c.b.s.e.-2011-sample-papers-for-ix-mathematics(5-sets)-summative-assessement-i.pdf

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SUMMATIVE ASSESSMENT I (2011)

Lakdfyr ijh{kk &I MATHEMATICS / xf.kr

Class IX / & IX

Time allowed: 3 hours Maximum Marks: 90 fu/kkZfjr le; % 3 ?k.Vs vf/kdre vad % 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) Question numbers 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.

lkekU; funsZk %

(i) lHkh izu vfuok;Z gSaA

(ii) bl izu i= esa 34 izu gSa, ftUgsa pkj [k.Mksa v, c, l rFkk n esa ckaVk x;k gSA [k.M & v esa 8 izu gSa ftuesa

izR;sd 1 vad dk gS, [k.M & c esa 6 izu gSa ftuesa izR;sd ds 2 vad gSa, [k.M & l esa 10 izu gSa ftuesa izR;sd ds 3 vad gS rFkk [k.M & n esa 10 izu gSa ftuesa izR;sd ds 4 vad gSaA

(iii) [k.M v esa izu la[;k 1 ls 10 rd cgqfodYih; izu gSa tgka vkidks pkj fodYiksa esa ls ,d lgh fodYi pquuk gSA

(iv) bl izu i= esa dksbZ Hkh loksZifj fodYi ugha gS, ysfdu vkarfjd fodYi 2 vadksa ds ,d izu esa, 3 vadksa ds 3 izuksa esa vkSj 4 vadksa ds 2 izuksa esa fn, x, gSaA izR;sd izu esa ,d fodYi dk p;u djsaA

(v) dSydqysVj dk iz;ksx oftZr gSA

Section-A

Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.

460011

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1. form of the number is :

(A) (B) (C) (D)

(A) (B) (C) (D)

2. Which of the following is a cubic polynomial ?

(A) x33x24x3 (B) x24x7

(C) 3x24 (D) 3(x2x1)

(A) x33x24x3 (B) x24x7

(C) 3x24 (D) 3(x2x1)

3. If a polynomial f (x) is divided by xa, then remainder is

(A) f (0) (B) f (a) (C) f (a) (D) f (a) f (0)

f (x) xa

(A) f (0) (B) f (a) (C) f (a) (D) f (a) f (0)

4. What is the remainder when x32x2x1 is divided by (x1) ?

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

x32x2x1 (x1)

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

5. In the figure below if ABAC, the value of x is :

p

q0 3.

3

10

3

100

1

3

1

2

0 3.p

q

3

10

3

100

1

3

1

2

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(A) 55 (B) 110 (C) 50 (D) 70

ABAC x

(A) 55 (B) 110 (C) 50 (D) 70

6. If ABC is congruent to DEF by SSS congruence rule, then :

(A) C < F (B)B < E

(C) A < D (D)A D, B E, C F

SSS ABCDEF

(A) C < F (B) B < E

(C) A < D (D)AD,BE,CF

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

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

16 m2

(A) 12 (B) 48 (C) 24 (D) 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 cm2 (C) 150 cm2 (D) 300 cm2

15 25

(A) 187.5 2 (B) 375 2 (C) 150 2 (D) 300 2

3

3

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Section-B Question numbers 9 to 14 carry two marks each.

9.

Simplify 2

364

125

2364

125

10. If (x1) is a factor of the polynomial p(x)3x44x3ax2 then find the value

of a ?

(x1) p(x)3x44x3ax2 a

11. Simplify : 3 2 3 2

3 2 3 2

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

x

13. In the figure, OAOB and ODOC. Show that

(i) AOD BOC (ii) ADBC

OAOB ODOC

(i) AOD BOC (ii) ADBC

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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.

120 40

14. A point lies on xaxis at a distance of 9 units from yaxis. 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

xaxis ?

x y - 9

y x (9)

Section-C Question numbers 15 to 24 carry three marks each.

15.

Find the value of

2 3

1 3

4

64 1 25

125 64256

625

.

2 3

1 3

4

64 1 25

125 64256

625

OR Represent on number line.

