II, 06-7 SUMMATIVE ASSESSMENT II, 06-7 / MATHEMATICS IX / Class IX : hours 90 Time Allowed : hours Maximum Marks: 90 7RCN0C.... 6 0 General Instructions:. All questions are compulsory.. The question paper consists of questions divided into four sections A, B, C and D. Section-A comprises of questions of mark each; Section-B comprises of 6 questions of marks each; Section-C comprises of 0 questions of marks each and Section-D comprises of questions of marks each.. There is no overall choice in this question paper.. Use of calculator is not permitted. / SECTION-A Question numbers to carry one mark each. ` y ` x The cost of petrol in a city is ` 70 per litre. Find a linear equation in two variables where y represents number of litres of petrol consumed and ` x is total cost. x 0 Linear equation x 0is parallel to which axis? Construct a right angle and draw its bisector. The volume of a cube is numerically equal to its surface area. Find the length of its edge. / SECTION-B 5 0 Question numbers 5 to 0 carry two marks each. Page of 8
5 ABCD ar ( DAE) ar( CBF) In the given figure, ABCD is a parallelogram. ( DAE) ar( CBF) If and, show that ar 6 P Q R S PRQ PSQ In the figure two circles with centres P and Q intersect at R and S. prove that PRQ PSQ. 7 5 Draw an angle of 5 using protractor. Bisect it using compass. 8 5 cm cm (. ) Determine the volume of a conical vessel having radius of the base as 5 cm and its slant height as cm. (Use.) 9 600,,,, 5 6 5 6 60 90 75 68 50 57 (i) (ii) A die is thrown 600 times and the frequencies for the outcomes,,,, 5 and 6 are given in the following table : Outcome 5 6 Frequency 60 90 75 68 50 57 Find the probability that in the next throw of dice Page of 8
(i) even number will come. (ii) odd number will come. 0 0 kg 798 g,.795 kg,.805 kg,.80 kg,.85 kg,.80 kg,.798 kg,.800 kg,.800 kg.87 kg. (a) (b) kg 800 g.800 kg Following are the actual weights of 0 boxes of dry fruits distributed on the occassion of diwali; kg 798 g,.795 kg,.805 kg,.80 kg,.85 kg..80 kg,.798 kg,.800 kg,.800 kg and.87 kg. A box is chosen at random. Find the probability that : (a) its weight is more than kg 800 g (b) its weight is.800 kg or less than it. / SECTION-C 0 Question numbers to 0 carry three marks each. x 0 ax by c 0 a, b c Write x 0 in the form of ax by c 0. Also write the values of a, b and c. Draw its graph. ` 5 ` 7 x ` y The auto fare in a town is as follows : For the first kilometre, the fare is ` 5 and for the subsequent distance, it is ` 7 per km. Taking the distance covered as x km and total fare as ` y, write a linear equation for this information and draw its graph. AB 0. cm AB Draw a line segment AB 0. cm. Find AB, using ruler and compass. AB CB O DB, ABC ADC In the figure, AB and CB are chords of a circle equidistant from the centre O. Prove that the diameter DB bisects ABC and ADC. Page of 8
5 PQRS S PR QR X ar (PQRS) ar ( PXQ) PQRS is a quadrilateral. A line through S parallel to PR meets QR produced in X. Show that ar (PQRS) ar ( PXQ). 6 00 cm 7 How many litres of water will a hemispherical bowl of radius 00 cm contain and find its curved surface area? 50-5 5-57 58-6 6-65 66-69 70-7 5.5 67.5 7 7 5 0 5 6 Convert the following frequency distribution into a continuous grouped frequency table : Page of 8
