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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-II, March-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-II, March-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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SUMMATIVE ASSESSMENT – II, 2012

II, 2012

MATHEMATICS /

Class – IX / IX

Time allowed : 3 hours Maximum Marks : 90

3 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 of 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 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.

(i)

(ii) 34 8

1 6 2 10

3 10 4

(iii) 1 8

(iv) 2 3 3 4 2

(v)

MA-1025

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SECTION–A /

Questions Number 1 to 8 carry 1 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 8 1

1. The graph of 3xy9 intersects x-axis at the point. (A) (3, 0) (B) (3 , 0) (C) (0 , 9) (D) (0 , 9)

3xy9 x-

(A) (3, 0) (B) (3 , 0) (C) (0 , 9) (D) (0 , 9)

2. In given fig., ABCD is a parallelogram. If ar (BFC)40 cm2 then ar (AEB) is equal to :

(A) 20 cm2 (B) 40 cm2 (C) 80 cm2 (D) 10 cm2

ABCD (BFC)40 cm2 (AEB)

(A) 20 cm2 (B) 40 cm2 (C) 80 cm2 (D) 10 cm2

3. A chord of a circle is equal to its radius. (See given fig). BAC is equal to :

(A) 90 (B) 60 (C) 30 (D) 45

BAC

(A) 90 (B) 60 (C) 30 (D) 45

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4. Which of the following is a linear equation ?

(A) x24x3(x21) (B) x23x4

(C) x1

x5 (D) (x1)1x

(A) x24x3(x21) (B) x23x4

(C) x1

x5 (D) (x1)1x

5. The class marks of a frequency distribution are 15, 20, 25,…. The class corresponding to

class mark 25 is : (A) 17.522.5 (B) 2030 (C) 22.527.5 (D) 2227

( class marks) 15, 20, 25,…. 25

(A) 17.522.5 (B) 2030 (C) 22.527.5 (D) 2227

6. A semi-circle is folded to form a cone, (See fig.). The radius OA will form :

(A) height of the cone (B) slant height of the cone (C) Circumference of the base (D) half of the circumference of the base

OA

(A) (B)

(C) (D)

7. The sum of probability of an event A and event not A is equal to :

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

‘A’ A

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

8. If diameter of a sphere is doubled then its surface area will be : (A) same (B) doubled (C) four times (D) eight times

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

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SECTION-B /

Question numbers 9 to 14 carry 2 marks each.

9 14 2

9. Show that the line segment joining the mid-points of opposite sides of a parallelogram, divide it into two equal parallelograms.

10. A cylinder 3 m high, is open at the. Top the circumference of its base is 22 m. Find its total

surface area (take 22

7)

3 22

(22

7 )

11. The following number of goals were scored by a team in a series of 10 matches :

2, 3, 4, 5, 0, 1, 3, 3, 4, 3. Find mode and median of the above data.

10

2, 3, 4, 5, 0, 1, 3, 3, 4, 3.

12. Three coins are tossed simultaneously 200 times with the following frequencies of different

outcomes.

Outcome : 3 heads 2 heads 1 head 3 tails

Frequency : 24 70 75 31

Compute the probability of getting (i) less than 2 heads (ii) 3 heads

200

3 2 1 3

24 70 75 31

(i) (ii) 3

13. In adjacent Fig., two chords AB and CD of a circle intersect at right angle. If ABD65,

find the measure of CAB.

AB CD

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ABD65 CAB

OR /

In the figure, ABBP prove that DPDC.

ABBP DPDC.

14. Calculate mean of first 5 prime numbers.

SECTION-C /

Questions numbers 15 to 24 carry 3 marks each.

15 24 3

15. Rohit is driving his car at a uniform speed of 80 km per hour. Draw time – distance graph taking time along x-axis and distance along y-axis.

80 /

x- y-

16. Prove that median of a triangle divides it into two triangles of equal area.

17. Draw an acute angled triangle ABC. Construct perpendicular bisectors of AB and BC

intersecting each other at O. Measure OA, OB and OC. Are they equal ?

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AB BC O OA,

OB OC

18. A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in

between.

4 cm

OR /

A river 4 m deep and 60 m wide is flowing at the rate of 0.31 km/hour. How much water will fall into the sea in a minute ?

