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Mark Scheme
Sample Assessment Material
GCSE
GCSE in Mathematics Specification A Higher Tier Paper 1:(Non-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 candidates 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
75
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
76
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 3. FE
N
o of
tile
s ar
ound
roo
m
= 2
le
ngth
s of
roo
m =
8,
16,
16,
12
Tota
l num
ber
of t
iles
= 8
16
+ 8
1
2 =
224
Cost
= 4
2
24
OR
Area
of
the
room
=
4
8 +
4
6 =
56
Area
of
a ti
le
= 0.
5
0.5
= 0.
25
Num
ber
of t
iles
= 56
0.25
=
224
Cost
= 4
2
24
89
6 6
M1
for
doub
ling
each
leng
th t
o sh
ow n
umbe
r of
tile
s fo
r ea
ch s
ide
B1 f
or 8
, 16
, 16
and
12
M1
for
a fu
ll m
etho
d of
fin
ding
the
num
ber
of t
iles
(12
16
+ 8
4)
A1 f
or a
t le
ast
one
sec
tion
co
rrec
t M
1 fo
r 4
22
4
A1 c
ao
OR
M1
for
full
met
hod
for
find
ing
the
area
of
the
room
A1
at
leas
t on
e ar
ea c
orre
ct
B1 f
or a
rea
of t
ile =
0.2
5m2
or 2
500
cm2
or 4
tile
s =
1 m
2
M1
for
area
of
room
a
rea
of a
tile
M
1 fo
r 4
nu
mbe
r of
tile
s A1
cao
Tota
l for
Que
stio
n: 6
mar
ks
4.
(a)
5p=
20
p=
4 2
M1
add
16 t
o bo
th s
ides
A1
cao
(b
) 9
= 3
q q
=
32
M1
corr
ect
met
hod
to is
olat
e 3
qA1
cao
(c
) 6x
3 1
0
6x =
1
3 2
M1
at le
ast
one
expa
nsio
n co
rrec
t A1
13
or a
sta
tem
ent
that
the
ans
wer
is in
dep
of x
dep
endi
ng o
n co
rrec
t w
orki
ng
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
77
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
78
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 8.
121
4x
x
215
x,
101x
OR
Choo
ses
a su
itab
le n
umbe
r of
ba
lls (
say
10)
5 w
ill b
e re
d Th
e ot
her
5 ne
ed t
o be
sh
ared
out
in t
he r
atio
1:4
, H
ence
1 y
ello
w a
nd 4
blu
e
1043
M1
121
4x
x
A1101
x
A1104
oe
Tota
l for
Que
stio
n: 3
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
79
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 9.
(a
) (i
)
(ii)
a2 6x4 y
3
3 B1
cao
B26x
4 y3
(B1
for
2 ou
t of
3 t
erm
s co
rrec
t in
a p
rodu
ct)
(b
) x2
+ 3
x +
7x +
21
x2 +
10x
+ 2
1 2
M1
3 or
4 t
erm
s ou
t of
4 c
orre
ct in
a 4
ter
m e
xpan
sion
A1
cao
(c
)
3p(q
4p
) 2
B2 c
ao
(B1
p(3q
12
p), 1
2p( 41
q
p), p
(aq
+ bp
) whe
re a
and
b a
re n
umbe
rs)
(d
)(i)
(ii)
)32
(1
)2(3
xx
OR
320
1012
123
2x
xx
=5
23
2x
x
(3y
1)(y
3
) )1)(5
3(x
x
4 B2
cao
(B
1 (3
y
m)(y
n
) whe
re m
n =
3 o
r m
+ n
=
10
M1
use
of t
he f
acto
rise
d fo
rm w
ith
y re
plac
ed t
wic
e by
3x
+ 2
A1 c
ao
OR
B15
23
2x
xB1
cao
Tota
l for
Que
stio
n: 1
1 m
arks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
80
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 10
.
Reds
6,
12,
18,
24,
30
G
reen
s 9,
18,
27
201
3 B1
list
of
red
and
gree
n m
ulti
ples
(bo
th t
o at
leas
t 18
) or
exp
licit
ly
stat
es
LCM
B1
wor
ks o
ut h
ighe
st n
umbe
r (9
0 se
en)
B1201
(ac
cept
1005
)
Tota
l for
Que
stio
n: 3
mar
ks
11.
