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Mark Scheme
Sample Assessment Material
GCSE
GCSE in Mathematics Specification A Higher Tier Paper 2: (Calculator)
Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH
General Marking Guidance
• All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last.
• Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions.
• All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme.
• Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited.
• Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response.
• Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows:
i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear Comprehension and meaning is clear by using correct notation and labelling conventions. ii) select and use a form and style of writing appropriate to purpose and to complex subject matter Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning. iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used.
Guidance on the use of codes within this mark scheme M1 – method mark A1 – accuracy mark B1 – working mark C1 – communication mark QWC – quality of written communication oe – or equivalent cao – correct answer only ft – follow through sc - special case
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
157
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 5.
(a
) 0:
8
1: 0
2357
8 2:
012
2233
3:
134
5 4:
456
Key
4 I
6 m
eans
46
min
utes
Corr
ect
stem
an
d le
af3
B3 F
ully
cor
rect
(B
2 Al
l ent
ries
cor
rect
, no
key
) (B
1 co
rrec
t en
trie
s un
orde
red,
key
or
no k
ey)
OR
(B2
Thre
e ro
ws
corr
ect,
key
or
no k
ey)
(B1
Two
row
s co
rrec
t, k
ey o
r no
key
)
(b
) O
ld m
edia
n =
22
New
med
ian
= 22
+ 5
27
min
utes
2
M1
find
s m
edia
n co
rrec
tly
for
orig
inal
dat
a an
d ad
ds 5
A1
cao
O
RM
1 Re
does
tab
le (
ft)
wit
h ea
ch v
alue
incr
ease
d by
5 a
nd a
ttem
pts
to
find
med
ian
A1 c
ao
(c
)
The
sam
e +
reas
on1
C1 A
ll th
e va
lues
hav
e in
crea
sed
by 5
min
utes
so
whe
n yo
u su
btra
ct t
he
5 m
inut
es w
ill c
ance
l out
.
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
158
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 6. FE QW
Cii,
iii
(a)
1 ga
llon
= 4.
54 li
tres
,
200
gal
lons
= 9
08 li
tres
=
908
000
cm3
Vol
of
tank
60
2xπ
180
=
2035
752.
04..
cm3
9080
00<
1017
876.
02
OR
Vol o
f ta
nk
602
π 1
80 =
203
5752
.04.
.cm
3
Hal
f vo
l of
tank
=
1017
876.
02 c
m3
= 10
17.8
76…
litre
s
1017
.876
÷ 4
.54
= 22
4 ga
llons
224
> 20
0
No
5 Re
spon
se m
ay c
onve
rt in
to g
allo
ns,
litre
s, o
r cm
3
Calc
ulat
ions
may
be
perf
orm
ed in
dif
fere
nt o
rder
s
M1
Usi
ng f
orm
ulae
to
find
vol
ume
of t
ank
B1 C
onve
rts
betw
een
litre
s an
d cu
bic
cent
imet
res
M1
read
s of
f gr
aph
for
1l,
2l ,
4l,
5l o
r 10
litr
es w
ithi
n to
lera
nce
(4.4
—
4.6)
A1 A
nsw
er in
cm
3 , lit
res
or g
allo
ns
C1 D
ecis
ion
and
reas
on Q
WC:
Dec
isio
n sh
ould
be
stat
ed,
wit
h ap
prop
riat
e su
ppor
ting
sta
tem
ent
(b
) “
9080
00”
cm3 ×
0.8
5 g/
cm3
= 77
1800
g
771.
8 3
M1
“908
000”
× 0
.85
M
1(de
p) 7
7180
0÷10
00
A1 7
70 —
772
To
tal f
or Q
uest
ion:
8 m
arks
7.
120
5522
524
515
045
106.
08 h
ours
4
M1
for
mid
inte
rval
val
ues
M
1 fo
r m
ulti
plyi
ng f
requ
enci
es b
y m
id-i
nter
val v
alue
s M
1 fo
r ad
ding
(fr
eq
mid
-int
erva
l val
ues)
÷ 1
20
A1 c
ao
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
159
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 8.
