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'lellSUMMATIVE ASSESSMENT -I (2011)

~~alT-1

MATHEMATICS/~

Class - IX / Cfl~ - IX

460011

Maximum Marks: 90~atq;: 90

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A,B,C and D. Section

A comprises of 8 questions of 1 mark each, section B comprises of 6 questions of 2 marks

each, section C comprises of 10 questions of 3 marks each and section D comprises 10

questions of 4 marks each.

(iii) Questionriumbers 1 to 10 in section-A are multiple choice questions where you are to

select one correct option out of the given four.

(iv) There is no overall choice. However, internal choice have been provided In 1 question- of

two marks, 3 questions of three marks each and 2 questions of four marks each. You have

to attempt only one of the alternatives in all such questions.

(v) Use of calculator is not permitted.

•

~~:

(i) ff~ ~ 3lf1crr<f ~ I •

(ii) ~ ~ 1Bl -q 34~ t ~. 'qR~ 3l, Ef, ff ~~ G-q ificT· Tf<rr51~ ~. 3l -q 8 ~~ fGRif~ 1 atcn cpT5, ~ -'- ~. -q 6 ~ ~ ~~ <f> 2·3fcp ~, ~ - ff -q 10~ ~ ~

~ ct> 3 3lcP 5 ~~ ~ - G -q 10~ ~. ftATi.~ *4 atcn~I'(iii) ~~ 31 -q ~~ 1 it 10 (fCj) qsfc) Cf) C'<n ~ ~. ~ \iffii 3TJ1rCf>T 'qR~ -q ~ ~ "fl1fi fcrrwq

~51

(iv) ~ ~ 1f;{ -q~ 'loft~fclcfJ~ ~ 5,~~ fcrrwq 2 3fCbT <f> ~ ~ -q, 3 3fCbT"ct> 3

~ -q 3TR 4 3fCbT ct> 2~ -q ~ ~ ~I ~ ~ -q~~ tnT"'q(R ~I

(v) $<'icgJlc'! cnT wITrr ~. 5 I

Section-A

Question numbers 1 to 8 carry one markeach. For each question, fouralternative choices have been provided of which onlyone is correct. You haveto select the correct choice.

Page 1 of 11

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(C) 3x2+4

(B) x2 +4x-7

(D) 3(x2+x+1)

(D) 3(x2 +x+ 1)

3. If a polynomial1(x) is divided by x - a, then remainder is

(A) f(O) (B) I(a) (C) I( -a) (D) I(a) - 1(0)

(A) f(O) (B) 1(a) (C) I( -a) (D) f(a) '-:- f(O)

4. What is the remainder when x3 - 2x2 +x +1 is divided by (x -1) ?.(A) 0 (B) -1 (C) 1 (D) 2

x3 - 2x2+x+l CfiT (x-I) ~ \Wl~1R~~:

(A) 0 (B) -1 (C) 1 (D) 2

5. In the figure below if AB= AC, the value of x is :

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(A) 55° (B) 110° (C) 50°

A

(A) 55° (B) 110° (C) 50°

6. IfdABC is congruent to dOH by SSS congruence rule, then:

(A) . LC < L.:F

(C) LA< LO

•{B)LB<LE

(O)LA= LO, LB= LE, LC= LF

•

(A) LC < LF

• (C) LA<LO

(B) LB<LE

(O)LA= LO,LB= LE,LC= LF

7. .The area of an equilateral triangle is 16 ,J3 m2• Its perimeter (in metres) is :

(A) 12 (B) 48 (C) 24 (0) 306

(A) 12 (B) 48 (C) 24 (0) 306

8.The base of a right triangle is 15 cm and its hypotenuse is 25 em. Then its area is :

