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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 1003

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SECTION–A /

Question numbers 1 to 8 carry one mark each. For each questions, 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 the equation 2x3y6, cuts the x axis at the point (A) (0. 3) (B) (3, 0) (C) (2, 0) (D) (0, 2)

2x3y6 x-

(A) (0. 3) (B) (3, 0) (C) (2, 0) (D) (0, 2) 2. If E is the mid point of the median AD of a triangle ABC, then ratio of areas of BED and

ABC will be (A) 1 : 2 (B) 2 :1 (C) 1 : 4 (D) 4 : 1

ABC AD E BED ABC

(A) 1 : 2 (B) 2 :1 (C) 1 : 4 (D) 4 : 1 3. In the figure ‘O’ is the centre of the circle, ABO20 and ACO30 where A, B, C are

points on the circle. The value of x is.

(A) 120 (B) 130 (C) 100 (D) 150

‘O’ A, B, C ABO20,

ACO30 x

(A) 120 (B) 130 (C) 100 (D) 150

4. Any point of the form (a, - a) always lie on the graph of the equation. (A) x a (B) ya (C) yx (D) xy0

(a, - a)

(A) x a (B) ya (C) yx (D) xy0 5. The mode of the following data is :

3, 15, 4, 19, 17, 11, 6, 22, 6 (A) 6 (B) 22 (C) 21 (D) 19.

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3, 15, 4, 19, 17, 11, 6, 22, 6 (A) 6 (B) 22 (C) 21 (D) 19.

6. If the volume of a sphere is numerically equal to its surface area then diameter of the sphere

is. (A) 6cm (B) 8cm (C) 4cm (D) 12cm.

(A) 6 (B) 8 (C) 4 (D) 12

7. In the throw of a die in a game of snakes and ladder the probability of getting an even

number is

(A) 1

2 (B)

1

3 (C) 1 (D)

1

6

(A) 1

2 (B)

1

3 (C) 1 (D)

1

6

8. A match box measures 6cm2cm1.5cm. The volume of a packet containing five such

boxes is

(A) 80cm3 (B) 180cm3 (C) 90cm3 (D) 100cm3

6cm2cm1.5cm 5

(A) 80cm3 (B) 180cm3 (C) 90cm3 (D) 100cm3

SECTION-B /

Question numbers 9 to 14 carry two marks each.

9 14 2

9. In the figure, diagonals AC and BD of a trapezium ABCD with ABCD intersect each other

at O. show that ar (AOD)ar(BOC)

ABCD ABCD AC BD O

(AOD) (BOC)

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10. Find the total surface area of a cone whose radius is

r

2 and slant height is 2l.

r

2 2l

11. The class marks of a frequency distribution are 104, 114, 124, 134, 144, 154, 164.

find the class size and class intervals

104, 114, 124, 134, 144, 154, 164

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

out comes.

Out come 3 Heads 2 Heads 1 Head No Head

Frequency 23 72 77 28

If the three coins are simultaneously tossed again, compute the probability of more than 2 heads coming up.

200

3 2 1 0

23 72 77 28

2

13. Prove that equal chords subtend equal angles at the centre.

OR /

In the figure, O is the centre of the circle Arc BCD subtends an angle of 140 at the centre. BC

is produced to P and CD is joined. Find measure of DCP.

O BCD 140 BC P

DC DCP

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14. For a particular year, following is the distribution of ages (in years) of primary school teachers in a district :

Age (in years) 15 – 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50

No. of teachers 10 30 50 50 30 6 4

(i) Write the lower limit of first class interval. (ii) Determine the class limits of the fourth class interval (iii) Find the class mark of the class 45 – 50. (iv) Determine the class – size.

15 – 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50

10 30 50 50 30 6 4

(i)

(ii)

(iii) 45 – 50

(iv)

SECTION-C /

Question numbers 15 to 24 carry three marks each.

15 24 3

15. Express the following statement as a linear equation in two variables by taking present ages

(in years) of father and son as x and y. respectively. Age of father 5 years ago was two years more than 7 times the age of his son at that time.

5 7 2

x y

16. XY is a line parallel to side BC of ABC If BEAC and CFAB meet XY at E and F respectively. Show that ar (ABE)ar(ACF)

ABC BC XY BEAC CFAB XY

E F ar (ABE) ar (ACF)

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17. Construct an angle of 45 at the initial point of a given ray OA, using a ruler and compasses.

