2025 Pearson Edexcel Level 3 GCE Further Mathematics Advanced Subsidiary PAPER 1: Core Pure Mathematics Combined
Question Paper & Final Marking 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
Monday 12 May 2025
Afternoon (Time: 1 hour 40 minutes)
Paper
reference 8FM0/01
Further Mathematics
Advanced Subsidiary
PAPER 1: Core Pure Mathematics
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
•• IfUse black ink or ball-point pen.
pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fillcentre
in the boxes at the top of this page with your name,
number and candidate number.
• Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer the questions in the spaces provided
– there may be more space than you need.
• You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
• Inexact answers should be given to three significant figures unless
otherwise stated.
Information
•• There
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 11 questions in this question paper. The total mark for this paper is 80.
• The
– usemarks
this asfor eachas
a guide question
to how are shown
much timeintobrackets
spend on each question.
Advice
• Read each question carefully before you start to answer it.
•• Check
Try to answer every question.
your answers if you have time at the end. Turn over
P75670A
©2025 Pearson Education Ltd.
Y:1/1/1/
,1. z = 3 – 3i
(a) Write z in the form r (cos θ + i sin θ) where –π < θ π
DO NOT WRITE IN THIS AREA
(2)
(b) Show and label on a single Argand diagram
(i) the point P representing z
(ii) the point Q representing iz
(2)
(c) Describe the geometrical transformation that maps P onto Q
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
Question 1 continued
(Total for Question 1 is 6 marks)
Turn over
3
, 2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
DO NOT WRITE IN THIS AREA
f (z) = 4z3 – 12z2 – 95z + 325
Given that f (–5) = 0
(a) determine f (z) in the form (z + a)(bz2 + cz + d) where a, b, c and d are integers.
(3)
(b) 8i
Hence show that the complex roots of f (z) = 0 are
2 (2)
(c) Determine the values of z such that f (2z – 1) = 0
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
Question Paper & Final Marking 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
Monday 12 May 2025
Afternoon (Time: 1 hour 40 minutes)
Paper
reference 8FM0/01
Further Mathematics
Advanced Subsidiary
PAPER 1: Core Pure Mathematics
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
•• IfUse black ink or ball-point pen.
pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fillcentre
in the boxes at the top of this page with your name,
number and candidate number.
• Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer the questions in the spaces provided
– there may be more space than you need.
• You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
• Inexact answers should be given to three significant figures unless
otherwise stated.
Information
•• There
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 11 questions in this question paper. The total mark for this paper is 80.
• The
– usemarks
this asfor eachas
a guide question
to how are shown
much timeintobrackets
spend on each question.
Advice
• Read each question carefully before you start to answer it.
•• Check
Try to answer every question.
your answers if you have time at the end. Turn over
P75670A
©2025 Pearson Education Ltd.
Y:1/1/1/
,1. z = 3 – 3i
(a) Write z in the form r (cos θ + i sin θ) where –π < θ π
DO NOT WRITE IN THIS AREA
(2)
(b) Show and label on a single Argand diagram
(i) the point P representing z
(ii) the point Q representing iz
(2)
(c) Describe the geometrical transformation that maps P onto Q
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
Question 1 continued
(Total for Question 1 is 6 marks)
Turn over
3
, 2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
DO NOT WRITE IN THIS AREA
f (z) = 4z3 – 12z2 – 95z + 325
Given that f (–5) = 0
(a) determine f (z) in the form (z + a)(bz2 + cz + d) where a, b, c and d are integers.
(3)
(b) 8i
Hence show that the complex roots of f (z) = 0 are
2 (2)
(c) Determine the values of z such that f (2z – 1) = 0
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
