OUR OWN HIGH SCHOOL, AL WARQA A, DUBAI CMLSTQT SUMMATIVE ASSESSMENT II (05-06) MATHEMATICS Class IX Time allowed : hours Maximum Marks : 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of questions divided into five sections A, B, C, D and E. Section-A comprises of questions of mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 8 questions of marks each and Section-D comprises of 0 questions of marks each. Section E comprises of two questions of marks each and question of marks from Open Text theme. (iii) There is no overall choice. (iv) Use of calculator is not permitted. Question numbers to carry one mark each. SECTION-A In the figure, O is the centre of the circle passing through A,D and B. If ADB 0, find the measure of AOB, corresponding to arc ADB. What is the ratio of the volume of cylinder and a hemisphere of equal radii and equal height? Find the mean of the data :,, 7, 9, 7,, 7, In a frequency distribution, the mid value of a class - interval is 0 and the width of the class - interval is 6. Find the lower limit of the class. Page of 5
SECTION-B Question numbers 5 to 0 carry two marks each. 5 In the given figure, O is the centre of the circle. Find the value of x. 6 Draw a line segment XY of length 96 mm. Using ruler and compass, bisect it measure the length XY. 7 In the figure, PQRS is a parallelogram. Find the values of x and y. 8 The curved surface area of a right circular cylinder of height cm is 88 cm. Find the volume of the cylinder. 9 If the probability of winning a game is 0.. What is the probability of losing it? 0 The marks obtained out of 00 by the students of a class are given in the following table : Marks 0-0 0-50 50-60 60-70 70-80 80-90 Number of students 8 0 0 8 If a student is selected at random, find the probability that he/she is a student who scored 50 or more but less than 70. SECTION-C Question numbers to 8 carry three marks each. The average monthly salary of worker in a factory is `,850. If the salary of the manager is included, the average becomes,550, what is the manager's salary? Page of 5
The points scored by a team in a series of matches are as follows : 7,, 7, 5, 5, 5,,./8, 0,, 0, 8, 7, 0 Find mean, median and mode for the data. WXYZ is a parallelogram. E, F, G and H are respectively the mid-points of sides WX, XY, YZ and ZW. Show that ar (EFGH) ar (WXYZ). In an isosceles triangle ABC with AB AC, a circle passing through B and C intersects the sides AB and AC at D and E respectively as shown in the figure. Prove that DE is parallel to side BC. 5 Draw a line segment AB cm and by ruler and compasses, obtain a line segment of length AB. 6 In parallelogram ABCD of the given figure, the bisector of C meets AD at E. CE and BA are produced to meet at F. Prove that BC BF. 7 In the given figure, ABCD is a trapezium in which AB DC. Prove that ar ( AOD) ar ( BOC). Page of 5
8 The diameter of garden roller is. m and it is m long. How much area will it cover in 5 revolutions ( 7 ) SECTION-D Question numbers 9 to 8 carry four marks each. 9 Following is the distribution of ages (in years) of teachers teaching in a primary school : Age (in years) -5 6-0 -5 6-0 -5 6-50 No. of teacher 70 0 65 0 00 5 Draw a histogram and frequency polygon to represent the given data. 0 In the given figure, AE BC and AE BC. If AB ED and A 0, then find B, ECD, CED and AED. In ABC, if A 60 and bisectors of B and C meet AC and AB at P and Q respectively and intersect each other at I, prove that APIQ is a cyclic quadrilateral. Construct LXY, if base angles X 60, Y 5 and its perimeter is cm. In a parallelogram ABCD, P and Q are the mid points of sides AB and CD respectively as shown in the figure. Show that the line segments DP and BQ trisect diagonal AC. Deepika on her way to home saw some homeless persons sleeping in the park in a winter night. She gave them her canvas of area 55 m. They uses it to make a conical tent with a base radius of 7 m. Assuming that all the stiching, margin and wastage incurred while cutting, amounts to approximately m, find volume of the tent that can be made with it. Which value is depicted by Deepika? (Use 7 ) Page of 5
5 A solid cylinder has total surface area 6 cm. Its curved surface area is one third of its total surface area. Find : (a) its radius. (b) its height. (c) its volume. 6 A dome of a building is in the form of a hemisphere. From inside, it was white- washed at the cost of ` 98.96. If the rate of white washing ` per square meter, find the : (i) Inside surface area of the dome (ii) Volume of the air inside the dome 7 It costs ` 00 to paint the inner curved surface of a cylindrical vessel 0 m high at the rate of ` 0 per sq metre. Calculate the inner surface area and the capacity of the vessel. 8 A company selected 00 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below : Monthly income (in `) Less than 7000 7000-0000 0000-000 000-6000 6000 or more Vehicles per family 0 Above 0 0 5 0 0 95 7 55 9 9 9 5 59 8 88 If a family is chosen at random, find the probability that the family is : (i) earning ` 7000-000 per month and owning exactly vehicle (ii) owning not more than one vehicles. (iii) earning more than ` 000 and owning or more than vehicles. (iv) owning no vehicle SECTION-E (Open Text) (* Please ensure that open text of the given theme is supplied with this question paper.) Theme : Childhood Obesity in India 9 Taking the height as 0 cm, form a linear equation in two variables taking BMI as x and weight as y kg. Draw its graph also. 0 Shweta wants to burn 00 Kcal in a day by spending an hour in Home activities and walking. Write a linear equation for the same and find the time she spends for home activities and walking. Children eat twice as many calories at restaurant as they do during a meal at home. (i) Represent this situation algebraically. (ii) Write the equation in standard form of ax by c 0 (iii) Write the value of a, b, c. ********* Page 5 of 5
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