SUMMATIVE ASSESSMENT II, / MATHEMATICS IX / Class IX CBSETODAY.COM. : 3 hours 90 Time Allowed : 3 hours Maximum Marks: 90

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1 SUMMATIVE ASSESSMENT II, 06-7 / MATHEMATICS IX / Class IX : hours 90 Time Allowed : hours Maximum Marks: 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. x y 6 x y 7 x Express x in term of y : y 6. 7 x y, y Find the coordinates of the point where the equation x y cuts y axis. 50 Construct an angle of measure 50 (using ruler and compasses only). cm The diagonal of a cube is 5 0 cm. Find its volume. / SECTION-B Question numbers 5 to 0 carry two marks each. 5 ABCD AB E ar ( EDC) 8 cm ABCD Page of 7

2 6 ABCD is a square. E is any point on side AB. If ar ( EDC) 8 cm, find the length of each side of ABCD. If diagonals of a cyclic quadrilateral are diameters of the circle through the opposite vertices of the quadrilateral, prove that the quadrilateral is a rectangle. 7 O x In the given figure, O is the centre of the circle. Find the value of x. 8.5 cm cm How much ice-cream can be put into a cone with base radius.5 cm and height cm? A coin is tossed 500 times with the following frequencies: Head : 655, Tail : 85 Compute the probability for each event. 0 kg 7.97, 7.05, 7.08, 6.0, 7.00, 6.06, 6.08, 6.0, 6.00, 6.98, 7.5, 7., 7., 6.9, kg In a store, bags of coal powder each contained the following weights of powder (in kg): 7.97, 7.05, 7.08, 6.0, 7.00, 6.06, 6.08, 6.0, 6.00, 6.98, 7.5, 7., 7., 6.9, 7. kg. Find the probability that any one of these bags chosen at random contains more than 7. kg of coal powder. / SECTION-C 0 Question numbers to 0 carry three marks each. x y 7 (a) x- (b) y- Represent x y 7 by a graph. Write the coordinates of the point where it meets : (a) x-axis (b) y-axis Page of 7

3 x, x, y 0 y Draw the graphs of x, x, y 0 and y in the same cartesian plane. Identify the figure so formed. 6 cm PQ P l PQ m l m Draw a line segment PQ of length 6 cm. Construct perpendicular at point P. Name it as l. Also construct perpendicular bisector of PQ. Name it as m. Is l m? AB CD O P MP NP OM AB ON DC AB CD In the figure, AB and CD are two chords of a circle with centre O, intersecting each other at P when produced such that MP NP. If OM AB and ON DC, show that AB CD. 5 ABE AE D F D AB DC BE C ar ( ACF) ar (BCFD) In figure, D and F are points on side AE of ABE. Through point D a line DC is drawn which is parallel to AB and meets BE in C. Prove that ar ( ACF) ar (BCFD). 6 6 m, 8 m 0 m Page of 7

4 Metallic spheres of radii 6 m, 8 m and 0 m, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere , 5, 55, 75, 85, 70,, 085, 77, 807, 780, 5, 80, 7, 5, 75,, 5, 55, 65, The electricity bills of twenty households in a locality are as follows : 75, 5, 55, 75, 85, 70,, 085, 77, 807, 780, 5, 80, 7, 5, 75,, 5, 55, 65, 575. Construct a frequency distribution table with class size 00..,.,.8,.,.,.5. Find the median and mean of the given data :.,.,.8,.,.,.5. / SECTION-D Question numbers to carry four marks each. x 5, x 0, y, y 0. Draw the graphs of the following equations on the same graph sheet : x 5, x 0, y, y 0. Also, find the area enclosed between these lines. 0 x y 70 (a) 0 (b) 0 In a certain test, Nikita scored marks x and y respectively in Mathematics and English. If her total score is 70, then form a linear equation in two variables for this. Also, draw its graph. Find graphically, her score in other subject if : (a) score in Mathematics is 0. (b) score in English is 0. DEF EF 7 cm, E 0 DE EF cm Construct a DEF in which EF 7 cm, E 0 and DE EF cm. PQRS PQ E QE PE RS F RF SF PERF ar(perf) ar(pqrs) PQRS is a parallelogram. E is a point on PQ such that QE PE and F is a point on RS such that RF SF. Show that PERF is a parallelogram and ar(perf) ar(pqrs) Page of 7

5 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. cm 98 cm 7 cm On his birthday in the month of January, Harish distributed soup. He had it in a cylindrical bucket with base radius cm and height 98 cm. He distributed the soup in a hemispherical bowl of radius 7 cm to the poor people and also gave a blanket to them. How many people were served the soup? What value do you learn from Harish s act? 5 5 cm The curved surface area of a cylinder is 5 cm. The total surface area of the cylinder is three times its curved surface area. Find the volume of the cylinder m. m A water storage tank is in the form of a cube. When it is full of water, the volume of water is 5.65 m. If its present depth is. m, find the volume of water used from the tank and also find its ratio with the volume of remaining water in the tank. 7 IX 7-7! 6,, 7, 68,, 5,, 6, 8, 7, 6, 8, 6, 57 9, 7, 5, 59, 8, 6, 88, 56, 6, 66, 5, 6, 5, 7 7,, 6, 58,, 8, 6, 6, 9, 50, 76, 8, 7 77, 6, 5, 0, 7, 60, 5,,, 6, 0, 59, (i) 9 (ii) 9 00 Two sections of Class IX having 7 students each appeared for mathematics Olympiad. The marks obtained by them are shown below : 6,, 7, 68,, 5,, 6, 8, 7, 6, 8, 6, 57 9, 7, 5, 59, 8, 6, 88, 56, 6, 66, 5, 6, 5, 7 7,, 6, 58,, 8, 6, 6, 9, 50, 76, 8, 7 77, 6, 5, 0, 7, 60, 5,,, 6, 0, 59, One student is selected at random. Find the probability that selected student is : (i) having marks more than 9. (ii) having marks between 9 and 00 Page 5 of 7

6 Draw a histogram to represent the following grouped frequency distribution : Age (in yrs) No. of persons Also draw frequency polygon. 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. AB, BC CA D, E F In the given figure of, let. If mid-point of side AB, BC and CA are D, E and F respectively then find. 0 PQRS C C SC = CQ SQ CC Page 6 of 7

7 Points C and C are taken on opposite sides of parallelogram PQRS (see figure) such that SC = CQ. Show that SQ and CC bisect each other. If D, E, F are the mid-points of side BC, CA and AB of an equilateral triangle ABC as shown in the figure, then prove that triangle DEF is also an equilateral triangle. -o0o0o0o- Page 7 of 7