1. science
2. mathematics

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
x
All candidates must receive the same treatment. Examiners must mark the
first candidate in exactly the same way as they mark the last.
x
Mark schemes should be applied positively. Candidates must be rewarded for
what they have shown they can do rather than penalised for omissions.
x
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.
x
Where some judgement is required, mark schemes will provide the principles
by which marks will be awarded and exemplification may be limited.
x
Crossed out work should be marked UNLESS the candidate has replaced it
with an alternative response.
x
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
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
75
76
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
4.
3.
FE
5p = 20
–9 = 3q
6x – 3 í10 – 6x =
(b)
(c)
No of tiles around room
= 2 × lengths of room = 8, 16,
16, 12
Total number of tiles
= 8 × 16 + 8 × 12 = 224
Cost = 4 × 224
OR
Area of the room
=4 × 8 + 4 × 6 = 56
Area of a tile
= 0.5 × 0.5 = 0.25
Number of tiles = 56 y 0.25
= 224
Cost = 4 × 224
Working
(a)
1MA0/1H
Question
–13
q = í3
p=4
£ 896
Answer
2
2
2
6
Mark
Total for Question: 6 marks
Total for Question: 6 marks
M1 at least one expansion correct
A1 –13 or a statement that the answer is indep of x depending on
correct working
M1 correct method to isolate ±3q
A1 cao
M1 add 16 to both sides
A1 cao
M1 for doubling each length to show number of tiles for each side
B1 for 8, 16, 16 and 12
M1 for a full method of finding the number of tiles (12 u 16 + 8 u 4)
A1 for at least one ‘section’ correct
M1 for 4 u ‘224’
A1 cao
OR
M1 for full method for finding the area of the room
A1 at least one area correct
B1 for area of tile = 0.25m2 or 2500 cm2 or 4 tiles = 1 m2
M1 for area of room y area of a tile
M1 for 4 × number of tiles
A1 cao
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
77
78
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
8.
1MA0/1H
Question
1,
x
2
1
2
1
10
1
Chooses a suitable number of
balls (say 10)
5 will be red
The other 5 need to be
shared out in the ratio 1:4,
Hence 1 yellow and 4 blue
OR
5x
x 4x Working
4
10
Answer
3
Mark
10
A1 4 oe
M1 x 4 x 1
2
1
A1 x
10
1
Total for Question: 3 marks
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
79
9.
(ii)
(d)(i)
(c)
(b)
(3y–1)(y – 3)
3p(q î 4p)
x2 + 10x + 21
= 3x 2 2x 5
(3 x 5)( x 1)
OR
2
3 x 12 x 12 10 x 20 3
3( x 2) 1( x 2 3)
x2 + 3x + 7x + 21
6x4y3
4
2
2
3
2
(ii)
Mark
Answer
a
Working
(a) (i)
1MA0/1H
Question
1
q í p), p(aq + bp) where a and b are numbers)
4
Total for Question: 11 marks
M1 use of the factorised form with y replaced twice by 3x + 2
A1 cao
OR
B1 3 x 2 2 x 5
B1 cao
B2 cao
(B1 (3y í m)(y í n) where mn = ±3 or m + n = ±10
(B1 p(3q í 12p), 12p(
B2 cao
M1 3 or 4 terms out of 4 correct in a 4 term expansion
A1 cao
B2 6x4y3
(B1 for 2 out of 3 terms correct in a product)
B1 cao
Additional Guidance
80
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
y
x5
9 or y
6
9
x 5
6
x
5
11.
2
4
Reds 6, 12, 18, 24, 30…
Greens 9, 18, 27…
Working
10.
1MA0/1H
Question
y =11.25
x = 2.5
1
20
Answer
4
3
Mark
1
5
(accept
)
20
100
A1 cao
y
5
9
4
y
x5
A1 cao
OR
M1
9 or y
9
6
x 5 oe
6
Total for Question: 4 marks
2 oe
4
Total for Question: 3 marks
M1 a correct expression for x involving ratios of sides, e.g. x
5
A1 cao
B1
B1 list of red and green multiples (both to at least 18) or explicitly
states ‘LCM’
B1 works out highest number (90 seen)
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
81
12.
(b)
(a)
1MA0/1H
Question
6
8
10
12
8
10
12
14
10
12
14
16
Number of wins = 6 u 80
16
Prob Ali wins = 6
16
1 1
u u4
4 4
OR
1 1
u
4 4
4
6
8
10
Working
30
4
16
Answer
3
3
Mark
4
4
4
16
A1 ft
M1 ' 6 'u 80
B1 Prob Ali wins =
4
oe
A1
16
4
6 oe
16
(M1 1 u 1 u 1 , 2 or 3)
M2 1 u 1 u 4
OR
Total for Question: 6 marks
Additional Guidance
M1 Attempts to list all outcome pairs
A1 all 16 found
A1 cao
82
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
13.
5
( y 10 6 )
100
1 .2 u 10 5
2.4 u 1012 u
(b)
7
Answer
3 . 4 u 10
Working
(a)
1MA0/1H
Question
2
1
Mark
Total for Question: 3 marks
Additional Guidance
M1 2 . 4 u 10 12 u 5 oe ( y 10 6 )
100
A1 cao
B1 cao
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
83
14.
