Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Edexcel Level 3 GCE
Friday 15 May 2026
Afternoon Paper
reference 8FM0/22
Further Mathematics
Advanced Subsidiary
Further Mathematics options
Mark Scheme (Results)
22: Further Pure Mathematics 2
(Part of option A only)
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Summer 2026
Candidates may use any calculator allowed by regulations. Calculators
must not have the facility for symbolic algebra lation, 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, Edexcel GCE
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are Advanced Sunsidiary Level
• – there may
labelled.
Answer the questions in the spaces provided
In Further Mathematics (8FM0)
• working may not gain
be more space than you need.
You should show sufficient working to make your methods clear. Answers without
Paper 22 Further Pure Mathematics 2
• otherwise stated. be given to three significant figures unless
full credit.
Inexact answers should
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The
total mark for this part of the examination is 40. There are 5 questions.
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.
• Check your answers if you have time at the end.
Try to answer every question.
Turn over
P79393A
P:1/1/1/1/
Education Ltd. *P79393A0120* for more:
for more:
, 1 3 1 3 Edexcel and BTEC Qualifications
1. α=1 β=– + i λ=– – i
2 2 2 2
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
where α, β and λ ∈
Edexcel and BTEC qualifications are awarded by the UK’s
(a) Complete the following Cayley table for the set {α, β, λ} with the largest awarding body. We provide a wide rang ications
operation multiplication including academic, vocational, occupational and specific
programmes for emplo fo
qualifications websites at or .
× α β λ
Alternatively, you c
contact us page at
α
β
λ
A spare copy of this table is given on page 5 if you need to rewrite your
Cayley table.
helping people progress, everywhere
(2)
(b) Hence, assuming associativity, show that the set {α, β, λ} with the operation
multiplication forms a group.
(3) aspires to be the world’s leading learning company. Our aim is to
help everyone progress in their lives through education. We believe in every
Determine the order of each element of the group.
(2) kind of learning, for all kinds of people, wherever they are in the world.
(d) Hence determine whether the group is cyclic, giving a reason for your answer. We’ve been involved in education for over 150 years, and by working across
(1)
70 countries, in 100 languages, we have built an international reputation for
_____________________________________________________________________________________
our commitment to high standards and raising achievement through
_____________________________________________________________________________________
_____________________________________________________________________________________ innovation in education. Find out more about how we can help you and your
_____________________________________________________________________________________ students at:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ Summer 2026
Question Paper Log Number P79393A
_____________________________________________________________________________________
Publications Code 8FM0_22_MS_2606
_____________________________________________________________________________________
All the material in this publication is
_____________________________________________________________________________________
Education Ltd 2026
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
2
for more:
*P79393A0220*
, General Marking Guidance
Question 1 continued
_____________________________________________________________________________________ These notes offer general guidance, but the specific notes for examiners
appertaining to individual questions take precedence.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________ 1 All candidates must receive the same treatment. Examiners must
_____________________________________________________________________________________ mark the last candidate in exactly the same way as they mark the first.
_____________________________________________________________________________________
Where some judgement is required, mark schemes will provide the
_____________________________________________________________________________________ principles by which marks will be awarded; exemplification/indicative
_____________________________________________________________________________________ content will not be exhaustive. When examiners are in doubt
_____________________________________________________________________________________ regarding the application of the mark scheme to a candidate’s
response, the response should be sent to review.
_____________________________________________________________________________________
_____________________________________________________________________________________ 2 All the marks on the mark scheme are designed to be awarded; mark
_____________________________________________________________________________________ schemes should be applied positively. Examiners should also be
prepared to award zero marks if the candidate’s response is not
_____________________________________________________________________________________
worthy of credit according to the mark scheme. If there is a wrong
_____________________________________________________________________________________ answer (or no answer) indicated on the answer line always check the
_____________________________________________________________________________________ working in the body of the script (and on any diagrams), and award
any marks appropriate from the mark scheme.
_____________________________________________________________________________________
_____________________________________________________________________________________ Questions where working is not required: In general, the correct
_____________________________________________________________________________________ answer should be given full marks.
_____________________________________________________________________________________ Questions that specifically require working: In general, candidates
who do not show working on this type of question will get no marks –
_____________________________________________________________________________________ full details will be given in the mark scheme for each individual
_____________________________________________________________________________________ question.
_____________________________________________________________________________________
3 Crossed out work
_____________________________________________________________________________________
This should be marked unless the candidate has replaced it with an
_____________________________________________________________________________________ alternative response.
_____________________________________________________________________________________
4 Choice of method
_____________________________________________________________________________________
If there is a choice of methods shown, mark the method that leads to
_____________________________________________________________________________________ the answer given on the answer line.
_____________________________________________________________________________________
If no answer appears on the answer line then mark both methods as
_____________________________________________________________________________________
far as they are identical and award these marks.
