Mark Scheme Summer 2008 - Higher Grade Maths · 4400 IGCSE Mathematics Summer 2008 Summer 2008...
46
Mark Scheme Summer 2008 IGCSE IGCSE Mathematics (4400) Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH
Transcript of Mark Scheme Summer 2008 - Higher Grade Maths · 4400 IGCSE Mathematics Summer 2008 Summer 2008...
Mark Scheme Summer 2008
IGCSE
IGCSE Mathematics (4400)
Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH
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Summer 2008
Publications Code UG020267
All the material in this publication is copyright © Edexcel Ltd 2008
4400 IGCSE Mathematics Summer 2008
Contents
1. 4400/1F 5
2. 4400/2F 13
3. 4400/3H 21
4. 4400/4H 37
4400 IGCSE Mathematics Summer 2008
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
5
Sum
mer
2008 IG
CSE M
ath
s M
ark
Schem
e –
Paper
1F
Q
Work
ing
Answ
er
Mark
N
ote
s
1.
(a)
7006
1
B1
cao
(b
)
9000
1
B1
cao
(c
)
hundre
ds
1
B1
Accept
500,
100
(d
)
326
1
B1
cao
Tota
l 4 m
ark
s
2.
(a)(
i)
cuboid
1
B1
Accept
recta
ngula
r box
(i
i)
pri
sm
1
B1
Condone o
mis
sion o
f ‘p
enta
gonal’
(i
ii)
cone
1
B1
(b
)
8
1
B1
cao
Tota
l 4 m
ark
s
3.
(a)
Egypt
and M
ala
ysi
a
1
B1
(b
)(i)
20
3
B1
cao
(i
i)
100
20
M
1
for
100
20
""
51
A1
ft f
rom
“20”
(c
)
14
1
B1
Accept
13 o
r 14
(d
)(i)
Kenya
2
B1
(
ii)
0.4
3
B1
cao
(e
)(i)
35 <
bar<
40
2
B1
(
ii)
61
B1
cao
Tota
l 9 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
6
4.
(a)
1
B1
(b
) 10 ×
2 +
1
2
M1
21
A1
cao
(c
)
2
137−
2
M1
18
A1
cao
(d
) eg 6
0 is
even,
num
ber
of
stic
ks
is a
lways
odd,
firs
t num
ber
is o
dd a
nd 2
is
added e
ach t
ime,
mult
iply
ing b
y 2
and a
ddin
g 1
will alw
ays
giv
e a
n
odd n
um
ber
of
stic
ks
1
B1
May r
efe
r to
num
ber
sequence o
f st
ick p
att
ern
– n
eed n
ot
do b
oth
(e
)
n =
2p +
1
3
B3
for
n =
2p +
1 o
e
eg n
= p
2 +
1,
1 +
p ×
2 =
n
B2 f
or
2p +
1 o
e B
1 f
or
n =
lin
ear
functi
on o
f p e
g n
= p
+ 1
Tota
l 9 m
ark
s
5.
(a)
25 −
18
2
M1
for
25 −
18,
18-2
5,
18 t
o 2
5 e
tc
7
A1
cao
(b
) 18 1
9 2
1 2
2 2
3 2
4 2
4 2
5
or
22,
23 o
r 28
or
4 o
r 29
or
4½
2
M1
Als
o a
ward
for
18 1
9 2
1 2
2 2
3 2
4 2
5
i.e.
wit
h o
ne 2
4 o
mit
ted
22.5
A1
cao
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
7
6.
(a)
24
2
B2
B2 f
or
23-2
5 inc B
1 f
or
22 o
r 26
(b
) 6 ×
2 +
(2
05
4.
.±
) × 2
oe
2
M1
for
6 ×
2 +
(2
05
4.
.±
) × 2
oe
20.6
-21.4
A1
for
20.6
-21.4
inc
SC if
M0,
aw
ard
B1 f
or
20
(c
)
0
1
B1
Accept
‘none’,
‘zero
’
(d
)
2
1
B1
cao
(e
)(i)
115°-1
19°
2
B1
(i
i)
obtu
se
B1
(f
)
4 ,
3
2
B2
B1 f
or
4 B
1 f
or
3
Tota
l 10 m
ark
s
7.
(a)
2p
1
B1
Accept
p2,
2 ×
p e
tc
(b
)
4xy
1
B1
Accept
xy4,
4×
xy e
tc
(c
)
9g −
5h
2
B2
B1 f
or
9g B
1 f
or −
5h o
r + −
5h
Tota
l 4 m
ark
s
8.
(a)(
i)
27
1
B1
cao
(i
i)
20
1
B1
cao
(i
ii)
25
1
B1
cao
(i
v)
23
1
B1
cao
(b
)
95
2
M1
A1
fracti
on w
ith
denom
inato
r of
9
num
era
tor
of
5
or
B2 f
or
0.5
5,
0.5
6,
55%,
56% o
r bett
er
but
not
for
0.6
, 60%
B1 f
or
5 in 9
, 5 :
9
5 o
ut
of
9
Tota
l 6 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
8
9.
(a)
188
, 27
12
etc
1
B1
(b
) 65 ÷
5 o
r 13 o
r 4 ×
65 o
r 260
2
M1
52
A1
cao
(c
) 0.8
75
0.9
0.8
5
0.8
8
2
M1
2 f
racti
ons
convert
ed t
o d
ecim
als
or
perc
enta
ges
or
fracti
ons
wit
h t
he s
am
e d
enom
inato
r
109
25
22
87
20
17
A1
SC if
M0,
aw
ard
B1 f
or
3 f
racti
ons
in c
orr
ect
ord
er
Tota
l 5 m
ark
s
10.
180 −
2 ×
73 o
e
3
M2
for
180 −
2 ×
73 o
e
M1 f
or
unm
ark
ed b
ase
angle
identi
fied a
s 73° o
r 146° s
een
34
A1
cao
Tota
l 3 m
ark
s
11.
(a)(
i)
6859
2
B1
cao
(
ii)
6860
B1
cao
(b
)
4.2
28
.17
2
M1
for
17.2
8 o
r 2.4
or −
0.1
14..
. s
een
7.2
A1
for
7.2
oe inc
517
and
536
Tota
l 4 m
ark
s
12.
