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8/9/2019 2015 09 Sp Mathematics Sa2 Solved 01 Ans Kme
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CBSE Sample Paper-01 (solved)
SUMMATIVE ASSESSMENT –II
MATHEMATICS
Class – IX
Time allowed: 3 hours Maximum Marks: 90
S!UTINS"
1. (c)
2. (a)
3. (c)
4. (d)
5. Let the ede o! the cu"e "e # x u$its
%$creased ede #10 11
100 10
x x x units+ =
&rii$al sur!ace area # 26 x
'ew sur!ace area # 2121
6 x100
x
%$creased i$ area #2
2 2121 1266 x 6
100 100
x x x− =
∴ erce$tae o! i$creases area #2
2
126 x 100
6 x 100
x
x# 21
*. +rra$i$ the data i$ asce$di$ order:
5,5,5,*,*,*,*,-,-,-,,,9,9,10,10,11
* is re/eated maximum $um"er o! times that is 4 times
∴ Mode #*
-. %$ OAB∆ a$d ' 'OA B∆
&+ # &+
& # &
+ # +
∴ OAB∆ # ' ' 'O A B∆
' ' AOB A OB⇒ ∠ = ∠
. ro"a"ilit ("atsma$ hits a "ou$dar) #4
30
ro"a"ilit ("atsma$ does $ot hit a "ou$dar) #4 30 4 26 13
130 30 30 15
or −
− = =
9. +rea o! the recta$le # Le$th x readth
# /roduct o! adace$t sides
# 1* x
# 12 cm2
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&r
+rea o! a /aralleloram # ase x +ltitude
# 10 x *
# *0 cm2
10. iameter # 3.5 cm
∴ adius (r) #3.5
1.752
m m=
e/th (h) # 12 m
∴ 6a/acit o! the co$ical /it # 21
3r hπ
# 2 31 22
(1.75) 123 7
x x x m
# 3.5 kl7ectio$ 8 6
11. 2x 8 3 # 12
2 12
3
x y
−=
he$ x #02(0) 12
43
y −
= = −
he$ x #32(3) 12
23
y −
= = −
he$ x #*2(6) 12
03
y −
= =
lotti$ the ordered /airs (0,4),(3,2) a$d (*,0) a$d oi$i$ them, we et a straiht
li$e ;.
Thus, ; is the ra/h o! 2x 8 3 # 12
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12. %$ APB∆ a$d CQD∆ we ha=e
APB CQD∠ = ∠
+ # 6
&//osite sides o! /aralleloram +6[ || ] APB CQD AB CD and AB is a transversal∠ = ∠
APB CQD∴ ∆ = ∆
7i$ce APB CQD∴ ∆ = ∆
∴ Their corres/o$di$ /arts are e>ual
+ # 6;
13. Let 3 2( ) 3 2 7 2 p x x x x= − − −
3 2(2) 3(2) 2(2) 14 2 p = − − −
2 is a ?ero o! /(x)3 2
1 1 1 13 2 7 2
3 3 3 3 p
− − − − = − − −
#1 2 7
2 09 9 3
−− + − =
1
3
−⇒ %s a ?ero o! /(x)
1( 2)
3 x x
− +
( ) ( )3 2 23 2 7 2 3 5 2 1 x x x x x x− − + − − = +
1 x∴ = − is the third ?ero o! /(x)
14. + /aralleloram +6 a$d is its diao$al
ABD∆ a$d CDB∆ are co$rue$t.
7i$ce +6 is a /aralleloram the$
+ # 6 a$d + # 6
# commo$
ABD CDB∆ = ∆
15. %$$er radius o! the ra/hite (r1) # 0.5 mm
&uter radius o! the /e$cil (r2) # 3.5 mm
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∴ @olume o! the wood # 2 22 1
( )r r hπ −
2 222[(3.5) (0.5) ] 140
7 x= −
# 520 mm2 &r
r # -m, h # 3m
@olume o! the wheat 21
3r hπ =
31 227 7 3 154
3 7 x x x x m= =
2 29 49 58l h r m= + = + =
222 58l m=
1*. || AB CD∵ a$d + is a tra$s=ersal.
