Mathematics - Class IX 2012 - Exam - Set 43, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 43 and more Exams Mathematics in PDF only on Docsity! Page 2 of 12 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) 45006 Page 3 of 12 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 (7, 5) lies on the graph of the linear equation (in two variables) 4xy8, then the value of  is : (A) 5 (B) 36 5 (C) 4 (D) 7 (7, 5) 4x y8  (A) 5 (B) 36 5 (C) 4 (D) 7 2. If the area of ABC is 800 cm2, AD is a median, E is the mid-point of AD, F is the mid- point of AB, then the area of AEF (in cm2) is : (A) 400 (B) 300 (C) 200 (D) 100 ABC 800 2 AD AD E AB F AEF (A) 400 (B) 300 (C) 200 (D) 100 3. In the circle with centre O, AOB60 and BOC30 the measure of ADC is : (A) 30 (B) 45 (C) 60 (D) 90 O AOB60 BOC30 ADC (A) 30 (B) 45 (C) 60 (D) 90 4. The point of intersection of the lines representing the equations 3x2y1 and 2x3y1 is : (A) (2, 3) (B) (3, 2) (C) (1, 1) (D) (0, 0) 3x2y1 2x3y1 (A) (2, 3) (B) (3, 2) (C) (1, 1) (D) (0, 0) 5. The class size and class mark respectively of the class 1520 is : (A) 17.5, 15 (B) 5, 15 (C) 5, 17.5 (D) 5, 20 1520 (A) 17.5, 15 (B) 5, 15 (C) 5, 17.5 (D) 5, 20 Page 6 of 12 RS NM, RS MRS29 NMS OR In the above given figure, chords BD and AC intersect at the point E such that BEC130 and ECD20. Find the measure of BAC. BD AC E BEC130 ECD20 BAC 14. If the following data are arranged in increasing order of magnitude, find the median of the data 14, 15, 15, 16, 17, 18, 18, 18, 19, 20, 20, 21 14, 15, 15, 16, 17, 18, 18, 18, 19, 20, 20, 21 SECTION-C / Question numbers 15 to 24 carry three marks each. 15. Plot the linear equation x2y50 on a graph paper. x2y50 Page 7 of 12 16. Prove that area of the quadrilateral formed by joining the mid-points of the sides of a parallelogram is half the area of the parallelogram. 17. Construct a ABC, in which BC5 cm, C60 and ACAB1.5 cm. ABC BC5 C60 ACAB1.5 18. Find the area of the metal sheet required to make two closed hollow cones each of height 24 cm and slant height 25 cm. 24 25 OR Find the volume of the largest right circular cone that can be placed in a cube of edge 7 cm. 7 19. Given below is the frequency distribution of salary (in Rs) of 100 workers in a factory : Salary (in Rs.) 10002000 20003000 30004000 40005000 Number of workers 10 30 20 40 Answer the following questions. How many workers : (i) have salary below Rs. 3000 (ii) have salary between Rs. 3000 and Rs. 5000. (iii) From Rs. 1000 to Rs. 5000 100 10002000 20003000 30004000 40005000 10 30 20 40 (i) 3000 (ii) 3000 5000 (iii) 1000 5000 OR Find the mean of first five prime numbers 20. Find two different solutions of the equation 2x6y10 and check whether (3, 2) is a solution of the given equation. 2x6y10 (3, 2) OR “Father’s age is 5 years more than 6 times the age of son” – Express this statement as a linear equation in two variables and plot the equation on a graph paper. 6 5 Page 8 of 12 21. 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, given that the cost of painting is Rs. 100 per sq. metre. 22 Use 7        17.6 100 22 7        22. ABCD is a trapezium in which ABCD and ADBC. Show that : (i) AB (ii) CD ABCD एक िमऱॊब है जििम ं ABCD है तथा ADBC है। दर्ािइए फक : (i) AB (ii) CD 23. Show that the diagonals of a rhombus are perpendicular to each other. दर्ािइए फक एक िमितभुुि के विकर्ि परस्पर ऱम्बित्त होत ेहं। 24. A die is tossed 100 times and the following data are recorded : Outcome 1 2 3 4 5 6 Frequency 20 15 20 15 20 10 The die is tossed again, then : (a) What is the probability of getting an even number ? (b) What is the probability of getting a number less than 3 ? एक पािे को 100 बार उछाऱिे पर सिम्ि आॉकड़े पाये गये : पररर्ाम 1 2 3 4 5 6 बारॊबारता 20 15 20 15 20 10 िह पािा फिर उछाऱा गया, तो : (a) एक िम िॊख्या आिे की प्रासयकता क्या है ? (b) 3 िे कम िॊख्या आिे की प्रासयकता क्या है ? Page 11 of 12 ABCD एक िमाॊतर ितभुुि है जििमं िम्मखु भिुाओॊ AB तथा CD के मध्य वबन्द ु क्रमर्ः P तथा Q हं। यफद AQ , DP को S पर प्रसतच्छेद करती है तथा BQ, CP को R पर प्रसतच्छेद करती है तो दर्ािइए फक PSQR एक िमाॊतर ितभुुि है। 31. Draw the graph of the equation 2y3x40. From the graph, verify that x2 and y5 is one of the solutions of the given equation. 2y3x40 x2 y5 32. ABCD is a cyclic quadrilateral whose diagonals AC and BD intersect at the point E. If DBC70 and BAC30, then find BCD. Further, if ABBC, find ECD. ABCD AC BD E DBC70 BAC30 BCD ABBC ECD 33. A cubical box has each edge of length 10 cm and another cuboidal box is 12.5 cm long. 10 cm wide and 8 cm high. Find the volume of the box which has greater lateral surface area. 10 12.5 10 8 34. In a city the weekly observations made in a study on the cost of living index are given in the following table : Cost of living index Number of weeks 140150 150160 160170 170180 180190 190200 15 5 6 2 20 4 Page 12 of 12 Total Draw a frequency polygon for the above data. 140150 150160 160170 170180 180190 190200 15 5 6 2 20 4 Total - o 0 o -