Mathematics - Class IX 2012 - Exam - Set 61, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 61 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) 45026 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. If (2, 0) is a solution of linear equation 2x3yk, then the value of k is : (A) 4 (B) 6 (C) 5 (D) 2 (2, 0) 2x3yk, k (A) 4 (B) 6 (C) 5 (D) 2 2. In the given figure, if ABCD is a parallelogram, CF AD and AE DC. If AB=16 cm, AE=4 cm and CF=10 cm, then length of BC is : (A) 5.8 cm (B) 6.4 cm (C) 7.5 cm (D) 12 cm ABCD CF AD AE DC AB=16 cm, AE=4 cm CF=10 cm BC (A) 5.8 cm (B) 6.4 cm (C) 7.5 cm (D) 12 cm 3. In the figure, O is the centre of the circle. The value of x is : (A) 50 (B) 40 (C) 60 (D) 20 O x  Page 6 of 10 13. In the figure, AB is diameter of a circle and AC is a chord. If O is the centre and OD is the perpendicular from O to AC, prove that BC2OD. AB AC O O AC OD BC2 OD OR In the figure, diameter AB and a chord AC have a common end point A. If the length of AB is 20 cm and of AC is 12 cm, how far is AC from the centre of the circle ? AB AC A AB 20 cm AC 12 cm AC 14. The points scored by a Kabaddi team in a series of matches are as follows. 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10 Find the median of the points scored. 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10 SECTION-C / Question numbers 15 to 24 carry three marks each. Page 7 of 10 15. Express the following statement in the form of a linear equation in two variables. ‘The cost of a table is 6 times the cost of a chair’. Draw the graph of the equation so obtained. 6 16. Show that median of a triangle divides it into two triangles of equal areas. 17. Construct an angle of 37 1 2  using a ruler and compass. 37 1 2  18. The curved surface area of a right circular cylinder is 4.4 m2. If the diameter of the base of cylinder is 1.4 m, find its volume. (Take  22 7 ) 4.4 2 1.4 ( 22 7 ) OR/ Show that each angle of a rectangle is a right angle. 19. Represent the following frequency distribution by means of a histogram. Marks 10 - 20 20 - 30 30 – 40 40 - 50 50 - 60 60 - 70 Number of Students 7 11 9 13 16 4 10 - 20 20 - 30 30 – 40 40 - 50 50 - 60 60 - 70 7 11 9 13 16 4 OR/ The distribution of weight (in kg) of 110 students is given below : Weight (in kg) 4045 4550 5055 5560 6065 6570 Frequency 15 25 35 20 10 5 Construct a frequency polygon to represent the data above. 110 4045 4550 5055 5560 6065 6570 15 25 35 20 10 5 20. Determine the point on the graph of the equations 2x5y20 whose x-coordinate is 5 2 times its ordinate. Page 8 of 10 2x5y20 x - 5 2 OR/ ABCD is a quadrilateral in which P, Q, R, S are mid points of the sides AB, BC, CD and DA respectively. Show that PQRS is a parallelogram. ABCD P, Q, R S AB, BC, CD DA PQRS 21. The height, breadth and length of a cuboidal box are in the ratio 1 : 2 : 3. Find the volume of the box if its surface area is 1078 dm2. 1 : 2 : 3 1078 2 22. Show that the diagonals of a rhombus are perpendicular to each other. 23. In ABC, D, E and F are respectively the mid points of sides AB, BC and CA. Show that ABC is divided into four congruent triangles by joining D, E and F. ABC D, E F AB, BC CA D, E, F ABC 24. The king, queen and jack of clubs are removed from a deck of 52 cards and then well shuffled. One card is selected at random from the remaining card. Find the probability of getting : (a) A heart (b) A king (c) The 10 of hearts 52 (a) (b) (c) SECTION-D / Question numbers 25 to 34 carry four marks each. 25. Prove that a diagonal divides a parallelogram into two congruent triangles. 26. Construct a ABC in which BC4.5 cm. ABAC7.9 cm and B 60   . ABC BC4.5 cm, ABAC7.9 cm B 60   OR/ A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of sheet required to make 20 such caps. (Take  22 7 ) 7 24 20 ( 22 7 ) 27. Draw the graph of linear equation 2xy8. From the line (graph) drawn for the given equation, take two points and show that these points satisfy the given equation.