2015 09 Sp Mathematics Sa2 Solved 01 Ans Kme

8/9/2019 2015 09 Sp Mathematics Sa2 Solved 01 Ans Kme

1/9

Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in

Portal for CBSE Notes, est Papers, Sample Papers, ips and ric!s

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


2/9



&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


3/9



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


4/9



∴ @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


5/9



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+ =


6/9



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.


7/9



∵ +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∴ =


8/9



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


9/9



")

Documents

2015 09 Sp Mathematics Sa2 Solved 01 Ans Kme