分析文凭计划du bi programa del elistama further mathematics paper 1 slOREF MATHEMATICS PAPER 1.pdf

M05/5/FURMA/SP1/ENG/TZ0/XX

IBDIPLOMAPROGRAMME

PROGRAMMEDUDIPLÔMEDUBI

PROGRAMADELDIPLOMADELBI

FURTHERMATHEMATICS

STANDARDLEVEL

PAPER1

Monday23May2005(afternoon)

1hour

INSTRUCTIONSTOCANDIDATES

Donotopenthiaminationpaperuntilinstructedtodoso.

Answerallthequestions.

Unlessotherwisestatedinthequestion,allnumericalanswersmustbegivenexactlyortothree

significantfigures.

2205-71013pages

–2–M05/5/FURMA/SP1/ENG/TZ0/XX

Pleasestarteachquestiononanege.Youareadvisedtoshowallworking,wherepossible.Wherean

answeriswrong,somemarksmaybegivenforcorrectmethod,providedthisisshownbywrittenworking.

Solutionsfoundfromagraphicdisplaycalculatorshouldbesupportedbysuitableworking,e.g.ifgraphs

areusedtofindasolution,youshouldsketchtheseaspartofyouranswer.

33

1.Giventhatf(x)=1+x,usetheMaclaurinseries,uptotheterminx,tofindanapproximatevalueof

31.2.Giveyouranswercorrectto5decimalplaces.

2.Provebymathematicalinductionthatatreewithnverticeshaactlyn−1edges,wheren∈+.

3.Considerthegroup(G,)withtheidentityelemente.Giventwoelementsaandbofthegroupsuch

that2anda2=b3=e,showthat

aba=b

(a)2;

ab=ba

2

2

(b)ab=e.

()

4.Thefollowingtabl