Its the class IX Mathematics paper held at St. John, chandigarh. Quite difficult, so be cautious.......!!

1. LL4 C48q jooeg
Tiqfud qfuT - tr,2013
SUMMATTVE ASSESSHE}IT _ IT, 2013
iSHI - X/CI--D(
TfiIa / MATHHATIcS
Aqtfragrrrr:3qrre
Time: 3 Hours
€rlnar F*r :
(i)safr eaa flffi Ft
(ii)gtrq?aqrfs4lndtffi'q-1 susl 3{,E,sd?Irctrrbffitt Erus-3Tilec?atRad'e;.ryorsia
+r t; $rc-E il o c?a H B-;rS rS€ d z sr+. d; tru-s{ tr ro crs S m+* s-Sfi t e :iq. t; arn srs< f 10
c-ra S F-dTjl c-Sfi A 4 3i+. tl
(iii)tru-s-3rit rradwr t t a r*.ildF*?fiq cedf T6iJrdqrlMd tt'*. sS A*;e'+ga-artt
(iv) {s rR;r q-r d 6tg S fu+-fl rfl' tt
(v) *-o{tcr +l s-qtr effid tl
General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into h.r sectbns A, B, C and D. Sedion-A comprises of 8
questions of 1 mark each; Section-B comprises of 6 questirrs cf 2 rnarks each; Section4 comprbes of 10 questions of 3
marks each and Sectio*.D comprises of 10 questions of 4 rntbed.
(iii) Question numbers 1 to B in Section-A are multiple cfxfte SEsf,ons where you are required b sele€t one conect option
out of the givpn four.
(iv) There is no overall choice.
(v) Use of calculator is not permifted.
gmori+lsw-r
Question numbers 1 to 8 carry one mark eaclu Faeach questioru four alternative choices have been provided of
b'hich onlyr one b correct You have to select the correct choice.
{"4} 1
{D} 4
If a poi*t {F. 4} lies on Bre lirre 3* * gr:!g €ran t}e ya}$e of p is ;
{A} 1
tD) 4 -F{
2 tci 3
qfr !s t€t :r+y: 1O rR +t fqg (p, 4) f€er,fr t, * p:fiT r{Ia € :
,-r'
{c)(E
,/
"z q.q'tfis'# {T*Ersr iEI slFrcr # A fmq Eq * sq F€ *q :
{A) 3 {B} 4
€)2{il}1
Mtrliartrm ltas:ber of sslrrtions cl a lirreal eqreatiaa rcqrrired for
drawing its graph is :
trr) 3 {Bi 4
{c} 3 {s} 1.
Page 1 ot 11

2. q{T$qa?:
(A) 4 Tqrq€tfr €
(ci zffi da €
A Quadrilahrattt*s :
tA) 4sides
{C} Zdiagcrsls
4{fr{ Era €
a1-* {e}, te} *{tc}ffit
4 vertices
A11oItue{A}, G} ad(c}
{8}
tB)
{E}
ts)
,,(
-11
'14
*il * ffi qut A s'.a qr *w qg-or* ? :
(A) filtr{ts (E} 'Ta{M
ic) qffir (D) ?{r€t
The regien tret*'een a chord' a:rd either of its arcs js calbd : '
tAi wtar tEi segrn+rrt
Fi cu*:r:nference (Di diasster
qi5, {fS Ei frrf*1 *'Ed 25 cm *t # v
"'** * Es*r w t =
(A) 18en ts) 26cEi tc) i$Bet -
g Z*ce'
If the sknt heigtrt of a coste is 25 6r sd'teigbt is 7 @' 8* ifs @
15:
{A} 18csr {B} ?6m {C} 4$cm {D} Be
1
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1
'-*]
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ta
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tF-I
tB) 64
fDl 52
'i
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II
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l
/ ga 32rstffi qr6fu T{qt cer#qr$ r{ e*qrdt'
ldearr sf first five 1xiar*rtt:rbes is :
tA) s,6 {,8} v'&
{c} 52 {D) 14
nd" rfu sTcnEI i*ffid a q*af :
iAl I tBl E*
tc) ?s {D} 517
*rernrmberaf4egrei:'b+swhi*tegtbe..'t1tfrcm'asclidG$ewtroseedge
isS2csrmre:
tAl I
fcl ?56
(Al 5-6
{c} 52
{B} 7a
{D} tit
Page 2 of 11

