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
•• 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
• Answer
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 without working may not gain full credit.
answers should be given to three significant figures unless
otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 11 questions in this question paper. The total mark for this paper is 80.
The marks each question are shown in brackets
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
P75670A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P75670A0136*
,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 DO NOT WRITE IN THIS AREA 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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P75670A0236*
, Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 6 marks)
3
*P75670A0336* Turn over
, 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 DO NOT WRITE IN THIS AREA 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)
8 i
(b) 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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4
*P75670A0436*
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
•• 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
• Answer
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 without working may not gain full credit.
answers should be given to three significant figures unless
otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 11 questions in this question paper. The total mark for this paper is 80.
The marks each question are shown in brackets
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
P75670A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P75670A0136*
,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 DO NOT WRITE IN THIS AREA 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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P75670A0236*
, Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 6 marks)
3
*P75670A0336* Turn over
, 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 DO NOT WRITE IN THIS AREA 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)
8 i
(b) 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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4
*P75670A0436*
