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DC (KN/SW) 64205/3 UCLES 2013 [Turn over

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSGeneral Certificate of Education Ordinary Level

READ THESE INSTRUCTIONS FIRST

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 AAnswer all questions.

Section BAnswer 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.For , use either your calculator value or 3.142, unless the question requires the answer in terms of .

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.

*0510348785*

MATHEMATICS (SYLLABUS D) 4024/21Paper 2 May/June 2013 2 hours 30 minutesCandidates answer on the Question Paper.Additional Materials: Geometrical instruments Electronic calculator

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SectionA[52marks]

Answerallquestionsinthissection.

1 (a) Solve4(x2)=7x.

Answer x=......................................... [2]

(b) Solvethesimultaneousequations. 2x+y=7 4x3y=19

Answer x=.........................................

y=......................................... [3]

(c) (i) Writedowntheintegervaluesthatsatisfy1n

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2 (a) Theinteriorangleofaregularpolygonis165o.

Howmanysideshasthepolygon?

Answer ............................................... [2]

(b)

D

B

C GEAF

p q

FAECG andADBarestraightlines.DEisparalleltoBC.

(i) FADt =pandAEDt =q. Findanexpressionintermsofpand/orqfor

(a) BCGt ,

Answer ............................................... [1]

(b) DBCt .

Answer ............................................... [1]

(ii) AE=7cm,EC=3cm,DE=5.6cmandDB=2.1cm.

(a) FindBC.

Answer ......................................... cm[1]

(b) FindAD.

Answer ......................................... cm[1]

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3 (a) Thediagramsshowparallelogramsmadefromsmalltriangles.

1Parallelogram 2 3 4 5

(i) Completethetablebelow.

Parallelogramm 1 2 3 4 5 6

Numberofsmalltriangles 2 4 6 8

[1]

(ii) Find an expression, in terms ofm, for the number of small triangles used tomakeParallelogramm.

Answer ............................................... [1]

(b) Thediagramsshowtrianglesmadefromthesamesmalltriangles.

1Triangle 2 3 4 5

(i) Completethetablebelow.

Trianglen 1 2 3 4 5 6

Numberofsmalltriangles 1 4 9 16

[1]

(ii) Find an expression, in terms of n, for the number of small triangles used to makeTrianglen.

Answer ............................................... [1]

(iii) Triangleqismadefrom324smalltriangles. Findq.

Answer ............................................... [1]

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(c) Thediagramsshowtrapeziumsmadefromthesamesmalltriangles.

1Trapezium 2 3

4Trapezium 5

(i) Bycomparingthediagramswiththoseinparts(a)and(b),findanexpression,intermsoft,forthenumberofsmalltrianglesusedtomakeTrapeziumt.

Answer ............................................... [1]

(ii) HowmanysmalltrianglesareusedtomakeTrapezium25?

Answer ............................................... [1]

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4 (a) Aboxofchocolatescontains10milkchocolatesand2plainchocolates. Sachaeats3chocolateschosenatrandomfromthebox. Thetreediagramshowsthepossibleoutcomesandtheirprobabilities.

milk

810

plain

milk

plain

milk

plain

milk

plain

milk........

........

........

........

........

........

plain

milk

plain

milk

plain

210

910

911

211

1012

212

110

Second chocolateFirst chocolate Third chocolate

(i) Completethetreediagram. [2]

(ii) Expressingeachanswerasafractioninitslowestterms,findtheprobabilitythatSacha

(a) eats3milkchocolates,

Answer ............................................... [1]

(b) eats2milkchocolatesand1plainchocolateinanyorder.

Answer ............................................... [2]

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(b) Thefrequencydiagramshowsthedistributionofthenumberoflettersreceivedbyafamilyeachdayovera31dayperiod.

00

1

2

3

4

5

6

7

8

9

1 2 3 4 5Number of letters

Numberof days

6

Forthisdistribution,find

(i) themode,

Answer ............................................... [1]

(ii) themedian.

Answer ............................................... [1]

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5 (a) (i)

Exchangerate

$1=0.72

EddietravelsfromtheUSAtoGermany. Hechanges$300intoeuros().

Howmanyeurosdoeshereceive?

Answer ............................................. [1]

(ii) WhenEddiereturnstotheUSAhehas51leftthatheexchangesfor$75.

