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# ICSE Board Exam 2013 : Mathematics

7 pages, 32 questions, 35 questions with responses, 187 total responses
 ICSE Indian Certificate of Secondary Education (ICSE), New Delhi
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MATHEMATICS (Two hours and a haff) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first lS minutes. This time is to be spent in reading rhe question paper. The time given at the heod of this Paper is the time All allowedfor writing the answers. Attempt all questions from Section A and any four questionsfrom Section B. working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essentiol working will result The intended marl<s for questions in loss of marks. or ports of questions are given in brackets I J. Mathematical tables ore provided. SECTION A (40 Marks) Attempt all questionsfrom this Section. Question I (a) Given o:12 -ul" u - L2 0l ol [-: 0l' '1., :lo 2) 14 L0 * 2X:28 + C. (b) At what rute o/o p.a. will a sum of { 4000 yield ( Find the matrix X such that A t3l 1324 as compound interest in 3 years? (c) t3l The median of the following observations I l, 12, 14, (x 32, 38, 47 arranged in ascending order is - 2),(x + 4),(x + 9) , 24. Find the value of x and hence find the mean. Tl3 5lI This Paper consists of 7 printed pages and e) Copyright reserved. 141 I blank page. Turn over

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Question 2 (a) What number must be added to each of the numbers 6,15,20 and 43 to make them proportional? (b) 13I lf (x-2) is a factor of the expression 2x3 +ax'+bx-14 expression is divided by (, - 3) , it and when ttr leaves a remainder 52, find the values of a [3] and b. (c) Draw a histogram from the following frequency distribution and find the mode from the graph: 0-5 Frequency 5-10 t0-15 t5-20 20-25 25-30 ) Class 5 l8 t4 8 5 t4l Question 3 (a) Without using tables evaluate 3 cos 80o. Cosec l0' + 2 sin 59o sec 3 1o t3l D (b) ln the given figure, IBAD= 65o IABD = 70o, IB,DC = 45" (i) Prove that AC is a diameter of the circle. (ii) Find ZACB (c) I3l AB is a diameter of a circle with centre C = (-2,5). If (i) (ii) A: (3,-7). Find the length of radius AC the coordinates of B. 14l Question 4 (a) Solve the following equation and calculate the answer correct to two decimal places: (b) t3l In the given figure, AB and DE are perpendicular to BC. (D (ii) Prove that AABC -ADEC If AB = 6cm: DE = 4cm and AC: Tl3 x'-5x-10=0. 511 15 cm. Calculate CD. A

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(iii) (c) Find the ratio of the area of AABC : area of ADEc. t3l Using a graph paper, plot the points A(6,4)and B(0, 4). (i) Reflect A and B in the origin to get the images (ii) (iii) (iv) A, and B,. Write the co,ordinates of A, and B,. State the geometrical name for the figure ABA,B,. Find its perimeter. I4l SECTION B (40 Marks) Attempt anyfoar questionsfrom this Sectiorr Question (a) 5 ,--' Solve the following inequation, write the solution set and represent it on the numberline: -r<{-t1.1 3-2'r-;,xeR (b) Mr' Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8% per annum and Mr. Britto gets T 8088 from the bank after 3 years, find the value of his monthry instalment. t3l , (c) Salman buys 50 shares of face varue t t3l 100 availab re atl r32. (i) What is his investment? (ii) If the dividend is 7.syo,what wil be his annuar income? (iii) If he wants to increase his annuar income by ( r50, how many . Question 6 (a) 511 t4) ' Showthat .@y I Tl3 extra shares should he buy? sinA +cosA l+cosA t3l Turn over

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In the given circle with centre O' IABC: 100"' ZACD:40" CT is a tangent to the circle at (b) C' Find IADC and IDCT and ' \|/ t3l (c) Bank A'/c pass book: Given below are the entries in a Savings Balance Particulars Withdrawals Deposit Date 8500 B/F Feb 8 t Feb 18 To self April t2 By cash June 15 To self July 8 < 4000 By cash < 2230 < 5000 < 6000 t4l CalculatetheinterestforsixmonthsfromFebruarytoJulyat6Yop.a, Question 7 (a) In A ABC, A(3, 5), B(7'8) and C(l'-10)' Find the equation of the median through A. t3l (b)Ashopkeepersellsanarticleatthelistedpriceof(1500andtherateofVATis 12o/oateachstageofsale.IftheshopkeeperpaysaVATof{36tothe Govemment,whatwastheprice,inclusiveofTax,atwhichtheshopkeeper purchased the article from the wholesaler? T13 5l I t3l

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(c) In the figure given, from the top of a building AB = 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30o and 60o respectively. Find: (i) (ii) the horizontal distance between AB and CD. the height of the lamp post. 14) Question 8 Findxandvif (a) [' "l Ly 4y) l'1 : [sl Lt.l Ltz) t3l A solid sphere of radius (b) 15 cm is merted and recast into sorid right circular cones of radius 2.5 cmand height 8 cm. Calculate the number of cones recast. (c) without solving the foilowing quadratic equation, find the varue of .p, for t3l which the given equation has real and equal roots: x2+(p-3)x*p=0. I4l Question 9 (a) In the figure alongside, OAB is a quadrant of a circle. The radius OA: 3.5 cm and OD : 2 cm. Calculate the area of the shaded portion. (Take t3l "= ?l (b) A box contains some black balls and 30 white balls. If A the probability of drawing a black balr is two-fifths of a white bail, find the number of brack balls in the box. (c) t3l Find the mean of nf the fhe f^n^.,;-^ -ti-+-jr^--r:- - rby foilowing distribution step deviation method: Class interval t4l Tl3 511 Turn over

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Question 10 (a) Using a ruler and comPasses onlY: (i) Construct a triangle ABC with the following data: AB:3'5 cm' BC = 6 cm and IABC=120" (iDlnthesamediagram,drawacirclewithBCasdiameter.FindapointPon thecircumferenceofthecirclewhichisequidistantfromABandBC. (iii) (b) Measure IBCP' t4l in a test are given below: The marks obtained by 120 students on a graph sheet' Draw an ogive for the given distribution estimate the following: Use suitable scale for ogive to (i) The median' (ii)ThenumberofstudentswhoobtainedmorethanT5Tomarksinthetest. (iiDThenumberofstudentswhodidnotpassthetestifminimummarks required to Pass is 40' t6l Question 11 (a)Inthefiguregivenbelow,thelinesegmentABmeetsX-axisatAandY.axisat B.ThepointP(-3,4)onABdividesitintheratio2:3,FindthecoordinatesofA and B. t3l 6 T13 sl l

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i_q@++9F(b) Using the properties of proportion, solve for x, given xa t_l _ 17 2x2 8' (c) A shopkeeper purchases a certain number of books for { 960. If the cost per book was t 8 less, the number of books that could be purchased for { 960 would be 4 more. write an equation, taking the original cost of each, book to be ( r, and solve it to find the original oos of the books. T13 5l I t3I 141

Additional Info : Solved ICSE Board exam paper study guide - ICSE 2013 : MATHEMATICS - I.C.S.E. Free Online Question Paper
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