Edexcel Maths A Level Paper 31
Statistics MS
,Pearson Edexcel
Mark Scheme (Results)
November 2021
Pearson Edexcel GCE
In Mathematics (9MA0)
Paper 31 Statistics
Pearson edexcel
,Edexcel and BTEC Qualifications
Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest awarding body. We provide a
wide range of qualifications including academic, vocational, occupational and specific programmes for
employers. For further information visit our qualifications websites at www.edexcel.com or
www.btec.co.uk. Alternatively, you can get in touch with us using the details on our contact us page at
www.edexcel.com/contactus.
Pearson: helping people progress, everywhere
Pearson aspires to be the world’s leading learning company. Our aim is to help everyone progress in their
lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in
the world. We’ve been involved in education for over 150 years, and by working across 70 countries, in 100
languages, we have built an international reputation for our commitment to high standards and raising
achievement through innovation in education. Find out more about how we can help you and your
students at: www.pearson.com/uk
October 2021
Question Paper Log Number P68828A
Publications Code 9MA0_03_2111_MS
All the material in this publication is copyright
© Pearson Education Ltd 2021
,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.
Examiners should mark according to the mark scheme not according
to their perception of where the grade boundaries may lie.
There is no ceiling on achievement. All marks on the mark scheme
should be used appropriately.
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.
When examiners are in doubt regarding the application of the mark
scheme to a candidate’s response, the team leader must be
consulted.
Crossed out work should be marked UNLESS the candidate has
replaced it with an alternative response.
, EDEXCEL GCE MATHEMATICS
General Instructions for Marking
1. The total number of marks for the paper is 100.
2. The Edexcel Mathematics mark schemes use the following types of marks:
M marks: method marks are awarded for ‘knowing a method and attempting to
apply it’, unless otherwise indicated.
A marks: Accuracy marks can only be awarded if the relevant method (M) marks
have been earned.
B marks are unconditional accuracy marks (independent of M marks)
Marks should not be subdivided.
3. Abbreviations
These are some of the traditional marking abbreviations that will appear in the mark
schemes.
bod – benefit of doubt
ft – follow through
the symbol will be used for correct ft
cao – correct answer only
cso - correct solution only. There must be no errors in this part of the
question to obtain this mark
isw – ignore subsequent working
awrt – answers which round to
SC: special case
oe – or equivalent (and appropriate)
dep – dependent
indep – independent
dp decimal places
sf significant figures
🞸 The answer is printed on the paper
, The second mark is dependent on gaining the first mark
4. For misreading which does not alter the character of a question or materially
simplify it, deduct two from any A or B marks gained, in that part of the question
affected.
5. Where a candidate has made multiple responses and indicates which response
they wish to submit, examiners should mark this response.
If there are several attempts at a question which have not been crossed out,
examiners should mark the final answer which is the answer that is the most
complete.
6. Ignore wrong working or incorrect statements following a correct answer.
7. Mark schemes will firstly show the solution judged to be the most common
response expected from candidates. Where appropriate, alternatives
answers are provided in the notes. If examiners are not sure if an answer is
acceptable, they will check the mark scheme to see if an alternative answer is
given for the method used.
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
,
, 9MA0-31 Mark Scheme October 2021(Final)
Qu 1 Scheme Marks AO
(a) Disadvantage: e.g. Not random; cannot use (reliably) for inferences B1 1.1b
(1)
(b) [Sight or correct use of] X ~B(36, 0.08) M1 3.3
(i) P(X = 4) = 0.167387… awrt 0.167 A1 1.1b
(ii) P( X …7) 1 P( X „ 6) 0.022233… awrt 0.0222 A1 1.1b
(3)
(c) P(In dance club and dance tango) = 0.4 0.08 = 0.032 or 4 or 3.2% 1.1b
B1
125
(1)
(d) [Let T = those who can dance the Tango. Sight or use of]
M1 3.3
T ~B(50, “0.032”)
[P(T < 3 ) = P(T „ 2) = ] 0.7850815… awrt 0.785 A1 1.1b
(2)
( 7 marks)
Notes
(a) B1 for a suitable disadvantage:
Allow (B1) Do NOT allow (B0)
Not random or less random (o.e.) Not representative
Cannot use (reliably) for inferences Less accurate
(More likely to be) biased Any comment based on time or cost
Any mention of skew
Any mention of non-response
(b) M1 for sight of B(36, 0.08) Allow in words: binomial with n = 36 and p = 0.08
may be implied by one correct answer to 2sf or sight of P( X „ 6) 0.97776... i.e. awrt 0.98
Allow for 36C4 0.084 0.9232 as this is "correct use"
(i) 1st A1 for awrt 0.167 NB An answer of just awrt 0.167 scores M1( )1st A1
nd
(ii) 2 A1 for awrt 0.0222
(c) B1 for 0.032 o.e. (Can allow for sight of 0.4 0.08 )
(d) M1 for sight of B(50, “0.032”) ft their answer to (c) provided it is a probability 0.08
may be implied by correct answer
or sight of [P(T „ 3)] = 0.924348…i.e. awrt 0.924 or P(T „ 2) as part of 1 – P(T „ 2) calc.