2 a
rcs,
radiu
s 6 c
m,
centr
es
A a
nd B
2
M1
tria
ngle
wit
hin
guid
elines
A1
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
9
13.
(a)
23500
1008
4×
. o
r 1128
3
M1
23 5
00 +
“1128”
M1
(dep)
or
M2 f
or
23 5
00 ×
1.0
48 o
e
24 6
28
A1
cao
(b
) 29 8
32 −
28 2
50 o
r 1582
3
M1
Als
o a
ward
for
15.8
2
100
28250
1582
× o
r 100
29832
1582
×
M1
for
28250
1582
or
29832
1582
or
0.0
56
or
0.0
53…
or
M1 f
or
28250
29832
or
1.0
56
or
105.6
M
1 f
or
“1.0
56” −
1
or
“105.6
” −
100
or
M1 f
or
29832
28250
or
0.9
469..
. or
94.6
9..
. M
1 f
or
1 −
“0.9
469”
or
100 −
“94.6
9”
5.6
A1
cao (
Do N
OT a
ward
for
5.3
)
Tota
l 6 m
ark
s
14.
2
60
1.
−
2
M1
for
1 −
0.6
or
0.4
or
2x w
here
0 <
x <
1
0.2
oe
A1
for
0.2
oe
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
10
15.
(a)
Enla
rgem
ent
scale
facto
r 2 c
entr
e (
1,
3)
3
B3
B1 f
or
enla
rgem
ent,
enla
rge e
tc
B1 f
or
2,
× 2
, tw
o,
12,
1 :
2,
2 :
1
B1 f
or
(1,
3)
Condone o
mis
sion o
f
bra
ckets
but
do n
ot
accept
⎟⎟ ⎠⎞⎜⎜ ⎝⎛ 31
(b
) Refl
ecti
on in t
he lin
e y
= x
2
B2
B1 f
or
refl
ecti
on,
refl
ect
etc
B1 f
or
y =
x o
e
inc e
g ‘
in lin
e f
rom
(2,2
) to
(5,5
)’,
‘in
dott
ed lin
e s
how
n’
These
mark
s are
in
dependent
but
aw
ard
no
mark
s if
answ
er
is n
ot
a s
ingle
tr
ansf
orm
ati
on
Tota
l 5 m
ark
s
16.
3 +
1 o
r 4 s
een
2
M1
for
3 +
1 o
r 4 s
een
210
A1
for
210 c
ao
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
11
17.
(a)(
i)
1,
9,
17
2
B1
cao
(
ii)
1,
5,
9,
13,
17,
25,
33
B1
cao (
B0 if
1 o
r 9 o
r 17 r
epeate
d)
Bra
ckets
not
necess
ary
(b
) eg N
o m
em
bers
in c
om
mon.
The inte
rsecti
on is
em
pty
. N
one o
f th
e m
em
bers
of
A &
C a
re t
he s
am
e.
They d
on’t
have t
he s
am
e n
um
bers
. N
o n
um
bers
are
in b
oth
A a
nd C
.
1
B1
Tota
l 3 m
ark
s
18.
(a)
2
38×
oe
2
M1
for
2
38×
oe
12
A1
cao
(b
) 375
.0
83ta
n=
=°
x
3
M1
A1
for
tan
for
83 o
r 0.3
75
or
M1 f
or
sin f
ollow
ing
corr
ect
Pyth
agora
s and
A1 f
or
0.3
511..
. or
M1 f
or
cos
follow
ing
corr
ect
Pyth
agora
s and
A1 f
or
0.9
363..
.
20.6
A1
for
20.6
or
bett
er
(A
ccept
20.5
5604…
rounded o
r tr
uncate
d t
o 4
sig
fig
s or
more
)
Tota
l 5 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
12
19.
(a)
7x −
7 =
5 −
2x
7x +
2x =
5 +
7 o
r 9x =
12
3
M1
M1
for
7x −
7 s
een
for
7x +
2x =
5 +
7 o
r 9x =
12
or
for
7x +
2x =
5 +
1 o
r 9x =
6 f
ollow
ing 7
x −
1 =
5 −
2x
31
1 o
e
A1
for
311
oe inc
34,
912
, 3.
1&,
1.3
3
(b
)(i)
16
4≤
x
4
M1
for
16
4≤
x
4
≤x
A1
for
4≤
x
(
ii)
1
2
3
4
B2
B1 f
or
3 c
orr
ect
and n
one w
rong
or
for
4 c
orr
ect
and 1
wro
ng
Tota
l 7 m
ark
s
20.
(i)
57.5
2
B1
Accept
94.
57
&,
57.4
99,
57.4
999 e
tc
(i
i)
56.5
B1
cao
Tota
l 2 m
ark
s
21.
4
M1
for
findin
g p
roducts
f ×
x c
onsi
stentl
y w
ithin
inte
rvals
(in
c e
nd p
oin
ts)
and s
um
min
g t
hem
55 ×
7 +
65 ×
21 +
75 ×
15 +
85 ×
14 +
95 ×
3
or
385 +
1365 +
1125 +
1190 +
285 o
r 4350
M
1
(dep)
for
use
of
half
way v
alu
es
(55,
65,
...
)
or
(55.5
, 65.5
, ..
.)
60
4350
""
M
1
for
60
4350
""
(dep o
n 1
st M
1)
for
div
isio
n b
y 6
0
or
for
60
"4380
"if
55.5
, 65.5
, ..
. use
d
72.5
A1
for
72.5
Accept
73 if
firs
t tw
o M
mark
s aw
ard
ed
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
13
Sum
mer
2008 IG
CSE M
ath
s M
ark
Schem
e –
Paper
2F
Q
W
ork
ing
Answ
er
Mark
N
ote
s
1.
(a)
800,
888,
1008,
1080,
1800
1
B1
This
ord
er
(b
)
-7
1
B1
(c
)
8,
14
2
B1B1
-B1 e
ach e
xtr
a
(d
)
1,
5,
7,
35
2
B2
B1 f
or
any t
wo,
wit
h n
o e
xtr
as.
Tota
l 6 m
ark
s
2.
