7/27/2019 Maths T STPM 2014 Sem 1 P1 Trial Pahang

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CONFIDENTIAL*

2014-1-PAHANG954/1

SectionA[45marks]

Answerallquestionsinthissection

1.

Thefunctionsfandgaredefinedby:

f:xax+4,

x

b

x

a

,

,

g:xax24x

,

x

,

4x

(a)

Byfindingthevaluesof

)1(g

and

)3(g

,explainwhytheinve

rsefunctiong-1(x

)isnot

defined

[2marks]

(b)

Giventhatthefun

ction

)(xf

go

isdefined,findtheminimum

valueofaandthe

maximumvalueo

fb.

[3marks]

2.(a)Evaluate

(

)

=

1001

1

3

3

r

r

r

,

giveyouranswerinthestandardform

n

A

10

.

[3marks]

(b)Express

x

x

3

1)

2(

4

+

intheformofincreasingpowerofxincludingthetermofx3.

Determinetherangeof

valuesofxsothatthisexpansionisvalid.

[6marks]

3.

MatrixPisinvertibleif

0

P

where

P

isthedeterminantofP

.

Thematrix

=

4

5

2

3

0

1

1

4

3

A

hasaninverse

1

A

because

10

4

5

2

3

0

1

1

4

3

=

.

(a)

Find

1

A

byusingthemethodofelementaryrowoperations.

[3marks]

(b)

Solvethefollowingsystemoflinearequationsbymethodofm

atricesthatinvolvesA

and

1

A

.

2

3

3

4

5

2

1

4

3

=

+

=

+

+

=

+z

x

z

y

x

z

y

x

[4marks]

(c)

Statethevalueof

(i)

4

5

4

3

0

2

1

4

6

(ii)

3

0

1

4

5

2

1

4

3

[2marks]

CONFIDENTIAL*

2

4.(a)Givenp(1+5i)2q=3+7i,

findthevaluesofpandqifpandqareboth

realnumbers.

[3marks]

(b)Expressthecomplexnumber

i+3

intheform

)

sin

(cos

i

r

+

,whereristhemodulusand

istheargumentofthecomplexnumber.

Hence,simplify

5

(3

).i+

[5marks]

5.

Showthatthetwocurves4x2+

9y2=36and4x2y2=4havethesamefoci

.

Forthehyperbola,statetheequ

ationsoftheasymptotes.

[6marks]

Sketchthecurves4x2+9y2=3

6and4x2y2=4onthesameaxes,showing

clearlythe

asymptotesofthehyperbola.

[4marks]

6.

ThepointsA,BandChavepo

sitionvectors

k

j

i

a

2+

+

=

,

k

j

i

b

4

2

3

+

+

=

and

k

j

i

c

4

4

+

=

respectively.

Find:

(a)

b

a

[1mark]

(b)

)

(

)

(

a

c

a

b

[3marks]

7/27/2019 Maths T STPM 2014 Sem 1 P1 Trial Pahang

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CONFIDENTIAL*

3

SectionB[15marks]

Answeranyonequestioninthissection

7.(a)ThepolynomialQ(x)is

definedbyQ(x)=x+mx+5xn.

IfQ(x)hasaquadratic

factor(x+5)andazeroof2,findthevaluesofmandn.

[3marks]

(b)Express

x

x

sin

2

cos

+

intheform

)

sin(

+x

R

whereRispositive

and

2

0