kerala-math sample paper-1-solution-class 10 question paper
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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_chpim ^cpmr3 _aiutka`
ww.tappmrimcr`k`j.oah 3
Emrcic _tctm Facrd
Oicss R Hctbmhctkos
_chpim ^cpmr 3 _aiutka`
3. U6X
c) Cijmfrcko larh, x`8 6` + =
Lkrst tmrh 8 x38 6 + = 8 :
@aw, tbm smoa`d tmrh8 x686(6) + = 8 ;
Oahha` dkllmrm`om 8 x6x38 ; : 8 6
3 `
` ` ` `f) _uhal lkrst '`'tmrhs (x x ) (: 6 =) (6` 36) 6(` (C`jim k` c smhk-okroim)
hRCF 8 32>;>4>8 => (suh al tbm c`jims al c )
hR[F 8 hRCF 8 => (c`jims k` tbm schm smjhm`t al cokroim)
?. Imt p(x) 8 px6
+ =x + r_k`om x 6 ks c lcotar, p(6) 8 > U6X
p(6)6+ =(6) + r 8 >
4p + 3> + r 8 >
r 8 (4p + 3>) (k)
_k`om x 3
6ks c lcotar, p
3
68 >
p
63
6 + =
3
6 + r 8 >
r 8 p 3>
4
(kk)
Lrah (k) c`d (kk), wm bcvm
(4p + 3>) 8 p 3>
4
3
8 p + 3>
3=p 8 ?> p 8 6
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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_chpim ^cpmr3 _aiutka`
ww.tappmrimcr`k`j.oah 6
^uttk`j p 8 6 k` (k), wm jmt r 8 (2 + 3>) 8 6
_a, p 8 r 8 6
Bm`om, pravmd.
4. Tatci surlcom crmc al tbm fuoemt U6X
8 Ourvmd surlcom crmc al tbm fuoemt + Crmc al tbm fattah
8 i(r3+ r6) +(r6)6
6 6
3 6@aw, i b +(r r )
i ;>> 3>> 3>>> 3> 3> oh oh 8 ?3.3> (6> + 3>) + ?.34 (3>)6
8 ?3.43> ?> + ?34
8 (;463> + ?34) oh6
=. Lrah tbm lkjurm, U?X
a a3 3h C^F h CAF 33> ==
6 6
(_k`om, c`jim hcdm fy c` cro ct c`y pak`t a` tbm citmr`ctm cro
ks mquci ta bcil tbm c`jim hcdm ct tbm om`trm)
K` CAF, ACF 8AFC (sk`om AC 8AF)a32> 33> :> ?=
6 6
_k`om, SF_ ks c tc`jm`t ct F c`d AF ks rcdkus, AF S_
a
a a a
h AFS ;>
@aw, h CFS h AFS h AFC ;> ?= ==
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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_chpim ^cpmr3 _aiutka`
ww.tappmrimcr`k`j.oah ?
Tbus, oa-ardk`ctms al tbm pak`t C crm (6oas?>, 6sk`?>)
? 36 ,66 6
?,3
f) @aw, hFAR 8 ;>+ ?>8 36>
@aw lrah (k), oa-ardk`ctms al F (6oas36>, 6sk`36>)
3 ?6 , 6
6 6
3, ?
:. c) Vmhck`dmr tbmarmh m`surms tbct x + ? wauid fm c huitkpim al q(x) 8 x?+ U?X
Tbus, wm ociouictm q(?) c`d obmoe
q (?) 8 (?)?+
_k`om, q(?) 8 >, fy Vmhck`dmr tbmarmh, x + ? ks c huitkpim al q(x).
f) Imt l(x) 8 x?px6+ x +
V V
?< ;p ?p ?>
c) @uhfmrs dkvkskfim fy 6crm 6, 4, , 36, 34, 3, k.m., 3> k` cii.
@uhfmrs dkvkskfim fy ?crm ?,
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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_chpim ^cpmr3 _aiutka`
ww.tappmrimcr`k`j.oah 4
f) @uhfmrs dkvkskfim fy 3>crm 3>, c`d 6>, k.m., 6 k` cii.
