ICSE- Mathematics Sample Paper-1-solution-Class 10 Question Paper

7/23/2019 ICSE- Mathematics Sample Paper-1-solution-Class 10 Question Paper

1/19

@K[D W | BM^GDBM^@K[

[mbpid Smpdr = [oiutòe

ww.toppdridmreèl.kob =

@K[D Aomrn

Kimss W Bmtgdbmt`ks


[DK^@OE

M (>3 Bmrjs)

]. =.

(m) Sut x 1 2 3 x 2 1 è 1 ; 6jx x Ay Fmktor ^gdordb, tgd rdbmèndr oatmèdn oe n`v`nèl 1jx -;x + 6 ay x 1

2 1j(1) -;(1) + 6

Sut ; 3 ;x x è 1; 4x x j

[`bìmriy, tgd rdbmèndr oatmèdn ay n`v`nèl ;x1+ 4x j ay x + ;

2 ;(;)1+ 4(;) j

Eow, 1j(1) - ;(1) + 62 11Z;(-;) + 4(-;) - jR

>j 6 + 6 2 1Z1< =4 jR

>j 2 1(=1 j)>j 2 1> 1j

>j + 1j 2 1>6j 2 1>

[o, j 2 >.

(a)

^gus, MA AM

= 3 3 = 3+3 =+3 3 =MA 2 2 23 -= = 3 3-= 3+3 -= 3

3 = = 3 3+3 3-= 3 -=AM 2 2 2

= 3 3 -= =+3 3-3 = 3


2/19



ww.toppdridmre`el.kob 1

(k) Idt tgd sub of boedy idet out 2 Qs. x

Mbouet rdkd`vdn mftdr oed ydmr

1

=133

er

S

1=

1

1

72 x =+

133

=2 x =+

14

162 x

14

60

(a);

1x 24x

11x - 4x - ;23

1x + = 2 3 or x ; 2 3

1x16x + x ; 2 3

1x(x 6) + =(x ;) 2 3-=

x21

or x 2 ;


3/19



ww.toppdridmre`el.kob ;

(k)

`. L`vde8 ]Q 2 ]S

]SQ 2 ]QS

b]SQ + bQS] + bS]Q 2 =73

1b]SQ +

b]QS 2 bQS] 2 4>

Eow, bSO] 2 1b]QS 2 =37

For melids `e mitdremtd sdlbdet

bK]S 2 b]QS 2 4>

Men bKS] 2 b]SK 2 4>

``. Eow, bK]S + bKS] + bSK] 2 =73

4>+ 4>+ bSK] 2 =73

=37+ bSK] 2 =73

bSK] 2 =73- =372


4/19



ww.toppdridmreèl.kob >

]. ;.

(m) ôtmi mbouet ndpos`tdn ay Bmeu è 4 ydmrs 2 Qs. 1>3 63 2 Qs. =>,>33

Dqu`vmidet prèk`pmi for = boetg 263(63 + =)

Qs.1>3 2 Qs.>,;0,133

1

Idt tgd rmtd of ètdrdst ad r%

@etdrdst oe Qs. >,;0,133 for = boetg= r

2 Qs.>;0133 2 Qs.;66r=1 =33

Bmtur`ty mbouet 2 =

Or =>>33 + ;66r 2 =

r 2 0%

(a)

Ideltg of n`mloemi 2 MK 2 1m 2 47 1 b 47 1

r 2 2 10 1 b1

Mrdm of wgoid imwe 2 mrdm of MAK + Mrdm of

sdb`-k`rkid oe MK ms n`mbdtdr.

1

1

= (10 1)2 47 47 +

1 1

11 7>= 1

2 10 47 + < 1

2 >;14.=> b


5/19




(k)

`. Ko-ornèmtds of kdetro`n, = 1 ;x + x + x

x 2

;

= + ; + < ==2 2

; ;

Men, = 1 ;y + y + y > + 1 + 4 ==

y 2 2 2; ; ;

[o,

== ==L 2 ,

; ;

``. ^gd dqumtòe of m ièd, tgroulg L men pmrmiidi to MA.