3

3

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16. Prove that .

.

17. Factorise : .

.

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

given below ?

Volume 12ky28ky20k.

12ky28ky20k

18. If x2y6 then find the value of x38y336xy216.

x2y6 x38y336xy216

19. In ABC, B45, C55 and bisector of A meets BC at a

point D. Find ADB and ADC.

ABC B45, C55 A BC D ADB

ADC

OR

In the figure below, l1l2 and a1a2. Find the value of x.

1 2 1 0

2 3 5 3 2 5

1 2 1 0

2 3 5 3 2 5

2 1

4 8

xx

2 1

4 8

xx

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l1l2 a1a2 x

20.

In the figure below, l1l2 and m1m2. Prove that 1 2180.

l1l2 m1m2 1 2180

21. In the given figure, ABAC, D is the point in the interior of ABC such that

DBCDCB. Prove that AD bisects BAC of ABC.

ABAC ABC D DBCDCB

AD ABC BAC

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22. In the given figure, ABBC and ADEC. Prove that ABE CBD .

ABBC ADEC ABE CBD

23. In the given figure, if ABCD, APQ50 and PRD127, find x and y.

AB CD, APQ50 PRD127, x y

24. The perimeter of a triangular field is 300 cm 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 cm.

300 5 : 12 : 13 130

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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 5 7 3 5 a 5b

3 5 3 5

7 3 5 7 3 5 a 5b

3 5 3 5

a b

OR

Evaluate after rationalizing the denominator of . It is being given

that

26.

Simplify : 1 1 1 1

2 5 5 6 6 7 7 8

.

1 1 1 1

2 5 5 6 6 7 7 8

.

27. Prove that : (a2b2)3(b2c2)3(c2a2)3

3 (ab) (bc) (ca) (ab) (bc) (ca)

(a2b2)3(b2c2)3(c2a2)3

3 (ab) (bc) (ca) (ab) (bc) (ca)

28. If remainder is same when polynomial p(x)x38x217xax is divided by

(x2) and (x1), find the value of a.

p(x)x38x217xax (x2) (x1) a

25

40 80

5 2.236 and 10 3.162

25

40 80

5 2.236 10 3.162

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29. Find and , if (x1) and (x2) are factors of x33x22x.

x33x22x (x1) (x2)

OR

Factorize : x33x29x5.

x33x29x5.

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

AOB.

A (4, 0) B (0, 4) O,A, B AOB

31. In the given figure, if PQST, PQR110 and RST130find QRS.

PQST, PQR110 RST130 QRS

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

PQR and PRS meet at point T, then prove that 1

QTR QPR2

.

PQR QR S PQR PRS

T 1

QTR QPR2

.

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

ABC.

ABCD ABC

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

D such that ADAB. Show that BCD is a right angle.

ABC ABAC BA D

ADAB BCD

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Class IX / & IX














lkekU; funsZk %







Section-A


460012

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1. The simplified form of 1

5

13

13

13

is :

(A) 2

1513 (B) 8

1513 (C) 1

313 (D) 2

1513

15

13

13

13

(A) 2

1513 (B) 8

1513 (C) 1

313 (D) 2

1513

2. Which of the following is a polynomial in one variable :

(A) 3x2x (B) 3 4x

(C) 3 3 7x y (D) 1

xx

(A) 3x2x (B) 3 4x

(C) 3 3 7x y (D) 1

xx

3. Which of the following is a quadratic polynomial ?

(A) 3x35x4 (B) 53x2x27x3

(C) (D) (x1) (x1)

(A) 3x35x4 (B) 53x2x27x3

(C) (D) (x1) (x1)

4. If 1, (x, y 0), then, the value of x3y3 is :

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

1, (x, y 0) x3y3

2 1 3xx

2 1 3xx

x

y

y

x

1

2

x

y

y

x

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

5. Value of x in the figure below is :

(A) 80 (B) 40 (C) 160 (D) 20

x

(A) 80 (B) 40 (C) 160 (D) 20

6. In ABC, if ABAC, B50, then A is equal to :

(A) 40 (B) 50 (C) 80 (D) 130

ABC ABAC, B50 A

(A) 40 (B) 50 (C) 80 (D) 130

7. A square and an equilateral triangle have equal perimeters. If the diagonal of the square is

12 2 cm then area of the triangle is :

