Mathematics - Class IX 2012 - Exam - Set 64, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 64 and more Exams Mathematics in PDF only on Docsity! Page 2 of 11 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) 45027 Page 3 of 11 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. In the figure, the graph of the equation is drawn. Choose the correct equation for which the graph has been drawn : (A) yx (B) yx (C) y2x (D) y3x (A) yx (B) yx (C) y2x (D) y3x 2. In the figure, PLM and rectangle KLMN are shown. The ratio of the area of PLM and rectangle KLMN is : (A) 2 : 1 (B) 3 : 2 (C) 1 : 2 (D) 2 : 3 PLM KLMN PLM KLMN Page 6 of 11 13. In the figure, two circles with centres A and B intersect each other at C and D. Prove that  ACB ADB . A B C D  ACB ADB OR/ Bisector AD of BACof ABC passes through the centre of the circumcircle of ABC as shown in the figure. Prove that ABAC. ABC BAC AD ABC O AB=AC 14. Find the mean of the data : x 20 25 32 40 50 100 f 5 4 10 2 1 3 x 20 25 32 40 50 100 f 5 4 10 2 1 3 SECTION-C / Page 7 of 11 Question numbers 15 to 24 carry three marks each. 15. In the figure, P (a, b) is a point on the graph of the linear equation 5x2yk. Find the value of k. 5x2yk P (a, b) k OR/ The point (2, 3) lies on the graph of the linear equation 3x(a1)y2a1. If the same point also lies on the graph of the linear equation 5x(12a)y3b, find the value of b. (2, 3) 3x(a1)y2a1 5x(12a)y3b b 16. Show that median of a triangle divides it into two triangles of equal area. OR/ In ABC, L and M are the points on sides AB and AC respectively such that LMBC. LC (a, b) 7, 27, 30.) (a, b) Page 8 of 11 and BM intersect at O. Prove that ar (LOB)ar (MOC) ABC L M AB AC LMBC LC BM O LOB  MOC 17. Draw an angle of 40 with a protractor and then construct an angle 80 using ruler and compass. 40 80 18. A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. (Use  22 7 ) 0.25 5 (  22 7 ) OR/ A solid cylinder has a total surface area 462 cm2. Its curved surface area is one-third of the total surface area. Find the height of the cylinder. 462 2 19. The following table gives life time of 100 neon lamps. Draw an histogram to represent the information : Life time (in hours) 300 – 400 400 – 500 500 – 600 600 – 700 700 – 800 800 – 900 Number of lamps 12 8 15 25 30 10 100 300 – 400 400 – 500 500 – 600 600 – 700 700 – 800 800 – 900 12 8 15 25 30 10 20. Express the linear equation 72x in the form axbyc0 and also write the values of a, b and c. 72x axbyc0 a, b c 21. The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling it at the rate of 30 paise per sq.metre (Use  22 7 ). 120 84 500 30 ( 22 7 ) 22. In the figure, ABCD is a parallelogram in which AB is produced to E so that ABBE. (a) Prove that ED bisects BC. (b) If AD10 cm, find OB.