(a)
12
1
B1
(b
)
7
1
B1
(c
)
Dave’s
Sport
s 1
B1
or
Sport
s or
Dave o
r th
e 4
th o
ne
(d
)
41/
4 c
ircle
s dra
wn
1
B1
Allow
if
inte
nti
on c
lear
Tota
l 4 m
ark
s
3.
(a)
5/8
1
B1
(b
)
3 s
ecto
rs s
haded
1
B1
Allow
if
inte
nti
on c
lear
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
14
4.
(a)(
i)
48,
96
2
B1B1f
Allow
wri
tten in t
he s
equence,
wit
h
noth
ing o
n lin
e o
r w
ith 1
92,
384 o
n lin
e
ft d
ep o
n f
irst
num
ber ≥
24
(a
)(ii)
x 2
oe
1
B1
or
doubling e
tc
(b
)(i)
8,
6
2
B1B1d
ep
(b
)(ii)
0
1
B1
(b
)(iii)
10 –
99x2 o
e
-188
2
M1
A1
Allow
10 –
100x2
or
-190
cao
Tota
l 8 m
ark
s
5.
(a)
Is
osc
ele
s 1
B1
Allow
any r
ecognis
able
spellin
g
(b
)
B &
D
1
B1
(c
)(i)
Enla
rgem
ent
1
B1
or
enla
rge o
r enla
rged o
r enla
rgin
g e
tc
Tota
l 3 m
ark
s
6.
(i)
Mark
A
A a
t 0.5
1
B1
(i
i)
Mark
B
B a
t 1
1
B1
(i
ii)
Mark
C
C 1
cm
– 3
cm
fro
m O
1
B1
If n
o c
ross
, m
ark
the p
oin
t on t
he lin
e
level w
ith t
he c
entr
e o
f th
e lett
er.
If
no
lett
ers
show
n,
no m
ark
s.
Tota
l 3 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
15
7.
(a)(
i)
m
or
cm
1
B1
(a
)(ii)
to
nnes
or
kg
1
B1
Not
ton
(a
)(iii)
m2,
are
, hecta
re
1
B1
or
metr
e s
quare
d o
r sq
uare
metr
e
(b
) 5.2
x 1
0 0
00
52 0
00
2
M1
A1
or
100 ×
100
Tota
l 5 m
ark
s
8.
(a)
12 –
(-4
) or
12 +
4 o
r -1
6
16
2
M
1
A1
Allow
wit
hout
bra
cket
(b
) -4
–3
-7
2
M
1
A1
Tota
l 4 m
ark
s
9.
(a)
1525
1
B1
Allow
wit
h a
ny p
unctu
ati
on o
r none
(b
) Att
em
pt
dif
fere
nce 3
:25 t
o 5
:10
1 h
our
+ 3
5 m
in +
10 m
in
1h 4
5m
ins
3
M1
M1
A1
Accept
1.8
5,
1hr
85m
in,
2.1
5,
2hr
15m
in
or
60 +
35 +
10,
120 –
15,
2hr
– 15m
in
cao
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
16
10.
(a)
70
1
B1
(b
) 180 –
(30 +
70)
80
2
M1
A1f
ft “
70” if
use
d.
(c
) 360 –
(70 +
130 +
85)
75
2
M1
A1
or
360 -
285
Tota
l 5 m
ark
s
11.
(a)
Measu
re a
ngle
s fo
r w
alk
& b
ike
“90”/ “
60” x
28 o
e
42 (
± 2
)
3
M1
M1
A1
Walk
60,
Bik
e 9
0,
allow
2o e
rror
Accept
“90”/”60”,
“60”/”90”,
“60”/”28”,
“2.1
4”,
“28”/”60”,
“0.4
66”
Inte
ger
requir
ed
(b
) 50/150 x
360
120
o
2
M1
A1
Accept
50/150,
150/50,
360/150,
150/360
cao
Tota
l 5 m
ark
s
12.
(a)
580 x
0.1
0 or
58(.
00)
+ 4
£62.(
00)
3
M1
M1
A1
dep
(b
) 78.6
0 –
4(.
00)
or
78.6
0/0.1
0
“74.6
0” /
0.1
0 o
e
746(.
00)
3
M1 M
1
A1
786 -
40
Tota
l 6 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
17
13.
(a)
3:5
1
B1
or
3 t
o 5
(b
) 15/40
3/
8
2
M1
A1
or
0.3
75
or
37.5
%
cao
Tota
l 3 m
ark
s
14.
(a)
6
1
B1
(b
) 8w
= 1
7 +
7
3
2
M1
A1
(c
) 6x –
2x =
7 –
13 o
r 2x –
6x =
13 -
7
4x =
-6 o
r –4
x =
6
x =
-1 ½
oe
3
M1
M1
A1
6x -
2x +
13 –
7 =
0 o
r 2x -
6x –
13 +
7 =
0
Accept
-6/4 o
r -3
/2 (
not
6/-4
or
3/-2
)
(d
) y –
2 x
5 =
4 x
5
or
y/5 =
4 +
2
y =
30
2
M1
A1
Tota
l 8 m
ark
s
15.
(a)
250±2
2
B2
B2 f
or
angle
248 t
o 2
52 inclu
sive.
B1 f
or
angle
190 t
o 2
60 inclu
sive
(b
)
305±3
2
B2
Aw
ard
B1 f
or
a b
eari
ng
270
o <
angle
< 3
60
o
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
18
16.
(a)
20/2 o
r (2
0 +
1)/
2
6
2
M1
A1
(b
)
Yes,
no o
r not
nec’y
w
ith c
onsi
stent
reaso
n
2
B2
Can’t
tell
B1
Tota
l 4 m
ark
s
17.
(a)
3 –
5 x
-2
13
2
M1
A1
(b
)
5y -
10
1
B1
(c
)
w
(w +
5)
2
B2
B1 f
or
two f
acto
rs t
hat
mult
iply
to g
ive a
t le
ast
one c
orr
ect
term
.
SC
w(w
+ 5
w)
B1
Tota
l 5 m
ark
s
18.
(a)
30 x
0.2
6
2
M1
A1
or
30 ÷
5
(b
) 0.2
+ 0
.1
0.3
oe
2
M1
A1
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
19
19.
