教你如何作笔试题math centre Numeracy大型外企业笔试必备.docx

教你如何作笔试题math centre Numeracy大型外企业笔试必备.docx

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教你如何作笔试题mathcentreNumeracy大型外企业笔试必备

ANumeracyRefresher

V2.January2005

ThismaterialwasdevelopedandtrialledbystaffoftheUniversityofBirminghamCareersCentreandsubsequentlyusedwidelythroughouttheHESector.ThecontributionsofTomFrank,EricWilliamsandClareWrightareparticularlyacknowledged.

www.mathcentre.ac.uk

©2004mathcentre

IMPROVE

YOUR

NUMERACY

UniversityofBristol

CareersAdvisoryService

INTRODUCTION

Manystudentsworryaboutanythingtodowithnumbers,havingdonelittlesincetheirGCSEs.Thisbooklethasbeendesignedtoofferpracticeandexplanationinbasicprocesses,particularlytoanyonefacingemployers’selectiontests.ItusesmaterialdevelopedbyClareWright,TomFrank,andEricWilliamsofBirminghamUniversityCareersCentre,whereithasbeensuccessfullyusedforsometime.

Regainingnumericalconfidencecantakealittlewhilebut,ifyouoncehadthebasicskills,practiceshouldbringthemback.If,however,youencounterrealproblemsperhapsyoushouldquestionyourmotives.Employersdon’ttestyoujusttomakelifedifficult.Theydoitbecausetheirjobsdemandaparticularlevelofproficiency.Ifyou’restrugglingtomeetthatlevel,ornotenjoyingit,istheirjobrightforyou?

CONTENTS

1.

Decimals……………………………………………………………………………………………….

page

2

2.

Fractions………………………………………………………………………………………………

5

3.

Approximations……………………………………………………………………………………

10

4.

Averages……………………………………………………………………………………………….

12

5.

Percentages………………………………………………………………………………………….

14

6.

Ratios…………………………………………………………………………………………………….

17

7.

Answers…………………………………………………………………………………………………

19

SECTION1-DECIMALS

Themostcommonuseofdecimalsisprobablyinthecostofitems.Ifyou’veworkedinashoporpub,you’reprobablyalreadyfamiliarwithworkingwithdecimals.

AdditionandSubtraction

Thekeypointwithadditionandsubtractionistolineupthedecimalpoints!

Example1

2.67+11.2=2.67

+11.20inthiscase,ithelpstowrite11.2as11.20

13.87

Example2

14.73–12.157=14.730againaddingthis0helps

-12.157

2.573

Example3

127.5+0.127=127.500

+0.127

127.627

Multiplication

Whenmultiplyingdecimals,dothesumasifthedecimalpointswerenotthere,andthencalculatehowmanynumbersweretotherightofthedecimalpointinboththeoriginalnumbers-next,placethedecimalpointinyouranswersothattherearethisnumberofdigitstotherightofyourdecimalpoint.

Example4

2.1x1.2.

Calculate21x12=252.Thereisonenumbertotherightofthedecimalineachoftheoriginalnumbers,makingatotaloftwo.Wethereforeplaceourdecimalsothattherearetwodigitstotherightofthedecimalpointinouranswer.

Hence2.1x1.2=2.52.

Alwayslookatyouranswertoseeifitissensible.2x1=2,soouranswershouldbecloseto2ratherthan20or0.2whichcouldbetheanswersobtainedbyputtingthedecimalinthewrongplace.

Example5

1.4x6

Calculate14x6=84.Thereisonedigittotherightofthedecimalinouroriginalnumberssoouransweris8.4

Check1x6=6soouranswershouldbecloserto6than60or0.6

Division

Whendividingdecimals,thefirststepistowriteyournumbersasafraction.Notethatthesymbol/isusedtodenotedivisioninthesenotes.

Hence2.14/1.2=2.14

1.2

Next,movethedecimalpointtotherightuntilbothnumbersarenolongerdecimals.Dothisthesamenumberofplacesonthetopandbottom,puttinginzerosasrequired.

Hence2.14becomes214

1.2120

Thiscanthenbecalculatedasanormaldivision.

Alwayscheckyouranswerfromtheoriginaltomakesurethatthingshaven’tgonewrongalongtheway.Youwouldexpect2.14/1.2tobesomewherebetween1and2.Infact,theansweris1.78.

Ifthismethodseemsstrange,tryusingacalculatortocalculate2.14/1.2,21.4/12,214/120and2140/1200.Theanswershouldalwaysbethesame.

Example6

4.36/0.14=4.36=436=31.14

1.1414

Example7

27.93/1.2=27.93=2793=23.28

1.2120

RoundingUp

Somedecimalnumbersgoonforever!

Tosimplifytheiruse,wedecideonacutoffpointand“round”themupordown.

Ifwewanttoround2.734216totwodecimalplaces,welookatthenumberinthethirdplaceafterthedecimal,inthiscase,4.Ifthenumberis0,1,2,3or4,weleavethelastfigurebeforethecutoffasitis.Ifthenumberis5,6,7,8or9we“roundup”thelastfigurebeforethecutoffbyone.2.734216thereforebecomes2.73whenroundedto2decimalplaces.

Ifweareroundingto2decimalplaces,weleave2numberstotherightofthedecimal.

Ifweareroundingto2significantfigures,weleavetwonumbers,whethertheyaredecimalsornot.