(A) 24 2 cm 2 (B) 24 3 cm2 (C) 48 3 cm2 (D) 64 3 cm2

12 2

(A) 24 2 2 (B) 24 3 2 (C) 48 3 2 (D) 64 3 2

8. The side of an isosceles right triangle of hypotenuse 5 cm is :

(A) 10 cm (B) 8 cm (C) 5 cm (D) 3 cm

5

(A) 10 (B) 8 (C) 5 (D) 3

1

2

2

2

2

2

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9. If x32 , then find whether x is rational or irrational.

x32 x

10. Without actually calculating the cubes, find the values of 553253303.

553253303

11. If xy8 and xy15, find x2y2.

xy8 xy15, x2y2

12. In the given figure, if POR and QOR form a linear pair and ab80, then find the

value of a and b.

POR QOR ab80 a b

13. In figure, BE, BDCE and 12. Show ABC AED.

BE, BDCE 12 ABC AED.

21

x

21

x

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OR In the figure given below AC > AB and AD is the bisector of A. Show that ADC > ADB.

AC > AB A AD ADC > ADB.

14. Find the co-ordinates of the point which lies on yaxis at a distance of 4 units in

negative direction of yaxis.

(A) (4, 0) (B) (4, 0) (C) (0, 4) (D) (0, 4)

y 4

(A) (4, 0) (B) (4, 0) (C) (0, 4) (D) (0, 4)


15. Represent 2 on the number line.

2

OR

Express 18.48 in the form of p

q where p and q are integers, q 0.

18.48 p

q p q q 0

16.

If then find the value of . 5 2 6x 22

1 x

x

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17. If

1 7x

x , then find the value of 3

3

1 x

x .

1

7xx

33

1 x

x

OR Factorise : x33x210x24

x33x210x24

18. Using suitable identity evaluate (998)3.

(998)3

19. In the given figure, lines AB and CD intersect at O. If and

, find and reflex .

AB CD O

OR In the following figure, PQST, PQR 115 and RST 130 .

Find the value of x.

5 2 6x 22

1 x

x

AOC BOE 70

BOD 40 BOE EOC

AOC BOE 70 BOD 40

BOE EOC

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PQST PQR 115 RST 130 x

20.

In the given figure, ABC is a triangle with BC produced to D. Also bisectors of ABC

and ACD meet at E. Show that .

ABC BC D ABC ACD

E

21.

In the given figure, sides AB and AC of ABC are extended to points P and Q

respectively. Also PBC < QCB. Show that AC > AB.

ABC AB AC P Q

PBC < QCB. AC > AB.

1

BEC BAC2

1BEC BAC

2

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22.

In the given figure, ACBC, DCA ECB and DBC EAC. Show that

DBCEAC and hence DCEC.

ACBC, DCA ECB DBC EAC DBCEAC

DCEC.

23. The degree measure of three angles of a triangle are x, y, and z. If

then find the value of z.

x, y, z z

24. The perimeter of a triangular ground is 900 m and its sides are in the ratio

3 : 5 : 4. Using Herons formula, find the area of the ground.

900 3 : 5 : 4


25.

If and then evaluate

x2y2.

x2y2

OR

If a 3 2

3 2

and b

3 2

3 2

, find the value of 2 2a b 5 ab .

z

2

x y

z

2

x y

1 1

2 2 2 5 2 5x 1 1

2 2 2 5 2 5y

1 1

2 2 2 5 2 5x 1 1

2 2 2 5 2 5y

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a 3 2

3 2

b

3 2

3 2

2 2a b 5 ab

26.

Rationalize the denominator of 4

2 3 7

4

2 3 7

27. Factorize : (a) 4a29b22a3b.

(b) a2b22(abacbc)

(a) 4a29b22a3b.

