KV AFS AVADI - SECONDARY SECTION QUESTION BANK AND HOME WORKS

KENDRIYA VIDYALAYA AFS AVADI, CHENNAI 55

MODEL QUESTION PAPER FOR SUMMATIVE ASSESSMENT- II – 2016

CLASS IX  MATHEMATICS

Maximum Marks:100                                                                                     Time : 3 to 3 hours

        General Instructions:

(I)                 All questions are compulsory.

(II)               The question paper consists of 35 questions divided into five sections A, B, C, D and E.

(III)              SECTION A has 4  Very Short Answer type questions carrying ONE mark each.

(IV)              SECTION B has 6   Short Answer- I type questions carrying TWO marks each.

(V)                SECTION  C has 10 Short Answer- II type questions carrying THREE marks each.

(VI)              SECTION  D has 11 Long  Answer type questions carrying FOUR marks each.

(VII) SECTION  E has 4 questions from a theme of OTBA carrying TEN marks

(VIII) All questions are compulsory.

(IX) Calculators, Cell phones and Electronic gadgets are not permitted in the Examination Hall.

SECTION A

      1. The equation  x = 2y represents a line (a) parallel to x-axis      (b) parallel to y-axis        

              (c)passing through the origin    (d)  passing through the point (1, 2)

       2. The demand of different shirt sizes as obtained in a survey is given below. Find the modal shirt size.

Size	38	39	40	41	42	43	44	Total
No of persons	26	39	20	15	12	7	5	125

      

      3.  In the given figure ABCD is a parallelogram.  

            If the area of ∆AQB  is 13 cm²  ,find the area of 

            parallelogram ABCD.

      4.     Find the total surface area of a cone of radius 2r and slant height .

     

SECTION B

5. If (a,6) lies on the graph of the equation 3x + y = 9. Find the values of ‘a’.

6.    The data  5, 7, 10, 12, 2x – 8, 2x + 10, 35, 41, 42, 50 is arranged in ascending order. If the median of 

        these observations  is  25,  find  x.

7. If the volume of a sphere is 288cm³  then find its radius.

8. The curved surface area of a cylinder is 3960 cm².Find its height if the radius is 21cm.

9. Find the median of first 10 prime numbers.

       10. A coin is tossed150 times and the outcomes noted. Find the probability of getting   a) a head        b) a tail

OUTCOME	HEAD	TAIL
FREQUENCY	85	65

SECTION C

11. Give the equations of two lines passing through (2 , 4). How many such lines are there

       and why?

12. In the given figure, AD and BE are medians of ABC and DF II BE. Show that AC = 4CF

13.In the given figure ABCDE is a pentagon ABCDE  BD II FC. Prove that

   

     i)  ar(BDC)  = ar(BDF)

     ii) ar( ABCDE) = ar(AFDE)

14. Prove that parallelograms on the same base and between the same parallels are equal

      in area.

15.In figure,PQ is the diameter of the circle with the centre O. If   

      ,and, find

      ,and .

16. Curved surface area of a solid cone is 308cm² and its slant height is 14cm.

     i) radius of base

     ii) total surface area of the cone

17. A shopkeeper has one spherical laddoo of radius 5cm. With the same amount of material

      how many laddoos of radius 2.5 cm can be made?                          

18.The value of  up to 50 decimal places is given below.

     3.14159265358979323846264338327950288419716939937510

      i) Make a frequency distribution of the digits from 0 to 9.

      ii) What are the most and the least frequently occurring digits.

 19. 1500 families with 2 children were selected randomly, and the following data were recorded:

Number of girls in the family	2	1	0
Number of families	475	814	211

Compute the probability of a family chosen at random ,to have

a) 2 girls                      b) 1 girl                       c) no girls

20. The distance ( in km) of 40 female engineers from their residence to their place of their

        work were found as follows.

       5         3          10        20        25        11        13        7          12        31

      19        10        12        17        18        11        32        17        16        2

      7          9          7          8          3          5          12        15        18        3

     

      12        14        2          9          6          15        15        7          6          12

       What is the  probability that an engineer lives

      

        i)  less than 7 km from her place of work?

        ii)  more than or equal to 7 km from her place of work?

        iii) within km from her place of work?

SECTION D

21. Draw the graph of the linear equation 3x + 2y = 12. Also find the points where their graph

      cuts x-axis and y-axis.

22. The cost of making a solid cylindrical pipe is Rs.7040 at the rate of Rs.5 per cubic metre. If      

      the height of the cylindrical pipe is 7m then find its radius.

23. ABCD is rectangle and P , Q , R and S are mid-points of the sides AB , BC , CD and DA

      respectively. Show that the quadrilateral PQRS is a rhombus.

24. In figure, ABCD is a parallelogram and BC is produced to Q such that AD = CQ, Prove that

    

       ar(BCP) = ar(DPQ)

                                             

   

     

   

25. ABCD is a parallelogram. Points P and Q on BC trisects BC in three equal parts. Prove that

       ar(APQ) = ar(DPQ) = ar(ABCD)

26. 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.

27. Show that the quadrilateral formed by angle bisectors of cyclic quadrilateral is  also cyclic.  

                                                     

28. Construct a right triangle whose base is 8 cm and the sum of hypotenuse and other side is  16 cm.

29. A metallic cuboid having dimension 100 x 80 x 64 cm³ melted and recast in to a cube. Find

      the surface area of the cube.

30.A social welfare organization decided to build a shelter for homeless people in the form of

     cylinder of diameter 4.2 m and height 4 m surmounted by a cone whose vertical height is

2.1  m. Then

i)  How many persons can take a shelter if each person need 5 m³ space.

ii) Which mathematical concept is used in it?

iii)Which values are depicted in their plan?

       31.   Draw a histogram and a frequency polygon for the given data

Cost of living index	120-129	130-139	140-149	150-159	160-169	170-179
Number of weeks	8	12	4	16	8	4