8/12 o
r 3/12
8/
12,
3/
12
2
M1
A1
Accept
(4x2)/
(4x3)
or
(3x1)/
(4x3)
SC
Mult
iply
bs
by 1
2
B1
Decim
al m
eth
ods
M0 A
0
Tota
l 2 m
ark
s
For
oth
er
resp
onse
s not
covere
d b
y t
his
mark
schem
e b
ut
whic
h,
in y
our
opin
ion,
may b
e w
ort
hy o
f cre
dit
, se
nd t
o r
evie
w.
20.
(a)
3
14
1
B1
(b
)
73
1
B1
(c
)
3
72
5
55
5×
=n
or
n
+ 3
– 7
= 2
n =
6
2
M1
A1
Accept
5n+3 =
59
Tota
l 4 m
ark
s
21.
½
x 3
x 4
3 x
15 a
nd 4
x 1
5 a
nd 5
x 1
5
192
4
M1
M2
A1
M1 f
or
any O
NE o
f th
ese
cao
Tota
l 4 m
ark
s
22.
8x =
12 o
r 8y =
-4
x =
1.5
o
e
y =
-0.5
oe
3
M1
A1
A1
Elim
inate
one v
ari
able
corr
ectl
y.
Accept
3x +
5x –
8 =
4 o
r 5(4
– y
)/3 –
y =
8 o
e
Tota
l 3 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
20
23.
(a)
4.8
1
B1
(b
) 5
2 -
“4.8
”2
or
1.9
6
\/(5
2 -
“4.8
”2)
1.4
3
M1
M1dep
A1
cao
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
21
Sum
mer
2008 IG
CSE M
ath
s M
ark
Schem
e –
Paper
3H
Q
W
ork
ing
Answ
er
Mark
N
ote
s
1.
4.2
28
.17
2
M1
for
17.2
8 o
r 2.4
or −
0.1
14..
. s
een
7.2
A1
for
7.2
oe inc
517
and
536
Tota
l 2 m
ark
s
2.
2
60
1.
−
2
M1
for
1 −
0.6
or
0.4
seen
or
2x w
here
0 <
x <
1
0.2
oe
A1
for
0.2
oe
Tota
l 2 m
ark
s
3.
(a)
Enla
rgem
ent
scale
facto
r 2 c
entr
e (
1,
3)
3
B3
B1 f
or
enla
rgem
ent,
enla
rge e
tc
B1 f
or
2,
× 2
, tw
o,
12,
1 :
2,
2 :
1
B1 f
or
(1,
3)
Condone o
mis
sion o
f
bra
ckets
but
do n
ot
accept
⎟⎟ ⎠⎞⎜⎜ ⎝⎛ 31
(b
) Refl
ecti
on in t
he lin
e y
= x
2
B2
B1 f
or
refl
ecti
on,
refl
ect
etc
B1 f
or
y =
x o
e
inc e
g ‘
in lin
e f
rom
(2,2
) to
(5,5
)’,
‘in
dott
ed lin
e s
how
n’
These
mark
s are
in
dependent
but
aw
ard
no
mark
s if
answ
er
is n
ot
a
single
tr
ansf
orm
ati
on
Tota
l 5 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
22
4.
3 +
1 o
r 4 s
een
2
M1
for
3 +
1 o
r 4 s
een
210
A1
for
210 c
ao
Tota
l 2 m
ark
s
5.
(a)(
i)
1,
9,
17
2
B1
cao
(
ii)
1,
5,
9,
13,
17,
25,
33
B1
cao
(B0 if
1,
9 o
r 17 r
epeate
d)
Bra
ckets
not
necess
ary
(b
) eg N
o m
em
bers
in c
om
mon.
The inte
rsecti
on is
em
pty
. N
one o
f th
e m
em
bers
of
A &
C a
re t
he s
am
e.
They d
on’t
have t
he s
am
e n
um
bers
. N
o n
um
bers
are
in b
oth
A a
nd C
.
1
B1
Tota
l 3 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
23
6.
375
.0
83ta
n=
=°
x
3
M1
A1
for
tan
for
83 o
r 0.3
75
or
M1 f
or
sin a
nd
"73
"3fo
llow
ing
corr
ect
Pyth
agora
s and A
1 f
or
0.3
511..
. or
M1 f
or
cos
and
"73
"8fo
llow
ing
corr
ect
Pyth
agora
s and A
1 f
or
0.9
363..
.
20.6
A1
for
20.6
or
bett
er
(A
ccept
20.5
5604…
rounded o
r tr
uncate
d t
o 4
sig
fig
s or
more
)
Tota
l 3 m
ark
s
7.
π
× 7
.8 o
r 2π
× 3
.9
2
M1
for π
× 7
.8 o
r 2π
× 3
.9
24.5
A1
for
24.5
or
for
answ
er
whic
h r
ounds
to
24.4
9,
24.5
0 o
r 24.5
1
(π →
24.5
044…
3.1
4 →
24.4
92
3.1
42 →
24.5
076)
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
24
8.
(a)
n =
2p +
1 o
e
3
B3
for
n =
2p +
1 o
e
eg n
= p
2 +
1,
1 +
p ×
2 =
n,
n =
p +
p +
1
B2 f
or
2p +
1 o
e
B1 f
or
n =
lin
ear
functi
on o
f p e
g n
= p
+
1
(b
) 2p =
n −
1 o
r 21
2+
=p
n
2
M1
for
2p =
n −
1 o
r 21
2+
=p
n
2
1−n
oe
A1
for
2
1−n
oe inc
21
2−
n
Tota
l 5 m
ark
s
9.
(a)
7x −
7 =
5 −
2x
7x +
2x =
5 +
7 o
r 9x =
12
3
M1
M1
for
7x −
7 s
een
for
7x +
2x =
5 +
7 o
r 9x =
12
or
for
7x +
2x =
5 +
1 o
r 9x =
6 f
ollow
ing 7
x −
1 =
5 −
2x
31
1 o
e
A1
for
311
oe inc
34,
912
, 3.
1&,
1.3
3
(b
)(i)
16
4≤
x
4
M1
for
16
4≤
x
4
≤x
A1
for
4≤
x
(i
i)
1
2
3
4
B2
B1 f
or
3 c
orr
ect
and n
one w
rong
or
for
4 c
orr
ect
and 1
wro
ng
Tota
l 7 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
25
10.
