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Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Monday 23 June 2025
Paper
Afternoon (Time: 1 hour 30 minutes)
reference 9FM0/4A
Further Mathematics
Advanced
PAPER 4A: Further Pure Mathematics 2
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have the facility for symbolic algebra 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).
• centre
Fill in the boxes at the top of this page with your name,
number and candidate number.
• clearly labelled.
Answer all questions and ensure that your answers to parts of questions are
• 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.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
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. Turn over
P75689A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P75689A0132*
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1. The set S = {1, 3, 5, 9, 11, 13} forms the group G, under the operation multiplication
modulo 14
DO NOT WRITE IN THIS AREA
(a) Complete the Cayley table below for the group G
×14 1 3 5 9 11 13
1 1 3 5 9 11 13
3 3 9 1 13 5 11
5 5 1 11
9 9 13 11
11 11 5 9
13 13 11 1
DO NOT WRITE IN THIS AREA
A spare table can be found on page 5 if you need to rewrite your Cayley table.
(3)
(b) Write down a subgroup of G of order 2
(1)
The group H is defined by the Cayley table below.
* p q r s t u
p p q r s t u
q q t u r s p
DO NOT WRITE IN THIS AREA
r r u t q p s
s s r q p u t
t t s p u r q
u u p s t q r
(c) Show that G and H are isomorphic.
(3)
2
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Question 1 continued
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3
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Turn over
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Question 1 continued
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DO NOT WRITE IN THIS AREA
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4
https://www.stuvia.com/uploads *P75689A0432*
https://www.stuvia.com/uploads 3/6/2026,9:10:19
AM
Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Monday 23 June 2025
Paper
Afternoon (Time: 1 hour 30 minutes)
reference 9FM0/4A
Further Mathematics
Advanced
PAPER 4A: Further Pure Mathematics 2
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have the facility for symbolic algebra 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).
• centre
Fill in the boxes at the top of this page with your name,
number and candidate number.
• clearly labelled.
Answer all questions and ensure that your answers to parts of questions are
• 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.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
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. Turn over
P75689A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P75689A0132*
https://www.stuvia.com/uploads https://www.stuvia.com/uploads 3/6/2026, 9:10:19 AM
,https://www.stuvia.com/uploads https://www.stuvia.com/uploads https://www.stuvia.com/uploads
1. The set S = {1, 3, 5, 9, 11, 13} forms the group G, under the operation multiplication
modulo 14
DO NOT WRITE IN THIS AREA
(a) Complete the Cayley table below for the group G
×14 1 3 5 9 11 13
1 1 3 5 9 11 13
3 3 9 1 13 5 11
5 5 1 11
9 9 13 11
11 11 5 9
13 13 11 1
DO NOT WRITE IN THIS AREA
A spare table can be found on page 5 if you need to rewrite your Cayley table.
(3)
(b) Write down a subgroup of G of order 2
(1)
The group H is defined by the Cayley table below.
* p q r s t u
p p q r s t u
q q t u r s p
DO NOT WRITE IN THIS AREA
r r u t q p s
s s r q p u t
t t s p u r q
u u p s t q r
(c) Show that G and H are isomorphic.
(3)
2
https://www.stuvia.com/uploads *P75689A0232*https://www.stuvia.com/uploads 3/6/2026,9:10:19
AM
, https://www.stuvia.com/uploads https://www.stuvia.com/uploads https://www.stuvia.com/uploads
Question 1 continued
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DO NOT WRITE IN THIS AREA
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3
https://www.stuvia.com/uploads
*P75689A0332*
https://www.stuvia.com/uploads 3/6/2026, 9:10:19 AM
Turn over
, https://www.stuvia.com/uploads https://www.stuvia.com/uploads https://www.stuvia.com/uploads
Question 1 continued
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4
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