7
CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/42 Paper 4 (Extended), maximum raw mark 120 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.theallpapers.com

0607 CAMBRIDGE INTERNATIONAL MATHEMATICS (0607)/0607_s13... · 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS ... n 1 e th)− 2 6 ww o. ro 2 ... www 3 3 M1 for 9882 + 10602 – 2 × 988

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Page 1: 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS (0607)/0607_s13... · 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS ... n 1 e th)− 2 6 ww o. ro 2 ... www 3 3 M1 for 9882 + 10602 – 2 × 988

CAMBRIDGE INTERNATIONAL EXAMINATIONS

International General Certificate of Secondary Education

MARK SCHEME for the May/June 2013 series

0607 CAMBRIDGE INTERNATIONAL MATHEMATICS

0607/42 Paper 4 (Extended), maximum raw mark 120

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

www.theallpapers.com

Page 2: 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS (0607)/0607_s13... · 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS ... n 1 e th)− 2 6 ww o. ro 2 ... www 3 3 M1 for 9882 + 10602 – 2 × 988

1

2

(a

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a) (

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2

4

5

7

9

2

7

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3

2

27.2

49 :

500

748

9 o

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7

2

+y

y

3 ×

5

1

2 (

: 45

0

8.8[

or 8

2( x

1=

+

y

2y

o.

(27

5 f

[0]

8.83

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3

1=

= y

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.22

fina

ca

3 (

)1

3

1

y +

2…

al a

ao f

8.8

3=

+ 1

)

answ

fina

829

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o.e

wer

al a

to

( +x

e.

IG

©

r

answ

8.8

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or

GC

Ca

wer

830

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bet

M

SE

amb

r

0)

o.e

tter

Mar

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brid

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r

rk S

M

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ay/

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che

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nter

eme

une

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e 2

tion

201

nal

13

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1

2

3

2

3

M2

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2

1

1

1

mina

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o

a

o

M

o

M

÷

S

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o

o

M

o

If

m

B

o

i.

y

atio

SC1

or B

answ

or 2

M2

or M

M1

÷ 12

SC2

M2

Allo

or M

or 6

M2

or M

f M

mis

B1

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y =

ons

1 fo

B1 f

wer

27.2

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M1

for

2 d

2 fo

for

ow

M1

650

for

M1

M0,

sin

for

fina

corr

5

1

s 20

or a

for

r)

2 (2

r 72

for

r 72

oes

or a

r lo

1.5

for

mu

r gr

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, B1

ng b

r x2

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013

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r 18

27.2

20

r 72

20

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og (

54

r 65

ulti

rap

r gr

1 fo

brac

2=

nsw

ct eq

S

3

we

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22.

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20

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ot s

we

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for

50

ipli

phs

rap

or

cke

x7=

wer

qua

Syll

06

er 4

see

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1.4

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er 8

000

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ied

tha

ph o

2x

ets

x

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atio

lab

607

45:4

n (

: 25

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144

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oil m

8.85

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000

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d by

at i

of y

2( xx

if c

o.e

, 7

on w

bus

7

49 o

ma

5 o

o.e.

4%

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met

5

50)

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5n =

y 1.

inte

y =

+x

corr

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wit

s

or

ay b

o.e.

se

im

tho

÷ l

50

= 1

.05

erse

= 1.

)1+

rec

or 2

tho

1.0

be i

en

mp

od

log

in m

100

at

ect

.05x

or

ct ex

2(2

ut f

09 (

imp

plie

g(1.

me

00

lea

as x

3r x

xpa

2x +

fra

P

(1.0

plie

d b

.05

etho

ast

sho

(xx

ans

+ 1)

ctio

Pa

4

088

ed b

by 7

)

ods

twi

ow

+x

sion

) =

ons

pe

42

8 to

by

749

.

ice

wn

)3

ns f

3(x

s le

er

o 1.

the

9.

co

Co

foll

x +

eadi

089

eir r

orre

ond

low

+ 3)

ing

9)

rati

ectl

done

w

) o.

g to

io

y

e

e.

www.theallpapers.com

Page 3: 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS (0607)/0607_s13... · 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS ... n 1 e th)− 2 6 ww o. ro 2 ... www 3 3 M1 for 9882 + 10602 – 2 × 988

3

(c

(a

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(i

a)

b) (

(i

age

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ii)

(i)

ii)

e 3

1

w

2

b

o

w

w

3

y

R

3

w

10

10

+w

bett

or

(ww

2w

3 h

=y

Rul

so

9

0

+

(10

ter

90

+w

9+

20

−=

led

oi

s

(w

9

0

+

9w

mi

−x

lin

soi

9+

)=

3−w

in

1−

ne th

)9 −

2=

36

ww

o.

hro

2×−

2

1

=

ww

.e. f

oug

10×

o.