[iopd of ièd 1 =

1 =

y - y 1 - > 1MA 2 2 2 - 2 -=

x - x ; - = 1

Eow, dqumtòe of ièd tgroulg L men pmrmiidi to MA,

= =y - y 2b(x - x )

== ==y - 2 -= x -

; ;

;y - ==2 -;x + ==

;x + ;y - 1123

]. >.

(m) 1 = =

1 x ; :x Q.; ; ;

7 = =3x

; ; ;

Zay suatrmktèl

=

;, wd ldtR

7 = = = =3 =x +

; ; ; ; ; ;

0 0x

; ;

; x ;

[oiutòe `s x 8 x Q, ; x ;


6/19




(a)

1o o o o

o o

sè(03 -

(k) ô iokmtd tgd bond frob tgd g`stolrmb, wd prokddn ms foiiows8

` Fèn tgd bonmi kimss. Qdktmelid MAKN `s tgd imrldst rdktmelid. @t rdprdsdets tgd

bonmi kimss, tgmt `s, tgd bond i`ds è tg`s rdktmelid. ^gd bonmi kimss `s =313.

`` Nrmw two ièds n`mloemiiy frob tgd vdrt`kds K men N to tgd uppdr koredrs of tgd two

mnhmkdet rdktmelids. Idt tgdsd rdktmelids ètdrsdkt mt poèt G.

``` ^gd x-vmiud of tgd poèt G `s tgd bond. ^gus, bond of tgd l`vde nmtm `s

mpprox`bmtdiy =4.

[o, bond 2 =4


7/19



ww.toppdridmre`el.kob 3 Bmrjs)

]. 4.

(m) B.S. 2 Qs. x, N`skouet 2 13% of x 2x

Qs.

4 Edw B.S. mftdr n`skouet 2

x >xQs. x 2 Qs.

4 4

Mlm`e n`skouet 2 4% of>x = >x x

2 2 Qs.4 13 4 14

Kgmeldn B.S. mftdr 1enn`skouet 2 >x x =0x

2 Qs.4 14 14

Eow, 1107.1> 2=0x =0x

+ 7% of14 14

=0x 7 =0x1107.1> 2 + 14 =33 14

=0x ;7x1107.1> 2 +

14 614

> 2

614

4=;x1107.1> 2

614

1107.1> 6142 x

4=;

x 2 Qs. 1733

B.S. 2 Qs. 1733


8/19




(a)

Ideltg of tgd w`rd usdn è oed rouen 2 ; bb 2 3.; kb

=1Eubadr of rouens rdqu`rdn to kovdr =1 kb of ideltg 2 2 >3

3.;

N`mbdtdr of tgd kyièndr 2 =3 kb Qmnùs of tgd kyièndr 2 4 kbIdeltg of w`rd rdqu`rdn

1

1

for oed rouen 2 1r 2 1 4 kb 2 =3 kb

Ideltg of w`rd rdqu`rdn for >3 rouens 2 =3 >3

2 >33 kb 2 >33 ;.=> 2 =146 kb

; ;Eow,rmnùs of tgd w`rd 2 bb2 kb

1 13

;Voiubd of tgd w`rd 2 r g 2 =14

13

;

1

6 kb

\d`lgt of tgd w`rd 2 Voiubd of tgd w`rd 7.77 lb

;2;.=> =146 7.77 2 m +


9/19




[iopd (S]) [iopd (MM) 2 =

> a =1 2 =

< m + 7

a + =3> 2 3

>m + men dqumtòe (1) ay < wd ldt

=6m + 17a 2 ;=1

>0m 17a 2 3

=3>3

m 2 2 =6,64

Sut m 2 =6 è dqumtòe, wd ldt

>m + , =) mrd piottdn to forb m

rdktmelid.

^gd rdktmelid so forbdn men tgd rdfidktdn rdktmelid mrd sgowe è tgd f`lurd8

@t `s rdfidktdn tgroulg x 2 4, tgde tgd koornèmtds of tgd edw rdktmelid adkobd

