stvijk jit sin taman sri rambai · 2009. 10. 28. · sultt 954t2 mathematics t paper 2 3 hours 954n...
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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
[see next page]SULIT
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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
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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
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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
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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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Jit Sin Trial 2009_Maths T P2Complete Answers_Maths T P2 jit sin
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