0

w

fin

gh (

IG

©

0w

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al a

(– 2

GC

Ca

5=

ans

2, 0

M

SE

amb

5w

swe

0) a

Mar

E –

brid

(ww

er

and

rk S

M

dge

9+

d (0

Sc

ay/

e In

))9

, 4)

che

/Ju

nter

o.e

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eme

une

rnat

e. o

e

e 2

tion

or

201

nal

2

13

Ex

B1

B1

M1

E1

4

2

2

2FT

xam

1

1

1

1

T

mina

If

w

i.

c

a

a

i.

E

li

B

M

q

c

o

a

s

s

T

tr

(u

B

h

B

B

B

o

o

F

S

atio

f no

wx =

.e.

corr

allo

also

.e.

Esta

ine

B3

M2

qua

com

or M

a +

ubs

imp

Tria

rial

unl

B1 F

hou

B1

B1

B1

or

or ti

FT

SC1

ons

ot s

= 1

cor

rect

w

o al

cor

abli

e wi

for

for

dra

mple

M1

b =

stit

plif

al a

ls f

less

FT

urs a

for

for

for

iny

on

1 fo

s 20

see

0 i

rrec

t fo

10(

llow

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ish

ith

r w

r (w

atic

etin

for

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tuti

fyin

and

for

s co

T fo

and

r y

r ru

r

y pa

ly i

or c

013

en o

is n

ct m

orm

(w +

w o

ct c

hed

no

= 3

+w

c sh

ng

r (w

or

ons

ng

im

com

orre

or 1

d m

−=

uled

art n

if p

corr

S

3

only

not

mul

mat

+ 9

over

coll

wi

err

3 or

12+

how

sq

w +

sk

s in

or

mpro

mp

ect

0 ÷

minu

x−

d lin

not

pos

rec

Syll

06

y im

suf

ltip

9) –

r co

lect

ith

ror

r fo

)(2 w

wing

quar

)a+

ketc

n qu

(w

ove

pari

t an

÷ th

ute

c+

ne t

t sh

itiv

ct a

lab

607

mp

ffic

plic

– 10

om

tion

at l

rs o

or w

−w

g z

re r

)(w

ch o

uad

+w

em

son

nsw

heir

s

c o.

thr

had

ve g

rea

bus

7

lied

cien

cati

0w

mmo

n o

leas

or o

w =

)3−

zero

reac

w +

of q

drat

) 22

9

ent

n o

wer

r po

e.

oug

ded

gra

a un

s

d b

nt.

on

= 2

on d

of tw

st o

omi

= 3

or

os o

chi

)b

qua

tic 2−

t –

f di

fou

osi

o

gh

die

nsh

by f

of

2.5

den

wo

one

issi

or

go

or q

ing

wi

adra

for

4

81−

allo

ista

und

tiv

r y

(0,

ent

hade

furt

f an

w(w

nom

ter

e m

ons

– 1

ood

qua

g −

ith

atic

rmu

3=

ow

anc

d w

e ro

=y

, 4)

and

ed

P

ther

eq

w +

min

rms

more

s

12

sk

adra

9 ±

ab

c or

ula

36 o

w M

ces

with

oot

kx

or

d c

Pa

4

r w

quat

+ 9

nato

s

e in

w

ketc

atic

2

±

= –

r co

be

o.e

M2 f

and

h 1

t co

1−

r gr

uts

pe

42

work

tion

) o

or

nter

ww

ch o

c fo

22

– 3

orre

efor

e.

for

d ti

or 2

orre

1 o

adi

s x-

er

kin

n in

.e.

rme

w

of

orm

5

36 o

ect

re

at

ime

2 tr

ectl

o.e.

ient

axi

ng.

n th

edia

mula

or

lea

es

rial

ly i

. se

t of

is

e.g

he

ate

a or

ast 3

ls)

into

een

f 2

g.

r

3

o

n

www.theallpapers.com

Page 4: 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS (0607)/0607_s13... · 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS ... n 1 e th)− 2 6 ww o. ro 2 ... www 3 3 M1 for 9882 + 10602 – 2 × 988

Page 4 Mark Scheme Syllabus Paper

IGCSE – May/June 2013 0607 42

© Cambridge International Examinations 2013

(c) 73 −= xy o.e. 3 B2 for cxy += 3 o.e. or 7−= kxy o.e.

or M1 for rise/run = 13

42

−−

o.e.

