Mathematics - Class IX 2012 - Exam - Set 59, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 59 and more Exams Mathematics in PDF only on Docsity! Page 2 of 9 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) 45019 Page 3 of 9 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. For what value of k, x2 and y1 is a solution of x3yk0 : (A) 1 (B) 2 (C) 2 (D) 3 k x2 y1 x3yk0 (A) 1 (B) 2 (C) 2 (D) 3 2. If a triangle and a parallelogram are on same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is (A) 1 : 3 (B) 1 : 2 (C) 3 : 1 (D) 1 : 4 (A) 1 : 3 (B) 1 : 2 (C) 3 : 1 (D) 1 : 4 3. Choose the correct statement : (A) Diagonals of a rectangle are perpendicular to each other (B) Diagonals of a rhombus are perpendicular to each other (C) A kite is a parallelogram whose adjacent sides are equal (D) Diagonals of a trapezium are always equal. (A) (B) (C) (D) 4. Which of the following is a linear equation in one variable : (A) 2x3y0 (B) x25x3 (C) 5xy23 (D) x56 (A) 2x3y0 (B) x25x3 (C) 5xy23 (D) x56 5. If 12 is the mean of 10 observations and 10 is added to each observation, then the new mean is : (A) 120 (B) 13 (C) 24 (D) 22 10 12 10 (A) 120 (B) 13 (C) 24 (D) 22 6. S is the curved surface area of a cylinder of radius r and height h. If its radius is doubled and height is halved then the CSA will be : (A) S (B) S 2 (C) S 4 (D) 2 S r h S (A) S (B) S 2 (C) S 4 (D) 2 S Page 6 of 9 Find the volume of a sphere whose surface area is 154 m2. 22 use 7        154 m2 22 7        19. Mean of 35 observations was found to be 78.4. But later it was found that 86 was misread for 68. Find the correct mean. 35 78.4 86 68 OR/ 20 children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows : 1 6 2 3 5 12 5 8 4 8 10 3 4 12 2 8 15 1 17 6 Make a grouped frequency distribution table for this data taking class width 5 and one of the class intervals as 510. How many children watched television for more than 10 hours a week ? 20 1 6 2 3 5 12 5 8 4 8 10 3 4 12 2 8 15 1 17 6 5 510 10 20. The food charges in a hostel are as follows : For the first day, the charges are Rs 100 and for the subsequent days it is Rs 50 per day. Taking the number of days as x and total charges as Rs y, write a linear equation for this information and draw its graph. 100 50 x y 21. A solid cuboid of dimensions 12 cm  18 cm  10 cm is cut into cubes of side 2 cm. How many such cubes can be cut from the cuboid ? Compare the total surface area of the cube and cuboid. 12 cm  18 cm  10 cm 2 cm 22. In a parallelogram ABCD, the bisector of Angle A also bisects BC at X. Prove that AD2AB ABCD A BC X AD2AB Page 7 of 9 23. Prove that a diagonal of a parallelogram divides it into two congruent triangles. 24. 1500 families with 2 children were selected randomly and the following data were recorded. No. of girls 0 1 2 No. of families 211 814 475 If a family is chosen at random, compute the probability that it has (i) No girl (ii) 2 girls (iii) Atmost 1 girl 2 1500 0 1 2 211 814 475 (i) (ii) 2 (iii) SECTION-D / Question numbers 25 to 34 carry four marks each. 25 34 4 25. ABC is an isosceles triangle in which ABAC. AD bisects exterior angle PAC and DCAB. Show that (i) DACBCA (ii) ABCD is a parallelogram ABC ABAC PAC AD DCAB (i) DACBCA (ii) ABCD Page 8 of 9 26. Construct a ABC, in which B60, C45 and ABBCCA11 cm. ABC B60, C45 ABBCCA11 cm 27. Express y in terms of x, it being given that 3xy120. Check whether point (3, 3), (4, 0) and (2, 12) satisfy the equation 3xy120 (without drawing graph) 3xy120 y x (3, 3), (4, 0) (2, 12), 3xy120 28. A circus tent is in the form of a cone of height 15 m and diameter 16 m. Find the length of the canvas needed to make the tent if the width of the canvas is 2 m (use 3.14) 15 m 16 m 2 m 3.14 OR/ th3 4 of a cylindrical can contains milk. The height of the can is 1.4 m and radius is 0.4 m. This milk is poured into small cylindrical glasses of height 10 cm and radius 5 cms. How many small glasses are needed to empty the can ? 3 4 1.4 m 0.4 m 10 cm 5 cm 29. Construct a triangle PQR such that Q45, R60 and PQQRRP20 cm PQR Q45, R60 PQQRRP20 OR/ Construct a XYZ in which YZ5 cm, Y60, and XYXZ9 cm. XYZ YZ5 cm, Y60 XYXZ9 30. ABCD is a rectangle. If P, Q, R, S are the mid points of the sides of AB, BC, CD, DA respectively show that the quadrilateral PQRS is a rhombus. ABCD P, Q, R, S AB, BC, CD, DA PQRS OR/ 31. Draw the graphs of each of the equation x2y30 and 4x3y10 on the same graph.