(a)
29 8
32 −
28 2
50 o
r 1582 s
een
3
M1
M
1
for
28250
1582
or
29832
1582
or
0.0
56 o
r 0.0
53…
or
M1 f
or
28250
29832
or
1.0
56
or
105.6
M
1 f
or
“1.0
56” −
1
or
“105.6
” −
100
or
M1 f
or
29832
28250
or
0.9
469..
. or
94.6
9..
. M
1 f
or
1 −
“0.9
469”
or
100 −
“94.6
9”
5.6
A1
cao (
Do N
OT a
ward
for
5.3
)
(b
)
052
.128141
or
2.105
100
28141×
3
M2
for
052
.128141
or
2.105
100
28141×
M1 f
or
2.105
28141
, 105.2
%=28141
or
267.5
(0)
seen
26
750
A1
cao
Tota
l 6 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
26
11.
(a)
70
60
≤<
p
1
B1
Accept
60-7
0
(b
) 4
M1
for
findin
g a
t le
ast
four
pro
ducts
f ×
x c
onsi
stentl
y w
ithin
in
terv
als
(in
c e
nd p
oin
ts)
and s
um
min
g t
hem
55 ×
7 +
65 ×
21 +
75 ×
15 +
85 ×
14 +
95 ×
3
or
385 +
1365 +
1125 +
1190 +
285 o
r 4350
M
1
(dep)
for
use
of
half
way v
alu
es
(55,
65,
...
)
or
(55.5
, 65.5
, ..
.)
60
4350
""
M
1
60
4350
""
(dep o
n 1
st M
1)
for
div
isio
n b
y 6
0
or
for
60
"4380
"if
55.5
, 65.5
, ..
. use
d
72.5
A1
for
72.5
Aw
ard
4 m
ark
s fo
r 7
3 if
firs
t tw
o M
mark
s aw
ard
ed
(c
) 30 (
or
30½
) in
dic
ate
d o
n g
raph o
r st
ate
d
2
M1
for
30 (
or
30½
) in
dic
ate
d o
n g
raph o
r st
ate
d
124 o
r 125
A1
Accept
any v
alu
e in r
ange 1
24-1
25 inc
eg 1
24,
124.5
, 125
(d
) U
se o
f p =
131 o
n g
raph
2
M1
for
use
of
p =
131 s
how
n o
n g
raph o
r im
plied b
y 4
7,
48 o
r 49 s
tate
d
≈
12
A1
Accept
any v
alu
e in r
ange 1
1-1
3 inc
Tota
l 9 m
ark
s
12.
3
2 o
r 9 o
r valu
e w
hic
h r
ounds
to
3.3
9 s
een
2
M1
for
32 o
r 9 o
r valu
e w
hic
h r
ounds
to 3
.39 s
een
36
A1
for
36 c
ao
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
27
13.
fi
nds
int
angle
of
hexagon
6
180
)2
6(×
−
finds
ext
angle
of
hexagon
6
360
5
M1
for
6
180
)26(
×−
or
6
360
120
60
A1
for
120 o
r 60
Aw
ard
M1 A
1 f
or
in
t angle
of
hexagon s
how
n a
s 120°
or
ext
angle
sh
ow
n a
s 60°
on
pri
nte
d d
iagra
m
or
on c
andid
ate
’s
ow
n d
iagra
m
If t
here
is
clear
evid
ence
the c
andid
ate
th
inks
the
inte
rior
angle
is
60° o
r th
e
exte
rior
angle
is
120°,
do n
ot
aw
ard
these
tw
o m
ark
s.
int
angle
of
poly
gon =
150
or
ext
angle
of
poly
gon =
30
B1
int
angle
of
poly
gon =
150
or
ext
angle
of
poly
gon =
30
Aw
ard
B1 f
or
int
angle
of
poly
gon
show
n a
s 150°
or
ext
angle
show
n
as
30° o
n p
rinte
d d
iagra
m o
r on
candid
ate
’s o
wn d
iagra
m
30
360
or
150
)2(
180
=−
nn o
e
M1
for
30
360
or
150
)2(
180
=−
nn o
e
12
A1
for
12 c
ao
Aw
ard
no m
ark
s fo
r an a
nsw
er
of
12 w
ith n
o w
ork
ing.
Aw
ard
5 m
ark
s fo
r an a
nsw
er
of
12 if
at
least
2 o
f th
e
pre
vio
us
4 m
ark
s sc
ore
d.
Tota
l 5 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
28
14.
(a)
5(2
y −
3)
1
B1
cao
(b
)
3pq(3
p +
4q)
2
B2
B1 f
or
3pq(…
) or
…(3
p +
4q)
or
3p(3
pq +
4q
2)
or
3q(3
p2 +
4pq)
or
pq(9
p +
12q)
or
3(3
p2q +
4pq
2)
ie
for
two f
acto
rs,
one o
f w
hic
h is
3pq o
r (3
p +
4q),
or
for
corr
ect,
but
incom
ple
te,
facto
risa
tion
(c
)(i)
(x −
2)(
x +
8)
3
B2
B1 f
or
one c
orr
ect
facto
r or
(x
+ 2
)(x −
8)
(
ii)
2,
−8
B1
ft f
rom
(i)
if
two lin
ear
facto
rs
Tota
l 6 m
ark
s
15.
(a)(
i)
57.5
2
B1
for
57.5
, 9
4.57
&,
57.4
99,
57.4
999 e
tc
but
NO
T f
or
57.4
9
(i
i)
56.5
B1
for
56.5
Als
o a
ccept
56.5
0
(b
) 62.5
− “
56.5
”
2
M1
for
62.5
− “
56.5
” A
ccept
94.
62
&,
62.4
99,
62.4
999 e
tc inst
ead
of
62.5
6
A1
for
6,
9.5&
, 5.9
99 e
tc
ft f
rom
“56.5
”
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
29
16.