(b) a2b22(abacbc)

28. If (x5) is a factor of x32x213x10, find the other factors.

x32x213x10 (x5)

29. Factorize a7ab6.

a7ab6

OR If ax3bx2x6 has x2 as a factor and leaves remainder 4 when divided by x2,

find the values of a and b.

x2 ax3bx2x6 (x2) 4

a b

30. In the given figure, PQR is an equilateral triangle with coordinates of Q and R

as (2, 0) and (2, 0) respectively. Find the coordinates of the vertex P.

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PQR Q R (2, 0) (2, 0)

P

31. In the adjoining figure, the side QR of PQR is produced to a point S. If the bisectors of

PQR and PRS meet at point T, then prove that 1

QTR QPR2

.

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PQR QR S PQR PRS

T 1

QTR QPR2

.

32. In the following figure, the sides AB and AC of ABC are produced

to D and E respectively. If the bisectors of CBD and BCE meet

at O, then show that A

BOC 90 2

.

ABC AB AC D E CBD

BCE OA

BOC 90 2

33. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that

the triangle ABC is isosceles.

ABC BE CF RHS ABC

34. In a triangle ABC, ABAC, E is the mid point of AB and F is the mid point of

AC. Show that BFCE.

ABC ABAC E AB F AC

BFCE.

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Class IX / & IX














lkekU; funsZk %







Section-A


460013

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1. The value of 0 0

0

2 7

5

is :

(A) 2 (B) 0 (C) 9

5 (D)

1

5

0 0

0

2 7

5

(A) 2 (B) 0 (C) 9

5 (D)

1

5

2. Which of the following expressions is a polynomial ?

(A) x1

x (B) x xx2

(C) 2 xx33x2 (D) x2x22

(A) x1

x (B) x xx2

(C) 2 xx33x2 (D) x2x22

3. What is the coefficient of x2 in the polynomial ?

(A) 3 (B) 4 (C) (D) 0

x2

(A) 3 (B) 4 (C) (D) 0

4. The maximum number of terms in a polynomial of degree 10 is :

(A) 9 (B) 10 (C) 11 (D) 1

10

(A) 9 (B) 10 (C) 11 (D) 1

5. In the figure below, if x, y and z are exterior angles of ABC, then

xyz is :

2 3 46

x x

6

2 3 46

x x

6

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(A) 180 (B) 360 (C) 270 (D) 90

x, y z ABC xyz

(A) 180 (B) 360 (C) 270 (D) 90

6. In ABC and DEF, ABFD, A D. The two triangles will be congruent by SAS

axiom if :

(A) BCDE (B) ACEF (C) BCEF (D) ACDE

ABC DEF ABFD, A D SAS

(A) BCDE (B) ACEF (C) BCEF (D) ACDE

7. The perimeter of a triangle is 36 cm and its sides are in the ratio a : b : c 3 : 4 : 5

then a, b, c are respectively :

(A) 9 cm, 15 cm, 12 cm (B) 15 cm, 12 cm, 9 cm

(C) 12 cm, 9 cm, 15 cm (D) 9 cm, 12 cm, 15 cm

36 a : b : c 3 : 4 : 5 a, b, c

(A) 9 , 15 , 12 (B) 15 , 12 , 9

(C) 12 , 9 , 15 (D) 9 , 12 , 15

8. The area of ABC in which ABBC4cm and is :

(A) 16 cm2 (B) 8cm2 (C) 4cm2 (D) 12 cm2

ABBC4

B 90

B 90

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(A) 16 2 (B) 8 2 (C) 4 2 (D) 12 2


9.

Simplify :

10. Find the remainder when x4x32x2x1 is divided by x1.

x4x32x2x1 x1

11. Using suitable identity prove that :

3 3

2 2

0.87 0.13 1

0.87 0.87 0.13 0.13

3 3

2 2

0.87 0.13 1

0.87 0.87 0.13 0.13

12. In the given figure, if AOB is a line then find the measure of BOC, COD and DOA.

AOB BOC, COD DOA

214

12

15

3

214

12

15

3

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13. In the given figure, AB > AC and BO and CO are the bisectors of B and C

respectively. Show that OB > OC.