Whatexchangeratehasbeenusedinthiscase?

Answer $1=.................................... [1]

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(b) Gregbuys60gardenplantsatacostpriceof$2.00eachtosellinhisshop. Hesells25ofthemataprofitof75%and18ofthemataprofitof35%. Hesellstherestoftheplantsfor 45 ofthecostprice.

(i) Calculatetheprofitorlosshemakesfromsellingthese60plants,statingifitisaprofitorloss.

Answer Gregmakesa...........................of$.....................[3]

(ii) Findthepercentageprofitorloss.

Answer ...........................................%[1]

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6 (a) ABCDisatrapeziumwithBCparalleltoAD.

A DE7

18

9

55

CB

EisthepointonADsuchthatBEisperpendiculartoAD. BDAt =55,AE=7cm,BE=18cmandBC =9cm.

Calculate

(i) BAEt ,

Answer ............................................... [2]

(ii) theareaofthetrapeziumABCD.

Answer .........................................cm2[4]

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(b)

S R

QP112

41

PQRSisanothertrapezium. PQRt =112andPRSt =41,eachmeasuredcorrecttothenearestdegree.

FindthesmallestpossiblevalueofQRPt .

Answer ............................................... [2]

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7 (a) InanathleticsmatchBenwonthe100mracein9.98sandCalvinwonthe200mracein19.94s.

Whatisthedifferenceintheiraveragespeeds? Giveyouranswerinmetrespersecond,correcttotwodecimalplaces.

Answer ......................................... m/s[2]

(b) Twocarseachcompleteajourneyof120km. Thefirstcarisdrivenatanaveragespeedofx km/h. Thesecondcarisdrivenatanaveragespeed3km/hfasterthanthefirstcar. Thefirstcartakes6minuteslongertocompletethejourney.

(i) Writedownanequationinxandshowthatitsimplifiestox2+3x3600=0.

[3]

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(ii) Solvetheequationx2+3x3600=0,givingeachanswercorrecttoonedecimalplace.

Answer x=..................or..................[3]

(iii) Howmanyminutesdoesthefirstcartaketotravelthe120km?

Answer ................................. minutes[2]

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SectionB[48marks]

Answerfourquestionsinthissection.

Eachquestioninthissectioncarries12marks.

8 (a) ( )f x x24 3

=-

Find

(i) f(2),

Answer f(2)=................................. [1]

(ii) f1(x),

Answer f1(x)=................................ [2]

(iii) thevalueofgsuchthatf(2g)=g.

Answer g=........................................ [2]

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(b)B

CA

E

D

BADandCAEarestraightlinesandBCisparalleltoED.

,BA ED BA BD12

123 4

1and=-

=-

=c cm m . (i) DescribefullythesingletransformationthatmapstriangleABContotriangleADE.

Answer..............................................................................................................................

...................................................................................................................................... [2]

(ii) Calculate BA .

Answer ............................................... [1]

(iii) FindCD .

Answer [2] (iv) FisthemidpointofBD. FindEF .

Answer [2]

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9 (a) ShapeIisacylinderwithradius4cmandheighthcm. ThevolumeofShapeIis1500cm3.

(i) Findh.

Answer ............................................... [2]

(ii) ShapeIismadebypouringliquidintoamouldatarateof0.9litresperminute. Findthenumberofsecondsittakestopourthisliquidintothemould.

Answer ................................. seconds[1]

(b) ShapeIIisaprismoflength8cmwithatriangularcross-section,shownshaded.

Twosidesoftheshadedtriangleareatrightanglestoeachotherandhavelengths5xcmand12xcm.

GiventhatShapeIIalsohasavolumeof1500cm3,findx.

Answer ............................................... [2]

h

4

Shape I

Shape II

12x

5x 8

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(c) ShapeIIIisalsoaprismoflength8cmwithatriangularcross-section,shownshaded.

Twosidesoftheshadedtriangleareatrightanglestoeachotherandhavelengths5ycmand12ycm.Thethirdsideisoflength13y cm.

y satisfiestheequation4y2+16y33=0.

(i) Factorise4y2+16y33.

Answer ............................................... [1]

(ii) Hencesolvetheequation4y2+16y33=0.

Answer y=..................or..................[1]

(iii) Findtheareaoftheshadedtriangle.

