PEARSON 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
o.e. – 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, alternative 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.
, General Principles for Further Pure Mathematics Marking
(But note that specific mark schemes may sometimes override these general principles)
Method mark for solving 3 term quadratic:
1. Factorisation
( x2 bx c) ( x p)( x q), where pq c , leading to x ...
(ax2 bx c) (mx p)(nx q), where pq c and mn a , leading to x ...
2. Formula
Attempt to use the correct formula (with values for a, b and c)
3. Completing the square
2
x2 bx c 0 : x q c 0, q 0 , leading to x ...
b
Solving
2
Method marks for differentiation and integration:
1. Differentiation
Power of at least one term decreased by 1. ( x n x n 1 )
2. Integration
Power of at least one term increased by 1. ( x n x n 1 )
Use of a formula
Where a method involves using a formula that has been learnt, the advice
given in recent examiners’ reports is that the formula should be quoted
first.
Normal marking procedure is as follows:
Method mark for quoting a correct formula and attempting to use it, even if
there are small errors in the substitution of values.
Where the formula is not quoted, the method mark can be gained by
implication from correct working with values but may be lost if there is any
mistake in the working.
, Assessment Objectives
Assessment Objective Definition
A01 Use and apply standard techniques
A02 Reason, interpret and communicate mathematically
A03 Solve problems within mathematics and in other contexts
Elements
Element Definition
1.1a Select routine procedures
1.1b Correctly carry out routine procedures
1.2 Accurately recall facts, terminology and definitions
2.1 Construct rigorous mathematical arguments (including proofs)
2.2a Make deductions
2.2b Make inferences
2.3 Assess the validity of mathematical arguments
2.4 Explain their reasoning
2.5 Uses mathematical language and notation correctly
3.1a Translate problems in mathematical contexts into mathematical processes
3.1b Translate problems in non-mathematical contexts into mathematical processes
3.2a Interpret solutions to problems in their original context
3.2b Evaluate (the) accuracy and limitations (of solutions to problems)
3.3 Translate situations in context into mathematical models
3.4 Use mathematical models
3.5a Evaluate the outcomes of modelling in context
3.5b Recognise the limitations of models
3.5c Where appropriate, explain how to refine (models)
, Question Scheme Marks AOs
2
1
1 2x 4 y
2 2 4
Special If 0 marks are scored on application of the mark scheme then allow
Case Special Case B1 M0 A0 (total of 1 mark) for any of
3
1 1 x
2x 4 y 2x 2 y x y 2 2
2 4 42
x y
2x 2 2
log2x log4 y x log2 y log4 or x log2 2 y log2
ln 2x ln 4 y x ln 2 y ln 4 or x ln 2 2 y ln 2
1
y log x o.e. {base of 4 omitted}
2 2 2
3
Way 1 2 x 22 y 2
2 B1 1.1b
3
3
2x 2 y 2 2
x 2y
y ... M1 2.1
2
1 3 1
E.g. y x or y (2 x 3) A1 1.1b
2 4 4
(3)
1
Way 2 log( 2 x 4 y ) log B1 1.1b
2 2
1
log 2 x log 4 y log
2 2 M1 2.1
x log 2 y log 4 log1 log(2 2) y ...
log(2 2) x log 2 1 3
y y x A1 1.1b
log 4 2 4
(3)
1
Way 3 log( 2 x 4 y ) log B1 1.1b
2 2
1 1
log 2 x log 4 y log log 2 y log 4 log
x
y ... M1 2.1
2 2 2 2
1
log (2 )
x
log
2 2 1 3 A1 1.1b
y y x
log 4 2 4
(3)
1
Way 4 log 2 ( 2 x 4 y ) log 2 B1 1.1b
2 2
1 3
log 2 2 x log 2 4 y log 2 x 2 y y ... M1 2.1
2 2 2
1 3 1
E.g. y x or y (2 x 3) A1 1.1b
2 4 4
(3)
(3 marks)
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
o.e. – 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, alternative 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.