AB > AC BO CO B C OB > OC

OR In the figure below, ray OC stands on the line AB. Ray OP bisects AOC and

ray OQ bisects BOC. Prove that POQ90.

OC AB OP, AOC OQ

BOC POQ90

14. Plot the point P (2, 6) on a graph paper and from it draw PM and PN perpendiculars

to x-axis and y-axis, respectively. Write the coordinates of the points M and N.

P(2, 6) P PM PN x - y -

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M N


15. Simplify : 3 45 125 200 50

3 45 125 200 50

OR

Simplify : 6 3 2 4 3

2 3 6 3 6 2

6 3 2 4 3

2 3 6 3 6 2

16.

Simplify the following :

17. If

1 3x

x , then find the value of 3

3

1 x

x .

1 3x

x 3

3

1 x

x

OR Factorise : x2y22x6y8

x2y22x6y8

18. Factorize : 8 a3b312 a2 b6ab2

8a3b312a2 b6ab2

19. The exterior angles obtained on producing the base of a triangle both ways are

2 1 3

5 3 3 2 5 2

2 1 3

5 3 3 2 5 2

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100 and 120. Find all the angles.

100 120

OR In the following figure, PQRS, MXQ 135 and MYR 35 .

Find XMY

PQRS, MXQ 135 MYR 35 XMY

20. In the given figure, PQR PRQ, then prove that PQS PRT.

PQR PRQ PQS PRT.

21.

In the figure, AB and CD are respectively the smallest and longest sides of a

quadrilateral ABCD. Show that A > C

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ABCD CD AB A > C

22. ABC is an isosceles triangle in which ABAC. Side BA is produced to D

such that ADAB. Show that BCD is a right angle.

ABC ABAC BA D

ADAB. BCD

23. In the given figure, if BE is bisector of and CE is bisector of , then

show that .

BE CE

.

24. Manisha has a garden in the shape of a rhombus. The perimeter of

the garden is 40 m and its diagonal is 16 m. She wants to divide it

into two equal parts and use these parts in rotation. Find the area of

each part of the garden.

40 16


ABC ACD

1BEC BAC

2

ABC ACD

1BEC BAC

2

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25. Rationalise the denominator of .

OR

Express with rational denominator .

26.

If a 3 2

3 2

and b

3 2

3 2

, find the value of 2 2a b 5 ab .

a 3 2

3 2

b

3 2

3 2

2 2a b 5 ab

27. If (xyz)0, then prove that (x3y3z3)3xyz.

(xyz)0 (x3y3z3)3xyz

28. The lateral surface area of a cube is 4 times the square of its edge, find the edge

of a cube whose lateral surface area is given by : 4x28 x.

4x28 x

29. If x2 is the root of the equation (xp)0 and is also the zero of the

polynomial px2kx2 then find the value of k.

(xp)0 x2 px2kx2

k

OR Without actual division prove that 2x46x33x23x2 is exactly divisible by

x23x2.

2x46x33x23x2 x23x2

1

7 6 13

1

7 6 13

1

2 3 5

1

2 3 5

128

128

2

2

2 2

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30. Plot the points A (3, 3), B (3, 3), C (3, 3), D (3, 3) in the

cartesian plane. Also, find the length of line segment AB.

A (3, 3), B (3, 3), C (3, 3) D (3, 3)

AB

31. Prove that if two lines intersect, then the vertically opposite angles are equal.

32. Q is a point on side SR of PSR as shown in the figure below such

that PQPR. Show that PS > PQ.

PSR SR Q PQPR

PS > PQ

33. Two sides AB and BC and median AM of one triangle ABC are respectively equal to

sides PQ and QR and median PN of PQR. Show that ABCPQR.

ABC PQR ABPQ, BCQR AM PN

ABCPQR.

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34. In the figure given below, x y and PQQR. Prove that PERS.

x y PQQR PERS.