OA 45

18. The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped into it.

Find the ratio of surface areas of the balloon in two cases.

7 14

OR /

A hemispherical bowl is 0.25cm thick. The inner radius of bowl is 5cm find the outer curved surface area and volume of the bowl [keep volume in ]

0.25 5

19. 100 Surnames were randomly picked up from a telephone directory and frequency

distribution of the number of letters in the English alphabet in the surnames was found to be as follows.

Number of letters Number of Surnames

2 – 4 6

4 – 6 30

6 – 8 44

8 – 12 16

12 - 14 4

Draw a histogram to depict the given information.

100

2 – 4 6

4 – 6 30

6 – 8 44

8 – 12 16

12 - 14 4

20. Find two linear equations in two variables whose graphs pass through (2, 14). How many

such equations are possible ?

(2, 14)

21. How many liters of milk can be put in six hemispherical bowls each of radius 35cm ?

35 6

22. Four angles of a quadrilateral are in the ratio 3 : 5 9 : 13 find the angles of the quadrilateral.

3 : 5 9 : 13

OR /

Show that the bisectors of angles of a parallelogram form a rectangle.

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

OR /

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 :

(A) D is mid point of AC (B) MDAC (C) CMMA1

2AB

ABC C AB M BC

AC D

(A) AC D (B) MDAC (C) CMMA1

2AB

24. A die is rolled 25 times and outcomes are recorded as under

Out comes 1 2 3 4 5 6

Frequency 9 4 5 6 1 0

It is thrown one more time Find the probability of getting (a) an even number (b) a multiple of 3 (c) a prime number

25

1 2 3 4 5 6

9 4 5 6 1 0

(a)

(b)

(c)

SECTION-D /

Question numbers 25 to 34 carry four marks each.

25 34 4

25. Show that the quadrilateral formed by joining the mid points of adjacent sides of a rectangle

is a rhombus.

26. Construct a ABC in which BC7.5cm, B45 and ABAC4cm.

ABC BC7.5 B45 ABAC4

27. Taxi fare in a city is Rs 8.00 for first kilometer and for the subsequent distance it is Rs 5.00

per km. Write an equation to represent this information in two variables taking distance covered as ‘x’ km and total fare as y (in Rs). Find the distance travelled by a person if he spent Rs 63.00.

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8.00 5.00

‘x’ ‘y’

63

28. A cube and a cuboid have the same volume. The dimensions of the cuboid are in the ratio 1 : 2 : 4. If the difference between the cost of painting the cuboid and cube (whole surface area) at the rate of Rs 5 / m2 is Rs 80. Find their volumes.

1 : 2 : 4

5 2 80

29. ABC is an isosceles triangle with ABAC. A circle through B and C intersect AB and AC at D and E respectively prove that BCDE.

ABC ABAC B C AB AC

D E BCDE

30. Show that, the line segments joining the mid points of the opposite sides of a quadrilateral bisect each other.

31. Draw graph of following linear equations on the same axes. (i) xy3 (ii) 3x2y4 Also shade the region formed by their graphs and y-axis.

(i) xy3 (ii) 3x2y4

y-

32. Show that angle subtended by minor arc at the centre is double the angle subtended by it at any point on the remaining part of a circle.

33. The diameter of a metallic ball is 4.2cm. what is the mass of the ball, if the density of the

metal is 8.9g per cm3 ?

4.2 8.9 3

OR /

A vessel is of the shape of a cone. Radius of the broader end is 2.1cm and height is 20cm. Find volume of the vessel.

2.1 20

34. Find the mean of the following data :- x 10 12 20 25 35 f 3 10 15 7 5

x 10 12 20 25 35

f 3 10 15 7 5

OR /

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A company manufactures car batteries of particular type. Lives (in years) of 40 butteries were recorded as follows :

2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5

3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7

3.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8

2.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4

4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6

Construct a grouped frequency distribution table for the above data using each class interval of size 0.5 starting from the interval 2 – 2.5. (2.5 not included)

40

2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5

3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7

3.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8

2.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4

4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6

0.5 2 – 2.5 2.5

- o O o -