time allowed : 3 hours maximum marks : 90 3 90...page 2 of 10 summative assessment – ii, 2012 ii,...

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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 1070

ANIL TUTORIALS,D-156,SECTOR-5,DEVENDRA NAGAR,RAIPUR,C.G,HELPLINE : 97525-09261

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SECTION – A /

Question numbers 1 to 8 carry 1 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. x2, y5 is solution of the linear equation :

(A) x2y7 (B) 5x2y7 (C) xy7 (D) 5xy7

x2, y5

(A) x2y7 (B) 5x2y7 (C) xy7 (D) 5xy7 2. If a triangle and a rhombus are on the same base and between the same parallels then ratio of

area of triangle and area of rhombus are in the ratio : (A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1

(A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1 3. In the figure, O is the centre of a circle and AOC130. ABC will be :

(A) 120 (B) 115 (C) 90 (D) 65

O AOC130 ABC

(A) 120 (B) 115 (C) 90 (D) 65

4. Graph of x2y3 will intersect x-axis at the point :

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

x2y3 x-

(A) (3, 0) (B) (0, 3) (C) (3, 0) (D) (0, 3) 5. Mode of the data 4, 6, 5, 4, 6, 4, 5, 7, 8, 9, 4, 10 is :

(A) 4 (B) 5 (C) 6 (D) 10

4, 6, 5, 4, 6, 4, 5, 7, 8, 9, 4, 10

(A) 4 (B) 5 (C) 6 (D) 10


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6. The diameter of a cone is 14 cm and its slant height is 9 cm. Area of the curved surface will be :

(A) 2220 cm

7 (B) 2198

cm7

(C) 220 cm2 (D) 198 cm2

14 9

(A) 220

7 2 (B)

198

7 2 (C) 220 2 (D) 198 2

7. In a survey it was found that out of 364 persons, 91 persons like potato chips. If one person is

selected at random, then the probability that he likes potato chips is : (A) 0.75 (B) 0.50 (C) 0.25 (D) 0.80

364 91

(A) 0.75 (B) 0.50 (C) 0.25 (D) 0.80 8. The total surface area of a solid hemisphere of radius 21 cm is :

(A) 2772 cm2 (B) 4158 cm2 (C) 3986 cm2 (D) 4628 cm2

21

(A) 2772 2 (B) 4158 2 (C) 3986 2 (D) 4628 2

SECTION – B /

Question numbers 9 to 14 carry 2 marks each.

9 14 2

9. Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar

(APB) ar (CPD) ar (APD)ar (BPC).

ABCD AC BD P

ar (APB)ar(CPD)ar(APD)ar(BPC). 10. Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the

cylinder is 0.7 m, find its height.

4.4 2 0.7

11. Find the median of the following observations :

46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33.

46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. 12. A die is thrown 400 times and outcomes are recorded as follows :

Outcome 1 2 3 4 5 6

Frequency 70 65 60 75 63 67

Find the probability of getting an odd number.

400 1, 2, 3, 4, 5 6

1 2 3 4 5 6

70 65 60 75 63 67


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13. Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Find the distance between their centres.

10 8 12

OR/

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

5 3

4

14. The distance in km of 32 engineers from their residence to their place of work were found as follows : 4, 6, 10, 12, 8, 13, 12, 9, 11, 16, 10, 18, 15, 3, 8, 4 10, 8, 7, 9, 5, 15, 18, 3, 11, 15, 2, 10, 14, 7, 6, 12. Construct a grouped frequency distribution table with class – size 5 for the data given above taking the first interval as 05.

32

4, 6, 10, 12, 8, 13, 12, 9, 11, 16, 10, 18, 15, 3, 8, 4 10, 8, 7, 9, 5, 15, 18, 3, 11, 15, 2, 10, 14, 7, 6, 12.

5 05

SECTION – C /


15 24 3

15. The cost of a notebook is thrice the cost of a pen. Write a linear equation in two variables to represent this statement. Express it graphically.

16. In the figure ar (DRC)ar (DPC) and ar (BDP)ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

ar(DRC)ar(DPC) ar(BDP)ar (ARC) ABCD DCPR

OR/


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P and Q are any two points lying on the sides DC and AD resp. of a parallelogram ABCD. Show that ar (APB)ar (BQC).

DC AD P Q ar(APB)

ar (BQC). 17. Construct a triangle ABC in which B45, C60 and ABBCCA12 cm.