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Class IX / & IX




(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) Question numbers 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.


lkekU; funsZk %







Section-A


1. Every rational number is :

460014

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(A) a natural number (B) an integer

(C) a real number (D) a whole number

(A) (B)

(C) (D)

2. If p(x)x3x2x1, then value of p( 1) p(1)

2

is :

(A) 1

4 (B) 4 (C) 0 (D) 2

p(x)x3x2x1, p( 1) p(1)2

(A) 1

4 (B) 4 (C) 0 (D) 2

3. If p(x)2x33x24x2, then p(1) is :

(A) 2 (B) 11 (C) 0 (D) 1

p(x)2x33x24x2 p(1)

(A) 2 (B) 11 (C) 0 (D) 1

4. If ABx3, BC2xand AC4x5, then for what value of x, B lies on AC?

(A) 8 (B) 5 (C) 2 (D) 3

ABx3, BC2x AC4x5 x B AC

(A) 8 (B) 5 (C) 2 (D) 3

5. Find the measure of the angle which is complement of itself :

(A) 30 (B) 90 (C) 45 (D) 180

(A) 30 (B) 90 (C) 45 (D) 180

6. In ABC and PQR, ABPR and AP. The two triangles will be congruent by SAS

axiom if :

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(A) BCQR (B) ACPQ (C) ACQR (D) BCPQ

ABC PQR ABPR AP SAS

(A) BCQR (B) ACPQ (C) ACQR (D) BCPQ

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

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

16 m2

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

8. The area of a triangle whose sides are 13 cm, 14 cm and 15 cm is :

(A) 42 cm2 (B) 86 cm2 (C) 84 cm2 (D) 100 cm2

13 14 15

(A) 42 2 (B) 86 2 (C) 84 2 (D) 100 2


9.

Simplify :

10. Factorize : x23 x6.

x23 x6

11. Write the expansion of (2x3y2z)2.

(2x3y2z)2

3

3

51 2

5

15

12

27

51 2

5

15

12

27

3

3

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12. In the adjoining figure, ACXD, C is midpoint of AB and D is midpoint of XY. Using an

Euclids axiom, show that ABXY.

ACXD C, AB D, XY (axiom)

ABXY.

13. In the figure below, O is the mid point of AB and CD, prove that ACBD.

O AB CD ACBD.

OR

In the figure below, AOC and BOC form a linear pair. If b80, find the

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value of a.

AOC BOC b80, a

14. Plot the point P (2, 6) on a graph paper and from it draw PM and PN perpendiculars to x-axis

and y-axis, respectively. Write the coordinates of the points M and N.

P(2, 6) P PM PN x - y -

M N


15.

Prove that 30 29 28

31 30 29

2 2 2 7

102 2 2

30 29 28

31 30 29

2 2 2 7

102 2 2

OR

If a2, b3 then find the values of the following :

(i) (abba)1 (ii) (aabb)1

a2, b3

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(i) (abba)1 (ii) (aabb)1

16.

If x32 , then find the value of .

x32

17. Divide the polynomial 3x44x33x1 by x1 and find its quotient and remainder.

3x44x33x1 x1

OR

If both (x2) and are factors of px25xr, show that pr.

(x2) px25xr pr

18. Using suitable identity evaluate (42)3(18)3(24)3.

(42)3(18)3(24)3

19. Prove that the sum of three angles of a triangle is 180.

180

OR In the following figure, lm and TR is a transversal. If OP and RS are

respectively bisectors of corresponding angles TOB and ORD, prove

that OPRS.

lm TR OP RS TOB ORD

OPRS

2 22

1 xx

2 22

1 xx

1

2x

1

2x

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20. In the given figure, X72, XZY46. If YO and ZO are bisectors of XYZ

and XZY respectively of XYZ, find OYZ and YOZ.

X72, XZY46 YO ZO XYZ XYZ XZY

OYZ YOZ

21. In Fig. given below, AD is the median of ABC. BEAD, CFAD. Prove that

BECF.

ABC AD BEAD CFAD BECF.

22. Prove that angles opposite to equal sides of an isosceles triangle are equal.

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23. In the given figure, if FDA85, ABC45 and ACB40, then prove

that DFAE.