0180 A D∠ + ∠ =
0180 D A∠ = − ∠ # 1440
+ai$ + AA 6 a$d 6 is a tra$s=ersal
0180 B C ∠ + ∠ =
0180C B∠ = − ∠
# 990
∴ The re>uired measures o! 0 0 144 99 A and D are and ∠ ∠
1-. %$itial radius (r1) # - cm
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Se#$%o& – '
19. Bi=e$ 2 6 x y+ =
6
2
x y
−⇒ =
he$ 0 x = , the$6 0
32
y −
= =
he$ 2 x = , the$6 2
22
y −
= =
he$ 4 x = , the$6 4
12
y −
= =
e et the !ollowi$ ta"le o! =alues x a$d y
x 0 2 4
3 2 1(x, ) (0,3) (2,2) (4,1)
ased o$ the ta"le =alues /lotti$ the ordered /airs (0, 3), (2, 2) a$d (4, 1) a$d the$ oi$i$
them, we et the ra/h o! 2 6 x y+ =
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20. %$ the a"o=e !iure /aralleloram +6 is 7aras /iece o! la$d a$d BOE ∆ is ahul /lot.
7i$ce co$rue$t tria$les ha=e same area.
∴ e a=e to cut o!! a$
∆ alo$ 6, which is co$rue$t to BOE
∆.
Coi$ & i$ the /aralleloram +6, + AA 6 a$d + # 6
D # 6
'ow i$ BOE ∆ a$d COD∆ , we ha=e
OBE OCD∠ = ∠
BOE COD∠ = ∠
D # 6
BOE COD∆ = ∆
( ) ( )ar BOE ar COD∆ = ∆
Thus tria$ular /ieces &D a$d 6& ca$ "e excha$ed.+reas o! /aralleloram a$d tria$les
6harit a$d 6oo/eratio$.
21. Let ede o! cu"e # x u$its
∴ 7ur!ace area # *x2 s>uare u$its
'ew ede #25 5
100 4
x x x units+ =
'ew sur!ace area # 225
616
x x s>uare u$its # 275
8
x square units
%$crease i$ sur!ace area #2 2 275 27
68 8 x x x− =
erce$tae o! i$crease #
2
2
27
8 100 56.25%6
x
x x
=
22. +6 is a /aralleloram a$d + a$d 6; are /er/e$dicular !rom =ertices + a$d 6 o$ diao$al
res/ecti=el.
a) %$ APB CQD∆ = ∆ , + # 6
ABP CDQ∠ = ∠
∵ + AA 6 a$d tra$s=ersal i$tersects them
APB CQD∠ = ∠
+s /er ++7 rule each 900
APB CQD∴ ∆ ≅ ∆
") ∵ APB CQD∆ ≅ ∆ !rom the a"o=e e>uatio$
The$
+ # 6; is /ro=ed.
&r
Bi=e$ a /aralleloram +6. + circle /assi$ throuh +, a$d 6 is drae$ such that it
i$tersects 6 at D.
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∵ +6D is a cclic >uadrilateral.
0180 AEC B∠ + ∠ = (i)
%! +6 is a /aralleloram
D B∴ ∠ = ∠ (ii)
ual
Ee$ce + # +D
23. Let +6 "e a$ e>uilateral tria$le such that
+ # 6 # +6 # 9 cm each
Let us draw a media$ + corres/o$di$ to 6
1
2 BD BC ∴ =
1 99
2 2 BD x cm cm= =
+$d also + is /er/e$dicular to 6
%$ riht ADB∆ 2 2 2
AD AB BD= − 2
2 2 9 9 9
9 9 92 2 2 AD
= − = − +
29 27 9 9 9
3 32 2 2 2 2
x x x
= = =
93
2 AD cm=
7i$ce i$ a$ e>uilateral tria$le, the ce$troid a$d circumce$tre coi$cide.
: 2 :1 AO OD∴ =
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2 2 93
3 3 2 AO AD x= =
#9
3 3 3
3
cm=
e>uired radius # 3 3cm
24. Le$th o! the metal /i/e # -- cm
∴ %t is i$ the !orm o! cli$der.
∴ Eeiht (h) o! the cli$der # -- cm
25. Bi=e$
%$$er diameter is 4 cm
∴ %$$er radius (r) #4
2# 2 cm
&uter radius () #4.4
2# 2.2 cm
a) 6ur=ed sur!ace area # 222
2 2 x x 2 x 777
rh cmπ =
# 9* cm2
")
&uter sur!ace area # 2222 2 x x 2.2 x 777
Rh cmπ =
22 x 22 x 22 x 11
10cm=
# 10*4. cm2
c) Total sur!ace area # Fi$$er cur=ed sur!ace areaG H F outer cur=ed sur!ace areaG
H FTwo "ase circular lami$aG
2 2[2 ] [2 ] [2 ( )]rh Rh R r π π π = + + −
2 2 2 222[986 ] [1064.8 ] 2 x (2.2 2 )
7cm cm= + + −
# 2032. cm2 H 5.2 cm2 # 203.0 cm2
Bi=e$ 8 +6D is a /e$tao$. + li$e throuh /arallel to +6 meets 6 /roduced at
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")