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SUMMATIVE ASSESMENT II 2013 MATHEMATICS CLASS 9Time 3 hours MAXIMUM MARKS 90GENERAL INSTRUCTIONS • All questions are compulsory. • The question paper consists of 34 questions divided into 4 sections A, B, C and D. A comprises of 8 questions of 1 mark each. Section B contains of 6 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each. Section D comprises of 10 questions of 4 mark each. • Question Numbers 1 to 8 in Section A are multiple choice questions where you are required to select one correct option out of the given four. • There is no overall choice • Use of calculator is not permitted. Section A 1. The point((1/2), (1/2)) is the solution of the linear equation 5x+2y=_____. (A) (3/2) (B) 0 (C) 7/2 (D)(1/2) 2. Any point on the line y=3x is of the form: (A) (a,3a) (B) (3a,a) (C) (a,(a/3)) (D) ((a/3),-a) 3. Area of parallelogram PQRS is: (A) PQ x QM (B) SR x QM (C) SR x SL (D) PS x SL 4. Given a circle with centre O and radius r. A point P lies in a plane such that CO<r. Point P lies (A) On the circle (B) on the exterior of the circle (C) in the interior of the circle (D) None of these 5. Which solid figure among the following has the total surface area same as curved surface area? (A) Right Circular Cylinder (B) Sphere (C) Right Circular Cone (D) Hemisphere 6. The total surface area of a hemisphere of radius 3.5cm is: (A) 110
(B) 115.5 (C) 120 (D) 125.57. The age(in years) of the 10 children are given below: 15, 15, 16, 16, 15, 14, 17, 16, 14, 16 The Modal age of the children is: (A) 4 (B) 15 (C) 16 (D) 178. The sum of heights of a number of players is 745 cm and the mean height of player is 149. The number of players are: (A) 10 (B) 9 (C) 5 (D) 6 Section B9. If ABCD is a parallelogram then prove that ar(ACD)=ar(BCD)10. If the base of an isosceles triangle is 8 cm and one of the equal sides is 5 cm, then find the area of the triangle.11. Curved Surface Area of a right circular cylinder is 5.5m2 If the radius of the base of the cylinder is 0.7 m Find its height12. Find the mean of first 10 prime number13. The distance in km of 32 engineers from their residence to their place of work were found as follows Construct a grouped frequency distribution tabl;e with class size 5 for the data given above taking first interval as 0-5.14. Two coins are tossed 500 times simultaneously and observations are as given below: Find the probability of getting (i) at least one head (ii) no head Section C
15. In the linear equation 2x+3y=11, Express y in terms of x and x in terms of y. Find the points where it cuts x axis and y axis.16. Give the equations of three lines passing through point (-3, 4)17. In a parallelogram ABCD, P Q R and S are midpoints of sides AB, BC, CD and DA respectively. Show that ar(PQRS) = 0.5 ar(ABCD)18. Construct a triangle ABC in which BC = 4.5 cm B=45deg, and AC = 5.5cm19. Construct a square whose diagonal is 6cm long.20. Show that diagonals AC and BD of a parallelogram ABCD divides it into four triangles of equal areas.21. The radius and height of a right circular cone are in ration 5:12. If its volume is 314 cu cm find slant height and curved surface area (use pi = 3.14)22. A conical tent is 10m high and radius of its base 24m. Find the cost of canvas required to make the tent when 1square metre canvas costs 70 rs23. In a test given to 12 students, the following marks are recorded: 41 39 48 52 46 52 54 40 96 52 40 52 Find median mode and mean24. Ages of workers in a factory are given below Find probability that the age of worker selected at random at least 25 years. Section D25. Perimeter of rectangle is 24cm. If the length of a rectangle is taken as x cm and breadth as y cm write the equation for the above statement and draw the graph.26. The auto fare in a city is charged as per the rates stated below: Rate for first km of journey is Rs 8 and for the subsequent distance it is Rs 5 per km. taking distance covered as x km and total fare as y write a linear equation for the above and draw its graph.
184.108.40.206.31. A man having a triangular plot of base 5800m and corresponding height 30000m decides to give one fourth of his plot which is also triangular in shape for a school to be builtfor the visually impaired children. Answer the following : • What is the area of the triangular plot? • Explain the figure how could this be implemented? What shape and area of land is left with the man? • What value of the man is depicted here?32. The sum of the base and radius and the height of a right circular cylinder is 37cm. If total surface area of the cylinder is 1628 square cm. Find the volume of the cylinder
33. Diameter of sphere is decreased by 10%. Find the percent of decrease in surface area.34.