A1 for awrt 0.785
MR Allow MR of 50 (e.g. 30) provided clearly attempting P(T „ 2) and score M1A0
,Qu 2 Scheme Marks AO
(a) Negative B1 1.2
(1)
(b) Marc’s suggestion is compatible because it’s negative correlation
B1 2.4
(1)
(c) (r = ) – 0.54458266… awrt – 0.545 B1 1.1b
(1)
(d) H0 : 0 H1 : 0 B1 2.5
[5% 1-tail cv = ] (+) 0.4259 M1 1.1a
(significant result / reject H0)
There is evidence of negative correlation between the number of letters in A1 2.2b
(or length of) a student’s last name and their first name
(3)
( 6 marks)
Notes
(a) B1 for “negative” Allow “slight” or “weak” etc
Allow a description e.g. “as x increases y decreases” or in context e.g. “people with longer
last names tend to have shorter first names”
A comment of “negative skew” is B0
Need to see distinct or separate responses for (a) and (b)
(b) B1 for a comment that suggests data is compatible with the suggestion and a suitable reason
such as “there is negative correlation” or a description in x and y or in context
or the points lie close to a line with negative gradient
or draw line y = x and state that more points below the line so supports (or is compatible
with) his suggestion
A reason based on just a single point is B0
e.g. “ 11 letters in last name has only 5 in first name”
(c) B1 for awrt – 0.545
(d) B1 for both hypotheses correct in terms of
M1 for a critical value compatible with their H1:
1-tail: awrt + 0.426 (condone + 0.425) or 2-tail (B0 scored for H1) : awrt + 0.497
If hypotheses are in words and can deduce whether one or two-tail then use their words.
If no hypotheses or their H1 is not clearly one or two tail assume one-tail
A1 for compatible signs between cv and r and a correct conclusion in context mentioning
correlation and number of letters or length and name (ft their value from (c))
Do NOT award this A mark if contradictory comments or working seen e.g. “accept H 0”
or comparison of 0.426 with significance level of 0.05 etc
NB The M1A1 can be scored independently of the hypotheses
, Qu 3 Scheme Marks AO
(a) Hectopascal or hPa B1 1.2
(1)
(b) 214
x y 1010 or 1010 M1 1.1b
30
= 1017.1333… awrt 1017 A1 1.1b
(2)
(c) x y (or statement that standard deviation is not affected by this
M1 3.1b
type of coding)
5912
"7.13[33...]" or 146.1822...
2
y
M1 1.1b
30
= 12.0905… awrt 12.1 A1 1.1b
(3)
(d) High pressure (since approx. mean + sd ) so clockwise
B1
Locations are (from North to South): Leuchars, Heathrow, Hurn
2.4
Wind direction is direction wind blows from
So: Heathrow (NE) Hurn (E) Leuchars (W) B1 2.2a
(2)
( 8 marks)
Notes
FYI 1 hPa = 100 Pa; 10hPa = 1 kPa; 1Pa = 1 Nm-2
(a) B1 for “hectopascal” or hPa (condone pascals, allow millibars or mb) o.e.
Do NOT allow kPa or kilopascals or Pa on its own
(b) M1 for a strategy to find x
Allow an attempt to find x that gets as far as x y 30 1010 [= 30 514]
A1 for awrt 1017 (accept 1020) [Ignore incorrect units]
(c) 1 M1 for an overall strategy using the fact x y (can be implied by correct final ans)
st
or for x 30 514 and x2 31 041192 (both seen and correct)
2nd M1 for a correct expression (with )(ft their y to 3sf) allow awrt 146 for 146.1822..
or for correct expression in x can ft their x 30 000 or their answer to (b)
A1 (dep on 2nd M1) for awrt 12.1 [Ignore incorrect units]
Final
answer Final ans of awrt 12.1 scores 3/3 but if they then adjust for x e.g. add 1010 (M0M1A1)
(d) 1st B1 for at least one of these reasons (these 2 lines) clearly stated (may see diagram)
Need “high pressure” and “clockwise” to score on 1st line
Contradictory statements B0 e.g. correct N~S list but say “anticlockwise”
2nd B1 (indep of 1st B1) for deducing the 3 correct directions either in the table or stated
as above
If the answers in table and text are different we take the table (as question says)
Statistics MS
,Pearson Edexcel
Mark Scheme (Results)
November 2021
Pearson Edexcel GCE
In Mathematics (9MA0)
Paper 31 Statistics
Pearson edexcel
,Edexcel and BTEC Qualifications
Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest awarding body. We provide a
wide range of qualifications including academic, vocational, occupational and specific programmes for
employers. For further information visit our qualifications websites at www.edexcel.com or
www.btec.co.uk. Alternatively, you can get in touch with us using the details on our contact us page at
www.edexcel.com/contactus.