FDA85, ABC45 ACB40,

DFAE

24. A triangular park has sides 120 m, 80 m and 50 m. A gardener has to

put a fence all around it and also plant grass inside. How much area

does he need to plant ? Find the cost of fencing it with barbed wire

at the rate of Rs. 20 per meter leaving a space 3 m wide for a gate on

one side.

120 80 50

20 3

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25. Rationalize the denominator of

4

2 3 7

4

2 3 7

OR

If a74 3 , find the value of 1

a a

a74 3 1

a a

26. Express as a fraction in simplest form.

27. The polynomials ax33x24 and 2x35xa when divided by (x2) leave the

remainders p and q respectively. If p2q4, find the value of a.

(x2) ax33x24 2x35xa p q

p2q4 a

28. If 4 is a zero of the polynomial p(x)x3x214x24, find the other zeroes.

p(x)x3x214x24 4

29. (i) Expand

(ii) Evaluate (102)3, using suitable identity.

(i)

(ii) (102)3

OR Factorise : a3b313ab.

1 32 0.35.

1 32 0.35.

21 1 a b 1

4 2

21 1 a b 1

4 2

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a3b313ab

30. Plot the points given in the table below in the Cartesian plane.

31. In the figure below, if PQST, PQR110 and RST130, find QRS.

PQST PQR110 RST130 QRS

32. Prove that the sum of any two sides of a triangle is greater than twice the length

of median drawn to the third side.

33. In the given figure, if AD is the bisector of BAC then prove that :

(i) AB > BD (ii) AC > CD

AD BAC

(i) AB > BD (ii) AC > CD

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34. In figure below, ABAD, ACAE and . Prove that BCDE.

ABAD, ACAE BCDE.

BAD CAE

BAD CAE

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Class IX / & IX




(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) Question numbers 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.


lkekU; funsZk %







Section-A

Questions number 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.

460015

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1. Value of is :

(A) (B) 9 (C) 3 (D)

(A) (B) 9 (C) 3 (D)

2. is a polynomial of degree :

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

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

3. Degree of the polynomial (x32)(x211) is :

(A) 0 (B) 5 (C) 3 (D) 2

(x32) (x211)

(A) 0 (B) 5 (C) 3 (D) 2

4. Degree of which of the following polynomials is zero :

(A) x (B) 15 (C) y (D)

(A) x (B) 15 (C) y (D)

5. Two angles measure (30a) and (1252a). If each one is the

supplement of the other, then the value of a is :

(A) 45 (B) 35 (C) 25 (D) 65

(30a) (1252a)

a

(A) 45 (B) 35 (C) 25 (D) 65

23

1

9

1

3

23

1

9

1

3

2

1

2

2

1

2

2 x x

2 x x

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6. In ABC, if BCAB and B80, then A is equal to :

(A) 80 (B) 40 (C) 50 (D) 100

ABC BCAB B80 A

(A) 80 (B) 40 (C) 50 (D) 100

7. The area of a triangle whose sides are 13 cm, 14 cm and 15 cm is :

(A) 42 cm2 (B) 86 cm2 (C) 84 cm2 (D) 100 cm2

13 14 15

(A) 42 2 (B) 86 2 (C) 84 2 (D) 100 2 8. The area of an equilateral triangle is 16 m2. Its perimeter (in metres) is :

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

16 m2

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


9.

Evaluate,

10. Find the value of a if (x1) is a factor of 2x2ax .

(x1) 2x2ax a

11.

Find the product of .

12. In figure, AEDF , E is the midpoint of AB and F is the midpoint of DC. Using an

3

3

4532

243

4532

243

2

2

2 42 4

1 1 1 1 , , and x x x x

x x x x

2 42 4

1 1 1 1 , , and x x x x

x x x x

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Euclid axiom, show that ABDC.

AEDF E AB F DC

ABDC

13. ABC is an isosceles triangle with ABAC. Draw AP BC. Show that BC.

ABC ABAC AB BC BC.

OR In the given figure, line segments PQ and RS intersect each other at a point T

such that PRT40, RPT95 and TSQ75. Find SQT.

