kerala-math sample paper-1-solution-class 10 question paper

7/23/2019 Kerala-Math Sample Paper-1-SOLUTION-Class 10 Question Paper

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EMVCIC R | HCTBMHCTKO_

_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` dkllmrmòm 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_kòm x 6 ks c lcotar, p(6) 8 > U6X

p(6)6+ =(6) + r 8 >

4p + 3> + r 8 >

r 8 (4p + 3>) (k)

_kòm 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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ûttk`j p 8 6 k` (k), wm jmt r 8 (2 + 3>) 8 6

_a, p 8 r 8 6

Bmòm, 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

(_kòm, 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 (skòm AC 8AF)a32> 33> :> ?=

6 6

_kòm, 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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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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f) @uhfmrs dkvkskfim fy 3>crm 3>, c`d 6>, k.m., 6 k` cii.

@uhfmrs wbkob crm àt dkvkskfim fy 3> 8 6> 6 8 32

Vmqukrmd prafcfkikty 832 ;

6> 3>

U?X

AV

c) Tatci ùhfmr al ocrds 8 =

Tatci ùhfmr 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 ùhfmr al rmhck`k`j ocrds wkiifm 4.

k) Tatci ùhfmr al coms 8 3

3^(jmttk`j c com)

4

kk) Cs qumm` ks cirmcdy drcw`, tbmrmlarm, tbm ùhfmr al qumm`s wkii fm >.

>^(jmttk`j c qumm`) >

4

;. Kt ks eàw` 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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ww.tappmrimcr`k`j.oah =

3>. U?X

Hkd vcium al oicss

(x)

Lrmqumòy

(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` dkllmrmòm 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) _kòm 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

_kòm 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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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` paiyàhkci.

Tbus, (?x + 6) sbauid fm cddmd ta ?x?6x6ta jmt c paiyàhkci 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 =

_kòm tbm dksorkhk`c`t ks pasktkvm, p(x) oc` fm wrkttm` cs tbm praduot al twa lkrst

dmjrmm paiyàhkcis.

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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f) Oa`skdmr x6+ 6x 3 8 >

Dksorkhk`c`t 8 f64co 8 4 + 4 8 2

_kòm tbm dksorkhk`c`t ks pasktkvm, p(x) oc` fm wrkttm` cs tbm praduot al twa lkrst

dmjrmm paiyàhkcis.

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 kòkroim.


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ww.tappmrimcr`k`j.oah ;

3; 334 8 3>4 3>; 8 =

Tbmrmlarm, tbm jkvm` smqumòm 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) _kòm 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 ùhfmrs

x y

6.=>> 4

6.> 3>

6.:=> 32

6.2>> 62

?.>>> 4>

?.3=> =>

?.6=> =2

?.?>> > :>

Bmrm tbm hmdkc` ks tbm ùhfmr wbkob jkvms y 8:>

68 ?=

Tbm ùhfmr 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 guòtka`. Imt C c`d F fm tbm pasktka` al tbm ocrs cltmr a`m baur. Imt x c`dx + 3> fm tbm dkstcòms 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 ?>

_kòm dkstcòm oc`àt fm `mjctkvm, bmòm x 8 ?>.

Tbm dkstcòm trcvmimd fy tbm ocr wbkob wm`t àrtbwcrds 8 ?> eh

Tbm dkstcòm trcvmimd fy tbm ocr wbkob wm`t wmstwcrds 8 4> eh


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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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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 kòrmcsmd 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 bmòm 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 smqumòm al pm`city larh c` C.^. wktb c (lkrst tmrh) 8 6>>, d (oahha` dkllmrmòm)

8 =>

Imt tbm oa`struotka` ware jat dmicymd fy ` dcys.

_`8 6::=>

`

6U6 6>> + (` 3) =>X 8 6::=>

Ù =>` + ?=> X 8 6::=> 6

=>Ù` + : X 8 6::=> 6

Dkvkdk`j fatb skdms al tbm mquctka` fy =>

Ù` + :X8 333>`6+ :` 333> 8 >

`(` + ?:) ?>(` + ?:) 8 >

(` ?>)(` + ?:) 8 >

` ?> 8 > ar ` + ?: 8 >

` 8 ?> ar ` 8 ?:

_kòm tbm ùhfmr al dcys oc`àt fm `mjctkvm, ` 8 ?>.

Tbus, tbm ùhfmr al dcys lar wbkob tbm oa`struotka` ware wcs dmicymd ks ?>.

kerala-math sample paper-1-solution-class 10 question paper

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