ran r 6$) +Vc = l,\ rnnn

' 6[ . t i '

r /s. l? bM h-l

s\n 6( '4 lo =

ftl g, = PJ'hor,rrf

Nt - -- l t t+-

N

vvI Vl

A

" -aL-

x p. 4vs'P knlh

- 'a---

Vs= ( t>;* e?l

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\ ( .o)P(A=((t \ . f , A\ b) P(B)= .rx6-IF BlP )= V (uw)+ r(eor)tf gW\r P(o0o) F / =L AI

.L- I * l r ( p lc) - - Y(Enc) ' +lnc " . [ oze , eoel * l

rL./ z: , I

P(* lc l = t Pn t) s lo

r lc)t 1. ." 7Glc1 f rG)

= ; J- l l

- tt- Il / . ,1 A rwt u*fct*La* El

6- a) X - vra,cs 6 n box of choco I l). a) F[r)= ax--b)LL , 1 SL <

X- N 1too, z") FC-t) '-o*a*b'-0

= Y(2. - l )5 b= -q k\

= P L? > t )3 ,- 7(>) = Ja-VL =/

= (0, ts 96 6)3 = o,oo 3qq7 ,+f )at Vq - lo=i +\b= -+ f t \

r(xrfA -,1-f (xs *) ^/t lb) p1 Tofaf M^sr u( tlnrz. bwu v4 unal; 3o-r4 )

=f IX1 +{2+(3 >3or) t ( t l q F(x t-r t t3) r r to* n1-J =-0= 0,0TSS +l :_ 4: f -703

c) P(X>l ' ls) ' f (+>t [g( 'll f@)= # Ml=?(t>J-I)

= 0.[6 ]l ft l

P(x>9.&)= PLz> Bl= ? +>-L)= d "fi{13 +l

f ( - - - )= 7x [o,e. t t 3)Lxo.0o6*!

= 0 .0 {3}- +l

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S.M.J.K. JIT SINBukit Mertajam.

Angka Giliran

Soalah Markah

JumlahNombor Pusat / Nama

Perkara

Jungun tulittupu-upu l irtrunS illr

1. To prlve: anqle betwzett 1!1s' d^ad a^A lne tanqent a+ the potvrf of

confotct 0 eqFal +o the aAql,e, fn 'the aLtsrnalz' seqMq

L Ni l= I ACI

Conrtructio,t , Drav,t 4,te d|ander To fo lnd"/Ker+ ftte uWrrrfzrzqa- o* B

fruuf B

01 /

/ , /

? T &

L BT& = ?o' (tanOent .b: radiur )

/ BT4 = qP' .L

L BAT = Qo' ( angle M serrti crYcte)

Bft L- |BA + LgTA.Qo"

Bur"t LTCA = I f BA I arr4ter r\r )rl/te rarne saf,M€lrt)

: ' v=>flenC-t, LN&= L*eT tlruveat3

1o Prove : A^Dc

h an ilorce{v trraqle

Pruof , Let LDftB=x

/4', \ \ \ L DoB > >o< ( anqte af centre = tx I Orcill\ BlL DCft = lSDo - .ro< (o??, k o{ ractld qLld,)

}< -/ L *Dc= l8r) ' - d: ( lgou - >- l l -) (suu rt Ct d kD)=xc 4tLCftD= L*DC--x

#znL?t ftDr il a4 i\octx-tez tr^ag\e-

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t f *D=DB, then z>AB-- LDBA = x

LftDB = l&oo- l .d( /vr.l

L ftDB = /_ DcB BI= l8D ' - )o ( a(fen"o*e s ol ne t )

IFI

*t

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v rru 4I l

..-Br?r4'Et

upu-Ltpd dtrLlutrg Dlt

I-11sin fi-- fr cos BE g

\\ ./ r! lta tA * l \g---+" l I r3 olcoJ f t=i s)n 8= +t^n ft= I ton e-- -+

i ) cor (a+ e) cosAcor B- srhAsfvr g

+ F+t- 11 L+:: ,J_13563/65 \-/

\ ; ) far t G- d= 1an f t - lan Bl+ tanf t fan B

= +- (-+). ,1

l+ t ' . F+)=5(

rC

-lrr=-+/e. L>tt t1 = 100 9 Y=lt)o->r

* hrea, A' xy_l , 1r (tOo - )-y-)

= t00x -2x'

f f i ' -{^r + loDPor A 1o ba

^*. # = o rvax arca he rai s4clfrre

-Vv- t l0g .P =LYq.>c =lr)O ' )E (so)

)c ? JSm l)5oML

9o

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3, e'-rL-3+* - t t ( - ; / \

D= r-gi*E = (- ' ,--- l l /. \ \ ,1\

a. b = I - t I ' l - iF-lFrt

\ . / " / \ , .

/2 \ v'G/"///q

.16 L \:,

t d pz an4le bfwrr L a"d k

A,bCoJ B = r ̂ t r l^ |

tb'.6r. llffii-l"

t6

JtdJ| 2,/

+ , , /=-l / . l+t? w0 -- 38.5 "

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5. c;.sec 0 col 9=L> \I cole - L,_

ct\no rA- o b

caso =Lrt\^-0 tb

J c.rrf t -- r{h }-0

J c,gr f = l - ubt D

cot ' '7 + ) cot I - | - -o '

Let a, (^! o

a7+7a-l zQ

(a+l) ' -L,O

(a+ t1 ' , L 7

at l = F, @ -f-

^= lz- l @*Ir- | (ry'e*Ll)

: . csr S= f i - l

a -- 59,53"

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8. V-- t r

S.M.J.K. JIT SINBukit Mertajam.

Soalan Markah

Jumlah

Nombor Pusat / Nama(t

Jungurt tu l isapu-upu 4rr l rul tg i l I1Angka Giliran

= -VfA

= -lr[h

+ -- -V d,L

t=or h= to ooC

- - -V[o) + c[o ooo

f i t l

) ! - - -?t , + 50

t - -1, h= SlDD

Gmo

) Y.= -5t t5o

hr 0,

J5= - !b t so

5t=50

+a lo rnr in*te' l

fi)4^e- t 6lc

tt.ei0b Ytt 4iavr 0-, ' 9]- q0 t) bn" ,/ \

= +? foo Ln^

0+ = W Qoo [c,.'r

Lrrfevq\)Lor,ne ryf '( = 0-t '&,? 74, o o lc*,a ,/

9trr",t- MtOf"q,acfr? ra.^f.e : Yj+r SqtD b^, ,/

t-) Lffespan,x ltcM rui"d p+a^{,x, {tey*g lxa '1.

T

0c *< 81 ,Eol &l- o 'oo t t ) t I s4 ooD l , SSqf*(or lSQgse (r t 59t5oo ?Io uo t0D t ) I I otf, Otro 1.0(569 )" l0r f

f,= lrc 0 fa-- Tf ic ' = 6,81)>4nzr4

ru(ar! = To *J) uvv

= P )3S o o 0 -Anr3-At ' l7h.' - |

\0. A)

2MM SQUARE 2OCM X 24CM 4OS

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