UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

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1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 May/June 2013 Candidates answer on the Question Paper. Additional Materials: Geometrical instruments Electronic calculator READ THESE INSTRUCTIONS FIRST 2 hours 30 minutes Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. This document consists of 24 printed pages. DC (KN/SW) 64205/3 UCLES 2013 [Turn over

2 2 Section A [52marks] Answerallquestionsinthissection. 1 (a) Solve4(x 2)=7 x. Answer x=...[2] (b) Solvethesimultaneousequations. 2x+y=7 4x 3y=19 Answer x=... (c) (i) Writedowntheintegervaluesthatsatisfy 1<n <2. y=...[3] (ii) Solve2 3y<8. Answer...[2]

3 3 2 (a) Theinteriorangleofaregularpolygonis165 o. Howmanysideshasthepolygon? Answer...[2] (b) B D p q F A E C G FAECG andadbarestraightlines.deisparalleltobc. (i) FAD t =p and AED t =q. Findanexpressionintermsofpand/orqfor (a) BCG t, (b) DBC t. (ii) AE=7cm,EC=3cm,DE=5.6cmandDB=2.1cm. (a) FindBC. (b) FindAD. Answer... cm[1] Answer... cm[1] [Turn over

4 3 (a) Thediagramsshowparallelogramsmadefromsmalltriangles. 4 Parallelogram (i) Completethetablebelow. Parallelogramm Numberofsmalltriangles (ii) Find an expression, in terms of m, for the number of small triangles used to make Parallelogramm. [1] (b) Thediagramsshowtrianglesmadefromthesamesmalltriangles. Triangle (i) Completethetablebelow. Trianglen Numberofsmalltriangles (ii) Find an expression, in terms of n, for the number of small triangles used to make Trianglen. [1] (iii) Triangleqismadefrom324smalltriangles. Findq.

5 (c) Thediagramsshowtrapeziumsmadefromthesamesmalltriangles. 5 Trapezium Trapezium 4 5 (i) Bycomparingthediagramswiththoseinparts(a)and(b),findanexpression,interms oft,forthenumberofsmalltrianglesusedtomaketrapeziumt. (ii) HowmanysmalltrianglesareusedtomakeTrapezium25? [Turn over

6 4 (a) Aboxofchocolatescontains10milkchocolatesand2plainchocolates. Sachaeats3chocolateschosenatrandomfromthebox. Thetreediagramshowsthepossibleoutcomesandtheirprobabilities. 6 First chocolate Second chocolate Third chocolate 8 10 milk milk milk plain plain milk 1 10 plain... milk 2 12 plain... milk plain milk... plain... plain (i) Completethetreediagram. [2] (ii) Expressingeachanswerasafractioninitslowestterms,findtheprobabilitythatSacha (a) eats3milkchocolates, (b) eats2milkchocolatesand1plainchocolateinanyorder. Answer...[2]

7 7 (b) Thefrequencydiagramshowsthedistributionofthenumberoflettersreceivedbyafamily eachdayovera31dayperiod Number of days Number of letters 6 thisdistribution,find (i) themode, (ii) themedian. [Turn over

8 5 (a) (i) 8 Exchangerate $1= 0.72 EddietravelsfromtheUSAtoGermany. Hechanges$300intoeuros( ). Howmanyeurosdoeshereceive? Answer...[1] (ii) WhenEddiereturnstotheUSAhehas 51leftthatheexchangesfor$75. Whatexchangeratehasbeenusedinthiscase? Answer $1=...[1]

9 9 (b) Gregbuys60gardenplantsatacostpriceof$2.00eachtosellinhisshop. Hesells25ofthemataprofitof75%and18ofthemataprofitof35%. Hesellstherestoftheplantsfor 4 5 ofthecostprice. (i) Calculatetheprofitorlosshemakesfromsellingthese60plants,statingifitisaprofit orloss. (ii) Findthepercentageprofitorloss. Answer Gregmakesa...of$...[3] Answer...%[1] [Turn over