(a)
95
95×
2
M1
for
95
95×
81
25
A1
for
81
25
or
0.3
1 o
r bett
er
Sam
ple
space m
eth
od
– aw
ard
2 m
ark
s fo
r a
corr
ect
answ
er,
oth
erw
ise n
o m
ark
s
(b
) 91
91×
or
811
3
M1
for
91
91×
or
811
SC
M1 f
or
81
91×
or
721
91
91×
× 4
oe
M1
for
91
91×
× 4
oe
M1 f
or
81
91×
× 4
oe
814
A1
for
814or
0.0
5 o
r bett
er
Sam
ple
space m
eth
od
– aw
ard
3 m
ark
s fo
r a
corr
ect
answ
er,
oth
erw
ise n
o m
ark
s
Tota
l 5 m
ark
s
17.
(a)
hk
d=
3
M1
for
hk
d=
but
not
for
hd=
Als
o a
ward
for
d =
som
e n
um
eri
cal valu
e ×
h
54 =
15k
M1
for
54 =
15k
Als
o a
ward
for
225
54
k=
h
6.3
oe
A1
for
h6.
3 o
e
Aw
ard
3 m
ark
s if
answ
er
is
hk
d=
but
k is
evalu
ate
d a
s 3.6
oe in a
ny p
art
(b
)
28.8
1
B1
ft f
rom
“3.6
”
8 × e
xcept
for
k =
1,
if a
t le
ast
M1 s
core
d in
(a)
(1 d
.p.
accura
cy o
r bett
er
in f
ollow
thro
ugh)
(c
)
"6.
3"
2.61
=h
2
M1
for
"6.
3"
2.61
=h
except
for
k =
1
289
A1
cao
Tota
l 6 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
30
18.
°=
°64
sin
8.6
35
sina
3
M1
for
corr
ect
state
ment
of
Sin
e r
ule
°°
=64
sin
35
sin
8.6
a
M1
for
corr
ect
rearr
angem
ent
4.3
4
A1
for
4.3
4 o
r 4.3
395…
rounded o
r tr
uncate
d t
o 4
fig
ure
s or
more
Tota
l 3 m
ark
s
19.
2
B1
for
use
of
22
8=
or
16
28
=×
for
mult
iplicati
on o
f num
era
tor
and d
enom
inato
r by
2 o
r
8
(in e
ither
ord
er)
eg
8
12
=2
212
=22
221
2×
=4
212
8
12
=2
212
=22
26×
=2
26
8
12
=88
8
12×
=8
812
=2
22
3×
8
12
=22
8
12×
=162
12
B1
SC B
1 f
or
16
312=
or
for
both
18
8
144
8
12
2
==
⎟ ⎠⎞⎜ ⎝⎛
and
18
29
)2
3(2
=×
=
NB o
nly
tota
l of
1 m
ark
for
eit
her
of
these
appro
aches
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
31
20.
(a)(
i)
59
2
B1
cao
(i
i)
angle
at
the c
entr
e
= t
wic
e a
ngle
at
the c
ircum
fere
nce
or
angle
at
the c
ircum
fere
nce
= h
alf
the a
ngle
at
the c
entr
e
B1
Thre
e k
ey p
oin
ts m
ust
be m
enti
oned
1.
angle
at
centr
e/m
iddle
/O
/ori
gin
2.
twic
e/double
/2× o
r half
/21
as
appro
pri
ate
3.
angle
at
cir
cum
fere
nce/edge/peri
mete
r
(N
OT e
.g.
angle
R,
angle
PRQ
, angle
at
top,
angle
at
outs
ide)
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
32
for
180 −
(x +
36)
oe s
een,
eit
her
on its
ow
n o
r as
part
of
an
equati
on
(This
mark
may s
till b
e s
core
d,
even if
bra
ckets
are
late
r re
moved incorr
ectl
y.)
20.
(b)
180 −
(x +
36)
oe s
een (
poss
ibly
m
ark
ed o
n d
iagra
m a
s si
ze
of
ACB
∠)
5
B1
SC
(Max o
f 2 M
mark
s)
for
om
issi
on o
f bra
ckets
in −
(x +
36)
or
their
in
corr
ect
rem
oval
x =
2(1
80 −
(x +
36))
or
)36
180
(2−
−=
xx
or
2)
36
(180
xx
=+
−
or
180 −
x −
36 =
21
x
M1
x =
2(1
80 −
(x +
36))
or
x =
2(1
80 −
x +
36)
or
180 −
x +
36 =
21
x
or
180 −
36 +
x =
21
x
M
1
72
2360
−−
=x
x
or
x +
21
x =
180 −
36
M1
x =
360 −
2x +
72
or
x +
21
x =
180 +
36
(Note
– incorr
ect
sim
plifi
cati
on r
esu
lts
in
an a
nsw
er
of
x =
144)
M
1
72
360
3−
=x
or
3x =
288
or
23x =
180 −
36 o
r 23
x =
144
M1
96
A1
cao
Ple
ase
note
that
there
is
an a
ltern
ati
ve m
eth
od o
n t
he n
ext
page.
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
33
20.
(b)
OR
2x o
e s
een
(poss
ibly
mark
ed o
n d
iagra
m a
s si
ze
of
ACB
∠)
5
B1
180
236
=+
+x
x
M1
96
A1
cao
Tota
l 7 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
34
21.
(a)
tan d
raw
n a
t (3
, 6.5
)
3
M1
tan o
r ta
n p
roduced p
ass
es
betw
een p
oin
ts (
2,
0 <
y <
4)
and
(4,
9 <
y <
12)
dif
fere
nce
hori
zonta
ldif
fere
nce
vert
ical
M
1
finds
their
dif
fere
nce
hori
zonta
ldif
fere
nce
vert
ical
for
two p
oin
ts o
n t
an
or
finds
their
dif
fere
nce
hori
zonta
ldif
fere
nce
vert
ical
for
two p
oin
ts o
n c
urv
e,
where
one o
f th
e p
oin
ts h
as
an x
-coord
inate
betw
een 2
.5
and 3
inc a
nd t
he o
ther
poin
t has
an x
-coord
inate
betw
een 3
and 3
.5 inc
2.5
-6.5
in
c
A1
dep o
n b
oth
M m
ark
s
(b
)
−1.7
1
B1
Accept
answ
er
in r
ange −
1.7
- −
1.6
5
(c
)(i)
line j
oin
ing (−1
,11)
& (
1,1
3)
4
M1
12
A1
cao
(i
i)
pro
duces
line t
o c
ut
curv
e a
gain
M
1
4
A1
ft f
rom
lin
e
Tota
l 8 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
35
fi
rst
part
– f
inds
are
a o
f BCD
∆ a
nd/or
length
of
BD
22.