@uhfmrs wbkob crm `at dkvkskfim fy 3> 8 6> 6 8 32
Vmqukrmd prafcfkikty 832 ;
6> 3>
U?X
AV
c) Tatci `uhfmr al ocrds 8 =
Tatci `uhfmr al qumm`s 8 3
@uhfmral lcvaurcfimautoahms 3^(jmttk`j c qumm`)
@uhfmr al tatci passkfim autoahms =
f) Zbm` tbm qumm` ks drcw` c`d put cskdm, tbm tatci `uhfmr al rmhck`k`j ocrds wkiifm 4.
k) Tatci `uhfmr al coms 8 3
3^(jmttk`j c com)
4
kk) Cs qumm` ks cirmcdy drcw`, tbmrmlarm, tbm `uhfmr al qumm`s wkii fm >.
>^(jmttk`j c qumm`) >
4
;. Kt ks e`aw` tbct tbm tc`jm`t ct c`y pak`t al c okroim ks pmrpm`dkouicr ta tbm rcdkus
tbraujb tbm pak`t al oa`tcot. U?X
hAT^ 8 ;>
K` c trkc`jim, tbm hmcsurm al c` mxtmrkar c`jim ks mquci ta tbm suh al tbm hmcsurms alkts k`tmrkar appasktm c`jims.
Tbmrmlarm, k` ^CT,
ACT 8C^T +CT^
ACT 8 x + yK` ACT, AC 8 AT (Vcdkk al tbm schm okroim)
ACT 8ATC
x + y 8 AT^ CT^
x + y 8 ;>y
x + 6y 8 ;>
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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_chpim ^cpmr3 _aiutka`
ww.tappmrimcr`k`j.oah =
3>. U?X
Hkd vcium al oicss
(x)
Lrmqum`oy
(l)
lx
= 36 3= : 3>=
6= 3< 4>>
?= 36 46>
4= 33 4;=
== : ?2=
>
Tatci l 8 3>> lx 8 4?>>
lx 4?>>Hmc` 4?
l 3>>
33. c) Imt us cssuhm tbm lkrst tmrh cs x c`d oahha` dkllmrm`om cs d. U?X
3=tbtmrh 8 x + 34d
_uh al tbm lkrst 3= tmrhs 8 ` 33
_uh al lkrst 3= tmrhs (x x )
6
33=(x 34d x) 3=x 3>=d
6
Cs tbks suh ks :?=, wm bcvm
3=x + 3>=d 8 :?= (k)
=tbtmrh 8 x + 4d 8 ?3 (kk)
(kk) 3= 3=x + d 8 4
6:>d > oh6
Fy Bmra`s larhuic7
Crmc al c trkc`jim s(s c)(s f)(s o), .
(c f o)wbmrm s ks tbm smhk-pmrkhmtmr
6
c 8 3?, f 8 3>, o 8 3? crm tbm skdms.
(3? 3> 3?) ?)(32 3?)
6
32 (=) (2) (=)
; (3 oh6
Tbus, tatci surlcom crmc al tbm pyrchkd
8 Crmc al tbm squcrm + Crmc al laur trkc`jims
8 3>> + 64>
8 ?4> oh6
3?. c) _k`om tbm vmrtkoms crm C, F, O, D tbm oa-ardk`ctms al tbm pak`ts crm C(?, 6), F(?, 6),O(?, 4), c`d D(?, 4). U?X
f) Im`jtbs al dkcja`cis
66
6 6
CO ? ? 6 4 ?< ?< < 6 u`kts
FD ? ? 6 4 ?< ?< < 6 u`kts
o) ^mrkhmtmr
_k`om CFOD ks c squcrm, pmrkhmtmr 8 4 a`m skdm 8 4 CF
6 6
CF ? ? 6 6 < u`kts
Tbus, pmrkhmtmr 8 4 < 8 64 u`kts
d) Crmc al c squcrm 8 < < 8 ?< sq. u`kts
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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ww.tappmrimcr`k`j.oah :
34. c) Twa mquci raats dksorkhk`c`t 8 >
f64co 8 >
(=)64 4 e 8 >
6= 3
3, wm bcvm ta cdd (?x + 6) ta tbm jkvm` paiy`ahkci.
Tbus, (?x + 6) sbauid fm cddmd ta ?x?6x6ta jmt c paiy`ahkci lar wbkob fatb (x
3) c`d (x + 3) crm tbm lcotars. U4X
AV
c) Oa`skdmr x6x 3 8 >
Dksorkhk`c`t 8 f64co 8 3 + 4 8 =
_k`om tbm dksorkhk`c`t ks pasktkvm, p(x) oc` fm wrkttm` cs tbm praduot al twa lkrst
dmjrmm paiy`ahkcis.