Pearson: helping people progress, everywhere
Pearson aspires to be the world’s leading learning company. Our aim is to help everyone progress in their
lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in
the world. We’ve been involved in education for over 150 years, and by working across 70 countries, in 100
languages, we have built an international reputation for our commitment to high standards and raising
achievement through innovation in education. Find out more about how we can help you and your
students at: www.pearson.com/uk
October 2021
Question Paper Log Number P68828A
Publications Code 9MA0_03_2111_MS
All the material in this publication is copyright
© Pearson Education Ltd 2021
,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.
Examiners should mark according to the mark scheme not according
to their perception of where the grade boundaries may lie.
There is no ceiling on achievement. All marks on the mark scheme
should be used appropriately.
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.
When examiners are in doubt regarding the application of the mark
scheme to a candidate’s response, the team leader must be
consulted.
Crossed out work should be marked UNLESS the candidate has
replaced it with an alternative response.
, EDEXCEL GCE MATHEMATICS
General Instructions for Marking
1. The total number of marks for the paper is 100.
2. The Edexcel Mathematics mark schemes use the following types of marks:
M marks: method marks are awarded for ‘knowing a method and attempting to
apply it’, unless otherwise indicated.
A marks: Accuracy marks can only be awarded if the relevant method (M) marks
have been earned.
B marks are unconditional accuracy marks (independent of M marks)
Marks should not be subdivided.
3. Abbreviations
These are some of the traditional marking abbreviations that will appear in the mark
schemes.
bod – benefit of doubt
ft – follow through
the symbol will be used for correct ft
cao – correct answer only
cso - correct solution only. There must be no errors in this part of the
question to obtain this mark
isw – ignore subsequent working
awrt – answers which round to
SC: special case
oe – or equivalent (and appropriate)
dep – dependent
indep – independent
dp decimal places
sf significant figures
🞸 The answer is printed on the paper
, The second mark is dependent on gaining the first mark
4. For misreading which does not alter the character of a question or materially
simplify it, deduct two from any A or B marks gained, in that part of the question
affected.
5. Where a candidate has made multiple responses and indicates which response
they wish to submit, examiners should mark this response.
If there are several attempts at a question which have not been crossed out,
examiners should mark the final answer which is the answer that is the most
complete.
6. Ignore wrong working or incorrect statements following a correct answer.
7. Mark schemes will firstly show the solution judged to be the most common
response expected from candidates. Where appropriate, alternatives
answers are provided in the notes. If examiners are not sure if an answer is
acceptable, they will check the mark scheme to see if an alternative answer is
given for the method used.
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
,
, 9MA0-31 Mark Scheme October 2021(Final)
Qu 1 Scheme Marks AO
(a) Disadvantage: e.g. Not random; cannot use (reliably) for inferences B1 1.1b
(1)
(b) [Sight or correct use of] X ~B(36, 0.08) M1 3.3
(i) P(X = 4) = 0.167387… awrt 0.167 A1 1.1b
(ii) P( X …7) 1 P( X „ 6) 0.022233… awrt 0.0222 A1 1.1b
(3)
(c) P(In dance club and dance tango) = 0.4 0.08 = 0.032 or 4 or 3.2% 1.1b
B1
125
(1)
(d) [Let T = those who can dance the Tango. Sight or use of]
M1 3.3
T ~B(50, “0.032”)
[P(T < 3 ) = P(T „ 2) = ] 0.7850815… awrt 0.785 A1 1.1b
(2)
( 7 marks)
Notes
(a) B1 for a suitable disadvantage:
Allow (B1) Do NOT allow (B0)
Not random or less random (o.e.) Not representative
Cannot use (reliably) for inferences Less accurate
(More likely to be) biased Any comment based on time or cost
Any mention of skew
Any mention of non-response
(b) M1 for sight of B(36, 0.08) Allow in words: binomial with n = 36 and p = 0.08
may be implied by one correct answer to 2sf or sight of P( X „ 6) 0.97776... i.e. awrt 0.98
Allow for 36C4 0.084 0.9232 as this is "correct use"
(i) 1st A1 for awrt 0.167 NB An answer of just awrt 0.167 scores M1( )1st A1
nd
(ii) 2 A1 for awrt 0.0222
(c) B1 for 0.032 o.e. (Can allow for sight of 0.4 0.08 )
(d) M1 for sight of B(50, “0.032”) ft their answer to (c) provided it is a probability 0.08
may be implied by correct answer
or sight of [P(T „ 3)] = 0.924348…i.e. awrt 0.924 or P(T „ 2) as part of 1 – P(T „ 2) calc.
