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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 1074

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SECTION – A /

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 8 1

1. The equation y3 in two variables can be written as

(A) 1.x1.y3 (B) 0.x1.y3 (C) 0.x0.y3 (D) 1.x0.y3

y3

(A) 1.x1.y3 (B) 0.x1.y3 (C) 0.x0.y3 (D) 1.x0.y3 2. If P, Q, R and S are the midpoints of a rectangle of area 36 sq. cm, then PQRS is a

parallelogram of area

(A) 24 cm2 (B) 18 cm2 (C) 12 cm2 (D) 9 cm2

36 cm2 P, Q, R S PQRS

(A) 24 cm2 (B) 18 cm2 (C) 12 cm2 (D) 9 cm2 3. In the figure, the magnitude of angle ABC if angle AOC120 will be :

(A) 125 (B) 120 (C) 130 (D) 135

ABC AOC120:

(A) 125 (B) 120 (C) 130 (D) 135

4. The point of the form (a, a) always lies on the line :

(A) xa (B) ya (C) yx (D) xy0

(a, a)

(A) xa (B) ya (C) yx (D) xy0 5. The class mark of the class interval 90120 is

(A) 90 (B) 105 (C) 115 (D) 120

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90120

(A) 90 (B) 105 (C) 115 (D) 120 6. The radius of a sphere is 2r, then its volume will be

(A) 43 r3 (B) 4r3 (C) 8

3 r3 (D) 323r3

2r

(A) 43 r3 (B) 4r3 (C) 8

3 r3 (D) 323r3

7. A coin is tossed once, then the probability of getting tail is

(A) 1 (B) 12 (C) 2 (D) 1

3

1

(A) 1 (B) 12 (C) 2 (D) 1

3

8. If the height of the cone is doubled then its volume is increased by

(A) 100% (B) 200% (C) 300% (D) 400%

(A) 100% (B) 200% (C) 300% (D) 400% SECTION – B /

Question numbers 9 to 14 carry two marks each.

9 14 2

9. In figure, AD is median of triangle ABC, E is the midpoint of AD and F is the midpoint of

AE. Prove that ar(ABF)1/8ar(ABC)

ABC AD AD E AE F

ar(ABF)1/8 ar(ABC)

10. Three cubes each of side 3 cm are joined end to end. Find the surface area of the resultant

cuboid.

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3 cm

11. If the mean of 16 observations is 8. If two is added to every observation, what will be the

new mean ?

16 8 2

12. A die is thrown. Find the probability of getting an odd number.

13. Angle in a semi circle is a right angle. Prove it.

OR/

In figure, O is the centre of the circle, CAO40 and CBO30 find x.

O CAO40 CBO30. x

14. Find the median of the first ten prime numbers.

SECTION – C /

Question numbers 15 to 24 carry three marks each.

15 24 3

15. If x2 and y1 is a solution of the equation axy5, find the value of a, also two more

solutions of the equation.

x2 y1 axy5 a

16. Show that the median of a triangle divides it into two triangles of equal areas.

17. Construct a triangle PQR, in which QR7 cm and measure of angle Q45 and

PQPR3 cm.

PQR QR7 cm Q45 PQPR3 cm

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18. A military tent is in the form of a circular cone of vertical height 6 m, the diameter of the base being 7 m. If 12 soldiers can sleep in it, find the average cubic metre of air space required per soldier.

6 2 7 12

OR/

The volume of a cylinder is 448 cubic cm and the height is 7 cm find its total surface area.

448 cm3 7 cm

19. Find the arithmetic mean of the following data

x 1 2 3 4 5 6 7

f 5 9 12 17 14 10 6

x 1 2 3 4 5 6 7

f 5 9 12 17 14 10 6

OR

In an election seats won by various political parties are as follows :

Political party A B C D E F

Seats won 75 55 37 29 10 37

(a) Draw the bar chart for the above data. (b) Which party won the maximum seats ?

A B C D E F

75 55 37 29 10 37

(a)

(b)

20. Show that the points A(1, 2), B(1, 16) and C(0, 7) lie on the graph of the linear

equation y9x7

A(1, 2), B(1, 16) C(0, 7) y9x7

OR/

Write 3 different solutions of 2xy7.

2xy7

21. A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm,

find the outer curved surface area of the bowl. (Take 3.14)

0.25 5

3.14

22. Show that each angle of a rectangle is a right angle.

23. ABCD is a parallelogram. E and F are mid points of BC and AD respectively. Prove that BF and ED trisect AC.

ABCD E F BC AD BF

ED AC

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24. Two coins are tossed simultaneously 300 times. The frequency of appearing. (I) both heads : 75 (II) One head : 160 (III) No head : 65 Find the probability of occurence of each of these events.

300

(I) : 75

(II) : 160

(III) : 65

SECTION – D /

Question numbers 25 to 34 carry four marks each.

25 34 4

25. ABCD is a rhombus. Show that the diagonal AC bisects angle A and angle C and the

diagonal BD bisects angle B as well as angle D.

ABCD AC BD A, C B, D

26. Construct a triangle XYZ, in which measure of angle Y90 measure of angle Z30. XYYZZX11 cm.

XYZ Y90, Z30 XYYZZX11 cm

OR/

Construct a right angled triangle whose base is 4 cm and sum of its hypotenuse and other side is 8 cm.

4 cm 8 cm

27. Draw the graph of the linear equation 3x4y6. At what points the graph cuts the x and y axes.

3x4y6 x y

28. A spherical iron shell with 8 cm external diameter weighs 1860

4

7g. Find the thickness of

the shell of the density of metal is 12 g/cm3.

(shell) 8 cm 18604

7

12 g/cm3

29. In figure, PSSR, angle RPS54 and angle PRQ46. Find the measure of angle TQR and measure of angle RTQ.

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PSSR, RPS54 PRQ46. TQR RTQ

30. Prove that the quadrilateral formed by joining the mid points of pairs of consecutive sides

of a quadrilateral is a parallelogram.

31. The Auto fare in a city is as follows. For the first kilometer the fare is Rs. 5 and for the

successive distance it is Rs. 2 per kilometer. Taking a distance covered as x kilometer and total fares as Rs. y, write a linear equation for the above said data and draw its graph.

5 2

x y

32. Prove that the angle subtended by an arc at the centre is double the angle subtended by it

at the remaining part of the circle.

OR/

If the non parallel sides of a trapezium are equal, prove that is a cyclic quadrilateral.

33. The diameter of the roller is 84 cm and its length is 120 cms. It takes 500 complete

revolutions to move once over the level a play ground and find the area of the playground in square meters.

84 cm 120 cm

500

34. The heights of the workers in a company are as follows :

Height (cm) 130 – 140 140 – 150 150 – 160 160 – 170 170 – 180 180 – 190

Number of workers 8 18 20 5 4 3

Draw a histogram to represent the above data.

130 – 140 140 – 150 150 – 160 160 – 170 170 – 180 180 – 190

8 18 20 5 4 3

- o 0 o -