M(6,=), A(6,=), K(=>,=) men N(=>,=)

Sdr`bdtdr of MAKN 2 MA + AK + KN + NM

2 1 + 7 + 1 + 7 2 13 ue`ts

Mrdm 2 I A 2 AK KN 2 7 1 2 =6 sq.ue`ts


10/19



ww.toppdridmreèl.kob =3

(a)>

1

x + = = 1

> 1

1 1

1 1

1

1

1 1

1 1

1

1

x + 1x + = =< + 72

x 1x + = =< 7(x + =) 14

2(x =) 0

(x + =) 42

(x =) ;

Tsèl kobpoedeno men n`v`ndeno mlmè,

x + = + x = 4 + ;2

x + = x + = 4 ;

1x 7

21 1

x 2 >

x2 1

(k)

Bè. amimekd for tgd boetg of Hued 2 7673.33

Bè. amimekd for tgd boetg of Huiy 2 6=73.33

Bè. amimekd for tgd boetg of Mul 2 6=73.33

Bè. amimekd for tgd boetg of [dpt 2 6=73.33

Bè. amimekd for tgd boetg of Okt 2 6=73.33

Bè. amimekd for tgd boetg of Eov 2 6463.33

Bè. amimekd for tgd boetg of Ndk 2 33.33

ôtmi 2 ;0, 063.33

S 2 Qs. ;0,063

@ 2 Qs. (40>3.73 4=) 2 Qs. =00.73

Q 2 ?,=

^ ydmrs=1

Tsd,S Q ^

@ 2=33

;0,063 Q ==00.73 2

=1 =33

=00.73 =1 =33Q 2 2 6%

;0063


11/19



ww.toppdridmre`el.kob ==

].a

m a + =2

x 1a

1max 2

a + =

(a)

1

; 1

1 ; 1 ; < =1M M.M

= 1 = 1 > 4M M .M

> < = 1 =4 16

Eow, I.G.[. 2 M;>M1+ M

16 >4 < =1 1 ;>

=4 16 > < = 1

16 >4 17 >7 1 ;

=4 16 =6 17 = 1

3 33 Q.G.[.

3 3


12/19




(k) Gdrd wd eddn to f`en tgd bdme ay tgd bdme ndv`mt`oe bdtgon.

`x `f , 4``x M

u g

g

` `

f u

=4 4 > 13

13 7 ; 1>

14 == 1 11

;3 13 = 13

M 2 ;4 1; 3 3

>3 =7 = =7

>4 =; 1 16

43 ; ; 0

44 = > >

=31`

f 10` `f u

Frob tgd tmaid,` ` `M ;4, f =31,g 4, fu 10

[o, Bdme ` ``

f ux 2 M + g

f

102 ; 4 + 4

=31

=>42 ;4

=312 ;4 =.>1

2 ;;.47


13/19



ww.toppdridmre`el.kob =;

].7.

(m)

[kordsOatm`edn Eubadr of[gootdrs K.f.

3-=3 4 4

=3-13 0 =>

13-;3 =6 ;3

;3->3 11 41

>3-43 16


14/19



ww.toppdridmreèl.kob =>

`. e 2 =13 (dvde)

^gd pos`tòe of tgd bdn`me `s l`vde aye =13

2 2 631 1

[o, frob tgd lrmpg, bdn`me 2 >; skords

``. ^gd pos`tòes of =] `s l`vde ay e =132 2 ;3> >

[o, frob tgd lrmpg,=

] 2 ;3 skords

^gd pos`tòe of;

] `s l`vde ay;e ; =13

2 2 03> >

[o, frob tgd lrmpg,;

] 2 4< skords

Eow, @etdr-qumrtìd rmeld 2;

] -=

] 2 4< ;3

2 1< skords

```. eubadr of sgootdrs wgo oatmèdn bord tgme 24 DIM AIK

DI MD DI 1AK

2 2 DI 2 1AIAI AK AI AK


15/19




]. 0.

