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pe of Question

e.Q.

Marks per question

1

Total No. of Questions

1 0

Total Marks

1 0

A 2 8 1 6

3 1 0 3 0

4 6 2 4

TOTAL 80

MCQ(1) SA-I(2) SAil LA(4) Total

(3)

bra 2 ( 2 ) 4 ( 2 ) 6 ( 2 ) 8 ( 2 ) 2 0 ( 8 )

metry 4 ( 4 ) 2 ( 1 ) 6 ( 2 ) 4 ( 1 ) 1 6 ( 8 )

6. Mathematics,

Summ ative Assessment - II

Class X

Design of the Question Paper

Blue P rint

Sample Question Paper

Mathematics,SA-IIClass

X

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Sam ple Question Paper

Mathematics(Code-041)

Class X, SA-II

3 hours. M.M.: 80

al Instructions

A l lquestionsarecompulsory.

The questionpaper consistsof 34 questionsdivided into foursectionsA, B, C and D.

SectionA contains10 questionsof1 mark each, which are mult iplechoice type

questions,

SectionB contains8 questions of 2 marks each,Section C contains 10 questions of 3

markseach, Section0 contains6 questionsof 4 markseach.

There isno overallchoiceinthe paper.However,internalchoice isprovidedinone

questionof 2 marks.3 questionsof 3 marksand two questions of 4 marks.

Use of calculators is not permitted.

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fi

ssctton-A

t ion numbers 1 to 10 carry 1 mark each. For each of the questions 1-10, four

native choices have beenp rovided of which onlyone is correct.You haveto sele ctorrect choice.

Whichof the followingequationshas the sum of its rootsas

3? (A)x2+3x-5=0 (8) -x2+3x+3=0

(e)fix2-_2_x-1

(0) 3X2-3x-3=0

The sum of first five multiplesof3 is

(A) 45 (8) 65

(e) 75 (0) 90

If radii of the two concentriccirc lesare 15cmand 17cm, thenthe length of each chord

ofone circle which is tangentto otheris

(A) 8cm (8) 16cm

(e) 30cm (0) 17cm

In Fig.1 , PO and PR are tangentsto the

circle withcentre0 such that LOPR=50,then LOOR is equalto p

(A) 25 (8) 30

(e) 40 (0) 50

Two tangentsmakingan angle of 120 with eah other,are drawn to a circ le of radius6cm,

then the length of each tangentisequal to

(A) J3cm

(e)

ficm

(8) 6J3cm

(0) 2J3cm

Todraw a pair of tangentsto a circle which are inclined to each other at an angle of

100, it is required to draw tangents at end points of those two radii of the circle,

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the angle betweenwhich shou ldbe

(A) 1000 (8) 500

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Ifthe circumferenceofa circle is equal to the perimeterofa squarethen the ratio of

their areasis

(A) 22:7

(C) 7:22

(8) 14:11

(0) 7:11

A pole 6m high casts a shadow 2.J3 m long on the ground ,then the sun'selevation is

(8) 45

(0) 90

W hich of the follow ing cannotbe the probabilityof an event?

(A) -5 (8) 0.3

5(C) 4% (0)

4

Section-B

on numbers 11 to 18 carry 2 marks each.

Find the rootsof the follow ing quadra ticequation:

Ifthe numbersx-2 , 4x-1 and 5x+2 are inA . P ., Find the value ofx.

Two tangents PA and P8 are drawn from an external point P to a circle with centre

O. ProvethatA08P is a cyclic quadrilateral.

In Fig.2,a circle ofradius7cm is inscribed in a square.

2Find the area ofthe shadedregion. [use n= 27 ]

Fig. 2

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oHow manysphericallead shots each havingdiame ter3cm can be madefrom a cubo idal

lead solid ofdimensions9cm x 11cm x 12cm?

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3

Section-C

ons num bers 19 to 28 carry 3 marks each.

1 1Find the rootsofthe equation 2x-3+ x-5= t

OR

Anatural number,when increasedby 12, becomesequalto 160times its reciprocal.Find

the number.

Find the sum of the integersbetween100 and 200 that are divisible by 9.

In Fig.3, two tangentsPO and PR are drawn p

to a circle with centre 0 from an externalpoint P.Provethat LOPR = 2LOOR.

ORFig. 3

Prove that the parallelogramcircumscribinga circle is a rhombus.

Drawa triang leABC with side BC=6cm,AB=5cmand LABC=60.Then constructa triangle

whose sides are '4 time the correspondingsides of ~ABC.

In FigA, OABC is a squareinscribed in a quadrantOPBO.

IfOA=20cm,find the area ofshadedregion.[Usen=3.14]

Fig. 4A

A hemisphericaldepressionis cut out from one face ofa cubicalwooden block such

that the diameter'e 'of the hemisphereisequalto the edge of the cube. Determinethe

surface

area ofthe remainingsolid.OR

A copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18m

ofuniformthickness.Find the thicknessof the wire.

A tower stands vertically on the ground. From a point on the ground which is 20m

away fromthe foot ofthe tower, the angle of elevation of the top ofthe tower isfound to

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be 60. Findthe heighto f the tower.

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Section-O

on n um bers29 to 34 carry 4 marks each.

A train travelsat a cer ta inaveragespe edfor adistanceof63km and then travelsadistance

of72km at an average speedof6km /hrm orethan its original speed. If it takes 3hours to

completethe totaljourney,what is its originalaveragespeed?