(A) 187.5 em2 (B) 375 em2 (C) 150 em2 (0) 300 cm2

(A) 187.5 ~.ljt.2 (B) 375 ~.ljt.2 (C) 150 ~.ljt.2 (0) 300 ~.ljt.2

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A

~B C

(A) 55° (B) 110° (C) 50°

A

(A) 55° (B) 110° (C) 50° (0) 70°

6. lfdABC is congruent to dOH by SSS congruence rule, then:

(A) . LC < .,(F

(C) LA< LO

•{B)LB<LE

(O)LA= LO, LB= LE, LC= LF

•

(A) LC < LF

• (C) LA< LO

(B) LB<LE

(O)LA= LO,LB= LE,LC= LF

7. The area of an equilateral triangle is16 J3 m2• Its perimeter (in metres) is :

(A) 12 (B) 48 (C) 24 (0) 306

(A) 12 (B) 48 (C) 24 (0) 306

8.The base of a right triangle is 15 cm and its hypotenuse is 25 cm. Then its area is :

(A) 187.5 cm2 (B) 375 cm 2 (C) 150 cm2 (0) 300 cm 2

(A) 187.s ~.l:ft.2 (B) 375 ~.l:ft.2 (C) 150 ~.l:ft.2 (0) 300 ~.l:ft.2

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9.

Section-B

Question numbers 9 to 14 carry two marks each.

2

Simplify (~,-73125)

10. If (x -1) is a factor of the polynomial p(x) = 3.x4 - 4x3 - ax +2 then find the value

of 'a'?

<.TR (x-1)~ p(x) = 3x4 -4x3 - ax+ 2 CfiT~ :!ul1€lu:S~m 'a' CfiT l1R~q~ I

11. Simplify: (-/3 + 2)(-/3 - 2)

12. In the given figure/find the value of x.

13. In the figure, OAo == OB and 00 = oc. Show that

•

(i) ~AOD '" ~BOC (ii) ADIIBC

f.p:;f ~-q, OA=OBo~OD=OC t m~fcf;:

(i) ~AOD '" ~BOC (ii) ADIIBC

Page4 of 11

OR

An exterior angle of a triangle is 120° and one of the interior opposite angles is

40°. Find the other two angles of a triangle.

<:Jfc: fc8:ft ftf:F CfiT~~ 120° ~ 3tR~~ ~: ~ it ~ ~ 40°maT ftf:F ~ ~ ~~~

~I

14. A point lies on x-axis at a distance of 9 units from y-axis. What are its coordinates?

What will be the coordinates of a point if it lies on y axis at a distance of - 9 units from

x-axis?

x - 31~ 'R~~ y - 31a:l ~ 9~ q,1 ~T"{f{ m.rn t m~~q<:ff t? ~ 31~~~~

~ iliT~~ y- a1~ 11\m.rn ~Cf~ x- a1ltl it (- 9)~q,1~ 11{ t-?

•

Section-C

•

15.

, Question numbers 15 to 24 carry three marks each.

2. (64)-- ·1 . J25.Find the value of - 3 + 1 + 3r-r-f •

125 (256)'4 ,,64

625

ORRepresent J3 on number line.

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16.

17.

18.

1 2 1Prove that . J3 + J5 J3 + J5 = 0 .

2+ 3 5- 3 2- 5

F . 2 x 1actonse : x + - - - .

4 8

x 1~OI"1l5js~ : x2 + - - - .

4 8

OR

What are the possible expressions for the dimensions of a cuboid whose volume is

given below?

Volume = 12ky2 +8ky- 20k.

If x = 2y +6 then find the value of x3 - 8y3 - 36xy - 216.

<:ifu:x=2y+6m, mx3-8y3-36xy-216 CflI+Wi~~1

19. In ~ABC, L:B =45°, LC = 55° and bisector of L.A meets BC at a

point D. Find L.ADB and LADC.

.D.ABC -q, LB=45°, LC=55° Cl~ A CflI W1%~~ BC ~ D "lR 11mffl tl LADB amLADC.~~I

OR

In the figure below, 111112 and a111a2. Find the value of x.

