Mark Scheme Sample Assessment Material GCSE in Mathematics Specification A

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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
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
155
156
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
157
5.
(c)
(b)
(a)
1MA0/2H
Question
Old median = 22
New median = 22 + 5
Key 4 I 6 means 46 minutes
0: 8
1: 023578
2: 0122233
3: 1345
4: 456
Working
The same +
reason
27 minutes
Correct stem
and leaf
Answer
1
2
3
Mark
Total for Question: 6 marks
C1 All the values have increased by 5 minutes so when you subtract the
5 minutes will cancel out.
M1 finds median correctly for original data and adds 5
A1 cao
OR
M1 Redoes table (ft) with each value increased by 5 and attempts to
find median
A1 cao
B3 Fully correct
(B2 All entries correct, no key)
(B1 correct entries unordered, key or no key)
OR
(B2 Three rows correct, key or no key)
(B1 Two rows correct, key or no key)
Additional Guidance
158
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
7.
6.
FE
QWC
ii, iii
(b)
(a)
1MA0/2H
Question
10 45 150 245 225 55
120
“908000” cm3 × 0.85 g/cm3
= 771800 g
224 > 200
1017.876 ÷ 4.54 = 224 gallons
Vol of tank
602 u ʌ u 180 = 2035752.04..cm3
Half vol of tank
= 1017876.02 cm3
= 1017.876…litres
OR
908000< 1017876.02
1 gallon = 4.54 litres,
200 gallons = 908 litres
= 908000 cm3
Vol of tank
602 u x ʌ u 180 =
2035752.04..cm3
Working
6.08 hours
771.8
No
Answer
4
3
5
Mark
Total for Question: 8 marks
Total for Question: 4 marks
M1 for mid interval values
M1 for multiplying frequencies by mid-interval values
M1 for adding (freq u mid-interval values) ÷ 120
A1 cao
M1 “908000” × 0.85
M1(dep) 771800÷1000
A1 770 — 772
C1 Decision and reason QWC: Decision should be stated, with
appropriate supporting statement
M1 Using formulae to find volume of tank
B1 Converts between litres and cubic centimetres
M1 reads off graph for 1l, 2l , 4l, 5l or 10 litres within tolerance (4.4 —
4.6)
A1 Answer in cm3, litres or gallons
Calculations may be performed in different orders
Response may convert into gallons, litres, or cm3
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
159
8.
(b)
(a)
1MA0/2H
Question
170
x
x 10
3
2
170
5 x 30
6
170
2 x 3 ( x 10 )
6
x
210
5x = 1050
x
x 10
3
2
2x + 3(x – 10) = 170 u 6
5x = 1050
x = 210
OR
x
x 10
3
2
Fred has 2 x left, so solving
3
for x using
pays x 10
2
Malcolm gets £170 for Fred
and Jim, so Malcolm gets
x
and Jim
3
Fred pays
Working
£140
Clear and
coherent
explanation
Answer
4
1
Mark
A1 cao
Total for Question: 5 marks
M1(dep) multiply through by 6 and collect terms
M1 collects terms over 6
M1(dep) expand 3(x í 10)
OR
A1 cao
M1 (dep)collect terms on each side correctly
M1 multiply through by 6 and cancels fractions
M1 (dep)expand 3(x í 10)
C1 a clear and coherent explanation
Additional Guidance
160
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
FE
9.
QWC
i, iii
1MA0/2H
Question
Makes a comparison of the
shape of the distribution by
drawing
Makes a comparison of the
modal classes(31—40, 11—20)
Makes a comparison of the
class intervals that contain
the medians.(31—40, 21—30)
Works out an estimate of the
total sales of each shop(2635,
3530)
Working
Correct
comparisons
Answer
4
Mark
Total for Question: 4 marks
C1 for comments on shape of the distributions
QWC: Decisions should be stated, and all comments should be clear
and follow through from any working or diagrams
Plots frequency polygon or produces table
compares modes
compares medians
compares total sales
B1, B1, B1 for any 4 of the following done correctly
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
161
162
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
FE
12.
QWC
ii, iii
FE
11.
(c)
sin 68 = AC
8.5
AC = 8.5 × sin 68o = 7.881
7.881 + 1 < 9
o
15% of 80 = 12
Reason
supported
by
calculation
Yes, with
correct
conclusion
26
68 – 42
(b)
Answer
28
Working
(a)
1MA0/2H
Question
4
2
2
1
Mark
1
sq tolerance on each)
2
Total for Question: 5 marks
AC
Note
AC
sin 68
8.5
u sin 68
sin 90
Total for Question: 4 marks
8.5 does not get marks until in the form
sin 90
C1 8.88(1… + conclusion QWC: Decision should be stated, supported by
clearly laid out working
M1 sin 68 = AC
8.5
M1 AC = 8.5 × sin 68o
A1 7.88(1…
o
M1 looks up 68 or 40 min on cumulative frequency
A1 correct conclusion
A1 26 — 30 (need
M1 68 — 42
B1 27 — 29
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
163
13.
