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, JSS INTERNATIONAL SCHOOL, DUBAI GRADE: 10 DATE:- 17-01-2018 PRE FINAL EXAMINATION 2018 Marks: 80 Duration: 2 Hrs MATHEMATICS Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Section A (40 Marks) Attempt all questions from this section Question 1 a) Ravish opened a cumulative time deposit account with Punjab National 3 Bank for years. If the rate of interest is 10% per annum and the bank 2 pays Rs 4662 on maturity. Find how much did Ravish deposit each month? [3] b)If A is the solution set of 5x 2 3 x+ 4, x N and B is the solution set of 3x+1 19 x , x N , find A B [3] c)If y = 1 3 1 3 1 3 1 3 ( p+1) +( p 1) ( p+1) ( p 1) - 3py +3y p . [4] , Using properties of proportion, find the value of y Question 2 a) A hemispherical bowl of internal diameter 36cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm.How many bottles are required to empty the bowl?. [3] Page 1 of 5 b)If A = is [3] [ 1 0 1 7 the ] and I = [ ] 1 0 0 1 identity then find k so that A = 8A + kI, where I matrix of order 2. c) If one root of the quadratic equation mx -9x -10 = 0 is 2,find the value of m and also find the other root [4] Question 3 a)Find [3] the b) middle Prove term of the AP. that [3] 213, 205, 197, tan cot = 37 2 2 si n 1 sin cos c)If x-2 is a factor of 2x - x +px -2 ,find the value of p. With this value of p factorise the given polynomial. [4] Question 4 a)The price of a TV set inclusive of value added tax of 9% is Rs 13407.Find its marked price.If the VAT is increased to 13% ,how much more does the customer has to pay for the TV? [3] b) AB is a tangent to the circle at Q.PQRS is a cyclic quadrilateral .If PSQ=38 , PQR=110 , QOR , PQA RQB find . [3] c)In an interview one candidate is to be selected out of 5 male and 6 female candidates. Find the probability that the selected candidate is a i) male ii) female iii) male or female iv) male and female. [4] Section B (40 marks) Page 2 of 5 Attempt any four questions from this section Question 5 a) Find a GP for which the sum of first two terms is -4 and fifth term is 4 times the third term. [3] b) A model of a ship is made to a scale of 1: 300. i) The area of the deck of the ship is 3,60,000 m .Find the area of the deck of the model. ii) The volume of the model is 250 litres .Calculate the volume of the ship in m . [3] c)Use a graph paper for this question. (Take 2cm = 1 unit on both axis) [4] i) Plot the following points : A(0,-4) ,B (2,-3) , C(1,-1) , D (2,0) ii) Reflect points B, C, D on the y axis and write down their coordinates. Name the images as B ,C , D respectively. iii) Join the points A,B ,C , D ,D ,C B and A in order so as to form a closed figure. iv) Write the equation of line CC . Question 6 a) Find a 2 x 2 matrix X which satisfies the equation [ ][ ] [ 3 7 0 2 +2 X = 1 5 2 4 5 3 4 6 ] [3] b)If P (9a-2,-b) divides the line segment joining A (3a+1, -3) and B ( 8a,5) in the ratio 3:1 .Find the values of a and b. [3] c)Using ruler and compasses only: [4] i) Construct a triangle ABC with following data: AB = 3.5 cm ,BC = 6cm and ABC =120 ii)Draw a circle with BC as diameter. Find a point P on circumference of circle which is equidistant from AB and BC. iii) Measure of BPC Question 7 Page 3 of 5 a)Find the equation of the perpendicular dropped from the point (-1,2) on to the line joining (1,4) and (2,3). [3] b) If [3] 4 a2+ 3 b 7 a2 2 a2 11 b2 = . Using properties of proportion , find the value of i ii 4 a 2 3 b 4 b2 2 a2 +11 b2 c) A farmer wishes to grow a 100m rectangular garden. Since he has only 30m barbed wire ,he fences three sides of the rectangular garden letting the compound wall of his house act as fourth side fence. Find the dimensions of his garden. [4] Question 8 a) Prove: 1+cosA =(CosecA+ cotA) [3] 1 cosA b) Shikha invests Rs 14950 in Rs100 shares of a company ,paying 14% dividend. If her annual income from shares be Rs 1610 ,find the market value of each share. [3] c) In the following figure ,PQ is the tangent to the circle at A.DB is the diameter and O is the centre of the circle.If ADB=30 CBD=60.Calculate i QAB ii PAD iii AOB [4] Question 9 a)To a circle of radius 4cm, construct two tangents which are inclined to each other at an angle of 60 . [5] b) A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13cm and 5 cm respectively. The radii of the hemispherical part and conical parts are the same as that of the cylindrical part .Calculate the surface area of the toy if height of the conical part is 12cm. [5] Question 10 a)A man standing on the deck of a ship which is 10m above water level observes the angle of elevation of the top of a hill as 60 depression of the base of hill as 30 Find the distance of the hill from the ship and the height of the hill. [4] Page 4 of 5 b) Using a graph paper, draw an ogive for the following distribution of weight of 50 workers. Taking 2cm = 10kg on one axis and 2cm = 5workers along other axis. 60-70 70-80 80-90 90-100 100110Weigh 50-60 110 120 t 4 7 11 14 6 5 3 No of worke rs Use the ogive to estimate: [6] i) Upper and lower quartile ii)If weighing 95kg and above is considered over weight find the number of workers who are over weight. Question 11 a) D is a point on BC such that i) Prove that BAD= C , AB = 7cm and BD = 4cm. Area ( ABC ) ABD CBA .ii Find BC iii Also find Area ( DBA ) [3] b)If the sum of first n terms of an AP is given by Sn = 3n + 4n .Determine the AP and the nth term. [3] c) Find the mean of the following distribution. Hence, find the modal class. [4] Marks Cumulati ve frequenc y Below 10 3 Below 20 12 Below 30 27 Below 40 57 Below 50 75 *************************************** Page 5 of 5 Below 60 80
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