3. i'
;
F (E) + P {*ot E} is equal to:
{A} o
tc) :
{B) 1
{D} theva}uebetrafdf
+ P {ETfr ) e{ffi{ t':
vP iE)
{A}
tc)
o
1
?
iB) 1
{D}'odfqr+d"dw
sEcTrIatffT
Question numbers 9 b lf clybo marks each-
,-{ frl€ Etq =-{gq Asc*e1 Tw{ AB * r=i qt E q{ ffi €
str g.srE AD E BC qa1+ q{ F q{ fid tr & z 456:sff'*t
t?,w.:5ff *, * zeag a*r zcFDsfir
E
I* figfFte, sides AB ild Dc c{ a cTdic Enadr:l*teral ABCD ue
to seet at E $fu AD s'J EC aeFffi&ed. tc set *t F'
If / ADC:flF, *ftal ./BEC: 5(F, Iltgl e"H{ I EAD ad Z C5:D..
Page3af 11

4. frq'rq f4'{ d r€Rs eq-. e.q'id{ qg{-a t t
FS
7%
1"0 x
* Ertt y sI EF{ ilq Etfa'qt
a
In the
and ry.
P
R
given figrrre PQRS is a parallela$aul Find frre value of :r
%
t0x
,r/ up na Tdrr*t{ *era al q€ wtq *rrss 55 az *r qR ssb 3ilrqR 61
ffi;fl s.z o.*, 'fi g.r*t ffi =n*
qfrR t
C'rsed stlfface are.a of a rigftt cifcdnt cylir,r,iter s 55 a2' If fu
ratlittsofthebaseoithecy{irrderisG.Tguthgrfinditsk|ght'
Ttrere are 1ffi students in a class' 4O of tlte* are gids' The avetage
$srks of tfte lrcys rn sciettce b ?5S unrd that af E.* gF !* i" 655' Fird
the average marks of tleclas-T science'
6 6'ar { 1oo ffir;i d, ffi * 4oEsi*d ?r f*gnq qqqi * 3il€d
75:63{6€aql6gfa.{I*.esg*rq-qrfFarEqle}sdF.ddlaeilfsE'|
V Tte btood gr<nrps of $o stnde$ts are r'ecorded as {olls$rs :
*8,dX g"{fr, !(,f,'F,&,
fr,& N,ra,g,& &8, & $,p' 14
*&,F,fi,p,8,F,xN.
ffi** a &eqr*ecrcy distribstisn table for the data
3offid?ii*-{tr €T6€s Y'*.nisrr* krrq:
&B-,9, *AF,g.4,9,9'+'
o; 9, *+B' -8, *: A9, 9 !' t' 7 4'
H.ffi? *f&*** ;is q*sfi f,qiq +ltilq r
Page 4 of 11

5. Fistd the cred;a* arrd. grode of fu d.r,
&&4&,q+,**4qb
fqgq affi q;lqTglw *** agqrc'er*qtr
/,1,1,fi,u,1,b,$,4,t
.&tr ?r ?4r?, +) 9t
sEcTKnCtrE{
Question numbers 15E Z|- c-r1lhree marks each.
@ PE f+-€ qt? q frq s:2, !:Z;fF+1) r-er+3) y -t:CI EFr €fr
dqz wt+rrr frfsq r
Fsr what value of p; -r : Z y : g is a soltrin
"{ b + 1) r - t2p + 3} y
-1:O and*-rite the equatio*
d'q Hrfqq to wr ti)
*I qr+rqlFqr
: 3 {nJ Q t*€y:O tfuq' Eq}"fi{q€"*
{Ire*ko,hethe the eqtrxtio*s {t} .tr -
+
:3 h} ,lf ** €y:o
rfr{,fuosdEErfifiwfl
ar*linea- I*=t{y"
qq--fr-q egrja ABcD ffi' AB licp t *
kG effiilql+ao:sc*r
The vertlees of a trqreatta ABCD lb s* a circle wi&r cskre o s1d: drat
AB ll CD. Prove rfiat llD) - BC.
Page 5 of 11

