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# ICSE Board Exam 2007 : Mathematics

7 pages, 44 questions, 44 questions with responses, 112 total responses
 ICSE Indian Certificate of Secondary Education (ICSE), New Delhi
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MATHEMATICS 2007 (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 thefirst 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 th~ 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 tl,e answer. Omission of essential working will result in the loss of marks. The intended marksfor questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. SECT~(40 Marks) Attempt all questions from this Section. _aLL - 1 ~ t ~ rl~+5"b -~ -/'1A) Show that (x - 1) is a factor of X3- 7X2 14x- 8. Hence, completely + Q'V"0n ~ (a) 1" (~ , :0-95 i~ 7" -?--- factorisethe aboveexpression. iC "v- ~ Dineshbought an article for Rs. 374, which includeda discountof 15% [3] . ~(b) on the markedprice and a salestax of 10%on the reducedprice. Findthe marked price of the article. (c) 400 Ramesh invests Rs.12800 for three ~t '3~c> [3] '31 ~v the rate of 10% per annum compoundinterest. Find:(i) The s~ due to Rameshat the end of the fifstyear. 1408"0 (ii) The interesthe earnsfor the secondyear. 1408' (iii) The.totalamountdue to hiin at the end ofthe third year. This Paper consists of 7 printed pages and 1 blank page. T07 511 t1 Copyright reserved. Turnover

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QU~2 (a) In the givenfigure,0 is the centreof the circleand LPBA =45 . Calculatethe valueof LPQB. p A (b) [3] In an equilateral !!!ABC of side 14 em, side BC is the diameter of a semi-circleas shown in the figure below. Find the area of the shaded region. (Take 7r= 22/7 and .fj = 1.732) [3] C A. B (c) Ifx= fH3b+ ~ ~ r:-n' a+3b-va-3b Prove that 3bx2 - 2ax + 3b = 0 [4] / ~on3 (0) 70 4 1 -f ),. ] + [ 0 1. j If 2[~ ! ~ = [ 10' 5] ..~ find the valuesofx and y. ~) '2- [3] f ~ Solvethe followinginequationand graphthe solutionon the numberline. 2 11 -2-~x+-<3-;xeR 3 33 [3] 2 T07 511

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(c) Use a graphpaperfor this question. (i) The point P (2, - 4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates ofQ.~ (H) c=. 2,- Lj) PointQ is reflected aboutthe liney = 0 to get the image R. Find L. "'1 the co-ordinatesof R. IZ C- L (Hi) Namethe figurePQR. (iv) Findtheareaof figurePQR. I Y ) l'vtl~/~ c-r--(v.-J " i , A [4] 16 &J (..A-,3t;' / ~n4 Sin.80 (a) Evaluate: (b) SalonidepositedRs.150per month in her bank for eight monthsunderthe [3] Cos 100 + Sin 59 Sec 31 Recurring Deposit Scheme. What will be the maturity value of her deposit, if the rate of interest is 8% per annum and the interest is calculatedat the end of everymonth? o"f (c) v::;/' [3] [4] 10~2020;30 I ~ON B (40 Marks) Attemptanyfour questionsfroTljhis Section t J 3 .1_~:.~' (, J~I L; of"I I cJ "''''~ ). , J I 1..1 I 3~,. .-1 r-? J . . Question 5 (a) LaA~ (b) 6 Findthe meanof the followIngdistribution:- D ~n.:- . f,,-,J [3] [} ~J [~ ~] B=[:1 ~l F~dA2+AB+B2 Ajay owns 560 shares of a company. The face value of each share is Rs.25. The companydeclaresa dividendof9%. Calculate:- IUD (i) The dividendthat Ajaywill get. (ii) The rate of intereston his investment,if Ajay had paid Rs. 30 for each share. (c) 7, ~ 1. [3] The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheresof diameter 3.5 em. "m many such spheres can be obtained? '1 [4] 3 T07 511 Turnover 1.\ ,'> :