Answer ........................................cm2[1]

(iv) FindthetotalsurfaceareaofShapeIII.

Answer ........................................cm2[3]

(d) FindVolume ofVolume of

Shape IIShape III

asafractioninitssimplestform.

Answer ............................................... [1]

Shape III

12y

5y 8

13y

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10 (a) Thetableshowssomevaluesofxandthecorrespondingvaluesofyfor yx62

= .

x 3 2.5 2 1.5 1 1 1.5 2 2.5 3

y 0.96 1.5 2.67 6 6 2.67 1.5 0.96

(i) Completethetable. [1]

(ii) Onthegriddrawthegraphof yx62

= for3GxG3.

123 0 1 2 3 x

y

2

4

6

7

8

1

3

5

[2]

(iii) Useyourgraphtofindthevaluesofxwheny=2.

Answer x=..................or..................[1]

(iv) Bydrawingatangent,findthegradientofthecurvewhenx=1.5.

Answer ............................................... [2]

(v) Bydrawingasuitablelineonthegrid,solvetheequationx

x6 22= - .

Answer x=......................................... [2]

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(b) Thegraphshowsasketchofy=5a x.

O

P

y

x

(4, b)

(2, 45)

Twopointsonthecurveare(2,45)and(4,b).

(i) Findthevaluesofaandb.

Answer a=.........................................

b=......................................... [2]

(ii) Findthecoordinatesofthepoint,P,wherethegraphcrossesthey-axis.

Answer (.....................,.....................) [1]

(iii) FindthegradientofthestraightlinejoiningthepointsPand(2,45).

Answer ............................................... [1]

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11 (a) Thescalediagramshowsthepositions,AandB,oftwoboats.

A

North

Scale: 1 cm to 50 mB

(i) Findtheactualdistancebetweenthetwoboats.

Answer ............................................m[1]

(ii) AthirdboatispositionedatC,suchthatAC=350mandBC=300m. CiseastofthelineAB.

UserulerandcompassestofindC. [2]

(iii) MeasurethebearingofCfromA.

Answer ............................................... [1]

(iv) AfourthboatispositionedatD,suchthatACisthelineofsymmetryofthe quadrilateralABCD.

CompletethequadrilateralABCD. [2]

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(b) Thediagramshowsthepositions,P,QandR,ofthreebuoys. ThebearingofQfromPis054o,PQ=250m,QR=340mandPR=160m.

P

Q

R

54

North 250

340

160

(i) CalculatethebearingofRfromP.

Answer ............................................... [4]

(ii) CalculatetheareaoftrianglePQR.

Answer .......................................... m2[2]

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12 (a) Thedistributionoftheweightsofluggagefor140passengersisshowninthetable.

Weightofluggage(wkg)

01wG6 61wG10 101wG14 141wG16 161wG18 181wG22 221wG30

Frequency 15 14 20 24 31 24 12

(i) Calculateanestimateofthemeanweightofluggage.

Answer ........................................... kg[3]

(ii) Onthegridopposite,drawahistogramtorepresentthisdata. [3]

(iii) Estimatetheprobabilitythatapassenger,chosenatrandom,hasluggageweighinglessthan13kg.

Answer ............................................... [2]

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0 2 4 6 8 10 12 14 16Weight of luggage (kg)

18 20 22 24 26 28 w30

TURNOVERFORTHERESTOFTHEQUESTION

24

UCLES2013 4024/21/M/J/13

Do not write in this

margin

(b) Thepiechartrepresentsthedistributionofthebirthplacesofagroupof60students.

Singapore

Pakistan

48126

54 42

UnitedKingdom

Australia

South Africa

(i) FindthenumberofstudentsinthegroupwhowereborninAustralia.

Answer ............................................... [1]

(ii) CalculatethepercentageofstudentsinthegroupwhowereborninSouthAfrica.

Answer ............................................%[1]

(iii) Fourmorestudentsjointhegroup. Ofthese,twostudentswereborninPakistan,oneinSingaporeandoneinChina. Anewpiechartistobedrawnusingtheinformationaboutthewholegroupofstudents.

Forthenewpiechart,calculatetheangleofthesectorthatrepresentsthestudentsborninPakistan.

Giveyouranswercorrecttothenearestdegree.

Answer ............................................... [2]

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