6. "Y
tuxqacllPD, Yltr"a*rr*eulPc?
r
fr**,#o.r* '
ti) ar{CQI}}:slcCP} a?r
1
(n) ariCQD): 'u4cneQ)€ r
, DCfiPB emd ADIIBC.
firove tlrat:
W ar{cQD}=attcQP}
1
{# ar(CaD}::ar{CDPQ}
@ PeBsEtr sqqgs ? ffi /PRQ:3€F?I ssn ffil*{l
FQ!15 is a rhssrbres strcla tlrat IFRQ:i!0f' FlnJ tki varw o{ ^ffR'
l
I
I
;r.-l
rl
/1^-/
(@j uq eABc qn qft*,a o 3tt{ cD J- BCA, * fiF=# qxkq f* zaau : JEAS
7
tr
HG is the ciffiiErc,efttre ol a i ABC and OD :" BC,6e*rlxove Elat .{BCD
: ZBAC,
g; ft-fir * sTrqr-{ qii fffiI ar{ ffi q eqfTlir4
'
stt * FffiI s{lffiq
2sl.4z.*3 d, ?ft +flT 4I qFF'
Y€ *Tq€ EH *ffiq t
The tadius r}f the lese a*d height of a <ylinfu se in fhe r*ti* 4 : 5' If
the v*lusre r* ?51.42- c**3, fhe, fi*d ihe cl:''c?d s:trf#e sea nf the
qrlinder-

7. qfi fT{ st fr at :+rq 4? crn x so...o tt Ut--f d g e mr rJ.s q1q{
qri qlt qq f r qrd E? fu Efr{ { t *trrg sn * gm f_eqr
Enrqr rrzn t r gs fAaA +1 qrfrdr Ard ffiql
sqrrares each of side 6 cil::ure clrt offfurthcongrs of aslrcet of
tin rcesring 112 cm l:y 3{} csr- ?bererri!1* of the tin sh€et is
made into aa op*rrbox by foldiag try te !p, ht Egr caprcity of Bre
box.
Draw a histosfan of tile &ta:
Cfass 10- 2e 2e -3' sCI-4t {t-51 t-50 6S-70
Frequec
cY
a 1fl x3 9 5 2
f{q"#+ftq W rrrqaR?ffEq:
Elt 10- 20 2*-3? 3(}-{ {o-51 x-60 €E-70
qfiqF{at 5 1B 13 ) 5 2
If r€i*s are toesed e Egdn, fu ee probebllity of
fd{ rtcnooemeflPdaCt'2b.;&
6 exaetlyslrc.rs
V no treads
/
-f Thm* coins are tossed. simhEodt ill firc and Ere fofiowiry
observdics a,re ..rde. Tk€e lba&=1!l#.iib€+ o<ar*ty trc
heads:3{14 tim€s. fficfry 1be*l:fuFsES r3rhs..lc:1fl} tigg5-
a1q fsq* rs' ETq tfln-K?d tRigr f{q sffi qtq .A fr fu : t16
<R,#6**tff*i€: s8{ix,#at*'g+ f'qa : mq.dfuar6,
13s ETr{ uq ftq+- {ir * * * qd, * f{q a1 sfTsd ffi +itsq r
{a} *-+..-#*. zfud;t aH
&) d}+-6tfi sfud
tc) *?{ fqd +gT
sEcTtoN-D / soir{
Cluesfin numbers 25to 34 carry four marks eactr.
?age7 of 11

8. Ti ffi H re"H q{ e|F*T| {Fq Ed d =ft fr fdq t sG rnt{-ash eE
sft Efr ? 10 {ffi *r gq effi fr idqtfirs sqt€,*q fdf€q ain aTrts
dtrsq r ;rr.i.s * s'fr + fldq {ffi sd alqq r
The pnrking drarge of a car arr lrGerar Deltri Raikr,'ay statiarr fc'r first
twohoursaret 50and? L0fox haurg Writeduyrmalirffi
eryraticn a:rd drar*. the grryh o{ rl** &ta- R€ad t}E .hargss for six
hsurs&sr the graph-
/
6 tfuHT q*ffi{str ?s + y :6:fn ::-y+Z:o* aT*H df{q I F{.r.l
s*r*-{q Ggsnqlfuqr :
Dran' the graph of linea'r equrtions ?t + y : 6, 2x - y + 2 :G Erd d
E:e poi*t of *re intessectifrr-
altpfr q, € AABC+'T *gat BC+i AD, a .
b q cfffiI fr, di ar{ABD) :
ar {ABC} Am +1itrgr
BffiP-aaMDbt-
In t$Fngure, irrAABC, if AD divides ECin Breratioa:b. trsr M
ariABD) : m {ABC}.
A
4
I
AAEC{ qffi a *te* e"sq€ tql{m€ + rrq?iqgga *qtgd
dt ;p+fl, fug* D *{ E qt frcr*' * t@ rrq } r fiqra Efrf'fi f* elq m
: Qp{cetr
I$ AAEC, thepeg1letrdii-'utrsrs fsosrriedir,.es A acrd S er thelr
oppesite sides tret {urhangro&rced} the {trcrlsrcilc{ecf t}te
tria+g1e at p*irrts D and E re.sp*cti-rie$y.
Frcve that*rcCD:alcCE.
C
?age & ai a'1