10 10 6 (a) ABCDisatrapeziumwithBCparalleltoAD. B 9 C 18 A 7 E 55 D EisthepointonADsuchthatBEisperpendiculartoAD. BDA t =55,AE=7cm,BE=18cmandBC =9cm. Calculate (i) BAE t, Answer...[2] (ii) theareaofthetrapeziumabcd. Answer...cm 2 [4]

11 11 (b) P Q 112 S 41 R PQRSisanothertrapezium. PQR t =112 andprs t =41,eachmeasuredcorrecttothenearestdegree. FindthesmallestpossiblevalueofQRP t. Answer...[2] [Turn over

12 12 7 (a) InanathleticsmatchBenwonthe100mracein9.98sandCalvinwonthe200mracein 19.94s. Whatisthedifferenceintheiraveragespeeds? Giveyouranswerinmetrespersecond,correcttotwodecimalplaces. Answer... m/s[2] (b) Twocarseachcompleteajourneyof120km. Thefirstcarisdrivenatanaveragespeedofx km/h. Thesecondcarisdrivenatanaveragespeed3km/hfasterthanthefirstcar. Thefirstcartakes6minuteslongertocompletethejourney. (i) Writedownanequationinxandshowthatitsimplifiestox 2 +3x 3600=0. [3]

13 13 (ii) Solvetheequationx 2 +3x 3600=0,givingeachanswercorrectto onedecimalplace. (iii) Howmanyminutesdoesthefirstcartaketotravelthe120km? Answer x=...or...[3] Answer... minutes[2] [Turn over

14 14 Section B[48marks] Answerfourquestionsinthissection. Eachquestioninthissectioncarries12marks. 8 (a) f( x) Find = 4x (i) f( 2), Answer f( 2)=...[1] (ii) f 1 (x), Answer f 1 (x)=...[2] (iii) thevalueofgsuchthatf(2g)=g. Answer g=...[2]

15 15 (b) B A C E D BADandCAEarestraightlinesandBCisparalleltoED BA = c m, ED = c m and BA = BD (i) DescribefullythesingletransformationthatmapstriangleABContotriangleADE. Answer......[2] (ii) Calculate BA. (iii) FindCD. (iv) FisthemidpointofBD. FindEF. Answer [2] Answer [2] [Turn over

16 16 9 (a) Shape Iisacylinderwithradius4cmandheighthcm. ThevolumeofShape Iis1500cm 3. (i) Findh. 4 h Shape I Answer...[2] (ii) Shape Iismadebypouringliquidintoamouldatarateof0.9litresperminute. Findthenumberofsecondsittakestopourthisliquidintothemould. Answer... seconds[1] (b) Shape IIisaprismoflength8cmwithatriangularcross-section, shownshaded. Twosidesoftheshadedtriangleareatrightanglestoeachotherand havelengths5xcmand12xcm. GiventhatShape IIalsohasavolumeof1500cm 3,findx. 12x 5x 8 Shape II Answer...[2]

17 17 (c) Shape IIIisalsoaprismoflength8cmwithatriangularcross-section, shownshaded. Twosidesoftheshadedtriangleareatrightanglestoeachotherand havelengths5ycmand12ycm.thethirdsideisoflength13y cm. y satisfiestheequation4y 2 12y +16y 33=0. (i) Factorise4y 2 +16y y 5y 8 Shape III (ii) Hencesolvetheequation4y 2 +16y 33=0. (iii) Findtheareaoftheshadedtriangle. Answer y=...or...[1] (iv) FindthetotalsurfaceareaofShape III. Answer...cm 2 [1] Volume of (d) Find Volume of Shape III asafractioninitssimplestform. Shape II Answer...cm 2 [3] [Turn over

