Mathematics - Class IX 2012 - Exam - Set 58, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 58 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) 45025 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. If the linear equation has solutions (5, 5), (0, 0), (5, 5) then equation is : (A) xy0 (B) xy0 (C) 2xy0 (D) x2y0 (5, 5), (0, 0), (5, 5) (A) xy0 (B) xy0 (C) 2xy0 (D) x2y0 2. In the figure, ABCD is a square. E and F are mid-points of AD and BC respectively. The ratio of areas of GAB and HAB is : (A) 4 : 1 (B) 1 : 4 (C) 1 : 2 (D) 2  ABCD E F AD BC GAB HAB (A) 4 : 1 (B) 1 : 4 (C) 1 : 2 (D) 2 : 1 3. In the figure, O is the centre of the circle. Quadrilateral PQTS is a cyclic quadrilateral. If POT 130   , then the measure of x is : (A) 50 (B) 65 (C) 115 (D) 130 O PQTS POT 130   x  (A) 50 (B) 65 (C) 115 (D) 130 Page 6 of 11 14. The blood groups of students of class IX are recorded as follows : A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, A, B, O, B, O, AB, A, B, O Represent this data in the form of a frequency distribution table. A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, A, B, O, B, O, AB, A, B, O SECTION-C / Question numbers 15 to 24 carry three marks each. 15. When 5 times the larger of the two numbers is divided by the smaller, the quotient and remainder are 2 and 9 respectively. Form a linear equation in two variables. Write it in standard from. 2 9 16. In the figure, ABP is a line and BDPC. Prove that ar (quad. ABCD)ar(APD). ABP BDPC ar ( ABCD)ar (APD) 17. Construct an angle of 52 1 2  with the help of compass and foot ruler. 52 1 2  18. The circumference of the cross section of a hemispherical bowl is 132 cm. Find the capacity of the bowl      22 Take 7  132 cm Page 7 of 11 22 7        OR/ Find the volume of a cylindrical tank of height 1.4 m and circumference of the base is 2 m. 1.4 m 2 m 19. Draw a bar chart of pass-percentage of students during 2005 to 2010 from the data given below : Year 2005 2006 2007 2008 2009 2010 Pass percentage 80% 75% 90% 70% 95% 85% 2005 2010 2005 2006 2007 2008 2009 2010 80% 75% 90% 70% 95% 85% OR/ The mean of the following distribution is 50. xi 10 30 50 70 90 yi 17 5p3 32 7p11 19 Find the value of p. 50 xi 10 30 50 70 90 yi 17 5p3 32 7p11 19 p 20. A part of monthly expenses of a family on milk is fixed which is Rs. 500 and the remaining varies with the quantity of milk taken extra at the rate of Rs. 20 per litre. Taking the quantity of milk required extra as x litres and the total expenditure on milk Rs. y, write a linear equation for this information and draw its graph. 500 20 x y 21. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. 10.5 m 3 m 22. Show that the diagonals of a rhombus are perpendicular to each other. OR/ Prove that a diagonal of a parallelogram divides it into two congruent triangles . 23. In the figure D, E and F are midpoints of sides AB, BC and CA respectively of ABC. Show that ADEF, BDFE and DFCE are parallelograms. Page 8 of 11 D, E F ABC AB, BC CA ADEF, BDFE DFCE 24. In a mathematics test, 90 students obtained (out of 100) the marks given in the following table : Marks 1 – 20 21 – 40 41 – 50 51 – 60 61 – 70 71 – 80 81 – 90 No. of students 8 12 15 20 13 17 05 Find the probability : (i) a student obtained less than 41, (ii) a student obtained more than 50, (iii) a student obtained between 41 and 80. 90 100 1 – 20 21 – 40 41 – 50 51 – 60 61 – 70 71 – 80 81 – 90 8 12 15 20 13 17 05 (i) 41 (ii) 50 (iii) 41 80 SECTION-D / Question numbers 25 to 34 carry four marks each. 25. Prove that angle bisectors of a parallelogram form a rectangle :