(a
) Fr
ed p
ays
3x a
nd J
im
pays
210x
Mal
colm
get
s £1
70 f
or F
red
and
Jim
, so
Mal
colm
get
s
170
2103
xx
Clea
r an
d co
here
ntex
plan
atio
n
1 C1
a c
lear
and
coh
eren
t ex
plan
atio
n
(b
) Fr
ed h
as
32x
left
, so
sol
ving
for
xus
ing
170
2103
xx 2x
+ 3(
x –
10) =
170
6
5x
= 1
050
x
= 2
10O
R
6)
10(3
2210
3x
xx
x
170
630
5x
5
x =
105
0
21
0x
£140
4
M1
mul
tipl
y th
roug
h by
6 a
nd c
ance
ls f
ract
ions
M
1 (d
ep)e
xpan
d 3(
x−
10)
M1
(dep
)col
lect
ter
ms
on e
ach
side
cor
rect
ly
A1 c
ao
OR
M1
colle
cts
term
s ov
er 6
M
1(de
p) e
xpan
d 3(
x−
10)
M1(
dep)
mul
tipl
y th
roug
h by
6 a
nd c
olle
ct t
erm
s
A1 c
ao
Tota
l for
Que
stio
n: 5
mar
ks
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
160
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 9.
QW
Ci,
iii
FE
M
akes
a c
ompa
riso
n of
the
sh
ape
of t
he d
istr
ibut
ion
by
draw
ing
M
akes
a c
ompa
riso
n of
the
m
odal
cla
sses
(31—
40,
11—
20)
Mak
es a
com
pari
son
of t
he
clas
s in
terv
als
that
con
tain
th
e m
edia
ns.(
31—
40,
21—
30)
Wor
ks o
ut a
n es
tim
ate
of t
he
tota
l sal
es o
f ea
ch s
hop(
2635
, 35
30)
Corr
ect
com
pari
sons
4
B1,
B1,
B1 f
or a
ny 4
of
the
follo
win
g do
ne c
orre
ctly
Plot
s fr
eque
ncy
poly
gon
or p
rodu
ces
tabl
e co
mpa
res
mod
es
com
pare
s m
edia
ns
com
pare
s to
tal s
ales
C1 f
or c
omm
ents
on
shap
e of
the
dis
trib
utio
ns
QW
C: D
ecis
ions
sho
uld
be s
tate
d, a
nd a
ll co
mm
ents
sho
uld
be c
lear
an
d fo
llow
thr
ough
fro
m a
ny w
orki
ng o
r di
agra
ms
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
162
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 11
. (a
)
28
1 B1
27
— 2
9
(b
) 68
– 4
2 26
2
M1
68 —
42
A1 2
6 —
30
(ne
ed 21
sq
tole
ranc
e on
eac
h)
FE(c
) 15
% of
80
= 12
Ye
s, w
ith
corr
ect
conc
lusi
on
2 M
1 lo
oks
up 6
8 or
40
min
on
cum
ulat
ive
freq
uenc
y A1
cor
rect
con
clus
ion
Tota
l for
Que
stio
n: 5
mar
ks
12.
QW
Cii,
iii
FE
sin
68o =
5.8AC
AC =
8.5
× s
in 6
8o = 7
.881
7.
881
+ 1
< 9
Reas
onsu
ppor
ted
byca
lcul
atio
n
4M
1 si
n 68
o =
5.8AC
M1
AC =
8.5
× s
in 6
8o
A1 7
.88(
1…
C1 8
.88(
1… +
con
clus
ion
QW
C: D
ecis
ion
shou
ld b
e st
ated
, su
ppor
ted
by
clea
rly
laid
out
wor
king
Not
e
90si
n5.868
sinAC
does
not
get
mar
ks u
ntil
in t
he f
orm
68si
n90
sin5.8
AC
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
163
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 13
.A
kT
; 40
=
100
kk
= 4
AT
460
4T
31.0
4
M1
Ak
TM
1 40
=
100
k
A1A
T4
A1 f
or 3
0.98
… o
r 31
(.0)
OR
M2
for
40T =
10
060
oe
M1
for
100
6040
T o
e
A1 f
or 3
0.98
… o
r 31
.0
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
165
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 16
. (a
) Vo
l =
2)
2(x
x=
51
Vol =
x
x4
22
– 51
=0
Der
ives
giv
en
answ
er a
nd
cond
itio
n
4M
1 Vo
l =
2)2
(xx
M1
expa
nds
brac
ket
corr
ectl
y A1
(E1
) se
ts e
qual
to
51
B12
x a
s th
e le
ngth
s of
the
cub
oid
have
to
be p
osit
ive.
