Pearson Edexcel
ACTUAL SUMMER 2024
8FM0/22
GCE
Advanced Subsidiary Level Further
Mathematics (8FM0)
Paper 22 Further Pure Mathematics 2
Question Paper + Mark Scheme
, Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 17 May 2024
Afternoon
Paper
reference 8FM0/22
Further Mathematics
🞍 🞍
Advanced Subsidiary
Further Mathematics options
22: Further Pure Mathematics 2
(Part of option A only)
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.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• Answer
centre number and candidate number.
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. Answers without
• Inexact
working may not gain full credit.
answers should be given to three significant figures unless
otherwise stated.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
The total
marksmark for this
for each part of are
question the shown
examination is 40. There are 5 questions.
in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read
Try
each question carefully before you start to answer it.
to answer every if
question.
Check your answers you have time at the end.
Turn over
P75672A
©2024 Pearson Education Ltd.
F:1/1/1/
, 1. (i) The table below is a Cayley table for the group G with operation °
DO NOT WRITE IN THIS AREA
° a b c d e f
a d c b a f e
b e f a b c d
c f e d c b a
d a b c d e f
e b a f e d c
f c d e f a b
(a) State which element is the identity of the group.
(1)
DO NOT WRITE IN THIS AREA
(b) Determine the inverse of the element (b°c)
(2)
(c) Give a reason why the set {a, b, e, f } cannot be a subgroup of G. You must
justify your answer.
(1)
(d) Show that the set {b, d, f } is a subgroup of G.
(2)
(ii) Given that H is a group with an element x of order 3 and an element y of
order 6 satisfying
yx = xy5
show that y3xy3x2 is the identity element.
(3)
DO NOT WRITE IN THIS AREA
2
🞍🞍🞍🞍
ACTUAL SUMMER 2024
8FM0/22
GCE
Advanced Subsidiary Level Further
Mathematics (8FM0)
Paper 22 Further Pure Mathematics 2
Question Paper + Mark Scheme
, Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 17 May 2024
Afternoon
Paper
reference 8FM0/22
Further Mathematics
🞍 🞍
Advanced Subsidiary
Further Mathematics options
22: Further Pure Mathematics 2
(Part of option A only)
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.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• Answer
centre number and candidate number.
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. Answers without
• Inexact
working may not gain full credit.
answers should be given to three significant figures unless
otherwise stated.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
The total
marksmark for this
for each part of are
question the shown
examination is 40. There are 5 questions.
in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read
Try
each question carefully before you start to answer it.
to answer every if
question.
Check your answers you have time at the end.
Turn over
P75672A
©2024 Pearson Education Ltd.
F:1/1/1/
, 1. (i) The table below is a Cayley table for the group G with operation °
DO NOT WRITE IN THIS AREA
° a b c d e f
a d c b a f e
b e f a b c d
c f e d c b a
d a b c d e f
e b a f e d c
f c d e f a b
(a) State which element is the identity of the group.
(1)
DO NOT WRITE IN THIS AREA
(b) Determine the inverse of the element (b°c)
(2)
(c) Give a reason why the set {a, b, e, f } cannot be a subgroup of G. You must
justify your answer.
(1)
(d) Show that the set {b, d, f } is a subgroup of G.
(2)
(ii) Given that H is a group with an element x of order 3 and an element y of
order 6 satisfying
yx = xy5
show that y3xy3x2 is the identity element.
(3)
DO NOT WRITE IN THIS AREA
2
🞍🞍🞍🞍
