Mathematics - Class IX 2012 - Exam - Set 56, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 56 and more Exams Mathematics in PDF only on Docsity! Page 2 of 12 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) 45020 Page 3 of 12 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. y3x5 has : (A) a unique solution (B) only two solution (C) infinitely many solution (D) none of these y3x5 (A) (B) (C) (D) 2. In figure, BE2 EC and area (ABC)60 cm2, then ar (AEC) is : (A) 15 cm2 (B) 20 cm2 (C) 30 cm2 (D) 40 cm2, BE2 EC ar (ABC)60 2, ar (AEC) (A) 15 cm2 (B) 20 cm2 (C) 30 cm2 (D) 40 cm2, 3. In figure, if OA5 cm, AB8 cm and ODAB then CD is equal to (A) 3 cm (B) 2 cm (C) 4 cm (D) 5 cm OA5 , AB8 ODAB, CD Page 6 of 12 SECTION-C / Question numbers 15 to 24 carry three marks each. 15 24 3 15. Determine the point on the graph of the linear equation xy6, whose ordinate is 2 times its abscissa. xy6 16. Show that the diagonals of a parallelogram divide it into four triangles of equal area. 17. In the given figure, PQQR and, if QPR55 find TSR. PQQR QPR55 TSR OR/ In the figure, ABCD is a cyclic parallelogram. Prove that ABCD is a rectangle. ABCD ABCD Page 7 of 12 18. The capacity of a closed cylindrical vessel of height 1 m, is 15.4 litres. How much m2. of metal sheet is needed to make it ? 1 m 15.4 m2 19. The marks obtained by 40 students of class IX in an examination are given below 12, 8, 18,8, 6, 16, 12, 5, 23, 2, 10, 20, 12, 9, 7, 6, 5, 3, 5, 13, 21, 13, 15, 20, 24, 1, 7, 16, 21, 13, 23, 18, 7, 3, 18, 17, 16, 16, 23, 12. Represent the data in the form of a frequency distribution using 1520 (20 not included) as one of the class intervals IX 40 12, 8, 18, 8, 6, 16, 12, 5, 23, 2, 10, 20, 12, 9, 7, 6, 5, 3, 5, 13, 21, 13, 15, 20, 24, 1, 7, 16, 21, 13, 23, 18, 7, 3, 18, 17, 16, 16, 23, 12. 1520 20 OR/ Find the mean for the weekly pocket money (in Rs.) using the following data : Pocket money in Rs. 55 50 49 81 48 57 65 Number of students 8 3 10 7 3 7 2 55 50 49 81 48 57 65 8 3 10 7 3 7 2 20. If the point (1, 5) lies on the graph of 3xay7, then find the value of ‘a’. 3xay7 (1, 5) ‘a’ 21. The radius and height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cm3, find slant height and curved surface area (use 3.14) 5 : 12 314 cm3 3.14 OR/ A hemispherical bowl of internal and external diameter 6 cm and 10 cm is melted and formed into a cylinder of diameter 14 cm. Find the height of the cylinder. 6 cm 10 cm 14 cm 22. In ABC, D, E and F are midpoints of sides AB, BC and CA. If AB6 cm, BC7.2 cm and AC7.8 cm, find the perimeter of DEF. ABC D, E F AB, BC CA. AB6 cm, BC7.2 cm AC7.8 cm DEF Page 8 of 12 23. Diagonal AC of a parallelogram ABCD bisects A show that : (i) It bisects C also (ii) ABCD is a rhombus ABCD AC, A (i) C (ii) ABCD 24. Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds which had germinated in each collection were counted and recorded as follows : Bag 1 2 3 4 5 Number of seeds germinated 40 48 42 39 36 What is the probability of germination of : (i) More than 40 seeds in a bag (ii) Less than 41 seeds in a bag (iii) 49 seeds in a bag ? 5 50 20 1 2 3 4 5 40 48 42 39 36 (i) 40 (ii) 41 (iii) 49 Page 11 of 12 ABCD AD BC X Y BX DY, AC P Q APPQQC OR/ In a parallelogram ABCD, the bisectors of A and B intersect at M. Show that AMB is a right angle. ABCD A B M AMB 33. A cylindrical tent has a conical top with dimension as shown in the figure. Calculate the total cost of the canvas required to make the tent, if the cost of canvas is Rs. 50/- per sq. m. 50 Page 12 of 12 34. The following data shows the daily expenses of a group of families living in a housing society. Daily Expenses (in Rs.) No. of Families 0200 200400 400600 600800 8001000 3 7 12 8 5 Draw a frequency polygon to represent the data above. 0200 200400 400600 600800 8001000 3 7 12 8 5 - o 0 o -