Table Of ContentA Level
Further
Mathematics
Sample Assessment Materials
Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0)
First teaching from September 2017
First certifi cation from 2019
Issue 1
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Original origami artwork: Mark Bolitho
Origami photography: Pearson Education Ltd/Naki Kouyioumtzis
ISBN 978 1 4469 3352 7
All the material in this publication is copyright
© Pearson Education Limited 2017
Contents
Introduction
1
General marking guidance
3
Paper 1 – sample question paper and mark scheme
5
Paper 2 – sample question paper and mark scheme
41
Paper 3A – sample question paper and mark scheme
71
Paper 4A– sample question paper and mark scheme
103
Paper 3B/4B – sample question paper and mark scheme
147
Paper 4E– sample question paper and mark scheme
183
Paper 3C/4C – sample question paper and mark scheme
221
Paper 4F – sample question paper and mark scheme
257
Paper 3D/4D – sample question paper and mark scheme
293
Paper 4G – sample question paper and mark scheme
333
Introduction
The Pearson Edexcel Level 3 Advanced GCE in Further Mathematics is designed for use in
schools and colleges. It is part of a suite of AS/A Level qualifications offered by Pearson.
These sample assessment materials have been developed to support this
qualification and will be used as the benchmark to develop the assessment students
will take.
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Pearson Edexcel Level 3 Advanced GCE in Mathematics
Sample Assessment Materials – Issue 1 – June 2017 © Pearson Education Limited 2017
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Pearson Edexcel Level 3 Advanced GCE in Mathematics
Sample Assessment Materials – Issue 1 – June 2017 © Pearson Education Limited 2017
General marking guidance
•
All candidates must receive the same treatment. Examiners must mark the last
candidate in exactly the same way as they mark the first.
•
Mark schemes should be applied positively. Candidates must be rewarded for what
they have shown they can do rather than be penalised for omissions.
•
Examiners should mark according to the mark scheme – not according to their
perception of where the grade boundaries may lie.
•
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/indicative content will not be
exhaustive. However different examples of responses will be provided at
standardisation.
•
When examiners are in doubt regarding the application of the mark scheme to a
candidate’s response, a senior examiner must be consulted before a mark is given.
•
Crossed-out work should be marked unless the candidate has replaced it with an
alternative response.
Specific guidance for mathematics
1.
These 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.
2.
Abbreviations
These are some of the traditional marking abbreviations that may appear in the mark
schemes.
•
bod
benefit of doubt
•
ft
follow through
•
this symbol is 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)
•
d…
dependent
or dep
•
indep independent
•
dp
decimal places
•
sf
significant figures
•
The answer is printed on
the paper or ag- answer
given
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Pearson Edexcel Level 3 Advanced GCE in Mathematics
Sample Assessment Materials – Issue 1 – June 2017 © Pearson Education Limited 2017
•
or d… The second mark is
dependent on gaining the
first mark
3. All M marks are follow through.
All A marks are ‘correct answer only’ (cao.), unless shown, for example, as A1 ft to
indicate that previous wrong working is to be followed through. After a misread
however, the subsequent A marks affected are treated as A ft, but answers that don’t
logically make sense e.g. if an answer given for a probability is >1 or <0, should
never be awarded A marks.
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. If no such
alternative answer is provided but deemed to be valid, examiners must escalate the
response to a senior examiner to review.
Centre Number
Candidate Number
Write your name here
Surname
Other names
Total Marks
Paper Reference
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Sample Assessment Materials – Issue 1 – June 2017 © Pearson Education Limited 2017
Centre Number
Candidate Number
Write your name here
Surname
Other names
Total Marks
Paper Reference
*S54438A0125*
S54438A
©2017 Pearson Education Ltd.
1/1/1/1/
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Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for algebraic manipulation,
differentiation and integration, or have retrievable mathematical
formulae stored in them.
Instructions
• Use black ink or ball-point pen.
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the boxes at the top of this page with your name, centre number and
candidate number.
• Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer the questions in the spaces provided
– there may be more space than you need.
• You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
• Answers should be given to three significant figures unless otherwise stated.
Information
• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• There are 9 questions in this question paper. The total mark for this paper is 75.
• The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.
• Try to answer every question.
• Check your answers if you have time at the end.
Further Mathematics
Advanced
Paper 1: Core Pure Mathematics 1
Sample Assessment Material for first teaching September 2017
Time: 1 hour 30 minutes
9FM0/01
You must have:
Mathematical Formulae and Statistical Tables, calculator
Pearson Edexcel
Level 3 GCE
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Answer ALL questions. Write your answers in the spaces provided.
1. Prove that
1
1
3
12
2
3
1 (
)(
)
(
)
(
)(
)
r
r
n an
b
n
n
r
n
+
+
=
+
+
+
=∑
where a and b are constants to be found.
(5)
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Question 1 continued
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(Total for Question 1 is 5 marks)
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2. Prove by induction that for all positive integers n,
f (n) = 23n +1 + 3(52n +1)
is divisible by 17
(6)
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(Total for Question 2 is 6 marks)
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3.
f (z) = z4 + az3 + 6z2 + bz + 65
where a and b are real constants.
Given that z = 3 + 2i is a root of the equation f (z) = 0, show the roots of f (z) = 0 on a
single Argand diagram.
(9)
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(Total for Question 3 is 9 marks)
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