Page 1 of 12

Important Instructions for the

School Principal

(Not to be printed with the question paper)

1) This question paper is strictly meant for use in school based SA-I, September-2012 only.

This question paper is not to be used for any other purpose except mentioned above under

any circumstances.

2) The intellectual material contained in the question paper is the exclusive property of

Central Board of Secondary Education and no one including the user school is allowed to

publish, print or convey (by any means) to any person not authorised by the board in this

regard.

3) The School Principal is responsible for the safe custody of the question paper or any other

material sent by the Central Board of Secondary Education in connection with school

based SA-I, September-2012, in any form including the print-outs, compact-disc or any

other electronic form.

4) Any violation of the terms and conditions mentioned above may result in the action

criminal or civil under the applicable laws/byelaws against the offenders/defaulters.

Note: Please ensure that these instructions are not printed with the question

paper being administered to the examinees.

Page 2 of 12

I, 2012

SUMMATIVE ASSESSMENT – I, 2012

/ MATHEMATICS

IX / Class – IX

3 90

Time allowed : 3 hours Maximum Marks : 90

(i)

(ii) 34 8

1 6 2 10

3 10 4

(iii) 1 8

(iv) 2 3 3 4 2

(v)

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

of 10 questions of 4 marks each.

(iii) Question numbers 1 to 8 in Section-A are multiple choice questions where you are required

to select one correct option out of the given four.

(iv) There is no overall choice. However, internal choices 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.

MA1-019

Page 3 of 12

SECTION–A

1 8 1

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.

1. b > 0 b2a a

(A) b (B) b (C) b (D) b2

If b > 0 and b2a then a is equal to :

(A) b (B) b (C) b (D) b2

1

2. 1

yx

y x , (x y, y 0) x3

y3

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

2

If 1yx

y x , (x y, y 0) then the value of x3

y3 is :

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

2

1

3. p(t)4t3

4t2t1 (2t1)

1p

2

(A) 1

2 (B)

1

2 (C) 1 (D) 0

If (2t1) is the factor of the polynomial p(t)4t34t2

t1 then the value of

1p

2

is :

(A) 1

2 (B)

1

2 (C) 1 (D) 0

1

4. p(x) 3

(A) 3 (B) 3 (C) 1 (D) 0

The degree of the polynomial p(x) 3 is :

(A) 3 (B) 3 (C) 1 (D) 0

1

5. BCD

(A) 180 (B) ACBABC

(C) ACBBAC (D) BACABC

1

Page 4 of 12

In the given figure, BCD is equal to :

(A) 180 (B) ACBABC

(C) ACBBAC (D) BACABC

6. (abcdefghij)

(A) 900 (B) 720 (C) 540 (D) 360

In the figure the measure of (abcdefghij) is :

(A) 900 (B) 720 (C) 540 (D) 360

1

7. (2ab, b)(6, 2) a

(A) 2 (B) 2 (C) 4 (D) 6

If (2ab, b)(6, 2) then the value of a is :

(A) 2 (B) 2 (C) 4 (D) 6

1

8. M, IV M

(A) (a, b) (B) (a, b)

(C) (a, b) (D) (a, b)

The point M lies in the IV quadrant. The co-ordinates of point M is :

(A) (a, b) (B) (a, b)

(C) (a, b) (D) (a, b)

1

/ SECTION-B

Page 5 of 12

9 14 2

Question numbers 9 to 14 carry two marks each.

9. 2 1.414 3.141

1

2

Taking 2 1.414 and 3.141, evaluate 1

2

upto three places of decimal.

2

10. 3x2x1 (x1)

Examine whether (x1) is a factor of 3x2x1 ?

2

11. x y x24y2

17 xy2

(x2y)

If x and y are two positive real numbers such that x24y2

17 and xy2, then

find the value of (x2y).

2

12. P Q PQQRPR

P and Q are the centres of two intersecting circles. Prove that PQQRPR.

2

13. AOB : BOC2 : 3 AOC75 AOB BOC

In figure AOB : BOC2 : 3. If AOC75 then find the measure of AOB

and BOC.