6
6
f f 4co 3 = 3 = 3 =x ,
6c 6 6 6
3 = 3 =x x 3 x x6 6
36x 3 = 6x 3 =
4
36x 3 = 6x 3 =
4
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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ww.tappmrimcr`k`j.oah 2
f) Oa`skdmr x6+ 6x 3 8 >
Dksorkhk`c`t 8 f64co 8 4 + 4 8 2
_k`om tbm dksorkhk`c`t ks pasktkvm, p(x) oc` fm wrkttm` cs tbm praduot al twa lkrst
dmjrmm paiy`ahkcis.
6
6
f f 4co 6 2 6 2 6 2x ,
6c 6 6 6
6 2 6 2x 6x 3 x x
6 6
36x 6 2 6x 6 2
4
36x 6 2 6x 6 2
4
x 3 6 x 3 6
3=. _tmps al oa`struotka`7 U4X
k. Drcw ^SV wktb jkvm` hmcsurmhm`ts.
kk. Drcw c`jim fksmotars al ^ c`d S, c`d imt tbmh k`tmrsmot ct A.kkk. Drcw c pmrpm`dkouicr lrah A_ a` ^S.
kv. Tcek`j A cs c om`trm c`d A_ cs c rcdkus, drcw tbm okroim.
v. Tbm okroim drcw` ks tbm rmqukrmd k`okroim.
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7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper
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ww.tappmrimcr`k`j.oah ;
3; 334 8 3>4 3>; 8 =
Tbmrmlarm, tbm jkvm` smqum`om ks c` C.^.
Lkrst tmrh, c 8 334
Lar lk`dk`j lkrst `mjctkvm tmrh, T`9 >
c + (` 3)d 9 >
334 + (` 3)(=) 9 >
334 =` + = 9 >
33; =` 9 >
=` 9 33;
=` 0 33;
33;`
=
` 0 6?.2
Tbmrmlarm lkrst `mjctkvm tmrh ks 64.
o) _k`om t 8 _` _`3
8 `6 + :` U(` 3)6 + :(` 3)X
8 6` +
3:. U4X
Zmkjbt (ej) @uhfmr al k`lc`ts
Fmiaw 6.=>> 4
Fmiaw 6.> 4 + < 8 3>
Fmiaw 6.:=> 3> + 2 8 32
Fmiaw 6.2>> 32 + 3> 8 62
Fmiaw ?.>>> 62 + 36 8 4>
Fmiaw ?.3=> 4> + 3> 8 =>
Fmiaw ?.6=> => + 2 8 =2
Fmiaw ?.?>> =2 + : 8 >
Vmictka` fmtwmm` tbm `uhfmrs
x y
6.=>> 4
6.> 3>
6.:=> 32
6.2>> 62
?.>>> 4>
?.3=> =>
?.6=> =2
?.?>> > :>
Bmrm tbm hmdkc` ks tbm `uhfmr wbkob jkvms y 8:>
68 ?=
Tbm `uhfmr y 8 ?= aoours fmtwmm` y 8 62 c`d y 8 4>
Lrah tcfim, wm smm tbct
y 8 62 oarrmspa`ds ta x 8 6.2>> c`d y 8 4> oarrmspa`ds ta x 8 ?.>>>
]sk`j prapartka`cikty cssuhptka`7
x 6.2>> ?= 62
?.>>> 6.2>> 4> 62
x 8 6.2>> + >.6>>
:
36 8 6.;3.
kk. Tcem CL 8 FO 8 = oh.kkk. Cjck` tcem hL 8 hO 8 36>c`d LM 8 OD 8 = oh.
kv. Oahpimtm tbm bmxcja` CFODML.
v. Drcw fksmotars al c`y twa _kdms scy, CF c`d FO, imt tbmh hmmt ct A.
vk. Gak` AF.
vkk. Tcem A cs c om`trm c`d AF cs c rcdkus, drcw tbm okroim.
CFODML ks tbm jkvm` rmjuicr bmxcja` al skdm = oh
Okroim wktb om`trm A ks tbm rmqukrmd okroim.
6>. K` tbm lkjurm A ks tbm gu`otka`. Imt C c`d F fm tbm pasktka` al tbm ocrs cltmr a`m baur. Imt x c`dx + 3> fm tbm dkstc`oms trcvmiimd fy tbm ocrs cltmr a`m baur.
@aw CAF ks rkjbt c`jimd ct A.