1MA0/1H
Question
Let AB = x, AD = y
Area of rectangle = xy
xy
Area AXD =
4
xy
Area CYZ =
8
Shaded area = 5 xy
8
Working
5
8
Answer
4
Mark
Additional Guidance
Total for Question: 4 marks
OR
M1 for deciding upon suitable side lengths for AD and AB and calculating
dimensions of internal shapes
B1 for area ADX
B1 for area ZCY
A1 cao
Substitution
M1 for deciding upon suitable side lengths for AD and AB and calculating
dimensions of internal shapes
B1 for area of DZX
B1 for area of ZXBY
A1 cao
M1 a full method to find the unshaded area and subtracting from 1
B1 area of AXD = area of ABCD y 4
B1 area of CYZ = area of ABCD y 8
A1 cao
OR
Diagram
M1 for dividing left into 2 congruent triangles
for dividing right into 4 congruent triangles
B1 left = 2A and 2A or
1= 1 = 2
shaded = 1 of
2 4
2
8
B1 right = 2A and A and A or
1
3
shaded = 3 of
=
2
8
4
A1 cao
84
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
15.
(b)
(ii)
(a)
(i)
1MA0/1H
Question
o
o
o
= 4(–a + 3b)
o
o
OX = 12b , AX =–4a + 12b
AQ = AO OB BQ
1
= –4a + 4b + (12a – 4b)
4
o
BC = CO OB
o
Working
o
o
Correct
reason, with
correct
working
3
4
12a – 4b
3b – a
Mark
Answer
o
o
B1 AX =–4a + 12b
C1 convincing explanation
o
o
B1 OX = 12b
M1 –4a + 4b + 1
4
‘(12a – 4b)’
A1 cao
A1 cao
o
M1 BC = CO OB
Total for Question: 7 marks
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
85
17.
16.
1MA0/1H
Question
(3 x 5)( x 7)
(3 x 5)(3 x 5)
6 5 4
120
+
u u +
720 10 9 8
6 4 5
u u
10 9 8
4 6 5 120
u u =
720
10 9 8
Working
x7
3x 5
Answer
360
720
3
4
Mark
B1
(3x 5)(3x 5)
x7
B1
3x 5
B1 (3 x 5)( x 7)
4 6 6
u u
10 10 10
4 6 6
u u ×3
M1
10 10 10
M1
SC with replacement
A1 cao
M1
Total for Question: 3 marks
Total for Question: 4 marks
'120'
+ 2 correct cases (M1 any 2 correct cases)
720
'120'
X3
or
720
4 6 5
u u
10 9 8
120
A1 for
oe
720
M1 for
Additional Guidance
86
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
19.
18.
3 ) u (1 3 )
x=3
y=0
(b)
53 3
Answer
1
2
Smooth
curve
= 22 3 3 9
(2 +
Working
(a)
(b)
(a)
1MA0/1H
Question
3
2
2
1
Mark
Additional Guidance
B1 cao
Total for Question: 5 marks
B1 for substituting a value of x into y = x(x – 3) and
x2 y
r2
2
B1 for substituting y into x = 3 into x(x – 3) and x y
r2
OR
9
Total for Question: 3 marks
M1 attempts to draw circle at origin
M1 uses radius 3 cm (using graph scale correctly)
A1 cao
B1 correct plot of their values
B1 smooth curve through their points
M1 4 term expansion with 3, 4 terms correct and sight of 3 or
A1 cao
B1
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
87
20.
QWC
ii, iii
1MA0/1H
Question
= 2 × 4n = 8n
(2n 1) (2n 1)(2n 1 2n 1))
( 2 n 1) 2 ( 2 n 1) 2 =
OR
= 8n
=
4 n 2 4 n 1 ( 4 n 2 4 n 1)
Working
( 2 n 1) ( 2 n 1) 2
2
Mark
6
Answer
Fully
algebraic
argument,
set out in a
logical and
coherent
manner
Total for Question: 6 marks
C1 conclusion based on correct algebra QWC: Conclusion should be
stated, with correct supporting algebra.
OR
B1 use of 2n + 1 and 2n –1 oe
M1 ( 2 n 1) 2 ( 2 n 1 ) 2
M1 (2n 1) (2n 1) (2n 1 2n 1))
C1 conclusion based on correct algebra QWC: Conclusion should be
stated, with correct supporting algebra.
M1 4n 2 4n 1 (4n 2 4n 1)
B2 the nth term for consecutive odd numbers is 2n – 1 oe
(B1 2n + k, k z 1 or n = 2n – 1 or 2x í1
B1 use of 2n + 1 and 2n – 1 oe
M1 ( 2 n 1) 2 ( 2 n 1) 2
Additional Guidance
88
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
21.
1MA0/1H
Question
0–10
10–20
20–40
40–80
>80
L
F
40
60
90
60
0
FD
4
6
4.5
1.5
0
Working
CF
40
100
190
250
250
82%
Histogram
OR
Cumulative
Frequency
polygon
Answer
6
Mark
Total for Question: 6 marks
M1 Use 50 on the horizontal scale of CF diagram read off vertical axis
(200-210)
or Use 50 on the horizontal scale of a histogram and covert area to the
left to a frequency
M1 convert to a percentage
A1 80 – 85
B1 Scales labelled and also marked on the vertical axis with frequency
density or with cumulative frequency
M1 frequency densities calculated, at least one non-trivial one correct.
A1 all correctly plotted
(M1 cumulative frequencies correct)
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
89
14.
Mar
Feb
Jan
2.
X
Z
D
0.13
0.125
0.1
Decimal
A
13
100
1
8
1
10
Fraction
13%
12.5%
10%
%
D
Z
C
B
C
X
Y
A
Y
B
14.56 kg
15 kg
Not known
kg
90
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
November 2009
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