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CONFIDENTIAL*

2014-1-NS-STPAUL-M

ARKINGSCHEME

MATHEMATICST954/1

Working

Marks

Note

1

D1

D1

[2]

Shape

Allcorrect

(a)

Substitute

intoy=kx

k=

M1

A1

[2]

(b)

A1

[1]

2(a)

Let

betwopointsonthe

curve,

TheGradientofPQ

EquationofchordPQ

(p2q+pq2)y+2x=2(p2+q2+pq)

Chordtangentwhe

nq=p,

EquationoftangentatPis

2p3y+2x=2(p2+p2

+p2)

M1

A1

M1

A1

[4]

Mustbesimplified.

(b)

B1

B1

[2]

Mustbeincoordinates

(c)

Mid-pointofQR(

8xy2

=27

Cartesianequationof

themid-pointofQRis

8xy2

=27

B1

M1

A1

[3]

Findthemid-point

Substituteoreliminatep

3-

-3-

+

-

+

x

y

CONFIDENTIAL*

2

3(a)

B1

CorrectAM

M1

M1

Equationsareconsistentif

k=3

A1

A1

[5]

Row-

echelonform

(b)

GeneralSolution,

B1

M1

A1

[3]

4(a)

sin

cos

1

i

z

=

2

sin

2

cos

2

i

z

+

=

2

sin

2

cos

12

i

z

=

cos

2

)

sin

(co

s

)

sin

(cos

1=

+

+

=

+

i

i

z

z

2

cos

2

)2

sin

2

(cos

)2

sin

2

(cos

12

2

=

+

+

=

+

i

i

z

zSquarebothsidesof

cos2

1=

+

z

z

B1

B1

M1

A1

A1

[5]

M1

(onecorrect)

(allcorrect)

(find

z

z

1+and

2

2

1z

z

+

)

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CONFIDENTIAL*

3

1

2

cos

cos

2

cos

4

2

2

cos

2

cos

4

2

1

)

cos

2(

12

2 2

2

2

2

2

+

=

=

+

=

+

+

=

+

z

z

z

z

A1

[2]

5

SolveforA,BandC

A=2,B=-1,C=-1

=2-2x+2x21

+x2-x+...

=13x+3x2+...

M1

M1

A1

M1

M1

A1

[6]

M1

M1

A1

[3]

6(a)

=

=

M1

A1

[2]

(b)

B1

M1

CONFIDENTIAL*

4

A1

[3]

(c)

ExactAreaofParallelogramOAPB

=

=

M1

A1

[2]

7(a)

1sttermofGP=1sttermofA

P=a

2nd

termofGP=4thtermof

AP

ar=a+3d

.....(1)

3rd

termofGP=6thtermofA

P

ar2=a+5d......(

2)

B1

B1

M1

M1

A1

[5]

Substi

tute(1)into(2)

ortrytoeliminatea

(b)

(3r2)(r1)=0

Since

thegeometryseriesisconvergent.

M1

A1

A1

M1

A1

[5]

(c)

SinceS>4a

n219n+72