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20. In the figure below, 111112 and m111m2' Prove that L:1 + L2 = 180°.

[1 12t

1n;

•2 ~

•11 12

1• n;

2 ~

21. In the given figure, AB = AC, 0 is the point in the interior of LlABC such that

L DBC= L DCB. Prove that AD bisects L BACof LlABC.

A

~TJt ~if, AB=AC~I ~ftr:p\ ABC~ 3Rf: 'l1TTTif~~D~~~%LDBC= LDCB

t en~~%AD ftr'iF ABC~ L BACem~~~ I

Page 7 of 11

A

22. In the given figure, AB= BC and AD= EC. Prove that MBE == ACBD.

B c

"eft7T{ ~if, AB=BCCf~ AD=EC%I ~~fcf; MBE == ACBD ~I

•

B

23. In the given figure, if ABnCD, APQ = 50° and PRD =127°, find x and y.•

A B

·c

"eft 7T{~ if,~ AB II CD,APQ =50° Cf~ PRD = 127°, or x Cf2TT Y Cfi lfR~~ I

A

24. The perimeter of a triangular field is 300 em and its sides are in the ratio 5 : 12 : 13..

Find the length of the perpendicular from the opposite vertex to the side whose length

is 130 em.

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Section-D

Question numbers 25 to 34 carry four marks each.

25. Find the values of a and b if 7 + 3: _ 7 - 3: = a + .JSb3+ 5 3- 5

OR

Evaluate after rationalizing the denominator of (j40 25 J80)' It is being given40 - 80 .

that J5 = 2.236 and .J1O = 3.162

26. S' l'f 1 1 1 1Imp 1y: 2 + J5 + J5 + 16 + 16 +·ff + .Ji+ J8 .

B'ffi~ : IJ5 + J5 1 .J6 + .J6 1,fi- +~ In .2 + 5 . 5 + 6 6 + 7 '/7 + ,,8

•

=3 (a+b) (b+c) (c+a) (a-b) (b-c) (c-a)

=3 (a+b) (b+c) (c+a) (a-b) (b-c) (c-a)

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28. If remainder is same when polynomial p(x) =x3 + 8x2 + 17x + ax is divided by

(x+ 2) and (x+ 1), find the value of a.

~~ p(x)=x3+8x2+17x+axcnT (x +2) am (x+l) ~fcr~CfiB1R~Wffim,maC1i11fR~~1

Page 9 of 11

~. 3 2Find a and /3, if (x +1) and (x +2) are factors of x +3x - 2ax + /3.

OR",

Factorize: x3 - 3x2 - 9x - 5.

30. Plot the points A (4, 0) and B (0, 4). Join AB to the origin O. Find the area of

~AOB.

f<q3TI A (4, 0) (i~ B (0,4) Cf>l~~ 3fu: ~3TI O,A, B Cf>l31l1ffi 1'4~(i~ ~AOB CfiT

~~~I

31. In the given figure, if PQIIST, LPQR = 110" and LRST= 130° find LQRS.

P

TI ~

p

T

32. In the given figure, the side QR of ~PQR is produced to a point S. If the bisectors of

LPQR and LPRS meet at point T, then prove that LQTR = .!. LQPR.2 .

eft ~~ 1'4 ~PQR Cfft~ QRCf>l f<q Sw.fi~~%I <iR L PQR (i~ L PRS t-~~

T 1:R firnij 'tmm~ fcF; LQTR = .!.LQPR .2

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33. A BCD is a parallelogram. If the two diagonals are equal. Find the measure of

LABC

34. In figure, ABC is an isosceles triangle in which AB = AC Side BA is produced to

D such that AD = AB. Show that BCD is a right angle.

D

3Wffu-q, i\.BC~fll1f6:"lI~ f,j'l;!~ %~ AB = AC ~ i ~ BA~ D (fif,- ~ w:nR~~ ~ -~ %

AD=AB~I ~fcoBCD~~tl

D

B.L.,....---~

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