(m) Bmrjdt vmiud of = sgmrd 216 ==3

Qs. 2 Qs.17.73=33

(`) Eubadr of sgmrds aoulgt 2 13,313 13,31,3332 2


16/19




(k)

I.G.[.

tmeM =

=tmeM(= tmeM)= tmeM

1

;

tme M =

(tme M =) tme M(tme M =)

tme M =

tmeM(tmeM =)

Tsd ; ; 1 1m a (m a)(m ma a ) 1

1 1

(tme M =)(tme M tme M =)

tmeM(tmeM =)

tme M = kot M

sè M kosM=

kosM sè M

sè M kos M == =

sè MkosM sè MkosM

= kosdkMsdkM

Q.G.[

Gdekd Srovdn

].=3.

(m)

Idt tgd eubadrs ad x men y:

[o 1=06

xy 2 =06 x 2 men ==1x 2 yy

Sut=06

x 2y

è 1==1x y , wd ldt

1==1 =06 2 yy

y 2 ==1 =06 y 2 17

Men=06

x 2 2 =33

;=14 Q

2 = +6> =33

;

; ;

=14 Q2 =+

6> =33

4 Q2 = +

> =33

^mjèl kuad of aotg tgd s`nds

4 Q 4 =33 + Q2 = + or 2

> =33 > =33

Or 433 2 >33 + >Q

Or >Q 2 =33 Q 2 14

Qmtd 2 14%


18/19




(k)

Idt W] 2 x b men SQ 2 g b tgde PQ 2 W] 2 x b

Men PW 2 Q] 2 >3 b

@e SQP, g

tme >4 g xx

@e S]W, g >3

tme63 g >3 ;xx

g >3 ;g Z g x R

>3 2 ;g g

>3 2 g( ; =)

Or

>3g 2

; =

; + =>3

2 ( ; =) ; + =

>3(=..6 + >3 2 0>.6 b

``. ^gd n`stmekd W] 2 x 2 g 2 4>.6 b

].==.

(m)

`. MB 2 BS Ztmeldets frob me dxtdremi poètR

BMS 2BSM

[`bìmriy, BS 2 BA

BAS 2BSA

Eow è MAS,

bSMA + bMAS + bMSA 2 =73

bBSM + bBSA + bBSM + bBSA 2 =73

(bBSM + bBSA) 2 =73

bMSA 2 03

``. MB 2 BS men BS 2 BA

MB 2 BA

^meldet mt S a`sdkts MA.


19/19



(a) ôtmi boedy for dxpdesds 2 Qs. ;63

Or`lèmi nurmtòe of tour 2 x nmys

Fèmi nurmtòe of tour 2 x + > nmys

Or`lèmiiy, = nmy dxpdesds 2;63

.Qs

x Fèmiiy, = nmy dxpdesds 2

;63.

>Qs

x Mkkornèl to tgd qudstòe,

1

1

1

1

;63 ;632 + ;

x x + >

;63x + =>>3 ;63x 2 ;x + =1x

;x + =1x =>>3 2 3

x + >x >73 2 3

x + 1>x 13x >73 2 3x(x + 1>) 13(x + 1>) 2 3

(x 13)(x + 1>) 2 3

^gus, x 2 13, 1>

Nmys kmeeot ad edlmt`vd, [o, x 2 13.

(k) Idt,MKW 2 menMAW 2

`. L`vde, dqumtòe of MA, x ;y = 3

[iopd of MA

kodff`k`det of x

kodff`k`det of y

= =2 2

; ;

[o,=

=(b ) 2 tme 2

;

2 ;3

Melid bmnd ay tgd ièd MA 2 ;3

Eow, dqumtòe of MK, x y 1 2 3

[iopd of MK 2kodff`k`det of x

2 kodff`k`det of y 2=

==

[o, 1

(b ) 2 2 =tme

2 >4

Melid bmnd ay tgd ièd MK 2 >4

``. bAMK 2 bK A 2 >4 ;32 =4

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ICSE- Mathematics Sample Paper-1-solution-Class 10 Question Paper