425x
695
xy
or6
59
xy
x =
2.5
y =1
1.25
4M
1 a
corr
ect
expr
essi
on f
or x
invo
lvin
g ra
tios
of
side
s, e
.g.
425x
oe
A1 c
ao
M1
695
xy
or6
59
xy
oe
A1 c
ao
OR
495y A1
cao
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
81
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 12
.
(a)
4
6
8
10
6
8 1
0
12
8 1
0 1
2 1
4 10
12
14
16
OR 41
41
441
41
1643
M1
Atte
mpt
s to
list
all
outc
ome
pair
s A1
all
16 f
ound
A1
cao
OR
M2
441
41
(M1
2,1
4141
or 3
)
A1164
oe
(b
) Pr
ob A
li w
ins
= 166
Num
ber
of w
ins
= 80
166
30
3 B1
Pro
b Al
i win
s =
166 o
e
M1
80'
166 '
A1 f
t
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
82
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 13
. (a
) 7
104.3
1 B1
cao
(b)
1005
104.2
12(
610
)5
102.1
2M
1 10
0510
4.212
oe (
610
)
A1 c
ao
Tota
l for
Que
stio
n: 3
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
83
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 14
.
Let
AB =
x,A
D =
yAr
ea o
f re
ctan
gle
=xy
Area
AXD
=
4xy
Area
CYZ
=8xy
Shad
ed a
rea
= 85xy
854
M1
a fu
ll m
etho
d to
fin
d th
e un
shad
ed a
rea
and
subt
ract
ing
from
1
B1 a
rea
of A
XD =
are
a of
ABC
D4
B1 a
rea
of C
YZ=
are
a of
ABC
D8
A1 c
ao
OR
Dia
gram
M1
for
divi
ding
left
into
2 c
ongr
uent
tri
angl
es
f
or d
ivid
ing
righ
t in
to 4
con
grue
nt t
rian
gles
B1
left
= 2
Aan
d 2A
or
sha
ded
= 21
of
21=
41 =
82
B1 r
ight
= 2
A an
d A
and
A or
shad
ed =
43of
21 =
83
A1 c
ao
Subs
titu
tion
M1
for
deci
ding
upo
n su
itab
le s
ide
leng
ths
for
ADan
d AB
and
cal
cula
ting
di
men
sion
s of
inte
rnal
sha
pes
B1 f
or a
rea
of D
ZXB1
for
are
a of
ZXB
YA1
cao
OR
M1
for
deci
ding
upo
n su
itab
le s
ide
leng
ths
for
ADan
d AB
and
cal
cula
ting
di
men
sion
s of
inte
rnal
sha
pes
B1 f
or a
rea
ADX
B1 f
or a
rea
ZCY
A1 c
ao
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
84
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 15
.
(a)
(i)
(ii)
BC =
O
BC
O
AQ =
BQ
OB
AO
=
4a +
4b
+ 41
(12a
4b
)
12a
4b
3b
a
4
M1
BC =
O
BC
OA1
cao
M1
4a
+ 4b
+ 41
(12
a
4b)
A1 c
ao
(b
) O
X=
12b
, AX
=4a
+ 1
2b=
4(a
+ 3
b)
Corr
ect
reas
on,
wit
h co
rrec
t w
orki
ng
3B1
OX
= 12
b
B1AX
=4a
+ 1
2bC1
con
vinc
ing
expl
anat
ion
Tota
l for
Que
stio
n: 7
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
85
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 16
.
8596
104 =
720120
720
120
+
8495
106 +
8594
106
720
360
4M
1 fo
r 85
96104
A1 f
or 7
20120
oe
M1
720'
120
' +
2 c
orre
ct c
ases
(M
1 an
y 2
corr
ect
case
s)
or72
0'12
0'
X 3
A1 c
ao
SC w
ith
repl
acem
ent
M1
106106
104
M1
106106
1043
Tota
l for
Que
stio
n: 4
mar
ks
17.
)53)(5
3()7
)(53(
xx
xx
53
7xx
3B1
)7)(5
3(x
xB1
)53)(5
3(x
x
B15
37
xx
Tota
l for
Que
stio
n: 3
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
86
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 18
. (a
)
211
B1
(b
) (2
+
3)
)31(
=9
33
22
33
52
M1
4 te
rm e
xpan
sion
wit
h 3,
4 t
erm
s co
rrec
t an
d si
ght
of 3
or
9A1
cao
Tota
l for
Que
stio
n: 3
mar
ks
19.
