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Class 10 CBSE Pre Board 2015 : Mathematics 2 (Kendriya Vidyalaya (KV) No. 2, Raipur)

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KENDRIYA VIDYALAYA SANGATHAN , RAIPUR REGION SUMMATIVE ASSESSMENT-II (2014-15) SUBJECT : MATHEMATICS CLASS:X Time: 3:00 Hrs M.M :90 General instructions: 1.All questions are compulsory. 2.The question paper consists of 31 questions divided into 4 sections A , B ,C and D. Section A comprises of 4 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 Section D comprises of 11 questions of 4 marks each 3.There is no overall choice in the paper .However , internal choice is provided in 1 question of 2 marks and 1 question of 4marks.you have to attempt only one of the alternatives in such questions. 4.Q.No.30 is value based problem. SECTION-A Q.1. If P(E) =0.05, what is the probability of ,notE,. 1 Q.2. Find the coordinates of the point which divides the join of (-1,7) and (4,3) In the ratio 2:3. Q.3.The height of a tower is 10m.what is the length of its shadow when suns altitude is 450. Q.4.The area of a circle is numerically equal to its circumference. Then find the area of the circle. SECTION-B Q.5. Find the roots of x2 3x 10 = 0 by factorisation. OR Write first four terms of the AP , when the 1st term a =4 and common difference d=-2 Q.6. From a point Q, the length of the tangent to a circle is 24cm and the distance of Q from the centre is 25cm.Find the radius of the circle. Q.7. Find the point on the x-axis which is equidistant from (2,-5)and (-2,9). Q.8. A box contains 5 red marbles,8 white marbles and 4 green marbles .one marble is taken out of the box at random .what is the probability that the marble taken out will be (i)red? (ii)not green? Q.9.One card is drawn from a well-shuffled deck of 52 cards .Find the probability of getting(i)the jack of spades (ii)a club. 2 1 1 Q.10. Prove that the points (a,0),(0,b)and (1,1) are collinear if, + =1. SECTION-C Q.11. Find the area of the triangle whose vertices are (-5,-1) , (3,-5) , (5,2) Q.12. A Coin is tossed 3 times find the probability of getting (i)at least two heads (ii)at most two tails Q.13. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 , find the sum of first 30 terms. Q.14. A train travels360 Km at a uniform speed. If the speed had been 5Km/h More, it would have taken 1 hour less for the same journey. Find the speed of the Train . Q.15. The angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary .prove that the height of the tower is 6m. Q.16. A 20m deep well with diameter 7m is dug and the earth from digging is evenly spread 22 out to form a platform 22m by 14m. find the height of the platform. ( = ) 7 Q.17. If the sum of the first n terms of an AP is 4n-n2 , what is the first term ?Find the sum of first 20 terms of the AP. 3 Q.18. AD and AF are two tangents to the circle at D and F respectively. CE touches the circle At B intersect AD and AF at C and E respectively. prove that AD = ( + + ) 2 Q.19. In the following circular figure of radius 32cm , a design is formed leaving an equilateral triangle ABC in the middle.Find the area of the design. ( =3.14). Q.20. If the points A(6,1),B(8,2) and C(9,4)are the three vertices of the parallelogram taken in order,find the coordinates of fourth vertex of the parallelogram. 4 SECTION-D Q.21. The altitude of a right triangle is 7cm less than its base.if the hypotenuse is 13cm , find the other two sides. Q.22. The first and the last terms of an AP are 17 and 350 respectively.If the common difference is 9,how many terms are there and what is their sum? Q.23. Prove that the parallelogram circumscribing a circle is a rhombus. Q.24. Find the sum of first 24 terms of the list of numbers whose nth term is given by an=3 + 2n Q.25. Draw a line segment AB of length 8cm.Taking A as centre , draw a circle of radius 4cm andtaking B as centre , draw a circle of radius 3cm.Construct tangent to each circle from the centre of the other circle. Q.26. Water in a canal,6m wide and 1.5m deep ,is flowing with a speed of 10Km/h. how much area will it irrigate in 30 minutes, if 8cm standing water is needed. Q.27. A bucket is in the form of a frustum of a cone and holds 15.25 litres of water. the diameters of the top and bottom are 25cm and 20cm 5 respectively. find its height ( =3.14). Q.28. A solid metallic sphere of diameter 28cm is melted and recast into a 2 number of smaller cones, each of