_____________________________________________________________________________________
_____________________________________________________________________________________ 5 Incorrect method
If it is clear from the working that the “correct” answer has been
_____________________________________________________________________________________
obtained from incorrect working, award 0 marks.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
for more:
3
*P79393A0320* Turn over
Candidate surname Other names
Centre Number Candidate Number
Edexcel Level 3 GCE
Friday 15 May 2026
Afternoon Paper
reference 8FM0/22
Further Mathematics
Advanced Subsidiary
Further Mathematics options
Mark Scheme (Results)
22: Further Pure Mathematics 2
(Part of option A only)
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Summer 2026
Candidates may use any calculator allowed by regulations. Calculators
must not have the facility for symbolic algebra lation, 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, Edexcel GCE
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are Advanced Sunsidiary Level
• – there may
labelled.
Answer the questions in the spaces provided
In Further Mathematics (8FM0)
• working may not gain
be more space than you need.
You should show sufficient working to make your methods clear. Answers without
Paper 22 Further Pure Mathematics 2
• otherwise stated. be given to three significant figures unless
full credit.
Inexact answers should
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The
total mark for this part of the examination is 40. There are 5 questions.
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.
• Check your answers if you have time at the end.
Try to answer every question.
Turn over
P79393A
P:1/1/1/1/
Education Ltd. *P79393A0120* for more:
for more:
, 1 3 1 3 Edexcel and BTEC Qualifications
1. α=1 β=– + i λ=– – i
2 2 2 2
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
where α, β and λ ∈
Edexcel and BTEC qualifications are awarded by the UK’s
(a) Complete the following Cayley table for the set {α, β, λ} with the largest awarding body. We provide a wide rang ications
operation multiplication including academic, vocational, occupational and specific
programmes for emplo fo
qualifications websites at or .
× α β λ
Alternatively, you c
contact us page at
α
β
λ
A spare copy of this table is given on page 5 if you need to rewrite your
Cayley table.
helping people progress, everywhere
(2)
(b) Hence, assuming associativity, show that the set {α, β, λ} with the operation
multiplication forms a group.
(3) aspires to be the world’s leading learning company. Our aim is to
help everyone progress in their lives through education. We believe in every
Determine the order of each element of the group.
(2) kind of learning, for all kinds of people, wherever they are in the world.
(d) Hence determine whether the group is cyclic, giving a reason for your answer. We’ve been involved in education for over 150 years, and by working across
(1)
70 countries, in 100 languages, we have built an international reputation for
_____________________________________________________________________________________
our commitment to high standards and raising achievement through
_____________________________________________________________________________________
_____________________________________________________________________________________ innovation in education. Find out more about how we can help you and your
_____________________________________________________________________________________ students at:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ Summer 2026
Question Paper Log Number P79393A
_____________________________________________________________________________________
Publications Code 8FM0_22_MS_2606
_____________________________________________________________________________________
All the material in this publication is
_____________________________________________________________________________________
Education Ltd 2026
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
2
for more:
*P79393A0220*
, General Marking Guidance
Question 1 continued
_____________________________________________________________________________________ These notes offer general guidance, but the specific notes for examiners
appertaining to individual questions take precedence.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________ 1 All candidates must receive the same treatment. Examiners must
_____________________________________________________________________________________ mark the last candidate in exactly the same way as they mark the first.
_____________________________________________________________________________________
Where some judgement is required, mark schemes will provide the
_____________________________________________________________________________________ principles by which marks will be awarded; exemplification/indicative
_____________________________________________________________________________________ content will not be exhaustive. When examiners are in doubt
_____________________________________________________________________________________ regarding the application of the mark scheme to a candidate’s
response, the response should be sent to review.
_____________________________________________________________________________________
_____________________________________________________________________________________ 2 All the marks on the mark scheme are designed to be awarded; mark
_____________________________________________________________________________________ schemes should be applied positively. Examiners should also be
prepared to award zero marks if the candidate’s response is not
_____________________________________________________________________________________
worthy of credit according to the mark scheme. If there is a wrong
_____________________________________________________________________________________ answer (or no answer) indicated on the answer line always check the
_____________________________________________________________________________________ working in the body of the script (and on any diagrams), and award
any marks appropriate from the mark scheme.
_____________________________________________________________________________________
_____________________________________________________________________________________ Questions where working is not required: In general, the correct
_____________________________________________________________________________________ answer should be given full marks.
_____________________________________________________________________________________ Questions that specifically require working: In general, candidates
who do not show working on this type of question will get no marks –
_____________________________________________________________________________________ full details will be given in the mark scheme for each individual
_____________________________________________________________________________________ question.
_____________________________________________________________________________________
3 Crossed out work
_____________________________________________________________________________________
This should be marked unless the candidate has replaced it with an
_____________________________________________________________________________________ alternative response.
_____________________________________________________________________________________
4 Choice of method
_____________________________________________________________________________________
If there is a choice of methods shown, mark the method that leads to
_____________________________________________________________________________________ the answer given on the answer line.
_____________________________________________________________________________________
If no answer appears on the answer line then mark both methods as
_____________________________________________________________________________________
far as they are identical and award these marks.
_____________________________________________________________________________________
_____________________________________________________________________________________ 5 Incorrect method
If it is clear from the working that the “correct” answer has been
_____________________________________________________________________________________
obtained from incorrect working, award 0 marks.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
for more:
3
*P79393A0320* Turn over