2

Page 6 of 12

/ OR

AOBBOCCODDOA360

In figure, prove that AOBBOCCODDOA360

14. x, x1 2x1 x 10 x

The sides of a triangle are x, x1, 2x1 and its area is x 10 . What is the value

of x ?

2

/ SECTION-C

15 24 3

Question numbers 15 to 24 carry three marks each.

15. 11

7

Find the decimal expansion of 1

17

.

/ OR

1

4 20 245 4052

Simplify : 1

4 20 245 4052

3

16. 2 2

5 2 2 5 8 3

Page 7 of 12

Evaluate : 2 2

5 2 2 5 8

17. 3x2

mxna xa m n

a 3

If xa is the factor of 3x2mxna then prove that

m na

3

.

/ OR

2x39x2

11x30.

Factorise using the remainder theorem 2x39x2

11x30.

3

18. (2yx)2(y2x)(2xy)2(2xy)

Factorise : (2yx)2(y2x)(2xy)2(2xy)

3

19. ab

In the given figure, find ab.

/ OR

180

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

3

20. AB CD

AFCE BEFD

Two equal pillars AB and CD are standing on either side of the road as shown in the figure.

3

Page 8 of 12

If AFCE then prove that BEFD

21. ABC ABBC CE BF

ABF ACE

ABC is an isosceles triangle with ABBC. If CE and BF are the medians then

prove that ABF ACE.

3

22. ABC AB > AC BC D AB > AD

Prove that in a ABC, if AB > AC and D is any point on the side BC, then

AB > AD.

3

23. PQR QR S PQR PRS

T 2QTRQPR

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

and PRS meet at T then prove that 2QTRQPR.

3

24. ABCD AC16 cm AB10 cm

3

Page 9 of 12

In the given figure ABCD is a rhombus with AC16 cm and AB10 cm. What is the area of the rhombus ABCD.

/ SECTION-D

25 34 4

Question numbers 25 to 34 carry four marks each.

25. a74 3

1a

a

If a74 3 then find the value of 1

a a

/ OR

3 3 34 281 25 5

16 9 2

Simplify :

3 3 34 281 25 5

16 9 2

4

26. 1 1 1

1 2 2 3 3 4

Prove that 1 1 1

1 2 2 3 3 4

is a rational.

4

27. f(x)x42x3

3x2axb (x1) (x1)

5 19 f(x) (x2)

4

Page 10 of 12

On dividing f(x)x42x3

3x2axb by (x1) and (x1) we get remainder

5 and 19 respectively. Find the remainder when f(x) is divided by (x2).

28. C 2x37x2

3xC, (2x3)

Find the value of C for which the polynomial 2x37x2

3xC is exactly divisible

by (2x3). Hence factorize the polynomial.

4

29. xyz0 x3y3

z33xyz.

If xyz0 then show that x3y3

z33xyz.

4

30. PQRS

P(1, 1), Q(4, 2), R(4, 8), S(1, 10) P x- y-

Plot the following points. Join them in order and identify the figure, PQRS thus obtained : P(1, 1), Q(4, 2), R(4, 8), S(1, 10). Write mirror image of point P on x-axis and y-axis.

4

31. ABC AB AC P Q CBP

BCQ BO CO O

BOC

1

2(yz)

The sides AB and AC of ABC are produced to point P and Q respectively. If

bisectors BO and CO of CBP and BCQ respectively meet at point O, then

prove that BOC

1

2(yz).

4

32. OAOB, OCOD AOBCOD ACBD 4

Page 11 of 12

In figure OAOB, OCOD and AOBCOD. Prove that ACBD.

/ OR

ADBD BD < AC

In the given figure ADBD. Prove that BD < AC.

33. ACB ACCD CDEF

FEC10 BDE

In figure ACB is a right angle and ACCD and CDEF is a parallelogram. If

FEC10 then calculate BDE.

4

34. 4

Page 12 of 12

Prove that two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and included side of the other triangle.

- o O o -