Mathematics - Class IX 2012 - Exam - Set 69, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 69 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) MA 1001 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 8 1 1. The maximum number of points that lie on the graph of the linear equation in two variables is (A) two (B) infinite (C) three (D) None of these (A) 2 (B) (C) 3 (D) 2. In ABC, E is the mid point of median AD. Then the ratio of areas of BED to area of ABC is (A) 1 : 2 (B) 2 : 1 (C) 4 : 1 (D) 1 : 4 ABC AD E BED ABC (A) 1 : 2 (B) 2 : 1 (C) 4 : 1 (D) 1 : 4 3. In the figure, ACP40, and BPD120. Then CBD (A) 40 (B) 60 (C) 20 (D) 30 ACP40 BPD120 CBD (A) 40 (B) 60 (C) 20 (D) 30 4. Which of the following is the solution of y40 ? (A) x0; y4 (B) x4; y0 (C) x4; y4 (D) x0; y0 y40 (A) x0; y4 (B) x4; y0 (C) x4; y4 (D) x0; y0 5. Mode of the following scores is :- 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18 (A) 18 (B) 28 (C) 14 (D) 25 Page 6 of 9 SECTION – C / Question numbers 15 to 24 carry three marks each. 15 24 3 15. Express x3y in the form axbyc0 and indicate the values of a, b and c. Write two solutions of the equation. x3y axbyc0 a, b c 16. In the figure, ABCD is a quadrilateral and BEAC, also BE meets DC produced at E. Show that ar(ADE)ar(ABCD) ABCD BEAC DC BE E (ADE) (ABCD) 17. Construct an angle of 45 at the initial point of a ray using scale and compasses only. 45 OR/ Construct a equilateral triangle with one side 6 cm.  6 18. The diameter of a roller is 42 cm and its length is 120 cm. It takes 500 complete revolutions to move once to land a playground. Find the area of the playground in m2. 120 42 500 2 OR/ A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm12 cm8 cm, how many bricks would be required ? 10 4 24 24 12 8 Page 7 of 9 19. Find the value of p if mean of following distribution is 20 : x 15 17 19 20p 23 f 2 3 4 5p 6 20 „p‟ x 15 17 19 20p 23 f 2 3 4 5p 6 20. Give the Geometrical representation of 2y70 as equation in (i) one variable (ii) two variables 2y70 (i) (ii) 21. The diameter of moon is approximately 1 4 th of the diameter of earth. What fraction of volume of earth is the volume of moon. 1 4 22. In a parallelogram ABCD, E and F are the mid points of sides AB, and CD respectively. Show that the line segment AF and EC trisect the diagonal BD. ABCD AB CD E F AF EC BD 23. “A diagonal of a parallelogram divides it into two congruent triangles” Prove it. OR/ The diagonals of a quadrilateral are perpendicular to each other. Show that the quadrilateral formed by joining the mid points of its sides is a rectangle. 24. 1500 families with 2 children were selected randomly and the following data was recorded : No. of girls 0 1 2 No. of families 211 814 475 If a family is chosen at random, find the probability that it has (i) at most one girl (ii) at least one girl. 2 1500 0 1 2 211 814 475 (i) (ii) Page 8 of 9 SECTION – D / Question numbers 25 to 34 carry four marks each. 25 34 4 25. Prove that “The diagonals of a rhombus are perpendicular to each other”. 26. Construct a XYZ in which Y45 and Z30. Also XYYZZX10 cm. XYZ Y45, Z30 XYYZZX10 27. Force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express the situation and plot the graph of the equation taking the constant to be 5 units. 5 28. If h, c, v are respectively the height, curved surface and the volume of a cone. Prove that 3vh3c2h29v20 h, c v 3vh3c2h29v20 29. Prove that “The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle”. OR/ “If two non parallel sides of a trapezium are equal then prove that it is cyclic quadrilateral”. 30. ABC is an isosceles triangle in which ABAC. AD bisects exterior PAC and CDAB. Show that (I) DACBCA (II) ABCD is a parallelogram ABC ABAC PAC AD CDAB (I) DACBCA (II) ABCD 31. Shade the triangle formed by the graphs of 2xy4, xy2 and the y-axis. Write the co-ordinates of vertices of the triangle. 2xy4, xy2 y- 32. Prove that the quadrilateral formed by internal angle bisectors of any quadrilateral is cyclic. OR/