Edexcel A Level In GCE further mathematics (9FM0/4A) paper 4A:Pure math 2 +
mark scheme JUNE 2025
surname names
Number Number
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
• IfUsepencil
black is ink
usedorfor diagrams/sketches/graphs
ball-point pen. it must be dark (HB or B).
• Fceilnl tinrethnuembboexresanadt tchaendtoidpaotfetnhiusmpbageer.with your name,
• 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 to answer every question.
©
• Check your answers if you have time at the end.
2
0
2
5
P
e
P75689A
a
r
s
,on 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
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
■■
mark scheme JUNE 2025
surname names
Number Number
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
• IfUsepencil
black is ink
usedorfor diagrams/sketches/graphs
ball-point pen. it must be dark (HB or B).
• Fceilnl tinrethnuembboexresanadt tchaendtoidpaotfetnhiusmpbageer.with your name,
• 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 to answer every question.
©
• Check your answers if you have time at the end.
2
0
2
5
P
e
P75689A
a
r
s
,on 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
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
■■