(a)
Sm
ooth
cu
rve
2 B1
cor
rect
plo
t of
the
ir v
alue
s B1
sm
ooth
cur
ve t
hrou
gh t
heir
poi
nts
(b
)
x =
3 y
= 0
3 M
1 at
tem
pts
to d
raw
cir
cle
at o
rigi
n M
1 us
es r
adiu
s 3
cm (
usin
g gr
aph
scal
e co
rrec
tly)
A1
cao
OR
B1 f
or s
ubst
itut
ing
a va
lue
of x
into
y =
x(x
3)
and
2
2r
yx
B1 f
or s
ubst
itut
ing
yin
tox
= 3
into
x(x
3
) and
2
2r
yx
B1 c
ao
Tota
l for
Que
stio
n: 5
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
87
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 20
.Q
WC
ii, ii
i
22
)12(
)12(
nn
=)1
44(
14
42
2n
nn
n
=8n
OR
22
)12(
)12(
nn
=))1
21
2()12(
)12(
nn
nn
=2
4n
= 8
n
Fully
alge
brai
c ar
gum
ent,
se
t ou
t in
a
logi
cal a
nd
cohe
rent
man
ner
6 B2
the
nth
term
for
con
secu
tive
odd
num
bers
is 2
n
1 oe
(B
12n
+ k
,1
kor
n=
2n
1 o
r 2x
1B1
use
of
2n +
1 a
nd 2
n
1 oe
M
1 2
2)1
2()1
2(n
nM
1)1
44(
14
42
2n
nn
n
C1 c
oncl
usio
n ba
sed
on c
orre
ct a
lgeb
ra Q
WC:
Con
clus
ion
shou
ld b
e st
ated
, w
ith
corr
ect
supp
orti
ng a
lgeb
ra.
OR
B1 u
se o
f 2n
+ 1
and
2n
1 o
e M
1 2
2)1
2()1
2(n
nM
1))1
21
2()12(
)12(
nn
nn
C1 c
oncl
usio
n ba
sed
on c
orre
ct a
lgeb
ra Q
WC:
Con
clus
ion
shou
ld b
e st
ated
, w
ith
corr
ect
supp
orti
ng a
lgeb
ra. T
otal
for
Que
stio
n: 6
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
88
1MA
0/1H
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 21
.
L
F FD
CF
0
10
40
4 40
10
20
60
6 10
0 20
40
90
4.5
190
408
0 60
1.
5 25
0 >8
0 0
0 25
0
His
togr
amO
RCu
mul
ativ
e Fr
eque
ncy
poly
gon
82%
6 B1
Sca
les
labe
lled
and
also
mar
ked
on t
he v
erti
cal a
xis
wit
h fr
eque
ncy
dens
ity
or w
ith
cum
ulat
ive
freq
uenc
y M
1 fr
eque
ncy
dens
itie
s ca
lcul
ated
, at
leas
t on
e no
n-tr
ivia
l one
cor
rect
. A1
all
corr
ectl
y pl
otte
d (M
1 cu
mul
ativ
e fr
eque
ncie
s co
rrec
t)
M1
Use
50
on t
he h
oriz
onta
l sca
le o
f CF
dia
gram
rea
d of
f ve
rtic
al a
xis
(200
-210
)or
Use
50
on t
he h
oriz
onta
l sca
le o
f a
hist
ogra
m a
nd c
over
t ar
ea t
o th
e le
ft t
o a
freq
uenc
y M
1 co
nver
t to
a p
erce
ntag
e A1
80
85
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
89
2.
Frac
tion
D
ecim
al
%
kg
Jan
1010.
110
%N
ot k
now
n
Feb
810.
125
12.5
% 15
kg
Mar
100
130.
13
13%
14.5
6 kg
14.
AB C
D
X
Y
Z
AB C
D
X
Y
Z
Edexcel GCSE Sample Assessment Materials Edexcel Limited 2009in Mathematics A
90
November 2009 For more information on Edexcel and BTEC qualifications please visit our website: www.edexcel.org.uk Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH. VAT Reg No 780 0898 07