(b
)
22
)51
(2
4)4
()4
(2
x
4424
4x
6.15
, -4
.15
both
to
3sf
3 M
1 co
rrec
t su
bsti
tuti
on (
allo
w s
ign
erro
rs in
a,
b an
d c)
into
qua
drat
ic
form
ula
M1
442
44
x
A1 6
.14(
7…, −
4.14
(7…
)
Tota
l for
Que
stio
n: 7
mar
ks
17.
An
gle
BAC
= 18
0º —
47º
— 5
8º
= 75
º
)58
sin
(75
sin22
047
sin
ABAC
AC
=75
sin
47si
n22
0 =
166
.57.
.
Area
=58
sin
'57.
166
'22
021
= 15
538
1550
0 m
2 5
B1 f
or 7
5º
M1
)58
sin
(75
sin22
047
sin
ABAC
M1
AC
=75
sin
47si
n22
0
M1
21 ×
220
× “
166.
57”
× si
n58
A1 1
5500
m2
Tota
l for
Que
stio
n: 5
mar
ks
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
166
1MA
0/2H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 18
.
Pent
agon
= 5
equ
al is
os
tria
ngle
s
5360
=72º
Base
ang
les
= (1
80 –
72)
2
=
54º
for
find
ing
equa
l sid
es o
f is
osce
les
tria
ngle
;
72si
n1054
sin
x=
8.50
6508
084…
area
of
isos
cele
s tr
iang
le =
72si
n21
2x
= 34
.409
5480
1..
area
of
pent
agon
=
5 3
4.40
9548
01
= 1
72.0
4774
01
area
of
dode
cahe
dron
=
12
172.
0477
401
OR
Usi
ng r
ight
-ang
led
trig
onom
etry
; h
= 5t
an54
º
= 6.
8819
…
Area
of
isos
cele
s tr
iang
le =
21 1
0 h
= 34
.409
5480
1…ar
ea o
f pe
ntag
on
= 5
34.
4095
4801
=
172.
0477
401
area
of
dode
cahe
dron
=
12
172.
0477
401
2065
cm
2 9
B1 f
or
5360
= 72
º
B1 (
180
–72
) 2
= 5
4º
M1
for
find
ing
equa
l sid
es o
f is
osce
les
tria
ngle
; x
=72
sin10
54si
nx
A1 f
or x
= 8
.506
5080
84…
M1
for
find
ing
area
of
isos
cele
s tr
iang
le =
72
sin
212 x
A1 f
or 3
4.40
9548
01…
(ft)
B1
for
are
a of
pen
tago
n =
5 (
ft)
= 17
2.04
7740
1…(f
t)
B1 f
or a
rea
of d
odec
ahed
ron
= 12
(
ft)=
206
4.57
2881
… c
m2
A1 f
or 2
065
cm2
(oe)
OR
B1 f
or
5360
= 72
º
B1 (
180
– 72
) 2
= 5
4 º
M
1 fo
r us
ing
righ
t-an
gled
tri
gono
met
ry;
h =
5 ta
n54º
A1
for
6.8
819…
M
1 fo
r fi
ndin
g ar
ea o
f is
osce
les
tria
ngle
= 21
10
h
A1 f
or 3
4.40
9548
01…
(ft)
B1 f
or a
rea
of p
enta
gon
= 5
(ft
) =
172.
0477
401…
(ft)
B1
for
are
a of
dod
ecah
edro
n =
12
(ft
) =
2064
.572
881…
cm
2
A1 f
or 2
065
cm2
(oe)
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
168
9.
102030405060
1020
3040
5060
0C
Ds s
old
Freq
uenc
y
Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2009in Mathematics A
169
14.
2468
24
0x
y