and M1 for correct method for finding c

Answer 3x – 7 implies M1 M1

4 (a) 125.7 or 126 2 M1 if at least 2 mid-values seen (60, 125 and

195)

or 2 from 1680, 5625, 5265 or sum of 12570

(b) Columns from 100 to 150 and 150 to 240

Heights 0.9 and 0.3

1

1,1

Accept freehand

5 (a) 534.6… www 3 3 M1 for 9882 + 10602 – 2 × 988 × 1060 cos 30

A1 for 285800 to 285802 or 286000

(b)

99811852

5359981185][cos

222

××

−+=

26.6 (26.62 to 26.65)

M2

A1

Allow use of 534.6… for 535

M1 for correct implicit statement

Strictly dependent on at least M1

SC2 if correct without working

(c) 353 (353.3 to353.4) 1FT FT 380 – their (b) only if answer between 270

and 360.

6 (a) 720 2 M1 for 0.5 × 12 × 6 × 20 o.e.

(b) (i)

700 (700.2 to 700.4)

4 Allow 432 + 120 5 as final answer for full

marks

M1 for [BC2]= 122 + 62

M2 for BC × 20 + 12 × 20 + 6 × 20 + 2 × area

triangle ABC

or M1 if one of the five areas missing or is

incorrect

(ii) 3.5[0] (3.501 to 3.502) 1FT FT their (i) × 0.005

(c) 14.4 (14.42 to 14.43) 3 M1 for 202 + 122 (544) or 202 + 122 + 62 (580)

(Square roots 23.323…, 24.08…)

M1 for tan = 22

1220

6

+their

or

sin = 222

61220

6

++their

or cos = 222

22

61220

1220

++

+

their

their o.e.

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7

8

9

(a

(b

(c

(a

(b

(a

(b

(c

Pa

a)

b)

) (

(i

a)

b)

a)

b)

)

age

(i)

ii)

e 5

[

6

7

0

0

x

x

x

9

9

9

5

0]6

669

752

0.41

– 1.

0.7

x Y

x >

x Y

9.18

9.77

9.02

6 30

9 (6

24

1

.49

798

Y –1

0

Y=0.

8 (9

7 or

2 to

0 o

669

cao

(–

(0

1.4

798

9.1

r 9

o 9.

o.e.,

9.0

o fi

1.4

0.79

9 o

8 o

77…

.78

.03

, [F

to

inal

496

976

or –

or 0

…)

8 (9

3

Feb

66

l an

6 to

6…

–1.4

0.79

)

9.77

b] 9

9.1

nsw

o –

…)

496

976

73 t

IG

©

9th

1)

wer

1.4

6 to

6…

to 9

GC

Ca

494

o –1

9.7

M

SE

amb

4)

1.4

75

w

Mar

E –

brid

94

….

ww

rk S

M

dge

.)

w 4

Sc

ay/

e In

che

/Ju

nter

eme

une

rnat

e

e 2

tion

201

nal

2

1

1

13

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3

1

1

2FT

B2

B1

B1

1FT

1

1FT

3

2

4

xam

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2

1

1

T

T

mina

B

B

o

s

F

0

B

S

o

C

F

F

M

o

w

M

A

e

M

o

M

atio

B1

B2

or M

een

FT

0.40

B1

Ske

or a

Con

FT

FT

M2

82

or M

with

M1

Allo

exac

M3

or M

M1

ons

for

for

M1

n

the

089

for

etch

a di

ndo

the

the

for2+

M1

hou

for

ow

ct

for

M1

for

(3

s 20

r [F

r [0

for

eir

9…

r po

h co

ffe

one

eir

eir

r 2

82

+

for

ut s

r 3

7

9

28

r 3

7

for

r 0

9.0

013

Feb]

]6

r 27

(d)

i.e

oor

ould

ren

< f

(a)

(a)

× 8

r

A

squa

360

70

9

360

70

r 3

7

.5 ×

09 t

S

3

] 9t

30

72

1

)(i)

no

qu

d b

nt fu

for

if

if

8 ×

8.2

8

2

AB

are

0×π

o.e

0×π

360

70

× 8

to 3

Syll

06

th.

o.e

+

÷

ot 2

uali

be w

func

r Y

on

on

× si

8.8

B

=

e ro

×π

e. a

×π

0×π

8 ×

39.

lab

607

e.

13

184

2 dp

ty s

with

ctio

etc

e n

e p

n35

cos

sin

oot

16×

as f

×π

8 s

10…

bus

7

so

400

p

ske

h d

on e

c

nega

posi

5 o

70s

n 35

6o.e

fina

8× a

sin7

…)

s

i or

0 B

etch

diffe

e.g

ativ

itiv

o.e.

