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ICSE Class X Board Exam 2017 : Mathematics

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Rajiv Khadye
Pawar Public School (PPS), Bhandup, Mumbai

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MATHEMATICS (Two hours and a half) 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 [ ]. Mathematical tables are provided. SECTION A (40 Marks) Attempt all questions from this Section. Question 1 (a) If b is the mean proportion between a and c, show that: [3] 4 + 2 2 + 4 2 = 4 + 2 2 + 4 2 (b) Solve the equation 4 2 5 3 = 0 and give your answer correct to two decimal [4] places. This paper consists of 7 printed pages and 1 blank page. T17 511 Copyright reserved. Turn over (c) AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm. If the radius of the circle [3] N A is 13 cm, find the distance between the two chords. B O C M D Question 2 (a) Evaluate without using trigonometric tables, [3] 1 sin2 28 + sin2 62 + tan2 38 cot 2 52 + 4 sec 2 30 (b) If A = [ 1 3 2 1 ] and B = [ ] and A2 5B2 = 5C. Find matrix C where C is a 3 4 3 2 [4] 2 by 2 matrix. (c) Jaya borrowed 50,000 for 2 years. The rates of interest for two successive years [3] are 12% and 15% respectively. She repays 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt. Question 3 (a) The catalogue price of a computer set is ` 42000. The shopkeeper gives a discount [3] of 10% on the listed price. He further gives an off-season discount of 5% on the discounted price. However, sales tax at 8% is charged on the remaining price after the two successive discounts. Find: (i) the amount of sales tax a customer has to pay (ii) the total price to be paid by the customer for the computer set. (b) P(1, 2) is a point on the line segment A(3, 6) and B(x, y) such that AP : PB is equal [4] to 2 : 3. Find the coordinates of B. (c) 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 marks is 48, find the value of x. Hence find the mode of the given data. T17 511 2 [3] Question 4 (a) What must be subtracted from 16x3 8x2 + 4x + 7 so that the resulting expression [3] has 2x + 1 as a factor? (b) In the given figure ABCD is a rectangle. It consists of a circle D C D A B [4] and two semi circles each of which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to three significant figures. (c) Solve the following inequation and represent the solution set on a number line. [3] 1 1 1 8 < 4 7 , 2 2 2 SECTION B (40 Marks) Attempt any four questions from this Section Question 5 (a) Given matrix = [ 1 1 ]. Find the matrix X if, = 2 4 . 8 3 5 Hence solve for and given [ ] = [ ] 50 [4] (b) How much should a man invest in ` 50 shares selling at `60 to obtain an income [3] of ` 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number. (c) Sixteen cards are labelled as a,b,c .m,n,o,p. They are put in a box and shuffled. [3] A boy is asked to draw a card from the box. What is the probability that the card drawn is: (i) a vowel. (ii) a consonant. (iii) none of the letters of the word median. T17 511 3 Turn Over Question 6 (a) Using a ruler and a compass construct a triangle ABC in which AB = 7cm, [4] CAB=60o and AC = 5cm. Construct the locus of: (i) points equidistance from AB and AC. (ii) points equidistant from BA and BC. Hence construct a circle touching the three sides of the triangle internally. (b) A conical tent is to accommodate 77 persons. Each person must have 16 3 of air [3] to breathe. Given the radius of the tent as 7 find the height of the tent and also its curved surface area. (c) If 7 + 2 7 2 = 5 3 [3] , use properties of proportion to find (i) m : n (ii) 2 + 2 2 2 Question 7 (a) A page from a saving bank account passbook is given below: Date Particulars Amount Withdrawn (`) Amount Deposited (`) [5] Balance (`) Jan. 7, 2016 B/F 3000.00 Jan 10, 2016 By Cheque Feb. 8, 2016 To Self 1500.00 4100.00 Apr. 6, 2016 By Cheque 2100.00 2000.00 May 4, 2016 By cash 6500.00 8500.00 May 27, 2016 By Cheque 1500.00 10000.00 2600.00 5600.00 (i) Calculate the interest for the 6 months from January to June 2016, at 6% per annum. (ii) If the account is closed on 1st July 2016, find the amount received by the account holder. T17 511 4 (b) Use a graph paper for this question (Take 2 cms = 1 unit on both x and y axis) [5] (i) Plot the following points: A(0,4), B(2,3), C(1,1) and 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. Write down the equation of the line of symmetry of the figure formed. Question 8 (a) Calculate the mean of the following distribution using step deviation method. Marks Number of Students (b) 0 10 10 20 20 30 30 40 40 50 50 60 10 9 25 30 16 10 [4] In the given figure PQ is a tangent to the circle at A. AB and AD are bisectors of [3] CAQ and PAC. IF BAQ = 30o, prove that: C (i) BD is a diameter of the circle. D (ii) ABC is an isosceles triangle. B P (c) A Q The printed price of an air conditioner is 45,000/-. The wholesaler allows a [3] discount of 10% to the shopkeeper. The shopkeeper sells the article to the customer at a discount of 5% of the marked price. Sales tax (under VAT) is charged at the rate of 12% at every stage. Find: (i) VAT paid by the shopkeeper to the government. (ii) The total amount paid by the customer inclusive of tax. T17 511 5 Turn Over Question 9 (a) In the figure given, O is the centre of the circle. DAE = 70 . Find giving suitable reasons, the measure of: [4] C (i) BCD (ii) BOD O (iii) OBD D B (b) A E A(-1, 3) , B(4, 2) and C(3, -2) are the vertices of a triangle. [3] (i) Find the coordinates of the centroid G of the triangle. (ii) Find the equation of the line through G and parallel to AC. (c) Prove that [3] sin 2 3 = 2 3 Question 10 (a) The sum of the ages of Vivek and his younger brother Amit is 47 years. The product [4] of their ages in years is 550. Find their ages. (b) The daily wages of 80 workers in a project are given below. Wages (in `) No. of workers [6] 400-450 450-500 500-550 550-600 600-650 650-700 700-750 2 6 12 18 24 13 5 Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = ` 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate: (i) the median wage of the workers. (ii) the lower quartile wage of workers. (iii) the number of workers who earn more than ` 625 daily. T17 511 6 Question 11 (a) The angles of depression of two ships A and B as observed from the top of a light [4] house 60 m high are 60o and 45o respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number. (b) 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 [3] P (i) Prove PQR SPR 8 cm 6 cm (ii) Find the length of QR and PS (iii) (c) Q R Mr. Richard has a recurring deposit account in a bank for 3 years at 7.5% p. a. simple interest. If he gets ` 8325 as interest at the time of maturity, find: (i) The monthly deposit (ii) The maturity value. T17 511 S 3 cm 7 [3]

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