diameter 4 cm and height 3cm.Find the 3 number of cones so formed. OR A Hollow sphere of internal and external diameters 4 and 8cm respectively is melted into a cone of base diameter 8cm.Find the height of the cone. Q-29. O is the centre of a circle of radius 5cm.T is a point such that OT=13cm and OT intersect the circle at E. If AB is the tangent to the circle at E, Find length of AB. Q.30. A juice seller was serving his customers using glasses as shown in figure. The inner diameter of the cylindrical glass was 5cm,but the bottom of the glass has a conical raised portion of height equal to base radius of the glass .if height of the glass is 10cm.Find actual capacity of the glass. What values given by the seller to others. ( use =3.14) 6 Q.31. There is a small island in the middle of a 100m wide river and a tall tree stands on the island. P and Q are points directly opposite to each other on two banks and in line with the tree. if the angles of elevation of the top of the tree from P and Q are respectively 300 and 450 , find the height of the tree. 7 KENDRIYA VIDYALAYA SANGATHAN, RAIPUR REGION MARKING SCHEME- SA-2 (2014-15) Class-X Subject-Mathematics SECTION - A Question No Marks Q-(1)0.95 1 Q-(2)(1,3) 1 Q-(3) 10m 1 Q-(4)4 sq unit 1 SECTION-B Q-(5)splitting middle terms 1 Obtaining roots 5,-2 1 OR 1 1 1 1 Finding each term of AP(2+2 + 2 + 2) 2 Q-(6)using Pythagoras property(assuming 1 Right triangle) Finding radius as 7cm 1 Q-(7)making equation from distance formula 1 Solving equation to get (-7,0) 1 5 Q-(8)probability for red17 1 13 Probability for not green 17 1 1 Q-(9)probability for the jack of spade 52 1 13 Probability for a club 52 1 Q-(10)Forming equation from area of a triangle 1 1 1 Solving the equation and find the + =1 1 SECTION-C Q-(11)putting values correctly in formula 1 1 Solving the expression 12 1 Finding the value as 32sq unit 2 Q-(12)listing outcomes correctly 1 1 Probability of getting at least two heads=2 7 Probability of getting at most two tails=8 1 1 Q-(13)let first term be a and common difference is d 7(2a+6d)/2=49 and 17(2a+16d)/2=289 1 Solving and getting a=1 and d=2 1 Sum of 30 terms is 900 1 Q-(14)FORMING 360 - 360 +5 = 1(x is the speed of the train) 1 Splitting the equation x2 = 5x 1800=0 1 Finding speed of train is 40Km/h 1 Q-(15)if the height of the tower is x then 1 Tan = 4 and tan(900- )=9 12 Finding x2=36 and x=6cm 12 Q-(16)Finding volume of earth and volume of the platform 12 Finding height=2.5m by solving the equation 12 Q-(17)Finding first term and common difference 12 Finding sum =440 from formula 12 Q-(18)finding AD=AF , CD=CB and EB =EF 12 Rearranging to find the proof part 12 Q-(19)Finding area of the triangle ABC 1 1 1 1 1 1 1 2 Finding area of the design=1888.25cm2 1 Q-(20)let coordinates of fourth vertex is (x,y) 1 Forming equations x+8=15 and y+2=5 12 Finding x=7 and y=3 1 SECTION-D 1 Q-(21)forming x2 +(x+7)2 = 132 12 Solving to get values of x= -12 or 5 12 Finding the sides as 5cm and 12cm 1 Q-(22)forming equation 17 + (n-1)9=350 and getting n=38 2 Getting sum from formula as 6973 2 Q-(23)given and to prove part 1 Steps to show sum of opposite sides are equal 2 To show adjacent sides are equal and proof of rhombus 1 Q-(24)to find terms of the AP 1 To find the first term and common difference 1 Finding sum as 672 by using the formula 2 Q-(25)to draw two circles at the end of the line segment AB 1 To find point of contacts by drawing circle 1 To draw 4 tangents 2 1 Q-(26)finding volume of water going to land Finding volume of water in the land 1.5 1 Equating and finding area of land as 562500m2 1.5 Q-(27)conversion of volume in cm3 1 Forming and solving equation using formula of volume 2 Finding height=38.22cm(approx) 1 Q-(28)finding volume of sphere and volume of cone 2 Formula to find number of cones and simplification 1 Finding number of cones as 168 1 OR Finding volume of hollow sphere 1 Finding volume of cone 1 Formula to find height of cone and simplification 1 Height of cone is 14cm 1 Q-(29)Finding length of PT 1 Finding equation using Pythagoras theorem in AET 2 Finding AB= 20 cm 1 Q-(30)apparent volume of glass 1 Volume of conical portion 1 3 Actual volume of glass 179.90cm3 1 Value judgement 1 Q-(31)using tan450 to express height in terms of distance 1 Applying tan 300 in another triangle and solving the equation 2 Height of the tree will be 50( 3 -1) m 1

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