, General Principles for Further Pure Mathematics Marking
(But note that specific mark schemes may sometimes override these general principles)
Method mark for solving 3 term quadratic:
1. Factorisation
( x2 bx c) ( x p)( x q), where pq c , leading to x ...
(ax2 bx c) (mx p)(nx q), where pq c and mn a , leading to x ...
2. Formula
Attempt to use the correct formula (with values for a, b and c)
3. Completing the square
2
x2 bx c 0 : x q c 0, q 0 , leading to x ...
b
Solving
2
Method marks for differentiation and integration:
1. Differentiation
Power of at least one term decreased by 1. ( x n x n 1 )
2. Integration
Power of at least one term increased by 1. ( x n x n 1 )
Use of a formula
Where a method involves using a formula that has been learnt, the advice
given in recent examiners’ reports is that the formula should be quoted
first.
Normal marking procedure is as follows:
Method mark for quoting a correct formula and attempting to use it, even if
there are small errors in the substitution of values.
Where the formula is not quoted, the method mark can be gained by
implication from correct working with values but may be lost if there is any
mistake in the working.
, Assessment Objectives
Assessment Objective Definition
A01 Use and apply standard techniques
A02 Reason, interpret and communicate mathematically
A03 Solve problems within mathematics and in other contexts
Elements
Element Definition
1.1a Select routine procedures
1.1b Correctly carry out routine procedures
1.2 Accurately recall facts, terminology and definitions
2.1 Construct rigorous mathematical arguments (including proofs)
2.2a Make deductions
2.2b Make inferences
2.3 Assess the validity of mathematical arguments
2.4 Explain their reasoning
2.5 Uses mathematical language and notation correctly
3.1a Translate problems in mathematical contexts into mathematical processes
3.1b Translate problems in non-mathematical contexts into mathematical processes
3.2a Interpret solutions to problems in their original context
3.2b Evaluate (the) accuracy and limitations (of solutions to problems)
3.3 Translate situations in context into mathematical models
3.4 Use mathematical models
3.5a Evaluate the outcomes of modelling in context
3.5b Recognise the limitations of models
3.5c Where appropriate, explain how to refine (models)
, Question Scheme Marks AOs
2
1
1 2x 4 y
2 2 4
Special If 0 marks are scored on application of the mark scheme then allow
Case Special Case B1 M0 A0 (total of 1 mark) for any of
3
1 1 x
2x 4 y 2x 2 y x y 2 2
2 4 42
x y
2x 2 2
log2x log4 y x log2 y log4 or x log2 2 y log2
ln 2x ln 4 y x ln 2 y ln 4 or x ln 2 2 y ln 2
1
y log x o.e. {base of 4 omitted}
2 2 2
3
Way 1 2 x 22 y 2
2 B1 1.1b
3
3
2x 2 y 2 2
x 2y
y ... M1 2.1
2
1 3 1
E.g. y x or y (2 x 3) A1 1.1b
2 4 4
(3)
1
Way 2 log( 2 x 4 y ) log B1 1.1b
2 2
1
log 2 x log 4 y log
2 2 M1 2.1
x log 2 y log 4 log1 log(2 2) y ...
log(2 2) x log 2 1 3
y y x A1 1.1b
log 4 2 4
(3)
1
Way 3 log( 2 x 4 y ) log B1 1.1b
2 2
1 1
log 2 x log 4 y log log 2 y log 4 log
x
y ... M1 2.1
2 2 2 2
1
log (2 )
x
log
2 2 1 3 A1 1.1b
y y x
log 4 2 4
(3)
1
Way 4 log 2 ( 2 x 4 y ) log 2 B1 1.1b
2 2
1 3
log 2 2 x log 2 4 y log 2 x 2 y y ... M1 2.1
2 2 2
1 3 1
E.g. y x or y (2 x 3) A1 1.1b
2 4 4
(3)
(3 marks)