18 (a) Thetableshowssomevaluesofxandthecorrespondingvaluesofyfor y =. 2 x x y (i) Completethetable. [1] 6 (ii) Onthegriddrawthegraphof y = for 3GxG3. 2 x y x [2] (iii) yourgraphtofindthevaluesofxwheny=2. Answer x=...or...[1] (iv) Bydrawingatangent,findthegradientofthecurvewhenx=1.5. Answer...[2] 6 (v) Bydrawingasuitablelineonthegrid,solvetheequation 2 x x 2 = -. Answer x=...[2]

19 19 (b) Thegraphshowsasketchofy=5a x. y (4, b) (2, 45) P O x Twopointsonthecurveare(2,45)and(4,b). (i) Findthevaluesofaandb. Answer a=... b=...[2] (ii) Findthecoordinatesofthepoint,P,wherethegraphcrossesthey-axis. Answer (...,...)[1] (iii) FindthegradientofthestraightlinejoiningthepointsPand(2,45). [Turn over

20 11 (a) Thescalediagramshowsthepositions,AandB,oftwoboats. North 20 A B Scale: 1 cm to 50 m (i) Findtheactualdistancebetweenthetwoboats. Answer...m[1] (ii) AthirdboatispositionedatC,suchthatAC=350mandBC=300m. CiseastofthelineAB. rulerandcompassestofindc. [2] (iii) MeasurethebearingofCfromA. (iv) AfourthboatispositionedatD,suchthatACisthelineofsymmetryofthe quadrilateralabcd. CompletethequadrilateralABCD. [2]

21 21 (b) Thediagramshowsthepositions,P,QandR,ofthreebuoys. ThebearingofQfromPis054 o,pq=250m,qr=340mandpr=160m. Q North 250 P R (i) CalculatethebearingofRfromP. Answer...[4] (ii) CalculatetheareaoftrianglePQR. Answer... m 2 [2] [Turn over

22 22 12 (a) Thedistributionoftheweightsofluggagefor140passengersisshowninthetable. Weightof luggage (wkg) 01wG6 61wG10 101wG14 141wG16 161wG18 181wG22 221wG30 Frequency (i) Calculateanestimateofthemeanweightofluggage. Answer...kg[3] (ii) Onthegridopposite,drawahistogramtorepresentthisdata. [3] (iii) Estimatetheprobabilitythatapassenger,chosenatrandom,hasluggageweighingless than13kg. Answer...[2]

23 w Weight of luggage (kg) TURN OVER FOR THE REST OF THE QUESTION [Turn over

24 24 (b) Thepiechartrepresentsthedistributionofthebirthplacesofagroupof60students. Do not write in this margin Singapore South Africa Pakistan Australia United Kingdom (i) FindthenumberofstudentsinthegroupwhowereborninAustralia. (ii) CalculatethepercentageofstudentsinthegroupwhowereborninSouthAfrica. Answer...%[1] (iii) Fourmorestudentsjointhegroup. Ofthese,twostudentswereborninPakistan,oneinSingaporeandoneinChina. Anewpiechartistobedrawnusingtheinformationaboutthewhole groupofstudents. thenewpiechart,calculatetheangleofthesectorthatrepresentsthestudentsborn inpakistan. Giveyouranswercorrecttothenearestdegree. Answer...[2] Permissiontoreproduceitemswherethird-partyownedmaterialprotectedbycopyrightisincludedhasbeensoughtandclearedwherepossible.Everyreasonableefforthasbeen madebythepublisher(ucles)totracecopyrightholders,butifanyitemsrequiringclearancehaveunwittinglybeenincluded,thepublisherwillbepleasedtomakeamendsat theearliestpossibleopportunity. UniversityofCambridgeInternationalExaminationsispartoftheCambridgeAssessmentGroup.CambridgeAssessmentisthebrandnameofUniversityofCambridgeLocal ExaminationsSyndicate(UCLES),whichisitselfadepartmentoftheUniversityofCambridge.

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 6 3 1 7 7 7 6 4 0 6 * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 October/November 2013 Candidates answer