Mathematics - Class IX 2012 - Exam - Set 46, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 46 and more Exams Mathematics in PDF only on Docsity! Page 2 of 10 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) 45023 Page 3 of 10 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 8 1 1 8 1. Which one of the following graphs represents the graph of xy0 ? xy0 2. In the figure, PQRS, ABCD is a parallelogram and AEB is a triangle. Area of the parallelogram ABCD is : (A) Half the area of triangle AEB (B) Equal to ar(AEB) (C) Thrice the area of AEB (D) Twice the ar(AEB) ABCD PQRS AEB ABCD (A) AEB (B) AEB (C) AEB (D) AEB 3. In the figure, ABD70, ADB30 then BCD is equal to : Page 6 of 10 75 55 37 29 10 37 SECTION-C / Question numbers 15 to 24 carry three marks each. 15 24 3 15. Given the equation 2xy7, (a) What is the value of x, when the value of y is 3 ? (b) What is the value of y, when the value of x is 4 ? (c) Find one more solution for the above equation. 2xy7 (a) x y = 3 (b) y x= 4 (c) 16. Prove that the parallelograms on the same base and between the same parallels are equal in area. 17. Construct a triangle ABC, where BC8 cm B45, ABAC3.5 cm. ABC BC8 cm B45 ABAC3.5 cm 18. Find the mean of the following distribution X 4 6 9 10 15 f 5 10 10 7 8 x 4 6 9 10 15 f 5 10 10 7 8 . OR/ If the mean of the following data is 15, find p. x 5 10 15 20 25 f 6 p 6 10 5 15 p x 5 10 15 20 25 f 6 p 6 10 5 . 19. The blood groups of 30 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, B, A, B, O. (1) Represent this data in the form of a frequency distribution table. (2) Which is the most common and which is the rarest blood group among these students ? 30 A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, Page 7 of 10 A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. (1) (2) 20. Find a solution for the equation 4xy20 where xy. Also check if (2, 25) is a solution for the given equation. Find k if (2, k) is a solution of the given equation 4xy20 xy (2, 25) k (2, k) OR/ Find k in each case if x2, y1 is a solution of the equation : (i) 3x2yk (ii) 2xky6 (iii) 5 k 4 3 yx   x2, y1 k (i) 3x2yk (ii) 2xky6 (iii) 5 k 4 3 yx   21. The radius of a spherical balloon increases from 7 cm to 14 cm as air is pumped into it. Find the ratio of surface areas of the balloon in two cases. 7 cm 14 cm OR/ The volume of a right circular cylinder is 3850 cm3. Find its height if it’s diameter is 14 cm. 3850 cm3 14 cm 22. Prove that equal chords of a circle subtend equal angles at the centre. 23. Two parallel lines l and m are intersected by a transversal p. Show that the quadrilateral formed by the bisectors of interior angles is a parallelogram. (see given fig.) p l m Page 8 of 10 24. A hemispherical dome of a stupa needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it at the rate of Rs. 5 per 100 cm2. 17.6 5 100 2 SECTION-D / Question numbers 25 to 34 carry four marks each. 25 34 4 25. ABCD is a rhombus and P, Q, R, S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. ABCD AB, BC, CD DA P, Q, R S PQRS OR/ ABC is a triangle, right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) MD  AC (iii) CM  MA  ½ AB ABC C AB M BC AC D : (i) AC D (ii) MD  AC (iii) CMMA½ AB 26. Construct a triangle XYZ in which Y60, Z45 and XYYZZX11 cm. XYZ Y60, Z45 XYYZZX11 cm 27. The sum of the present ages of Ram and twice that of his father is 65. Form a linear equation in two variables and draw its graph. Find the points where the line meets the x and y axis. 65 x y 28. The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m, how much concrete mixture would be required to build 14 such pillars ? 20 cm 10 m 14 OR/ A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m