Class - Interval Frequency 50-5 7 5-57 7 58-6 5 6-65 0 66-69 5 70-7 6 In which intervals would 5.5 and 67.5 be included? 8 50 55 9 The mean of 9 numbers is 50. If one number is included, their mean becomes 55. Find the included number. / SECTION-D Question numbers to carry four marks each. x 0, y 0, x y. Draw the graphs of the following equations on the same graph sheet : x 0, y 0, x y. Also, find the area enclosed between these lines. 0 8 The difference between two numbers is. Write the given data in form of a linear equation in two variables. Also, represent it graphically. If smaller number is 8, then find graphically the value of the larger number. EFG F 60, G 80.5 cm Construct EFG in which F 60, G 80 and perimeter is.5 cm. ABCD O ar( AOB) : ar(abcd) ABCD is a square whose diagonals intersect at O. Calculate ar(aob) : ar(abcd). Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle. Page 5 of 8
(a) 0 8. 7 ` 500 (b) - ( ) 7 (a) A well having 0 m inside diameter is dug 8. m deep. Earth taken out of it is spread all around it to a width of 7 m to form a beautiful embankment. Find the height of the embankment. The contractor charged ` 500 per metre for digging and making the circular embankment on its total height of well and embankment. He measured the height of the embankment as m. how much extra money he made. (b) The concerned officer accepted his calculations and paid the money to him as demanded. Who is guilty-the contractor or the officer? Comment. (Use 7 ). 5 0 m ` 00 ` 0 m (a) (b) (c) : It costs ` 00 to paint the inner curved surface of a 0 m deep well. If the cost of painting is at the rate of ` 0 per m, find : (a) inner curved surface area. (b) diameter of the well. (c) capacity of the well. 6 50 cm, 0 cm 0 cm 9600 cm 00 0 cm 0 cm 0 cm 0 The length, breadth and height of a cuboidal tank are 50 cm, 0 cm and 0 cm respectively. The tank has 9600 cm of water in it. 00 porous bricks each having dimensions 0 cm 0 cm 0 cm are placed in the tank. Calculate the rise in the water level of the tank, if each brick absorbs of its own volume. 0 7 IX 0-0 6,, 7, 68,, 5,, 6, 8, 8, 7, 6, 8, 6, 57, 9, 7, 5, 59, 8, 6, 88, 75, 56, 6, 66, 5, 6, 5, 7, 7,, 6, 58,, 8, 6, 67, 6, 9, 50, 76, 8, 7, 55, 77, 6, 5, 0, 7, 60, 58, 5,,, 6, 0, 59,, 9, (i) 59 (ii) 9 00 Page 6 of 8
8 Two sections of Class IX having 0 students each appeared for mathematics Olympiad. The marks obtained by them are shown below: 6,, 7, 68,, 5,, 6, 8, 8, 7, 6, 8, 6, 57, 9, 7, 5, 59, 8, 6, 88, 75, 56, 6, 66, 5, 6, 5, 7, 7,, 6, 58,, 8, 6, 67, 6, 9, 50, 76, 8, 7, 55, 77, 6, 5, 0, 7, 60, 58, 5,,, 6, 0, 59,, 9, A student is selected at random. Find the probability that student selected from the class is: (i) having marks more than 59 (ii) having marks more than 9 but less then 00, 6,,, 5,, 5, 8,, 8, 0,,,,, 8, 5,, 7, 6,,, 8, 5, 9, 6, 8, 7,, 5 5-0 5 Thirty children were asked about the number of hours they watched TV programs in the previous week. The results were found as follows :, 6,,, 5,, 5, 8,, 8, 0,,,,, 8, 5,, 7, 6,,, 8, 5, 9, 6, 8, 7,, Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5-0. Also draw histogram. How many children watched television for 5 or more hours a week? य/SECTION-E ( /Open Text) (* Please ensure that open text of the given theme is supplied with this question paper.) Theme : Quadrilateral in Architecture, WAH TAJ. 9 ABC C AB BC, 00m 80m AMD M D AB AC Page 7 of 8
In the given figure of triangle ABC, right angled at C, If its sides AB and BC are 00m and 80m, then find the perimeter of AMD, where M and D are mid-points of AB and AC respectively. 0 AD, AC E F DCFE In the given figure of if E and F are mid-points of AD and AC then prove that sum of angles of quadrilateral DCFE is 60 0. ABED Prove that in trapezium ABED (see figure), if middle points of its all sides are joined in order, then figure so formed is a parallelogram. -o0o0o0o- Page 8 of 8