页共三一学院预科课程数学入学期末feb14t2.pdfVIP

TRINITYCOLLEGEFOUNDATIONSTUDIES

MATHEMATICS2(FEBRUARYINTAKE)

SEMESTER1EXAMINATION

JUNE2014

Timeallowed:3hours.ReadingTime:10minutes

Thereare10questions.Totalmarksavailable:78

Alistofformulaeisattached.CalculatorsareNOTallowed.

Showworkingforeachofyoursolutions

1.Findthevalue(s)ofxsothatthesequencexx+3+x6is

(a)arithmetic

(b)geometric.

[3+3=6marks]

1

2.ConsiderthesetS=--–1:nN,whereNisthesetofnaturalnumbers.

n

(a)Whatistheadditiveidentity?

1

--

(b)Whatistheadditiveinverseof–?

2

(c)Whatisthemultiplicativeidentity?

1

--

(d)Whatisthemultiplicativeinverseof–?

2

(e)Giveacounter-exampletoshowthatSisnotclosedunderaddition.

[3+2+2+2+1=10marks]

1

z==i–1

3.(a)Simplify,where.

1+3i

(b)Convertyouranswertopart(a)topolarform.

6

(c)Hencefindzforzwrittenintermsoftheprincipalvalueofitsargument.

(WriteyouranswerinCartesi