Are
a o
fBCD
∆ =
2
6
B1
for
are
a o
f tr
iangle
BCD
22
22
2+
=)(B
D o
r 2
22
22
2=
⎟ ⎠⎞⎜ ⎝⎛
+⎟ ⎠⎞
⎜ ⎝⎛BD
BD
or
°=
45
cos
2
2/
BD
or
sin45°
or
°=
45
cos
22BD
or
2 s
in45°
M1
for
corr
ect
start
to P
yth
agora
s or
trig
for
findin
g B
D o
r ⎟ ⎠⎞
⎜ ⎝⎛2BD
8)
(=
BD
or
22
or
2.8
3 o
r bett
er
(2.8
284..
.)
or
22
= ⎟ ⎠⎞⎜ ⎝⎛B
D o
r 28
or
1.4
1 o
r bett
er
(1.4
142..
.)
A1
for
length
s BD
or
⎟ ⎠⎞⎜ ⎝⎛
2BD
corr
ect
se
cond p
art
m
eth
od 1
– u
ses
Pyth
agora
s to
fin
d A
M,
where
M is
mid
poin
t of
BD
22
2
210
⎟ ⎠⎞⎜ ⎝⎛
−=
BD
AM
M
1
98
=A
Mor
27
or
9.9
0 o
r bett
er
(9.8
994..
.)
A1
for
98
or
27
9.9
0 o
r bett
er
16
A1
for
16 o
r answ
er
roundin
g t
o 1
6.0
Tota
l 6 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
36
se
cond p
art
m
eth
od 2
– f
inds
angle
A e
ither
usi
ng C
osi
ne R
ule
or
by f
irst
fin
din
g 2A
usi
ng t
rig
10
10
2
10
10
cos
22
2
××
−+
=BD
A o
r 200
192
or
0.9
6
or
10
2/
2si
nBD
A=
or
208
or
0.1
41 o
r bett
er
(0.1
4142..
.)
M1
(A =
) 16.3
or
bett
er
(16.2
602..
.)
A1
for
angle
A c
orr
ect
16
A1
for
16 o
r answ
er
roundin
g t
o 1
6.0
Tota
l 6 m
ark
s
se
cond p
art
m
eth
od 3
– f
inds
angle
ABD
(or
angle
AD
B)
usi
ng t
rig o
r Cosi
ne R
ule
10
2/
)(c
os
BD
ABD=
∠ o
r BD
BD
ABD
××
−+
=∠
10
2
10
10
)(c
os
22
2
or
=∠
ABD
cos
208
or
0.1
41 o
r bett
er
(0.1
4142..
.)
M1
°=
∠9.
81
)(
ABD
or
bett
er
(81.8
698..
.)
A1
16
A1
for
16 o
r answ
er
roundin
g t
o 1
6.0
Tota
l 6 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
37
Sum
mer
2008 IG
CSE M
ath
s M
ark
Schem
e –
Paper
4H
Q
W
ork
ing
Answ
er
Mark
N
ote
s
1.
(a)
6x –
2x =
7 –
13 o
r 2x –
6x =
13 -
7
4x =
-6 o
r –4
x =
6
x =
-1 ½
oe
3
M1
M1
A1
6x -
2x +
13 –
7 =
0 o
r 2x -
6x –
13 +
7 =
0
Accept
-6/4 o
r -3
/2 (
not
6/-4
or
3/-2
)
(b
) y –
2 x
5 =
4 x
5
or
y/5 =
4 +
2
y =
30
2
M1
A1
Tota
l 5 m
ark
s
2.
(a)
250±2
2
B2
B2 f
or
angle
248 t
o 2
52 inclu
sive.
B1 f
or
angle
190 t
o 2
60 inclu
sive
(b
)
305±3
2
B2
Aw
ard
B1 f
or
a b
eari
ng
270
o <
angle
< 3
60
o
Tota
l 4 m
ark
s
3.
(a)
20/2 o
r (2
0 +
1)/
2
6
2
M1
A1
(b
)
Yes,
no o
r not
nec’y
w
ith c
onsi
stent
reaso
n
2
B2
Can’t
tell
B1
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
38
4
(a)
3 –
5 x
-2
13
2
M1
A1
(b
)
5y -
10
1
B1
(c
)
w(w
+ 5
)
2
B2
B1
fo
r tw
o f
acto
rs th
at
mu
ltip
ly to
giv
e a
t le
ast o
ne
co
rre
ct te
rm.
SC
w(w
+ 5
w)
B1
Tota
l 5 m
ark
s
5.
(a)
30 x
0.2
6
2
M1
A1
or
30 ÷
5
(b
) 0.2
+ 0
.1
0.3
oe
2
M1
A1
Tota
l 4 m
ark
s
6.
8/12 o
r 3/12
8/
12,
3/
12
2
M1
A1
Accept
(4x2)/
(4x3)
or
(3x1)/
(4x3)
SC
Mult
iply
bs
by 1
2
B1
Decim
al m
eth
ods
M0 A
0
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
39
7.
(a)
3
14
1
B1
(b
)
73
1
B1
(c
)
3
72
5
55
5×
=n
or
n
+ 3
– 7
= 2
n =
6
2
M1
A1
Accept
5n+3 =
59
(d
) Pro
duct
of
posi
tive inte
ger
pow
ers
of
both
2 a
nd 3
only
24 o
r 2
3 x
3
2
M1
A1
Pow
ers
and/or
pro
ducts
may b
e
evalu
ate
d.
Tota
l 6 m
ark
s
8.
½
x 3
x 4
3 x
15 a
nd 4
x 1
5 a
nd 5
x 1
5
192
4
M1
M2
A1
M1 f
or
any O
NE o
f th
ese
. cao
Tota
l 4 m
ark
s
9.
8x =
12 o
r 8y =
-4
x =
1.5
o
e
y =
-0.5
oe
3
M1
A1
A1
Elim
inate
one v
ari
able
corr
ectl
y.
Accept
3x +
5x –
8 =
4 o
r 5(4
– y
)/3 –
y =
8 o
e
No w
ork
ing M
0 A
0 A
0
Tota
l 3 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
40
10.