9. ,/
rV qs frTq aec r,? Til ecq{ ?dE
Rerrtk ae:er t r'+
'afu c q €iq{' i6rr{r: ac ait{ pa *-**u* og 6 qr fu n .n
sffiq *r* * +Hr rs r{" f f€'* nt *rh rq*cD rsqfriq qg .tre *r
BPc
P is a point sn the
ltte ac rr
"
dfui" AE d that AB : Ap.rhrough A and c' rines are drar.,a t;dd -F*,J **
;TT"Ty: T
t: intetrs:c-ts ar D c sla _il;;;. showthat ABCD is a cyclic
gaanUretrl-
y qs ftW aec6i rqqt #*q, ffi Bc:4.F*.*., AB+AC:* *.qi.
H*lf gg:45o fr 1
Coqrstn*ct a AABC ln q&khK:4.5 <a,.dB +AC:g cnsrd/B=45 .
.t
i*
5 t
Page g al 11

10. $afffi*qralpwiarEigf{*miFIq{rz*ffie€EryqrqqqFI{
deil a.ft w_ffi qm * *-*m-Ef" e .er+-fi ar *sa itrci ai at ? a-a
t r rffa q qA,.€ q€ ar c *i *' E6'Rq fu dqt qn eirai a1 firqq +qr tr
FrqhfisaY*iiq's<tdFils- :
i4 qrtkq fu qfu *rft"iq fqts Y* q,giiqd kql
(iil qaAl.EI fEn{?r a-fr qr?
i*r qe t qi-{ € {e,{ a-di n 'r*r
ert F?
-qlF€fi t?
.$hnt
,il
A oralrwho had a pf{ irt the shape o{ ep*allelagrao dieidEd*i5 tb
equa! g*ds and g*ve L" tf*oa Pat tcf*i*
"*rshieh
sgainwls iB6' -'F
of a parallelograar' The sotr J**g $at 6trte w85 rto s€*too{
i
* r|;e
decides to ogea a school tltece'
Answer the following qrrestions:
t4 51tow lrcw .ttl;tli. decisiur o{ furm be b}Pb@f€d. ryF
did tlre scr gPt ? EryPlala-wi& EglE€
tiil Was the son'e decision riglt ?
i"if lttrat vatue of tlre strr is deeictedhere ?
V wrtre +r sTFr?rt 3sss8 arstt ErrfiTdq tr*q:f, x'm alfqqr
The t'olllme of sphe:e * 38€ffi m9' Find its surfrce al=a'
'/
q4 Er*-d erd*qn*T{ q-'dt u,1 sidft€ g1{ ffil 1'*qFEr{l: 24 cm*
' 2F ** € t qE Efi* 5s *eq,ft d t{+ E,r €r{ { s'05 sfr o'd' * d'{
*1qqr ffiwrq?r;;;?r;*fqet
The ir3te'rral and exteffial dimreters of iE holtronn ae**$uecat vesel
ilriF
24 csr,artd 25 clrr reqrectively' If tle tost d Pak*it€ 1 csta sf *re
s*rface a*ea is ? o.0F fi*d. &e iotal cest of p€ir'tisg &e *esset all aver.
?age 1A of 11

11. Mavks Itlffarbes af stud:rfs
30-40 11
40-50
1*-ffi I
68 -70 2*
70-80 22
EO-90 2
90 -1BO .}
q*'
Drarv a freqrtency pctl'gcn of ihe fofqb,
Tage 11 at
31€S' ]?I€*FTqI EFT€@I}
30 -4S 11.
40-50
50-6& I
@-74 20
7S- 80 22-
88-S .,
?s-1@ J