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'Question (a) 6 Mr. AshokSharma'sincomefromhis salaryin the year2005-2006was Rs.2,96,000. Savinszs: . ContributiontowardsProvidentFund: Rs.I,500 per month. . ContributiontowardsLICpremium: Rs. 10,000 per year . NationalSavingCertificates Rs. 15,000 Donations: . To Prime Minister's Relief Fund Rs.12,000 (eligible for 100% tax exemption) If a sum of Rs. 4,000 was deducted every month towards Income Tax from his salaryfor the first II monthsof the year, calculateMr. Sharma's incometax liabilityin the lastmonthof the financialyear. Tax slab:Upto Rs.50,000 No tax. Rs.50,001 to Rs. 60,000 10% of the income exceeding I Rs.50,000. Rs.I,OOO 20% of the income + Rs.60,00 I to Rs.I ,50,000 exceeding Rs.60,000. Above Rs.I ,50,000 Rs.19,000 + 30% of the income exceeding Rs.I ,50,000. Standard Deduction Rs.20,000. Rebate in tax 20% of the of the total savings or Rs.14,000 whichever is less Surcharge 10% of the total tax payable after rebate. [6] Five years ago, a woman's age was the square of her son's age. Ten years . henceher agewill be twicethat of her son's age. Find:, . (i) (ii) The age of the son five yearsago S' The presentageof the woman. ::>0 4 T07 511 ~() lC> 4 ;v> -vS S' [4]

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~Question7 (a) Cf+? Solvethe following quadratic equation forx andgiveyouranswercorrect to two decimal places:-. . / - '3 t ~ ~ f,' [3] . 3x - 9 = 0 tr n- - I ~ ; :3(I.!~~ ') : I &; (:1 .J1 ) 1 Using a ruler, constructa triangle ABC with BC = 6.4 em, CA = 5.8 em X2 - (b) '" and LABC = 60 . Drawits incircle. Measureand recordthe radiusof the incir'cle. (c) [3] Mrs. Kumarhas an accountwith The Bankof India. The followingentries are fromher pass book:Deposits Rs. P -- -- Balance Rs. P. 8500.00 18.02.06 To self 4000.00 -- ..... 12.04.06 By cash -- 2238.00 ..... 15.06.06 To self 5000.00 -- ..... 08.07.06 By cash --- 6000.00 ..... Date Particulars Withdrawals Rs. P 08.02.06 B/F Completethe above page of her pass book and calculatethe interest for the six months,Februaryto July2006, at 4.5% per annum. I t I .it 3 [4] Question 8 SecA -1 l-CosA (a) Provethe identity: SecA + 1 - 1+CosA (b) [3] The mid point of the line segmentjoining (2a, 4) and (-2, 2b) is (1, 2a + 1). Findthe valuesof a and b. (c) [3] In the givenfigure,if LACE = 43 andLCAF = 62 find the values of a, b and c. [4] F 5 T07 511 Turnover

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Question9 (a) .. . A functlOnInx ISdefined as f( x ) - Find the value of the expression: (b) 3x2 + 2x -1. x+l ; X E R an d x ;f.- 1. f~j) + 1. Findthe equationof the lineparallelto the line3x + 2y = 8 andpassing [3] throughthe point (0, 1). (c) " ?' - [3] From the top of a hill, the angles of depression of two consecutive kilometerstones,due east are found to.be 30 and 45 respectively. Find the distanceof the two stonesfromthe foot of the hill. [4] J Question10 (a) The table below shows the distribution of the scores obtained by 120 shooters in a shootingcompetition. Using a graph sheet, draw an ogive for the distribution. Numberof shooters Scoresobtained o - 10 5 10 - 20 9 20 - 30 16 30 - 40 22 - 50 50 - 60 60 - 70 26 70 - 80 6 80 -90 4 40 18 11 90 - 100 3 Use your ogive to estimate:- LJ2..' -~ (i) The Median L\J r.1 (ii) TheinterqUartileange "~1 r (Hi) Thenumberof sli~oterswho obtainedmorethan 75%scores. '1 0 0 g - 22. 6 T07511 :: ~ [6]

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(b) A In the givenfigure,ABC is a triangle. DE is parallelto BC and AD DB 3 -2' 2>~S 3:.f' (i) . ' AD D th etermme e ratIOs AB' (ii) Provethat !J.DEF is similarto !J.CBF. DE BC C Hence,find EF 'J '.SFB (iii) What is the ratioof the areasof !J.DFE !J.BFC? cr: 1-5 and [4] Question 11 (a) If the linejoining the points A(4, -5) and B(4, 5) is dividedby the point P [3] suchthat ~~ =~, find the co-ordinatesofP. (b) In the figure given below, PT is a tangent to the circle. Find PT if AT = 16em and AB = 12em. [3] , (c) Constructa triangleBCPgivenBC = 5 em,BP= 4 emandLPBC = 45 . (i) Completethe rectangleABCDsuchthat (1) (2) (ii) P is equidistantfromAB and BC P is equidistantfrom C and D Measureand recordthe length of AB. 7 T07 511 [4] -

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