surname names
Number Number
June 2025 Edexcel: A Level Further
Mathematics 9FM0/4A Further Pure
Mathematics 2 – Merged Question Paper
& Mark Scheme.
Further Mathematics
🟐 🟐
Advanced
PAPER 4A: Further Pure Mathematics 2
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).
• Fill in the
centre boxesand
number at the top of this
candidate page with your name,
number.
• Answer all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Inexact answers should be given to three significant figures unless otherwise stated.
Answers without working may not gain full credit.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The are 9 questions in this question paper. The total mark for this paper is 75.
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
• your answers if you have time at the end.
to answer every question.
Check Turn over
P75689A
©2025 Pearson Education Ltd.
Y:1/1/1/
,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
■■■■
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
3
Turn over
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
4
Number Number
June 2025 Edexcel: A Level Further
Mathematics 9FM0/4A Further Pure
Mathematics 2 – Merged Question Paper
& Mark Scheme.
Further Mathematics
🟐 🟐
Advanced
PAPER 4A: Further Pure Mathematics 2
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).
• Fill in the
centre boxesand
number at the top of this
candidate page with your name,
number.
• Answer all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Inexact answers should be given to three significant figures unless otherwise stated.
Answers without working may not gain full credit.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The are 9 questions in this question paper. The total mark for this paper is 75.
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
• your answers if you have time at the end.
to answer every question.
Check Turn over
P75689A
©2025 Pearson Education Ltd.
Y:1/1/1/
,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
■■■■
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
3
Turn over
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
4
