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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.

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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.

MA1-042

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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. 2. 9

p

q p q q 0

(a) 2999

1000 (b)

19

10 (c) 3 (d)

26

9

The value of 2. 9

in the formp

q, where p and q are integers and q 0, is

(a) 2999

1000 (b)

19

10 (c) 3 (d)

26

9

1

2. abc0 a3b3c3

(a) abc (b) 3abc (c) 2abc (d) 4abc

If a b co, then a3 b3 c3 is equal to :

(a) abc (b) 3abc (c) 2abc (d) 4abc

1

3. f(x)2x27x3 x 2

(a) 19 (b) 3 (c) 3 (d) 0

Value of f(x) 2x2 7x 3 at x 2 is :

(a) 19 (b) 3 (c) 3 (d) 0

1

4. 52524752

(a) 100 (b) 10000 (c) 50000 (d) 100000

Value of 5252 4752 is : (a) 100 (b) 10000 (c) 50000 (d) 100000

1

5. 130

(a) 45 (b) 65 (c) 75 (d) 35

An exterior angle of a triangle is 130 and its two interior opposite angles are equal. Each of the interior angle is equal to : (a) 45 (b) 65 (c) 75 (d) 35

1

6.

(a) 15 (b) 25 (c) 30 (d) 35

In a right angled triangle, if one acute angle is half the other, then the smallest

angle is :

(a) 15 (b) 25 (c) 30 (d) 35

1

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7. ( 3, 9) x

(a) (3, 9 ) (b) (9, 3 ) (c) (3, 9 ) (d) (3, 9)Mirror image of point ( 3, 9) on x axis is : (a) (3, 9 ) (b) (9, 3 ) (c) (3, 9 ) (d) (3, 9)

1

8.

(a) I (b) II

(c) III (d) IV

A point both of whose co-ordinates are positive will be in : (a) I Quadrant (b) II Quadrant (c) III Quadrant (d) IV Quadrant

1

/ SECTION-B

9 14 2

Question numbers 9 to 14 carry two marks each.

9. 5 8 2 32 2 2

Simplify : 5 8 2 32 2 2

2

10. 2x3 11x2 4x 1 2x1

Show that 2x1 is a factor of 2x3 11x2 4x 1

2

11. x33x2

3x1 (x 1)

Find the remainder, when x3 3x2 3x 1 is divided by (x 1)

2

12.

State fifth postulate of Euclid.

2

13. (3x58) (x 38) x

If (3x 58) and (x 38) are supplementary angles, find x and the angles.

/ OR

PQR QP RQ S T

SPR 135 PQT110 PRQ

2

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In the figure sides QP and RQ of PQR are produced to points S and T

respectively. If SPR 135 and PQT 110 find PRQ.

14. 3 : 4 : 5 144 cm

The length of sides of a right angled triangle are in the ratio 3 : 4 : 5 and perimeter is 144 cm. Find its sides and area.

2

/ SECTION-C

15 24 3

Question numbers 15 to 24 carry three marks each.

15. 7 5.

Represent 7 5. on the number line geometrically.

/ OR

11 11 433 3281 (64 125 )

Evaluate :

11 11 433 3281 (64 125 )

3

16.

5 3 5 3

7 4 3 7 4 3

Simplify : 5 3 5 3

7 4 3 7 4 3

3

17. x3 3x29x5

Factorize : x3 3x2 9x 5

/ OR

3 3 32 2 a 16 2 b c 12abc

Factorize : 3 3 32 2 a 16 2 b c 12abc

3

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18. px2 5x r (x2) (2x1) pr

If both (x 2) and (2x1) are factors of px2 5x r show that p r

3

19.

POQ OR PQ OS, OP OR

1

ROS QOS POS2

In figure POQ is a line. Ray OR is to PQ. OS is another ray lying between OP

and OR.

Prove that

1

ROS QOS POS2

/ OR

OP RS, OPQ110 QRS130 PQR

In figure if OP RS, OPQ 110 and QRS 130, then determine PQR.

3

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20. ABC ABAC B C O

A O

(i) OBOC (ii) A AO

In an Isosceles triangle ABC, with AB AC, the bisectors of B and C

intersect each other at O. Join A to O. Show that (i) OB OC, (ii) AO bisects A

3

21.

l m p q

ABC CDA

l and m are two parallel lines intersected by another pair of parallel lines ‘p’ and

‘q’ (see figure ). Show that ABC CDA

3

22.

PQR QR S PQQRRP > 2 PS

In figures is any point on QR of PQR. Prove that PQ QR RP >2PS

3

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23.

ABC ABAC BA D

ADAB BCD

Triangle ABC is an isosceles triangle AB AC. Side BA is produced to D, such

that AD AB. Show that BCD is a right angle.

3

24. 3 : 5 : 7 300 m

The sides of a triangular park are in the ratio 3 : 5: 7 and the perimeter is 300 m. Find its area and the length of perpendicular drawn on the biggest side.

3

/ SECTION-D

25 34 4

Question numbers 25 to 34 carry four marks each.

25.

2 6 6 2 8 3

2 3 6 3 6 2

Simplify : 2 6 6 2 8 3

2 3 6 3 6 2

/ OR

2 5

a 2 5

2 5b

2 5

(ab)3

If 2 5

a 2 5

, and 2 5

b 2 5

then find (a b )3

4

26. a8 3 7 b

1

a a2

b2

If a 8 3 7 and b 1

a, what will be the value of a2 b2 ?

4

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27. 2x33x2

17x30

Factorize : 2x3 3x2 17x 30

4

28. k2 x3kx2

3kxk ( x3) k

k 0

Find the value of k ( k 0) if ( x3 ) is a factor of k2 x3 kx2 3kx k.

4

29.

(ab)3(bc)3

(ca)33(ab) (bc) (ca)2(a3

b3c3

3abc)

Prove that :

(ab)3 (bc)3 (ca)3 3(ab) (bc) (ca) 2(a3 b3c3

3abc)

4

30. PQRS P(4, 0), Q(1, 0), R(1,5)

S

Three vertices of a square PQRS are P(4, 0), Q (1, 0) R(1, 5). Plot the points.

Also find the co-ordinates of the missing vertex S.

4

31.

PQR QR S PQR PRS T

QTR1

2QPR

The side QR of PQR is produced to point S. If the bisector of PQR and PRS

meet at point T, then prove that QTR 1

2QPR.

4

32. PQR S SQSR < PQPR

S is any point in the interior of PQR. Show that SQ SR < PQ PR.

/ OR

4

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ABC AB, BC AM PQR PQ, QR

PN

(i) ABM PQN, (ii) ABC PQR

Two sides AB, BC and median AM of one ABC are respectively equal to sides PQ, QR and median PN of PQR. Prove that : (i) ABM PQN (ii) ABC PQR

33.

ABCD O OAOC D, O B

In a rhombus ABCD, O is any interior point such that OA OC. Then prove that D, O and B are collinear.

4

34.

ABC AB AC BE CF

4

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ABC is an isosceles triangle in which BE and CF are altitudes drawn to equal sides AB and AC. Show that these altitudes are equal .

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