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, JSS INTERNATIONAL SCHOOL, DUBAI GRADE: 10 Marks: 80 MOCK I EXAMINATION (2019-2020) MATHEMATICS DATE:17-11-2019 Duration: 2 Hrs 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) A man invests Rs 1680 in buying shares of nominal value Rs 25 and selling at 12% premium.The dividend on the shares is 15% per annum.Calculate : i) the number of shares he buys ii) the dividend he receives annually. [3] b) Solve the inequation and graph the solution set on the number line [3] c)Using properties of proportion, find the ratio a:b , given [4] Question 2 a)Find the 9th term from the end of the A.P: 10, 7, 4, . ..-62. Also find the number of terms of A.P. [3] b)Given a line segment AB joining the points A(-4,6) and B (8,-3).Find : i) the ratio in which AB is divided by the y axis ii) the coordinates of the point of intersection iii) the length of AB. [3] c) Construct a triangle ABC such that BC = 6.4 cm ,CA = 5.8cm and incircle. Measure and record the radius of the incircle. Draw its [4] 1 Question 3 a)If 1 is a root of quadratic equation 3x + ax -2 =0 and the quadratic equation a(x +6x) b=0 has equal roots, find the value of b. [3] b)The trunk of a tree is cylindrical and its circumference is 176cm.If the length of the trunk is 3m ,find the volume of the timber that can be obtained from the trunk. [3] c) The 5th term of a G.P is 48 and 8th term is 384.Find the 12th term of the G.P. [4] Question 4 a)Prove the identity : [3] b) The marks of 10 students of a class in an examination arranged in ascending order is as follows: 13, 35, 43, 46, x, x+4, 55, 61, 71, 80.If the median mark is 48,find the value of x. Hence find the mode of the given data. [3] c)Let A = [4] Section B (40 marks) Attempt any four questions from this section Question 5 a)The sum of first 20 terms of an A.P is 630 and its first term is 3.Find the 13th term. [3] b) Vicky had a recurring deposit in a bank. He deposited Rs 300 per month for some months. If he received Rs 525 as interest at 7% per annum find the duration of the deposit. [3] c)A hollow sphere of internal and external diameter 12cm and 16cm respectively is melted and recast into small cones of base radius 2cm and height 8cm.Find the number of cones. [4] Question 6 a) If a,b,c are in continued proportion ,prove that b) AB is the diameter of the circle with center O.OD//BC and numerical values of i) . . [3] Calculate the [3] c)Cards bearing numbers 1,3,5,7,9,11,13,15,17,19 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is i) a prime number ii) a number divisible by 3 iii) a number that is a multiple of 5 iv) an even number. [4] 2 Question 7 a) Find the equation of a line which passes through the point A(-3,4) and is perpendicular to the line 2x + 3y 2=0. [3] b) Find the number of integers between 50 and 500 which are divisible by 7? [3] c) Take 2cm = 2 unit on a graph paper [4] i)Plot the points A(-1,0), B(-3,0), C(-3,2) and D(-1,-3). ii) Reflect the points A,B,C,D on y axis and name them as A ,B ,C and D respectively. iii) Write down the coordinates of A , B ,C , D iv) Join the points DABCC B A D and give a name the closed figure. Question 8 a) When divided by x-3 , the polynomials x - mx + x +6 and 2x - x - (m+3)x 6 leave the same remainder. Find the value of m . [3] b) A company, with 10,000 shares of Rs100 each, declares an annual dividend of 5%. (i)What is the total amount of dividend paid by the company? (ii)What should be the annual income of a man who has 72 shares in the company? (iii)If he received only 4% of his investment, find the price he paid for each share [3] c) In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively. Find the equation of median through vertex A. Also, find the equation of the line through vertex B and parallel to AC. [4] Question 9 a) PQR is a triangle. S is a point on the side QR of PQR such that PSR = QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm. i) Prove PQR SPR. ii) Find the length of QR. iii) b)If i)m:n [3] ii) 3 c) If the mean of the following distribution is 24 ,find the value of a . Marks Number of students 0 10 7 10 -20 a 20 - 30 8 30 - 40 10 [4] 40 -50 5 Question 10 a)Find the volume and total surface area of a solid in the form of a right circular cylinder with hemispherical ends, given that the length of the cylinder is 28cm and the radius of the cylinder is 3.5cm. [4] b)The following distribution represents the height of 160 students of a school. Height in 140 -145 145 -150 150 -155 155 -160 160 -165 165 -170 170 -175 175 -180 cn Number 12 20 30 38 24 16 12 8 of students Take 2cm = height of 5 cm along one axis and 2cm = 20 students along the other axis draw an ogive of the above distribution. Use the graph to estimate the following : i) the median height ii) lower quartile iii)the number of students whose height is above 172cm. [6] Question 11 a)Find two consecutive odd positive integers ,sum of whose squares is 290. [3] b)On a map drawn to scale of 1: 250,000 , a triangular plot of land has the following measurements: AB = 6 cm, BC = 8cm and .Calculate i) actual length of AC in km ii)the area of the plot in sq km. [3] c) An aeroplane at an altitude of 1200 metres finds that two ships are sailing towards it in the same direction. The angles of depression of the ships as observed from the aeroplane are 60 and 30 respectively. Find the distance between the two ships. Give your answer to nearest whole number. [4] *************************************** 4
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