CBSE Mathematics SAMPLE PAPER

7/23/2019 CBSE Mathematics SAMPLE PAPER

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SUMMATIVE ASSESSMENT –I (2011)

Lkdfyr ijh{kk &

I

MATHEMATICS / xf.kr

Class – IX / & IX

Time allowed: 3 hours Maximum Marks: 90fu/kkfjr le; 3 ?k.V vf/kdre vd 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 8 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; fun”k

(i) lHkh iz”u vfuok;Z gS aA

(ii) bl iz”u i= es a 34 iz”u gSa, ftUgsa pkj [k.Mks a v, c, l rFkk n es a ckaVk x;k gSA [k.M & v esa 8 iz”u

gS a ftues a izR;sd 1 vad dk gS, [k.M & c es a 6 iz”u gSa ftues a izR;sd ds 2 vad gSa, [k.M & l es a 10iz”u gS a ftues a izR;sd ds 3 vad gS rFkk [k.M & n es a 10 iz”u gS a ftues a izR;sd ds 4 vad gS aA

(iii) [k.M v es a iz”u la[;k 1 ls 8 rd cgqfodYih; iz”u gS a tgka vkidks pkj fodYiks a es a ls ,d lghfodYi pquuk gSA

(iv)

bl iz”u i= es a dksbZ Hkh loks Zifj fodYi ugha gS, ysfdu vka rfjd fodYi 2 vadks a ds ,d iz”u es a, 3vadks a ds 3 iz”uks a es a vkSj 4 vadks a ds 2 iz”uks a es a fn, x, gS aA izR;sd iz”u esa ,d fodYi dk p;u djsaA

(v) dSydqysVj dk iz;ksx oftZ r gSA

Section-A

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

1.

Rationalisation factor of1

2 3 5 is :

460038



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(A) 5 2 3 (B) 3 2 5

(C) 12 5 (D) None of these

1

2 3 5

(A) 5 2 3 (B) 3 2 5

(C) 12 5 (D)

2. Which of the following is not a polynomial ?

(A) 3 (B) (C) (D) t73t24

(A) 3 (B) (C) (D) t73t24

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.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

5. In ABC, . Then the measure of A is :

(A) 60 (B) 30 (C) 40 (D) 20

ABC , A

23 5x x2

2

1 4x

x

23 5x x2

2

1 4x

x

2 3 46

x x

6

2 3 46

x x

6

CBA 2 6

CBA 2 6



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(A) 60 (B) 30 (C) 40 (D) 20

6.In the given figure, ABC is an isosceles triangle with ABAC and A50,

B is equals to :

(A) 50 (B) 65 (C) 90 (D) 130

ABC ABAC A50 , B

(A) 50 (B) 65 (C) 90 (D) 130

7.

The sides of a are 7 cm, 24 cm and 25 cm. Its area is :

(A) 168 cm2 (B) 84 cm2

(C) 87.5 cm2 (D) 300 cm2

7 24 25

(A) 168 2 (B) 84 2

(C) 87.5 2 (D) 300 2

8. Two sides of a triangle are 13 cm and 14 cm and its semi perimeter is 18 cm. Then third side of

the triangle is :

(A) 12 cm (B) 11 cm (C) 10 cm (D) 9 cm

13 14 18

(A) 12 (B) 11 (C) 10 (D) 9



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Section-B

Question numbers 9 to 14 carry two marks each.

9. Express 0.25 in the form of

p

q, where p and q are integers and q0.

0.25 p

q p q q0

10.If (x3) is a factor of 22 1 3 2x xk, find k.

(x3) 22 1 3 2x xk k

11. Check whether 73x is a factor of 3x37x or not.

73x 3x37x

12.

In figure, PQ and RS intersect at T and PRT 40 , RPT 95 and TSQ 75 , find

SQT

PQ RS T PRT 40 , RPT 95 TSQ 75

SQT

13. In PQR,

P70,

Q30. Which side of this triangle is the longest. Give reasons for youranswer.



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PQR P70, Q30

OR

In given figure is AB CD ? Justify your answer.

AB CD ?

14. Plot the points A (3, 0), B (3, 3) and C (0, 3) in a Cartesian plane. Join OA, AB, BC and CO.

Name the figure so formed and write its one property.

A (3, 0), B (3, 3) C (0, 3) OA, AB, BC CO

Section-C

Question numbers 15 to 24 carry three marks each.

15. If a 2 3 5 and b3 3 5 , prove that a2b24a6b30

a 2 3 5 b3 3 5 a2b24a6b30

OR

Find the value of ‘a’ and ‘b’ if3 1

3 1

a b 3 .

‘a’ ‘b’3 1

3 1

a b 3



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16. If a 9 4 5 find the value of 2

2

1a

a

a 9 4 5 22

1a

a

17.If x32 2 , find x2 2

1

x.

x32 2 x22

1

x

OR

If f (x) x25x1

Evaluate f (2) f (1) f 1

3

f (x) x25x1, f (2) f (1) f 1

3

18. If x 2, find the value of

x 2

19. In the figure given below, PQRS and T is any point as shown in the figure, then show that

.

PQRS T

.

33

1 x

x

3

31

x x

PQT QTS RST 360

PQT QTS RST 360



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OR

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

20. In the figure below, ABAC, DBDC. Prove that ABDACD.

ABAC, DBDC ABDACD

21.

In the given figure, X62, XYZ54. If YO and ZO are the bisectors of XYZ and

XZY respectively, find OZY and YOZ.

X62, XYZ54. YO ZO XYZ XZY

OZY YOZ

22. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such

that BADABE and EPADPB. Show that DAPEBP.



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AB P D E AB

BADABE EPADPB. DAPEBP.

23. If two parallel lines are intersected by a transversal, prove that the bisectors of the two pairs of

interior angles enclose a rectangle.

24. In a parallelogram measure of adjacent sides are 34 cm and 20 cm. One of the diagonals is

42 cm. Find the area of the parallelogram.

34 20 42

Section-D

Question numbers 25 to 34 carry four marks each.

25. Find the rational numbers a and b in the following :

.

a b

.

OR

If3 2

3 2x

and

3 2

3 2y

then, show that 2 2 99x xy y .

3 23 2

x

3 23 2

y

2 2 99x xy y

5 2 3 a b 3

7 4 3

5 2 3 a b 3

7 4 3



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26.Express 32.1235 in the form

p

q.

32.1235 p

q

27. Without actual division prove that x42x32x22x3 is exactly divisible by x22x3.

x42x32x22x3 x22x3

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

(xyz)0 (x3y3z3)3xyz

29.Factorise : x39x26x56.

x39x26x56.

OR

If xyz12 and x2

y2

z2

70, then find the value of x3

y3

z3

3xyz.

xyz12 x2y2z270 x3y3z33xyz

30. Write the co-ordinates of the vertices of a rectangle in III Quadrant whose length and breadth

are 5 and 2 units respectively, one vertex is at the origin and the shorter side is on y-axis

III 5

2 y-

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

32. Prove that the sum of the interior angles of a triangle is 180

180

33. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (as shown



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in figure below). Show that A > C.

ABCD AB CD

A > C.

34. In figure, PS is bisector of . Show that

PS

.

QPR and PT QR

1TPS

2 ( Q R)

QPR PT QR

1TPS

2 ( Q R)

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CBSE Mathematics SAMPLE PAPER