Fy ^ytbcjarcs Tbmarmh, x6+ (x + 3>)68 =>6
x6 + x6 + 6>x + 3>> 8 6=>>
6x6+ 6>x 64>> 8 >
x6+ 3>x 36>> 8 >
(x + 4>)(x ?>) 8 >
_a x 8 4> ar ?>
_k`om dkstc`om oc``at fm `mjctkvm, bm`om x 8 ?>.
Tbm dkstc`om trcvmimd fy tbm ocr wbkob wm`t `artbwcrds 8 ?> eh
Tbm dkstc`om trcvmimd fy tbm ocr wbkob wm`t wmstwcrds 8 4> eh
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_chpim ^cpmr3 _aiutka`
ww.tappmrimcr`k`j.oah 3?
AV U=X
Imt b fm tbm bmkjbt al tbm ikjbt bausm.
Imt O, D fm tbm pasktka`s al tbm twa sbkps.
OD 8 6>> h
Imt FO 8 x h
K` CFO,
aCF tc`4=FO
b3
x
b x
K` CFD,
CFtc`?>
FD
b 3
x 6>> ?
? b 8 x + 6>>
Fut b 8 x
? b 8 b + 6>>
? b b 8 6>>
? 3 b 8 6>>
6>>b
? 3
6>> ? 3b
? 3 ? 3
b 3>>( ? 3)
b 8 3>> 6.:?6 8 6:?.6 h
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ww.tappmrimcr`k`j.oah 34
63. c) Tbm mquctka` al tbm jkvm` ik`m ks ?x 6y + ; 8 > U=X
?x 6y 8 ; ... (k)
Ta obmoe wbmtbmr (3, pcssms tbraujb tbm pak`t (3,
Tbks ks tbm rmqukrmd mquctka` al tbm ik`m.
o) Kl (x3, y3) ks c pak`t a` tbm ik`m ?x 6y + ; 8 >, tbm`,
?x36y38 ; ... (3)
Kl (x6, y6) ks c`atbmr pak`t a` tbct ik`m, tbm`,
?x66y68 ; ... (6)
Lrah (3) c`d (6),?x36y38 ?x66y6
?x6?x38 6y66y3
?(x6x3) 8 6(y6y3)
_iapm 8 6 3
6 3
y y ?
x x 6
_iapm al tbm ik`m ?x 6y + ; 8 > ks?
6
_k`om tbm siapms al tbm twa ik`ms crm mquci, tbm ik`ms crm pcrciimi.
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66. Imt ikst prkom al tbm faae 8 Vs. x U=X
C`d k`ormcsmd prkom al tbm faae 8 Vs (x + 3>)
Cooardk`j ta qumstka`,
36>> 36>>3>
x x 3>
3 3
36>> 3>x x 3>
x 3> x
36>> 3>x(x 3>)
36>> 8 x(x + 3>)
x6 + 3>x 36>> 8 >
(x + 4>)(x ?>) 8 >
x 8 4> ar x 8 ?>
Fut x ks tbm oast al tbm faae c`d bm`om oc`'t fm `mjctkvm. _a, x 8 ?>.
Tbus, ikst prkom al tbm faae ks Vs. ?>
6?. ^m`city lar 3stdcy 8 Vs. 6>> U=X
^m`city lar 6`ddcy 8 Vs. 6=>
^m`city lar ?rddcy 8 Vs. ?>>, c`d sa a`.
Tatci pm`city 8 Vs. 6::=>
Tbm smqum`om al pm`city larh c` C.^. wktb c (lkrst tmrh) 8 6>>, d (oahha` dkllmrm`om)
8 =>
Imt tbm oa`struotka` ware jat dmicymd fy ` dcys.
_`8 6::=>
`
6U6 6>> + (` 3) =>X 8 6::=>
`U =>` + ?=> X 8 6::=> 6
=>`U` + : X 8 6::=> 6
Dkvkdk`j fatb skdms al tbm mquctka` fy =>
`U` + :X8 333>`6+ :` 333> 8 >
`(` + ?:) ?>(` + ?:) 8 >
(` ?>)(` + ?:) 8 >
` ?> 8 > ar ` + ?: 8 >
` 8 ?> ar ` 8 ?:
_k`om tbm `uhfmr al dcys oc``at fm `mjctkvm, ` 8 ?>.
Tbus, tbm `uhfmr al dcys lar wbkob tbm oa`struotka` ware wcs dmicymd ks ?>.
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