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 15 May 2026
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,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• – there may
labelled.
Answer the questions in the spaces provided
• working may not gain
be more space than you need.
You should show sufficient working to make your methods clear. Answers without
• 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
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P79393A0120*
, 1 3 1 3
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
where α, β and λ ∈
(a) Complete the following Cayley table for the set {α, β, λ} with the
operation multiplication
× α β λ
α
β
λ
A spare copy of this table is given on page 5 if you need to rewrite your
Cayley table.
(2)
(b) Hence, assuming associativity, show that the set {α, β, λ} with the operation
multiplication forms a group.
(3)
(c) Determine the order of each element of the group.
(2)
(d) Hence determine whether the group is cyclic, giving a reason for your answer.
(1)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P79393A0220*
, Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3
*P79393A0320* Turn over
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 15 May 2026
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,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• – there may
labelled.
Answer the questions in the spaces provided
• working may not gain
be more space than you need.
You should show sufficient working to make your methods clear. Answers without
• 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
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P79393A0120*
, 1 3 1 3
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
where α, β and λ ∈
(a) Complete the following Cayley table for the set {α, β, λ} with the
operation multiplication
× α β λ
α
β
λ
A spare copy of this table is given on page 5 if you need to rewrite your
Cayley table.
(2)
(b) Hence, assuming associativity, show that the set {α, β, λ} with the operation
multiplication forms a group.
(3)
(c) Determine the order of each element of the group.
(2)
(d) Hence determine whether the group is cyclic, giving a reason for your answer.
(1)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P79393A0220*
, Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3
*P79393A0320* Turn over