A1 for awrt 0.785
MR Allow MR of 50 (e.g. 30) provided clearly attempting P(T „ 2) and score M1A0
,Qu 2 Scheme Marks AO
(a) Negative B1 1.2
(1)
(b) Marc’s suggestion is compatible because it’s negative correlation
B1 2.4
(1)
(c) (r = ) – 0.54458266… awrt – 0.545 B1 1.1b
(1)
(d) H0 : 0 H1 : 0 B1 2.5
[5% 1-tail cv = ] (+) 0.4259 M1 1.1a
(significant result / reject H0)
There is evidence of negative correlation between the number of letters in A1 2.2b
(or length of) a student’s last name and their first name
(3)
( 6 marks)
Notes
(a) B1 for “negative” Allow “slight” or “weak” etc
Allow a description e.g. “as x increases y decreases” or in context e.g. “people with longer
last names tend to have shorter first names”
A comment of “negative skew” is B0
Need to see distinct or separate responses for (a) and (b)
(b) B1 for a comment that suggests data is compatible with the suggestion and a suitable reason
such as “there is negative correlation” or a description in x and y or in context
or the points lie close to a line with negative gradient
or draw line y = x and state that more points below the line so supports (or is compatible
with) his suggestion
A reason based on just a single point is B0
e.g. “ 11 letters in last name has only 5 in first name”
(c) B1 for awrt – 0.545
(d) B1 for both hypotheses correct in terms of
M1 for a critical value compatible with their H1:
1-tail: awrt + 0.426 (condone + 0.425) or 2-tail (B0 scored for H1) : awrt + 0.497
If hypotheses are in words and can deduce whether one or two-tail then use their words.
If no hypotheses or their H1 is not clearly one or two tail assume one-tail
A1 for compatible signs between cv and r and a correct conclusion in context mentioning
correlation and number of letters or length and name (ft their value from (c))
Do NOT award this A mark if contradictory comments or working seen e.g. “accept H 0”
or comparison of 0.426 with significance level of 0.05 etc
NB The M1A1 can be scored independently of the hypotheses
, Qu 3 Scheme Marks AO
(a) Hectopascal or hPa B1 1.2
(1)
(b) 214
x y 1010 or 1010 M1 1.1b
30
= 1017.1333… awrt 1017 A1 1.1b
(2)
(c) x y (or statement that standard deviation is not affected by this
M1 3.1b
type of coding)
5912
"7.13[33...]" or 146.1822...
2
y
M1 1.1b
30
= 12.0905… awrt 12.1 A1 1.1b
(3)
(d) High pressure (since approx. mean + sd ) so clockwise
B1
Locations are (from North to South): Leuchars, Heathrow, Hurn
2.4
Wind direction is direction wind blows from
So: Heathrow (NE) Hurn (E) Leuchars (W) B1 2.2a
(2)
( 8 marks)
Notes
FYI 1 hPa = 100 Pa; 10hPa = 1 kPa; 1Pa = 1 Nm-2
(a) B1 for “hectopascal” or hPa (condone pascals, allow millibars or mb) o.e.
Do NOT allow kPa or kilopascals or Pa on its own
(b) M1 for a strategy to find x
Allow an attempt to find x that gets as far as x y 30 1010 [= 30 514]
A1 for awrt 1017 (accept 1020) [Ignore incorrect units]
(c) 1 M1 for an overall strategy using the fact x y (can be implied by correct final ans)
st
or for x 30 514 and x2 31 041192 (both seen and correct)
2nd M1 for a correct expression (with )(ft their y to 3sf) allow awrt 146 for 146.1822..
or for correct expression in x can ft their x 30 000 or their answer to (b)
A1 (dep on 2nd M1) for awrt 12.1 [Ignore incorrect units]
Final
answer Final ans of awrt 12.1 scores 3/3 but if they then adjust for x e.g. add 1010 (M0M1A1)
(d) 1st B1 for at least one of these reasons (these 2 lines) clearly stated (may see diagram)
Need “high pressure” and “clockwise” to score on 1st line
Contradictory statements B0 e.g. correct N~S list but say “anticlockwise”
2nd B1 (indep of 1st B1) for deducing the 3 correct directions either in the table or stated
as above
If the answers in table and text are different we take the table (as question says)
