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ICSE Prelims 2017 : Mathematics (W. W. A. Cossipore English School (WWA CES), Kolkata)

3 pages, 35 questions, 33 questions with responses, 53 total responses,

Aviree Mukhopadhyay
Loreto Day School, Bow Bazar, Kolkata
1st to XII and contd. ISC

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This question paper consists of 3 no .of pages REHEARSAL TEST (2016-2017) SUBJECT:NL\THENL\TICS CLASS: X FULL MARKS: 80 TIME: 2YzHOURS 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. Attempt all questions from SectionA 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 giveninbrackets[ ]. SECTION: A (Answer all questions in this section) ~g polynomial: the remainder theorem facto rise completely the following 3 xl + 2 Xl - 19 x + 6 . (3) ~ hollow sphere of internal and external diameters 4 em and 8 em respectively, is melted into a cone of base diameter 8 cm.Find the , ,L height of the cone. (3) ~rind the ratio compounded of the reciprocal ratio of 15: 28, the subduplicate ratio of 36: 49 and the triplicate ratio of 5:4 (4) 2. (~e adjoining figure, AT is tangent to a circle at A . (3) IfLBAT = 4So and LBAC = 6So ,find LADC. B T ~Ive: Xl -3x-9 = 0.( correct to 2 significant figures). (3) ~ind the value of a and b if x-I and x-2 are factors of x3 - ax + b. (4) 3.(~ d~ are thrown simultaneously. What is the probability that: -...(iJ /' 4 will not come up either time? J ~ 4 will come up at least once? (3) WThe weights of SOapples were recorded as given below. Calculate the mean weight, to the nearest gram, by the Step Deviation Method. (3) 80-85 85-90 90-95 9S-100 100-10S 10S-110 110-11S S 8 10 12 8 Page-1 ( Class: X MATH) Weight (gm) No. of apples 4 Continued to page-2 3 ~What least number must be added to each of the numbers 5,11,19 and 37 sO~!Jhey are in proportion? (4) J.(~e hotel bill for a number of people for overnight stay is ~ 4800. If there were 4 more, the bill each person had to pay would have reduced by~200. Find the number of people staying overnight. (3) /nev bought an article for'!' 374 which includes a discount of 15 % on the / listed price and a sales tax at the rate of 10% on the reduced price. Find the listed price of the article. (3) ('C)Solve: cos ( 50 + 8) = sin ( 30 + 8). (4) SECTION: B (ANYFOURl 5.(a) Construct a triangle ABC with BC = 6.4 cm , CA = 5.8 em and L ABC = 60 Draw its incircle. Measure the radius of incircle. (3) (b) Prove that sec4A (1- sin4A) - 2 tan2 A = 1. (c) Given 4(81 -2) x= (3) (:~). Write down (i) the order of the matrix X, (ii) the matrix X. ~ (4) line joining P(-4,5) and Q(3,2) intersects the y-axis at R. PM and QN are ~~r",n perpendiculars fr?~ ~nd Q on the x-axis. Find ~ne co-ordinates of R,~he area of the quadrilateral PMNQ. (3) ~o dice are thrown simultaneously. Find the probability that the sum of the numbers appearing on the top of two dice is less than or equal tol0.(3) ~e roots of the equation 2 x' - 2 c x + a b = 0 be real and distinct, prove that the roots of x2 imaginary. - 2 ( a + b) x + ( a2 + b2 + c2 ) = 0 will be (4) . 7.~he radii of two concentric circles are 17 em and 10 cm; a line PQRS cuts the larger circle at P and S and the smaller circle at Q and R. __ . /_ If QR = 12 em , calculate PQ. (3) W"A letter of English alphabet is chosen at random. Determine the probabili that the letter is a consonant. (3) The ratio of the radii of two right c!pcular cones of the same height is 1:2. Find the ratio of their (!),/oiumes , Qi}'turved surface areas when the height of each cone is 3 times the smaller radius. (4) Page-2 ( Class: X MATH) Continued to page-3 8.(a) If the line x - 4y - 6 = 0 is the perpendicular bisector of the line segment PQ and the coordinates of Pare ( 1, 3), find the co-ordinates of Q. (3) (b) A map of a square plot of land is drawn to a scale of 1: 25,000. If the area of the plot in the map is 72 cm2 , find (i) the actual area of the plot of land, and (ii) the length of the diagonal in the actual plot of land. (3) (c) The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30 and 45 respectively. Find the height of the multi-storeyed building and the distance between the two buildings, correct to two decimal places. (4) 9. (a) A manufacturer sells a washing machine to a wholesaler for ~ 15,000.The wholesaler sells it to a trader at a profit of ~ 1,200and the trader sells it to a consumer at a profit of ~ 1,800 .If the rate of VAT is 8% find: (i) The amount of VAT received by the State Government on the sale of this machine from the manufacturer and the wholesaler. (ii) The amount that the consumer pays for the machine. (3) (b) A man borrows ~ 40,000 at 8 % p. a. compound interest, compounded yearly, and repays ~ 5,000 at the end of each year. Find out the amount of the loan outstanding at the beginning of the fourth year.( Give your answer correct to the nearest rupee). ' (3) Graph the solution set on the number line. o < A < 90 , /~en ~n' ~ove (4) solvethe followingequation: A - 3 ( sec A-I) . (3) that: ( sin A + cos A) (sec A + cosec A ) = 2 + sec A cosec A. (3) ~ind the equation of the line through the intersection of 2 x + 5 y - 4 = 0 with x- axis and parallel to the line 3 x -7 Y+ 8 = o. (4) 2 COS 2 A-l ove that: cot A - tan A = sin A cos A (3) ~chords AD ,CD of a circle intersect externally at a point P. If PA = PC, prove that AD = CD. (3) \ (~A solid sphere and a solid hemisphere have the same total surface areas. Fi(d~the ratio of their volumes. . (4) Page-3( Class: X END MATH)

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