(a)
4.8
1
B1
(b
) 5
2 -
“4.8
”2
or
1.9
6
\/(5
2 -
“4.8
”2)
1.4
3
M1
M1dep
A1
cao
Tota
l 4 m
ark
s
11.
123.4
7 &
123.5
3
2
B2
B1 f
or
123.3
7 &
123.4
3
(e
qual to
1dp)
o
r 1
23.5
7 &
123.6
3
Tota
l 2 m
ark
s
12.
(a)
6
3
1
B1
cao
(b
) 4 x
5/8
oe
2.5
2
M1
A1
or
8 ÷
2 =
4 s
o 5
÷ 2
= …
, or
4 ÷
1.6
or
(62 +
52 –
2 x
6 x
5 c
os
20
o)
or
(5 x
sin
20
o)
/ s
in 6
3o
2.1
5
1.9
2
M1 f
or
com
ple
te t
rig m
eth
od.
A1 f
or
answ
er
to 3
SF.
(c
) 6 x
8/5
oe
9.6
2
M1
A1
or
(42 +
82 –
2 x
4 x
8 c
os
‘97
o’)
or
(8 x
sin
‘97
o’)
/si
n 6
3o
or
(4 x
sin
‘97
o’)
/si
n 2
0o
9.3
7
8.9
1
11.6
M1 f
or
com
ple
te t
rig m
eth
od.
A1 f
or
answ
er
to 3
SF.
Tota
l 5 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
41
13.
(a)
2/
3 c
orr
ectl
y p
laced
once
Corr
ect
stru
ctu
re
All c
orr
ect
3
B1
B1
B1
corr
ect
4 n
ew
lin
es,
ignore
la
bels
/pro
bs
inclu
din
g labels
/pro
bs
(b
) 2/
3 x
2/
3
1-2
/3 x
2/
3 o
r 1/
3 +
2/
3 x
1/
3 or
1/
3 x
2/
3 +
2/
3 x
1/
3 +
1/
3 x
1/
3
5/
9
oe
3
M1
M1
A1
1/
3 x
2/
3 o
r 2
/3 x
1/
3 or
1/
3 x
1/
3
Tota
l 6 m
ark
s
14.
(a)(
i)
vert
dif
f/hori
z dif
f fo
r any 2
poin
ts o
n L
0.5
o
e
2
M1
A1
(a
)(ii)
y =
“0.5
”x +
const
ant
Y =
“0.5
”x +
1 o
e
2
M1f
A1f
SC “
0.5
”x +
1 o
r L =
“0.5
”x +
1 B
1
(b
)
x <
4
y >
-1
Y <
0.5
x +
1
oe
3
B1
B1
B1
Allow
<
SC
All inequaliti
es
Allow
>
w
rong w
ay r
ound B
1
Allow
<
To
tal 7
ma
rk
s
15.
3.1
2 +
3.9
2 –
2 x
3.1
x 3
.9 x
cos8
0o
9.6
+ 1
5.2
– 4
.2
4.5
4
3
M1
M1
A1
3.1
2 +
3.9
2 –
24.2
x c
os8
0o
or
20.6
Tota
l 3 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
42
16.
(a)
5 ±
\/((
-5)2
– 4
x3)
2
5 ±
\/13
2
4.3
0 a
nd 0
.697
3
M1
M
1
A1
allow
4.3
and 0
.697
(b
) y <
3 o
r y >
-3
-3 <
y <
3
2
M1
A1
Allow
y <
3 o
r y
≥ -
3
Tota
l 5 m
ark
s
17.
(a)
Try
to f
ind a
rea o
f 2-4
blo
ck.
Try
to f
ind t
ota
l are
a.
40%
3
M1
M
1
A1
or
8
M0 f
or
2/8 o
r 9 -
1
Wit
h c
onsi
stent
scale
.
(b
) H
alf
tota
l are
a
or
try t
o f
ind m
iddle
of
dis
trib
uti
on
4
2
M1f
A1
ft d
ep o
n M
1 f
or
tota
l are
a in (
a)
Cao
Tota
l 5 m
ark
s
18.
x
x 4
= 3
x 1
4
oe
x =
10.5
o
e
2
M1
A1
x/ 1
4 =
¾,
3/ (
3 +
4) =
x/ (
x +
14),
4/ (
3 +
4) =
14/ (
x +
14
)
Tota
l 2 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
43
19.
(a)
2t
- 6
2
B1B1
(b
) 2 x
5 -
6
4
2
M1f
A1
Su
b t
= 5
in
“ds/dt”
de
p o
n lin
ea
r f(
t)
M0 f
or
(2 x
5 -
6)/
5
Cao
(c
) d(“
2t
– 6”)/
dt
2
2
M1
A1
Atte
mp
t d
iff
“ds/dt”
de
p o
n lin
ea
r f(
t)
Cao
Tota
l 6 m
ark
s
20.
(a)
14 x
10
12 o
e
1.4
x 1
013
2
M1
A1
or
1.4
e13
(b
)(i)
16
1
B1
cao
(b
)(ii)
(p +
q)
x 1
015 =
r x
10
n
(p
+ q
)/10 o
e
2
M1
A1
may b
e s
een in (
i)
0.1
(p +
q),
(p +
q)
x 1
0-1,
16
15
15 10
10
10
×+
×q
p
Tota
l 5 m
ark
s
21.
(a)(
i)
a +
b
oe
1
B1
(a
)(ii)
-a
oe
1
B1
(a
)(iii)
b –
a
oe
1
B1
(b
)
5
1
B1
Tota
l 4 m
ark
s
4400 IG
CSE M
ath
em
ati
cs
Sum
mer
2008
44
22.
1/
2 x
6 x
8 x
sin
xo =
12
sinx
o =
0.5
30
x =
150
4
M1
M1
A1
A1
allow
x =
30
Tota
l 4 m
ark
s
23.
(a)
(x –
3)(
x +
3)
x(x
+ 3
)
x
x3
−
3
M1
M1
A1
x31−
(b
)
2
2
1
31
x
x−
or
2131
x
−
1 –
3x
2
2
M
1
A1
ft
x
x3
+ o
nly
cao
Tota
l 5 m
ark
s
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