Example8

243.7684=243.77（2decimalplaces）

=240（2significantfigures）

1973.285=1973.29（2decimalplaces）

=2000（2significantfigures）

2.4689=2.47（2decimalplaces）

=2.5（2significantfigures）

0.99879=1.00（2decimalplaces）

=1.0（2significantfigures）

Trytheseexamples.Giveallyouranswersto2decimalplacesand2significantfigures

1.2.45+7.682.3.17+12.153.2.421+13.1

4.162.5+2.1735.12.5–3.76.9.6–7.8

7.163.5–2.1738.2.416–1.49.26.95–1.273

10.1.5x7.211.2.73x8.1412.6.25x17x3

13.2.96x17.314.4.2/1.715.53.9/2.76

16.14.2/6.117.2.5/0.0318.250/2.35

Answersonpage19

SECTION2-FRACTIONS

CancellingDown

Whenweuseafraction,weusuallygiveitinitssimplestform.Todothiswelookatthetop（thenumerator）andthebottom（denominator）andseeifthereisanumberbywhichbothcanbedividedanexactnumberoftimes.

Hence2=1x2=1sincethetwos“cancelout”

84x24

E.G.6=3x2=3

84x24

15=3x5=3

357x57

16=8x2=2OR16=4x4=4=2x2=2

248x33246x463x23

Useasmanystepsasyouneedtoreachtheanswer.

AddingFractions

Whenthedenominators（thebottomlines）areallthesame,yousimplyaddthetopline（numerators）

Eg:

2+3=2+3=55+3=5+3=8

66669999

Remembertocanceldownifnecessary.

Whenthedenominatorsaredifferent,weneedtochangethefractionssothatthedenominatorsarethesamethenwecanaddthetoplineasabove.

Supposewewishtocalculate1+1

24

Fromthecancellingdownprocess,weknowthat1=1x2=2

22x24

Thedenominatorsofbothfractionsarenowthesamesowecancalculate

1+1=2+1=2+1=3

244444

Sometimesthedenominatorsarenotmultiplesofeachother

Eg:

1+2

43

Inthiscasewecanmake12thecommondenominatorusing

1=1x3=32=2x4=8

44x31233x412

Wecanthenaddthesetwofractionsdirectly:

1+2=3+8=3+8=11

4312121212

Eg:

2+1=?

56

2=2x6=121=1x5=5

55x63066x530

2+1=12+5=12+5=17

5630303030

SubtractingFractions

Thisworksinthesamewayasaddition.Ifthedenominatorsarethesame,simplysubtractalongthetopline:

5-3=5–3=2=1x2=1

66663x23

12-1=12-3x1=12-3=12–3=9

155153x515151515

Cancellingdowngives9=3x3=3

153x55

NB:

analternativemethodwouldhavebeentocanceldown12/15to4/5initiallyleavinganeasiersumof4/5–1/5=3/5

MultiplicationofFractions

Itmayhelptounderstandmultiplicationifyouinterpretthe‘x’signas‘of’.

Hence:

1x2means1of2=1

25255

Thecalculationinvolvesmultiplyingbothnumeratorsandbothdenominatorsthencancellingdown:

Eg:

1x2=1x2=21=1

252x51055

4x2=4x2=8

535x315

7x3=7x3=21

11811x888

Notethatwhenmultiplying,youcancanceldownduringthesumaswellasatthefinalstage–itoftenmakesthecalculationeasier:

Eg:

31x2=2

133113

41x3=1x31=1x1=1

982932326

5x61=5x1=5

24474x728

DividingFractions

Thetrickwithdivisionoffractionsistoturnthesecondfractionupsidedownandthentomultiply:

Eg.21=2x5=10

35313

Notethatthisanswercanalsobewrittenas31/3

24=21x5=5

7574214

27=2x8=16

383721

ImproperFractions

Animproperfractionisonewherethenumeratorislargerthanthedenominator,eg.10/3

Toconvertthistoamixednumber（onecombiningawholenumberandafraction）,thinkof10/3inthefollowingway:

1

3

3x1/3=1sooutoftheten1/3’s,ninecanbegroupedintothreewholeunits,leavingonly1/3leftover.Hence,10/3=31/3

Similarly,12/5=22/5

16/11=15/11

21/15=16/15=12/5（bycancelling）

Wecanalsogofrommixednumberstoimproperfractions:

21/8=（2x8）+1=16+1=17

88888

31/4=（3x4）+1=12+1=13

44444

Additionofmixednumbers

Eg.2½+31/5=2+3+½+1/5

=5+5/10+2/10

=5+7/10

=57/10

17/8+52/3=1+5+7/8+2/3

=6+21/24+16/24

=6+37/24

=6+113/24

=713/24

MultiplicationandDivisionofmixednumbers

Here,itisusuallyeasiesttoconverttoimproperfractionsandmultiplyordivideasnormal:

Eg:

25/6x31/8=17/6x25/8=425/48=841/48

12/32¾=5/311/4=5/3x4/11=20/33

2½x41/31¼=5/2x13/35/4=5/2x13/3x4/5=260/30=26/3=82/3

Nowtrytheseexamples:

Notethatinthesequestions2/5isthesameas2

5

1.2/5+1/32.7/8–1/53.5/8+2/34.2/9+4/11

5.6/7–4/96.7/8–1/37.2½-15/88.7¼-52/3

9.24/5+67/810.2/3x4/511.8/9x1/312.7/12x4/5

13.8/92/314.2/114/515.6/79/816.2¼x3½

17.51/7x21/518.3