4 m 60 m 0.31 km/hr

19. Find the mean of the following distribution :

Variable (x) : 4 5 6 7 8 9

Frequency (f) : 12 10 8 7 8 5

(x) : 4 5 6 7 8 9

(f) : 12 10 8 7 8 5

OR /

The number of books in different shelves of a library are as follows : 25, 27, 32, 24, 28, 34, 20, 25, 28, 30, 20, 35, 25, 27, 31, 37, 22, 24, 27, 28, 27, 20, 36, 21, 20, 29 30, 29, 36, 30. Prepare a frequency distribution table with class size 4 for the data given above taking the first interval as 1822. (22 not included)

(shelves)

25, 27, 32, 24, 28, 34, 20, 25, 28, 30, 20, 35, 25, 27, 31, 37, 22, 24, 27, 28, 27, 20, 36, 21, 20, 29 30, 29, 36, 30.

4 1822 22

20. Find three different solutions for the equation 6x8y320.

6x8y320

OR /

If the point (2, 4) lies on the graph of the equation 2yax10, find the value of a. Now express this as a linear equation in two variables.

2yax10 (2, 4) a

21. The outer diameter of spherical shell is 10 cm and the inner diameter is 8 cm. Find the

volume of the metal contained in the shell.

10 cm 8 cm

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22. Prove that a diagonal of a parallelogram divides it into two congruent triangles.

23. ABCD is a rhombus with ABC50 Determine ACD.

ABCD ABC50 ACD

24. 30 plants were planted in each school out of 12 schools. After a month the number of

plants that survived are given below. School : 1 2 3 4 5 6 7 8 9 10 11 12

Number of plants survived :

22 15 12 24 27 10 13 22 17 9 20 25

What is the probability of survival of : (i) more than 20 plants in a school (ii) less than 10 plants in a school (iii) exactly 22 plants in a school

12 30

1 2 3 4 5 6 7 8 9 10 11 12

22 15 12 24 27 10 13 22 17 9 20 25

(i) 20

(ii) 10

(iii) 22

SECTION-D /

Question numbers 25 to 34 carry 4 marks each.

25 34 4

25. Prove that the bisectors of angles of a parallelogram encloses a rectangle.

26. Construct a triangle PQR such that R75, Q45 and PQQRRP11 cm.

PQR R75, Q45 PQQRRP11

OR /

Construct a triangle ABC in which BC8 cm, B45 and ABAC3.5 cm.

ABC BC8 cm B45 ABAC3.5 cm

27. Draw the graph of linear equation 5y3x18 on Cartesian plane. From the graph check

whether (2, 4) is the solution of linear equation or not.

5y3x18 (2, 4)

28. What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and

base radius 6 m ? Assume that the extra length of material required for sticking purpose will be approx. 20 cm. (Take 3.14).

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3 m 6 m

8 m 20 cm

(3.14 )

29. If a line intersects two concentric circles with centre O at A, B, C and D. Prove that ABCD.

(See fig.)

O A, B, C D

ABCD.

30. ABC is a triangle right angled at C. A line through the mid point M of hypotenuse AB and parallel to BC intersects AC at D show that

(i) D is the mid point of AC (ii) CMMA1

2AB.

ABC C AB M BC

D AC

(i) AC D (ii) CMMA1

2AB.

OR /

ABCD is a parallelogram and X and Y are points on the diagonal BD, such that DXBY. Show that (i) AYCX is a parallelogram (ii) CXAY.

ABCD BD X Y DXBY

(i) AYCX (ii) CXAY.

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31. Give the geometrical representation of 4 (y3)2 y5 as an equation (i) in one variable (ii) in two variables.

4 (y3)2 y5 (i) (ii)

32. If circles are drawn taking two sides of a triangle as diameters, prove that the point of

intersection of these circles lie on the third side.

33. Twenty cylindrical pillars of a building are to be cleaned. If the diameter of a pillar is 0.5 m

and height is 4 m, what will be the cost of cleaning them at the rate of Rs. 3 per m2. (Take 3.14)

20 0.5

4 3 (3.14 )

34. Draw a histogram representing the following frequency distribution.

Marks : 010 1020 2030 3040 4050 5060

No. of students : 3 5 8 10 7 2

010 1020 2030 3040 4050 5060

3 5 8 10 7 2

- o O o -