O R

Find two con secut iveodd positive integers ,sum of whose squares is 290.

A sum of Rs. 1400 is to be used to give sevenca sh prize s to stud entsof a schoo lfortheir

overall academic performance. I f each prize is Rs. 40 less than the prece ding price ,

find the value of each of the prizes.

Provethat the lengthsof tange ntsdraw nfrom an externalpoint to a circleare equal.

A well of diameter 3m and 14m deep is dug. The earth, taken out of it, has been

evenly spreadall around it in the shape of a circular ring of width 4m to form an

embankm ent. Findthe height of the embankment.

O R

21 glass sphereseach of radius2 cm are packedin a cubo idalbox of internaldim ens ions

16cmx8cmx8cmand then the box is fil led w ith water.F ind the vo lumeof water filled in the

box.

The slan theighto f the frustumof a cone is 4cm and the circum ferencesof its circularends

are 18cmand 6cm . Find curved sur faceare a of the frustum.

From a point on the ground,the ang lesof elevationof the bottomand top of a transm issio n

tow er fixed at the top of a 20m high bu ild ing are 45 and 60 respectively.Find he ight of

the tower.

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= >

Marking Scheme

Mathematics,SA-II

Class X

Section-A

8) 2. (A) 3. (8) 4. (A) 5. (0)

C) 7. (C) 8. (8) 9. (A) 10. (0)

1x10=10

Section-B

2x2-6X+x-3=0

2x(x-3)+1 (x-3)=0

(2x+1 )(x-3)=0

1~ x=3,

x=--2

2(4x-1 )=x-2+5x+2

8x-6x=2 = >x=1

LPAO+LP80=90o+90o=180

= > LAP8+LA08=180

A08P is a cyclic quadrilateral

Side of square = 14cm

:. Shaded area = 22(14)2_-x7x77

ern-8

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(0),9x11x12

No. of lead shots = 4 22 3 3 3

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IS:. Q (5

-2+

-1'

--23--5)

or (3,-4)

P,A, B shouldbe collinear

.. Clearlythe three points lie on the line x=-4 1%

P (differentnumbers) = 1-P (samenumber)

= 1-366=1-~=% 1%

ORP (atmostone head) = P (IT orHT orTH)

1-P(HH)=1 3

1--=-4 4

Section-C

1 1--+ - = 1 => x-5+2x-3= (2x-3)(x-5) 1%2x -3 x-5

=> 2x2-16x+23 =0 => x=4 3..[2 1%2

OR

1x+12 = 160-

x

x2+12x-160=0(x+20)(x-8)=0=>x=-20,x=8

:. the numberis 8

Integersare 108, 117,126, .., 198

198= 108+(n-1)9=>n=11

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s, = 11"2(108+198)

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1

OR

~_..;.;..._~c ABCD is a I Igm =>AB=CD andAD=BC

AP=AS )Q BP=BQ

RC=QC

DR=DSA p 8

= > (AP+PB)+(RC+DR)= (AS+DS)+(BQ+QC)

AB+CD = AD+BC

= > 2AB = 2AD = >AB=AD

= >ABCD is a rhombus

Drawing~ABC correctly

Constructionofsimilar~

Radius = .JON+AB2 = 20.ficm

:. Shadedarea = ' 4x 3.14x800-(20)2

= 628-400=228cm2

RequiredSA = 6t2- 7 r ( % f+2 J r ( % f

2

1 ' 1 2

1 ' 1 2

OR

1 ' 1 2

1~ r=-cm

30

~ thickness= 2r=_!_cm

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AB=.J4+ 1=..j5,CD=.Ji+4"=..j5 i.e.AB=CD

BC=.J100 + 1=.J1Q1,AD=.J100 + 1 =.J1Q1 i.e.

BC=AD

= > ABCD is Ilgm

C (5,5) AB2+BC2=AC2

= > (a-2)'+16+(a-5)2=9+16

=> 2a2-14a+20=0=> a2-7a+10=0

(a-5)(a-2)=0,a*5 = > a=2

A(2,9)

B(a,5) . A r e a= ~ .ABx sc0(4X3)=6sq uits

2 2

TotalNumberof cards=100 ' 1 2

Perfectsquaresare4,9,16,25,36,49,64,81,100 i.e.9 1 ' 1 2

:. Probability= ~100

Section-D

Let averagespeedbex km/hr

= > 63 +~=3x x+6

= > 21(x+6)+24x= x2+6x

or x2-39x-126=0

= > (x-42)(x+3)=0

=> x - 42 km/hr

OR

x2+(x+2)2=290

2x2+4x-286=0orx2+2x-143=0

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(x+13)(x-11)=0 =>x=11

.. Numbersare 11 and 13

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=

Correct proof 2

Volume of earth dug out=

nx(~J x14

Vol. of embankment = n[(S.S)2 -(1.SnXh

= > ~x14=7x4xh4

9 14 9= > h=-x-=-m

4 7x4 8

O R

4 22Vol. of 21 spheres = 21x-x-x8=704cm3 1%

3 7

Vol. of cuboid = 16x8x8= 1024cm3 1%

.. Vol of water = 1024-704=320cm3

2nr, = 18 = > nr, = 9

SA = n e ( r ,+ r2) = 12x4 = 48cm2

Correct fig.

20- = tan 4S 1x

20

=> x=20m

h+20 M-- = tan60 =..;3

x