PQ RS T PRT40,

RPT95 TSQ75 SQT

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14. Which of the following points lies on x-axis ? Which on yaxis ?

A(0, 2), B(5, 6), C(3, 0), D(0, 3), E(0, 4), F(6, 0), G(3, 0)

x y

A(0, 2), B(5, 6), C(3, 0), D(0, 3), E(0, 4), F(6, 0), G(3, 0) Section-C Question numbers 15 to 24 carry three marks each.

15. Find the value of :

OR Represent 3.2 on the number line.

3.2

16. Simplify the following into a fraction with rational denominator.

17. If p2a, prove that a36app380.

2 3

3 4

4 1

216 256

2 3

3 4

4 1

216 256

1

5 6 11

1

5 6 11

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p2a a36app380.

OR

Factorize .

.

18. Using suitable identity evaluate (32)3(18)3(14)3.

(32)3(18)3(14)3

19. Prove that if two lines intersect, the vertically opposite angles are equal.

OR If the bisector of a pair of interior alternate angles formed by a

transversal with two given lines are parallel, prove that the given

lines are parallel.

20. ABC is a right angled triangle in which A90 and ABAC, find the values of B

and C.

ABC A90 ABAC B C

21. In given figure below, ABC is a triangle in which altitudes BE and CF to sides

AC and AB are equal. Show that

(i)

33

1 2 2 x x

xx

33

1 2 2 x x

xx

ABE ACF

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(ii) ABAC

ABC BE CF AC AB

(i)

(ii) ABAC

22. In given figure below, C is the mid point of AB. ACEBCD and

CADCBE. Show that

(i)

(ii) ADBE

AB C ACEBCD CADCBE

(i)

(ii) ADBE

23. In figure, prove that l m.

ABE ACF

DAC EBC

DAC EBC

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l m.

24. Find the height of the trapezium in which parallel sides are 25 cm and 10 cm and nonparallel sides are 14 cm and 13 cm.

25 10 14

13


25.

Simplify : .

.

OR

If and , find the value of x2xyy2.

2 6 6 2 8 3

2 3 6 3 6 2

2 6 6 2 8 3

2 3 6 3 6 2

3 2

3 2x

3 2

3 2y

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, x2xyy2

26. If x94 , find the value of x

2

x94 x2

27. (i) Expand

(ii) Evaluate (102)3, using suitable identity.

(i)

(ii) (102)3 28. If 3a2b5c5 and 6ab10bc15ac14, find the value of

27a3125c390abc8b3.

3a2b5c5 6ab10bc15ac14 27a3125c390abc8b3

29. State Factor theorem. Using this theorem factorise x33x2x3

x33x2x3

OR Find the value of a if the polynomias ax33x23 and 2x35xa

when divided by (x4), leave the same remainder.

ax33x23 2x35xa (x4) a

30. Plot the points A (0, 3), B (5, 3), C (4, 0), and D (1, 0) on the graph paper

Identify the figure ABCD and find whether the point (2, 2) lies inside the figure

or not ?

A (0, 3), B (5, 3), C (4, 0), D (1, 0)

ABCD (2, 2)

3 2

3 2x

3 2

3 2y

52

1

x

52

1

x

21 1 a b 1

4 2

21 1 a b 1

4 2

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31. In figure given below, if ABCD, EF CD and GED126, find AGE, GEF

and FGE.

ABCD, EF CD GED126 AGE, GEF FGE

32. In figure below, D is a point on side BC of ABC such that ADAC. Show that

AB > AD.

ABC BC D ADAC

AB > AD

33. In the given figure, if ABFE, BCED, AB BD and FE EC, then prove that ADFC.

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ABFE, BCED, AB BD FE EC ADFC.

34. ABC is an isoceles triangle in which ABAC. Side BA is produced to D such

that ADAB. Show that is a right angle.

ABC ABAC BA D

ADAB

BCD

BCD

c.b.s.e.-2011-sample-papers-for-ix-mathematics(5-sets)-summative-assessement-i.pdf

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