Paper2 4A
Please check the examination details below before entering your candidate information
Candidate surnameOther names
Centre Candidate
Number Number
Pearson Edexcel Level 3 GCE
Monday 23 June 2025
Afternoon (Time: 1 hour 30
minutes)
Paper
reference 9FM0/4A
Further Mathematics
🟐 🟐
Advanced
PAPER 4A: Further Pure Mathematics 2
You must have: Total
Mathematical Formulae and Statistical Tables (Green), Marks
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
• If pencil is used for diagrams/sketches/graphs it must be dark
• Fill
(HB
in the boxes at the top of this page with your
pen.or B). centre number and candidate number.
• Answer
name,
all questions and ensure that your answers to parts of
• Answer
questions are 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
• Inexact answers should be given to three significant figures unless otherwise stated.
clear. Answers without working may not gain full credit.
Informatio
n
• A booklet ‘Mathematical Formulae and Statistical Tables’ is
• There are 9 questions in this question paper. The total mark for this paper is 75.
• The marks for each question are shown in
–provided.
use this as a guide as to how much time to spend on each question.
Advic
brackets
•
e Read each question carefully before you start to answer it.
• Try to answer every P75689A
• Check your answers if you have time at the ©202
5
question.
end. P
e
a
r
s
o
n
Paper2 4A
,Education Ltd. Y:1/1/1/
Turn over
,1. The set S = {1, 3, 5, 9, 11, 13} forms the group G, under the operation multiplication
modulo 14
AREA
DO NOT WRITE IN THIS
(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
AREA
DO NOT WRITE IN THIS
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
r r u t q p s
AREA
DO NOT WRITE IN THIS
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 DO NOT WRITE IN THIS DO NOT WRITE IN THIS
AREA AREA AREA
■
■■■
Question 1 continued
Turn
over
3
Please check the examination details below before entering your candidate information
Candidate surnameOther names
Centre Candidate
Number Number
Pearson Edexcel Level 3 GCE
Monday 23 June 2025
Afternoon (Time: 1 hour 30
minutes)
Paper
reference 9FM0/4A
Further Mathematics
🟐 🟐
Advanced
PAPER 4A: Further Pure Mathematics 2
You must have: Total
Mathematical Formulae and Statistical Tables (Green), Marks
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
• If pencil is used for diagrams/sketches/graphs it must be dark
• Fill
(HB
in the boxes at the top of this page with your
pen.or B). centre number and candidate number.
• Answer
name,
all questions and ensure that your answers to parts of
• Answer
questions are 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
• Inexact answers should be given to three significant figures unless otherwise stated.
clear. Answers without working may not gain full credit.
Informatio
n
• A booklet ‘Mathematical Formulae and Statistical Tables’ is
• There are 9 questions in this question paper. The total mark for this paper is 75.
• The marks for each question are shown in
–provided.
use this as a guide as to how much time to spend on each question.
Advic
brackets
•
e Read each question carefully before you start to answer it.
• Try to answer every P75689A
• Check your answers if you have time at the ©202
5
question.
end. P
e
a
r
s
o
n
Paper2 4A
,Education Ltd. Y:1/1/1/
Turn over
,1. The set S = {1, 3, 5, 9, 11, 13} forms the group G, under the operation multiplication
modulo 14
AREA
DO NOT WRITE IN THIS
(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
AREA
DO NOT WRITE IN THIS
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
r r u t q p s
AREA
DO NOT WRITE IN THIS
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 DO NOT WRITE IN THIS DO NOT WRITE IN THIS
AREA AREA AREA
■
■■■
Question 1 continued
Turn
over
3