ABC B45, C60 ABBCCA12

18. A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm.

Find the area of the sheet required to make 10 such caps.

7

24 10

19. The following data gives the number (in thousands) of applicants registered with an

Employment Exchange during 20052010.

Year 2005 2006 2007 2008 2009 2010

No. of applicants registered (in thousands)

19 21 23 30 32 36

Construct a bar graph to represent the above data.

20052010

2005 2006 2007 2008 2009 2010

19 21 23 30 32 36

20. Express y in terms of x, it being given that 3xy90. Check whether the point (3, 0) and

(2, 2) lie on the equation.

3xy90 y x (3, 0) (2, 2)

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.

0.25 5

OR/

A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of

15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which

container has greater capacity and by how much ?

(Take 22

7)

(soft drink)

(i) 5 4 15

(ii) 7 10

22

7


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

23. ABCD is a parallelogram and AP, CQ are perpendiculars from vertices A and C on diagonal BD (see fig)

Show that

(i) APB CQD (ii) APCQ.

ABCD A C BD AP CQ

(i) APB CQD (ii) APCQ.

OR/

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see fig.) AC is a diagonal.

Show that

(i) SRAC and SR 1

2 AC

(ii) PQSR (iii) PQRS is a parallelogram.

ABCD P, Q, R S AB, BC, CD DA AC

(i) SRAC SR 1

2 AC

(ii) PQSR

(iii) PQRS


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24. In a box, there are 9 red, 8 white and 3 black balls. One ball is taken out of the bag. Find the probability that it is : (i) white, (ii) red or black (iii) not-red

9 8 3

(i) (ii) (iii)

SECTION – D /


25 34 4

25. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD res P. (see fig.).

Show that the line segment AF and EC trisect the diagonal BD.

ABCD E F AB CD AF EC

BD

26. Construct a triangle ABC in which BC7 cm, B75 and ABBC13 cm.

ABC BC7 B75 ABBC13

OR/

Construct a triangle ABC in which BC8 cm, B60 and ABAC2.5 cm.

ABC BC8 B60 ABAC2.5

27. Draw a graph of the line x2y3. From the graph, find the coordinates of the point.

When (i) x5, (ii) y0.

x2y3

(i) x5, (ii) y0.

28. The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of leveling this ground at the rate of 50 paise per square metre.

84 1.5 100

50

OR/

The cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq. d.m. is Rs. 237.60. The height of the tank is 6 times the radius of the base of the tank. Find its volume correct to two decimal places.


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237.60

60 dm 6 2

29. ABC and ADC are two right triangles with common hypotenuse AC. Prove that

CADCBD.

ABC ADC AC CADCBD.

30. Prove that the line segment joining the mid-points of two sides of a triangle is parallel to the third side.

31. Linear Equation for converting Fahrenheit temperature to Celcius one is

F9

5C32

(i) Draw the graph for the above equation representing Celcius temperature on x-axis and Fahrenheit temperature on y-axis.

(ii) Read the value of F for C35from the graph. (iii) Is there any temperature which is numerically equal in both Fahrenheit and Celcius

scale of temperature if yes, find it.

(Fahrenheit) (celcius)

F9

5C32

(i) x- y-

(ii) C35 F

(iii) (scales)

32. In the figure, P is the centre of a circle.

Prove that 2(XZYYXZ)XPZ

P

2(XZYYXZ)XPZ

33. A teak wood log is cut first in the form of a cuboid of length 2.3 m, width 0.75 m and of a


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certain thickness. Its volume is 1.104 m3. How many rectangular plants of size 1.104 m3. How many rectangular plants of size 2.3 m0.75 m0.04 m can be cut from the cuboid ?

2.3 0.75

1.104 3

2.3 0.75 0.04

34. Marks secured by a group of 10 students are as follows :

16, 18, 29, 31, 20, 23, 26, 25, 32, 20 (i) Find the mean of the data (ii) If 32 is replaced by 23 in the data, find the new mean. (iii) If each observation in the given data is increased by 5 marks, then what will be the

mean ? (iv) If two students securing 16 and 32 leave the group, then find the mean of remaining 8

students.

10

16, 18, 29, 31, 20, 23, 26, 25, 32, 20

(i)

(ii) 32 23

(iii) 5

(iv) 16 32 8

- o 0 o -


time allowed : 3 hours maximum marks : 90 3 90...page 2 of 10 summative assessment – ii, 2012 ii,...

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