Mathematics - Class IX 2012 - Exam - Set 57, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 57 and more Exams Mathematics in PDF only on Docsity! Page 2 of 10 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) 45021 Page 3 of 10 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. Equation of a line passing through origin is : (A) xy1 (B) x2y4 (C) xy0 (D) yx1 (A) xy1 (B) x2y4 (C) xy0 (D) yx1 2. In the figure, ABCD is a parallelogram. If area (AOD)12 cm2, then area (ABCD) is : (A) 3 cm2 (B) 24 cm2 (C) 48 cm2 (D) 36 cm2 ABCD ar (AOD)12 cm2 ar (ABCD) (A) 3 cm2 (B) 24 cm2 (C) 48 cm2 (D) 36 cm2 3. In the given figure ABC80, BDC40 then ACB is : (A) 120 (B) 60 (C) 80 (D) 40 ABC80 BDC40 ACB (A) 120 (B) 60 (C) 80 (D) 40 4. If the point (2, 1) lies on the graph of the equation 3xky4, then the value of k is (A) 1 (B) 1 (C) 2 (D) 2 (2, 1) 3xky4 k (A) 1 (B) 1 (C) 2 (D) 2 5. The median of first 5 odd multiples of 5 is (A) 15 (B) 25 (C) 35 (D) 45 Page 6 of 10 ABC A BC D AD E ar (BEC)½ ar (ABC). 17. In given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If DBC55, BAC45, COD95then find BCD and DCO. ABCD AC BD DBC55, BAC45, COD95, BCD DCO OR/ If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords. 18. A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs. 105/m, sheet being 2 m wide. 12 m 9 m 4 m 105 2 m Page 7 of 10 OR/ Diameter of a road roller is 98 cm and its length is 100 cm It takes 800 complete revolutions to level a playground. Find the area of the playground. (Use  22 7 ). 98 cm 100 cm 800  22 7 19. 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 the mean, median and mode of the data. 12 41, 39, 48, 52, 46, 52, 54, 40, 96, 52, 40, 52. OR/ Find the median of the following data 19, 25, 59, 48, 35, 31, 30, 32. If 25 is replaced by 52 and 48 is replaced by 32, find the new median. 19, 25, 59, 48, 35, 31, 30, 32. 25 52 48 32 20. Draw the graphs of the equations xy100 and xy40 on the same graph paper. xy100 xy40 21. A hemispherical dome of a building is to be white washed. The total cost of white washing of dome building is Rs. 924 at the rate of Rs. 3/m2. Find the. (a) radius of the hemisphere (b) volume of air in the dome 3 m2 924 (a) (b) 22. Two parallel lines l and m are intersected by a transversal p. Show that the quadrilateral formed by the bisectors of interior angles is a rectangle. l m p 23. Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other. 24. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes : Outcome 3 Heads 2 Heads 1 Head No Head Frequency 23 72 77 28 Find the experimental probability of getting (i) 2 Heads (ii) at least 2 Heads 200 Page 8 of 10 3 2 1 23 72 77 28 (i) 2 (ii) 2 SECTION-D / Question numbers 25 to 34 carry four marks each. 25 34 4 25. In figure ABCD is a trapezium in which side AB is parallel to side DC and E is the mid-point of side AD. If F is a point on the side BC such that the segment EF is parallel to the side DC, prove that F is the mid-point of BC and EF 1 2 (ABDC). ABCD AB, DC E, AD BC F EF DC F EF 1 2 (ABDC). 26. Prove that parallelograms on the same base and between the same parallels are equal in area. 27. Bhavya has a piece of canvas whose area is 552 m2. She uses it to make a conical tent with a base radius of 7 m. Assuming that all the stiching margins and the wastage incurred while cutting amounts to approximately 2 m2. Find the volume of the tent that can be made with it (Take 22/7). 552 m2 7 2 2 22/7 OR/ A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm and outer diameter is 5.0 cm. Find its (i) Inner curved surface area (ii) Outer curved surface area.