Mathematics - Class IX 2012 - Exam - Set 66, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 66 and more Exams Mathematics in PDF only on Docsity! Page 2 of 8 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 1074 Page 3 of 8 SECTION – A / Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1 8 1 1. The equation y3 in two variables can be written as (A) 1.x1.y3 (B) 0.x1.y3 (C) 0.x0.y3 (D) 1.x0.y3 y3 (A) 1.x1.y3 (B) 0.x1.y3 (C) 0.x0.y3 (D) 1.x0.y3 2. If P, Q, R and S are the midpoints of a rectangle of area 36 sq. cm, then PQRS is a parallelogram of area (A) 24 cm2 (B) 18 cm2 (C) 12 cm2 (D) 9 cm2 36 cm2 P, Q, R S PQRS (A) 24 cm2 (B) 18 cm2 (C) 12 cm2 (D) 9 cm2 3. In the figure, the magnitude of angle ABC if angle AOC120 will be : (A) 125 (B) 120 (C) 130 (D) 135 ABC AOC120: (A) 125 (B) 120 (C) 130 (D) 135 4. The point of the form (a, a) always lies on the line : (A) xa (B) ya (C) yx (D) xy0 (a, a) (A) xa (B) ya (C) yx (D) xy0 5. The class mark of the class interval 90120 is (A) 90 (B) 105 (C) 115 (D) 120 Page 6 of 8 18. A military tent is in the form of a circular cone of vertical height 6 m, the diameter of the base being 7 m. If 12 soldiers can sleep in it, find the average cubic metre of air space required per soldier. 6 2 7 12 OR/ The volume of a cylinder is 448 cubic cm and the height is 7 cm find its total surface area. 448 cm3 7 cm 19. Find the arithmetic mean of the following data x 1 2 3 4 5 6 7 f 5 9 12 17 14 10 6 x 1 2 3 4 5 6 7 f 5 9 12 17 14 10 6 OR In an election seats won by various political parties are as follows : Political party A B C D E F Seats won 75 55 37 29 10 37 (a) Draw the bar chart for the above data. (b) Which party won the maximum seats ? A B C D E F 75 55 37 29 10 37 (a) (b) 20. Show that the points A(1, 2), B(1, 16) and C(0, 7) lie on the graph of the linear equation y9x7 A(1, 2), B(1, 16) C(0, 7) y9x7 OR/ Write 3 different solutions of 2xy7. 2xy7 21. 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. (Take 3.14) 0.25 5 3.14 22. Show that each angle of a rectangle is a right angle. 23. ABCD is a parallelogram. E and F are mid points of BC and AD respectively. Prove that BF and ED trisect AC. ABCD E F BC AD BF ED AC Page 7 of 8 24. Two coins are tossed simultaneously 300 times. The frequency of appearing. (I) both heads : 75 (II) One head : 160 (III) No head : 65 Find the probability of occurence of each of these events. 300 (I) : 75 (II) : 160 (III) : 65 SECTION – D / Question numbers 25 to 34 carry four marks each. 25 34 4 25. ABCD is a rhombus. Show that the diagonal AC bisects angle A and angle C and the diagonal BD bisects angle B as well as angle D. ABCD AC BD A, C B, D 26. Construct a triangle XYZ, in which measure of angle Y90 measure of angle Z30. XYYZZX11 cm. XYZ Y90, Z30 XYYZZX11 cm OR/ Construct a right angled triangle whose base is 4 cm and sum of its hypotenuse and other side is 8 cm. 4 cm 8 cm 27. Draw the graph of the linear equation 3x4y6. At what points the graph cuts the x and y axes. 3x4y6 x y 28. A spherical iron shell with 8 cm external diameter weighs 1860 4 7 g. Find the thickness of the shell of the density of metal is 12 g/cm3. (shell) 8 cm 1860 4 7 12 g/cm3 29. In figure, PSSR, angle RPS54 and angle PRQ46. Find the measure of angle TQR and measure of angle RTQ. Page 8 of 8 PSSR, RPS54 PRQ46. TQR RTQ 30. Prove that the quadrilateral formed by joining the mid points of pairs of consecutive sides of a quadrilateral is a parallelogram. 31. The Auto fare in a city is as follows. For the first kilometer the fare is Rs. 5 and for the successive distance it is Rs. 2 per kilometer. Taking a distance covered as x kilometer and total fares as Rs. y, write a linear equation for the above said data and draw its graph. 5 2 x y 32. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at the remaining part of the circle. OR/ If the non parallel sides of a trapezium are equal, prove that is a cyclic quadrilateral. 33. The diameter of the roller is 84 cm and its length is 120 cms. It takes 500 complete revolutions to move once over the level a play ground and find the area of the playground in square meters. 84 cm 120 cm 500 34. The heights of the workers in a company are as follows : Height (cm) 130 – 140 140 – 150 150 – 160 160 – 170 170 – 180 180 – 190 Number of workers 8 18 20 5 4 3 Draw a histogram to represent the above data. 130 – 140 140 – 150 150 – 160 160 – 170 170 – 180 180 – 190 8 18 20 5 4 3 - o 0 o -