0 (

5 o.

e.

al a

0.5

and

70

)

r B

1F

h

fere

g. y

ve r

ve r

. e

( 8

e.

ans

5 ×

d

o.e

B1 f

FT f

ent w

=y

roo

root

.g.

.84

or

we

8 ×

e.

(

P

for

for

win

2

x

ot

t

22.

r ab

er b

× 8

(30

Pa

4

17

0.4

ndo

− x

....

bov

but

sin

.1 o

pe

42

30

409

ow.

3−x

)

ve e

mu

n70

or 3

er

0 o

9 or

.

2−

exp

ust

0 o

30.

or 0

r

2

[1

pres

be

o.e

.07

3 0

14]

ssio

.

….

00

on

..)

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Page 6: 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS (0607)/0607_s13... · 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS ... n 1 e th)− 2 6 ww o. ro 2 ... www 3 3 M1 for 9882 + 10602 – 2 × 988

10

11

0 (a

(b

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(f)

(g

(a

(b

Pa

a) (

(i

b)

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d)

) (

(i

)

g)

a) (

(i

(ii

b) (

(i

age

(i)

ii)

(i)

ii)

(i)

ii)

ii)

(i)

ii)

e 6

x

(

7

2

0

4

C

1

3

6

x =

180

720

2

0 Y

–2 Y

42.9

Cor

6

4

6

2

1 o

6

5,

36

1

18

0, –

0

Y g(

Y g

9 (4

rrec

o.

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6

1

cao

0

– 1

(x)

g(x

42.

ct a

.e.

.e.

.

an

o

)

Y

) Y

94…

area

nd

2

Y 2

…)

a sh

6

5,

), 3

had

6

1

17

ded

an

IG

©

(3

.

nd

GC

Ca

17.

6

5

M

SE

amb

.0 t

Mar

E –

brid

to 3

rk S

M

dge

317

Sc

ay/

e In

7.1)

che

/Ju

nter

)

eme

une

rnat

e

e 2

tion

201

nal

13

Exxam

minaatio

1

1

ons

2

2

1

1,1

1

1

1

1

1,1

1

1

1

1

2

2

s 20013

B1

B1

Co

Co

Co

Co

or

in

Fo

pe

fo

Do

ca

Do

SC

B1

po

M

(0

0.

S

3

1 fo

1 fo

ond

ond

ond

ond

r y f

equ

or a

erc

or 3

o n

anc

o n

C1

1 fo

osit

M1 f

0.02

027

Syll

06

or i

or i

don

don

don

don

for

ual

all

cent

3 sf

not

cell

not

for

or a

tion

for

278

778

lab

607

ina

ina

ne π

ne π

ne 4

ne s

g(x

itie

pa

tag

f.

pe

ing

ac

r 0.

any

n

the

8 or

8)

bus

7

ccu

ccu

π f

π f

4 π

stri

x) a

es in

arts

ges

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Page 7: 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS (0607)/0607_s13... · 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS ... n 1 e th)− 2 6 ww o. ro 2 ... www 3 3 M1 for 9882 + 10602 – 2 × 988

Page 7 Mark Scheme Syllabus Paper

IGCSE – May/June 2013 0607 42

© Cambridge International Examinations 2013

(iii)

36

11cao

2 M1 for 1 –6

5

6

5theirtheir ×

(0.306 or 530.0 or 0.3055 to

0.3056)

or 6

5

6

1

6

1×+

or (ii) + 2 × 6

5

6

1theirtheir ×

or 6

1

6

1theirtheir × + 2 ×

6

5

6

1theirtheir ×

(c) 5 2 SC1 for answer of 4 or 65 = 7776

seen or 54 = 625 seen

or M1 for attempted products of

1,6

1

6

5>×

ktheirtheir

k

12 (a) 18.75 (18.7 or 18.8)

18.5

23.5

13

1

1

1

1

(b) (i) r = –4.31t + 120 2 – 4.313…., 120.0…. B1 for

r = –4.31t + c or r = kt + 120

Allow x for t

(ii) Negative 1

(iii) 25 (25.1 to 25.4) 1FT FT their equation only if linear

13 (a) 3

2p + 3

1q o.e.

2 M1 for correct route from O to X or

PQ = q – p o.e. or correct

unsimplified answer

(b) –

3

2p + 3

5q o.e.

3 B2 for kp + 3

5q or –

3

2p + kq,

k≠ 0 or correct unsimplified

expression or

M1 for correct route from X to Y

or –3

2p + mq + nq, m 0,0 ≠≠ n

(c) 4± 1,1 If 0 scored , M1 for 22253 =+ k

o.e.

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