1MA0/2H
Question
k A
4 A
4 60
A1 for 30.98… or 31.0
Total for Question: 4 marks
Additional Guidance
60
oe
100
60
oe
100
40 u
T
=
40
M1 for T
M2 for
OR
A1 for 30.98… or 31(.0)
4 A
A1 T
M1 T
T
T
4
Mark
M1 40 = k 100
31.0
Answer
T k A ; 40 = k 100
k=4
Working
164
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
165
17.
16.
(b)
(a)
1MA0/2H
Question
220 sin 47
sin 75 = 166.57..
220
AB
(
)
sin 75 sin 58
= 15538
1
u 220u'166.57 'u sin 58
Area= 2
AC =
AC
sin 47
Angle BAC = 180º — 47º — 58º
= 75º
(4) r (4)2 4u 2u(51)
2u 2
4 r 424
x
4
x
Vol = x u ( x 2 ) u 2 = 51
Vol = 2 x 2 4 x – 51 =0
Working
15500 m
5
3
6.15, -4.15
both to 3sf
2
4
Mark
Derives given
answer and
condition
Answer
4r
4
424
1
× 220 × “166.57” × sin58
2
A1 15500 m2
M1
AC
220
AB
(
)
sin 58
M1 sin 47 sin 75
220 sin 47
M1 AC = sin 75
B1 for 75º
A1 6.14(7…, î 4.14(7…)
M1 x
Total for Question: 5 marks
Total for Question: 7 marks
M1 correct substitution (allow sign errors in a, b and c) into quadratic
formula
M1 Vol = x u ( x 2 ) u 2
M1 expands bracket correctly
A1 (E1) sets equal to 51
B1 x ! 2 as the lengths of the cuboid have to be positive.
Additional Guidance
166
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
18.
1MA0/2H
Question
sin 72
Using right-angled
trigonometry; h = 5tan54º
= 6.8819…
Area of isosceles triangle =
1 u 10 u h
2
= 34.40954801…
area of pentagon
= 5 u 34.40954801
= 172.0477401
area of dodecahedron
= 12 u 172.0477401
OR
= 34.40954801..
area of pentagon
= 5 u 34.40954801
= 172.0477401
area of dodecahedron
= 12 u 172.0477401
1 2
x sin 72
2
area of isosceles triangle =
8.506508084…
sin 54
Pentagon = 5 equal isos
triangles
360 =72º
5
Base angles = (180 – 72) y 2
= 54º
for finding equal sides of
isosceles triangle;
x
10
=
Working
2065 cm
2
Answer
9
Mark
x
sin 54
2
10
sin 72
A1 for 34.40954801…(ft)
B1 for area of pentagon = 5 u (ft) = 172.0477401…(ft)
B1 for area of dodecahedron = 12 u (ft) = 2064.572881… cm2
A1 for 2065 cm2 (oe)
M1 for using right-angled trigonometry; h = 5 tan54º
A1 for 6.8819…
M1 for finding area of isosceles triangle = 1 u 10 u h
B1 for
360
= 72º
5
B1 (180 – 72) y 2 = 54 º
OR
A1 for 34.40954801…(ft)
B1 for area of pentagon = 5 u (ft) = 172.0477401…(ft)
B1 for area of dodecahedron = 12 u (ft)= 2064.572881… cm2
A1 for 2065 cm2 (oe)
M1 for finding area of isosceles triangle = 1 x 2 sin 72
2
A1 for x = 8.506508084…
M1 for finding equal sides of isosceles triangle; x =
B1 for 360 = 72º
5
B1 (180 – 72) y 2 = 54º
Additional Guidance
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
167
60
CDs sold
50
40
30
20
10
0
10
20
30
40
50
60
Frequency
9.
168
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
x
4
2
0
2
4
6
8
y
14.
Edexcel GCSE
in Mathematics A
Sample Assessment Materials
© Edexcel Limited 2009
169
October 2009
For more information on Edexcel and BTEC qualifications
please visit our website: www.edexcel.org.uk
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Registered Office: One90 High Holborn, London WC1V 7BH. VAT Reg No 780 0898 07

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