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St. Francis Xavier School Rehearsal Examination(2017 18) Subject Mathematics Class X Time 2 hrs 30 min F.M. 80 Answer 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 answer. 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 [] Mathematical tables are provided. Section A (40 MARKS) (Attempt All Questions) Question 1: a) [3 + 3 + 4 = 10] Find the matrix X such that A + 2X = 2B + C b) Find the values of x which satisfy the inequation: -17/6 < 1/2 - 2x/3 2, x W. Graph the solution set on the number line. c) A die has 6 faces marked by given numbers as shown below: The die is thrown once. What is the probability of getting (i) a positive integer? (ii) an integer greater than -3? (iii) the smallest integer? 1 This question paper consists of 5 pages Question 2: [3 + 3 + 4 = 10] a) What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional? b) If (x - 2) is a factor of the expression 2x3 + ax2 + bx -14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the value of a and b. c) The median of the following observations 11, 12, 14, (x 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean. Question 3: [3 + 3 + 4 = 10] a) Without using tables, evaluate: 3 cos 80o . Cosec 10o + 2 sin 59o . Sec 31o b) In the figure, angle BAD = 65o, angle ABD = 70o, angle BDC = 45o i) Prove that AC is a diameter of circle. ii) Find angle ACB c) AB is a diameter of a circle wit centre C = (-2, 5). If A = (3, -7), find (i) the length of the radius AC, and (ii) the coordinates of B. Question 4: [3 + 3 + 4 = 10] a) Solve the following equation and calculate the answer correct two decimal places: x2 - 5x -10 = 0 b) In the given figure, AB and DE are perpendicular to BC. (i) Prove that ABC ~ DEC. (ii) If AB = 6 cm, DE = 4 cm and AC = 15 cm, calculate CD. (iii) Find the ratio of the area of ABC : area of DEC. 2 This question paper consists of 5 pages c) Using a graph paper, plot points A(6, 4) and B(0, 4). (i) Reflect A and B in the origin to get the images A and B . (ii) Write the coordinates of A and B . (iii) State the geometrical name for the figure ABA B (iv) Find its perimeter. Section B (40 MARKS) (Attempt any four Questions) Question 5: [3 + 3 + 4 = 10] a) A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find (i) the VAT paid by the shopkeeper, and (ii) the total amount that the consumer pays for washing machine b) If (x2 + y2) / (x2 y2) = 17 / 8 then find the value of (i) x : y , (ii) (x3 + y3) / (x3 y3) c) In ABC , angle ABC = angle DAC, AB = 8 cm, AC = 4 cm, AD = 5 cm. (i) Prove that ACD is similar to BCA. (ii) Find BC and CD. (iii) Find area of ACD : area of ABC. Question 6: [3 + 3 + 4 = 10] a) Find the value of a for which the following points A (a, 3), B (2, 1) and C (5, a) are collinear. Hence, find the equation of the line. b) Salman invests a sum of money in Rs. 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is Rs. 600, calculate (i) the number of shares he bought, (ii) his total investment, and (iii) the rate of return on his investment. c) The surface area of a solid metallic sphere is 2,464 cm2. It is melted and recast into solid right circular cones of 3.5 cm radius and 7 cm height. Calculate: (i) the radius of sphere, and (ii) the number of cones recast. (Take pi = 22/7). 3 This question paper consists of 5 pages Question 7: [3 + 3 + 4 = 10] a) Calculate mean of the distribution given below using the shortcut method. Marks No. of Students 11- 20 21 30 31 40 41 50 51 60 61 70 71 - 80 2 6 10 12 9 7 4 b) In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find (i) AB (ii) the length of tangent PT. c) Given: Find A2 + AC 5B Question 8: [3 + 3 + 4 = 10] a) If the x-intercept of a line is -5 and y-intercept is 16, find the equation of the line. b) Construct a ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. construct the incircle of the triangle. Measure and record the radius of incircle. c) Draw a histogram from the following frequency distribution and find mode from the graph. Class 0-5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 2 5 18 14 8 5 Frequency 4 This question paper consists of 5 pages Question 9: [3 + 3 + 4 = 10] a) If (x - 9) : (3x + 6) is the duplicate ratio of 4 : 9, find the value of x. b) Mohan deposits Rs. 80 per month in a cumulative deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is 6% per annum. c) Which term of the progression 18, -12, 8 . is 512/729 ? Question 10: [3 + 3 + 4 = 10] a) Prove the identity: (sinA + cosA) (tanA + cotA) = secA + cosecA b) A two-digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number. c) An aeroplane at an altitude of 250 m. observes the angle of depression of two boats on the opposite banks of a river to be 45o and 60o respectively. Find the width of the river. Write the answer correct to nearest whole number. 5 This question paper consists of 5 pages
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