Mathematics - Class IX 2012 - Exam - Set 52, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 52 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) 45014 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. The graph of ym is a straight line parallel to : (A) x-axis (B) y-axis (C) Both axes (D) None of these ym (A) x (B) y (C) (D) 2. In the figure, the area of parallelogram PQRS is : (A) PQQB (B) QRQC (C) SRQC (D) PSSA PQRS (A) PQQB (B) QRQC (C) SRQC (D) PSSA 3. In the fig AB is a diameter. BDC35 then ABC is : (A) 35 (B) 55 (C) 90 (D) 125 AB BDC35 ABC (A) 35 (B) 55 (C) 90 (D) 125 4. The equation of the line, whose graph passes through the origin is : Page 6 of 11 x, x2, x4, x6, x8 11 SECTION-C / Question numbers 15 to 24 carry three marks each. 15. Given a point (2, 3), form an equation of a line on which it lies. How many such equations are possible ? (2, 3) OR/ For what value of a and b, the points (2, 3) and (4, 0) lie on the graph of the equation axby7 ? a b (2, 3) (4, 0), axby7 16. In the figure. PQRS and ABRS are parallelograms. X is any point on BR. Prove that ar (AXS) 1 2 ar (PQRS) PQRS ABRS BR X ar(AXS) 1 2 ar (PQRS) 17. Construct a ABC with BC5.5 cm, B 60, AB  AC  8cm. ABC BC5.5 cm, B 60, ABAC  8 cm 18. A sphere and a cube have the same surface area. Show that the ratio of the volume of the sphere to that of the cube is 6 :  . 6 :  19. Find the value of x and y in the following distribution if it is known that the mean of the distribution is 1.46 : No. of accident 0 1 2 3 4 5 Total Frequency 46 x y 25 10 5 200 Page 7 of 11 x y 1.46 0 1 2 3 4 5 46 x y 25 10 5 200 OR/ Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 30 workers of a factory taking one of the class interval as 84408540, 85408640, ….. etc. 8740, 8780, 8760, 8740, 8450, 8200, 8440, 9080, 8880, 8840, 8340, 8140, 8660, 8960, 8400, 9100, 8460, 8880, 8540, 8140, 8760, 8300, 8350, 8660, 8950, 9120, 9100, 8320, 8150, 9080. 30 84408540, 85408640, ….. 8740, 8780, 8760, 8740, 8450, 8200, 8440, 9080, 8880, 8840, 8340, 8140, 8660, 8960, 8400, 9100, 8460, 8880, 8540, 8140, 8760, 8300, 8350, 8660, 8950, 9120, 9100, 8320, 8150, 9080. 20. If the point (3, 5) lies on the graph of equation 2ypx2, find p. Also find two more solutions for the given equation. (3, 5) 2ypx2 p 21. What length of canvas 3m wide will be required to make a conical tent of height 8m and radius of base 6 m ? (use 3.14) 8 m 6 m 3 m 3.14 OR The diameter of a sphere is decreased by 25 %. By what percent will its curved surface area decreased ? 25 % 22. Show that the diagonals of a rhombus are perpendicular to each other 23. E and F are points on the diagonal AC of a parallelogram ABCD such that AECF. Show that DFBE is a parallelogram. ABCD AC E F AECF DFBE Page 8 of 11 24. In a survey of 500 families, number of vehicles owned per family were found to be as follows. Number of vehicles owned 0 1 2 3 4 Number of families. 35 213 170 65 17 Find the probability that a family selected at random has (a) No vehicle (b) 2 or 3 vehicles (c) more than 1 vehicle 500 0 1 2 3 4 35 213 170 65 17 (a) (b) 2 3 (c) SECTION-D / Question numbers 25 to 34 carry four marks each. 25. In given figure ABCD is a trapezium in which ABDC, BD is the diagonal and P is the midpt. of AD. A line is drawn through P, parallel to AB intersecting BC at Q. Show that CQ is equal to QB. ABCD ABDC BD AD P P PQAB BC Q CQQB