surname names
Number Number
Further Mathematics
🟐 🟐
Advanced Subsidiary
PAPER 1: Core Pure Mathematics
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.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the
centre boxesand
number at the top of this
candidate page with your name,
number.
• Answer 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.
• 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.
are 11 questions in this question paper. The total mark for this paper is 80.
• – use this asfora guide
The marks each as
question
to how are
muchshown
timeintobrackets
spend on each question.
Advice
• Read each question carefully before you start to answer it.
•• Try to answer every question.
Check your answers if you have time at the end.
2025 Pearson Edexcel As level further Mathematics Question Paper Option 1 June+
Mark scheme
,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)
3
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
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
■■■■
Number Number
Further Mathematics
🟐 🟐
Advanced Subsidiary
PAPER 1: Core Pure Mathematics
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.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the
centre boxesand
number at the top of this
candidate page with your name,
number.
• Answer 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.
• 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.
are 11 questions in this question paper. The total mark for this paper is 80.
• – use this asfora guide
The marks each as
question
to how are
muchshown
timeintobrackets
spend on each question.
Advice
• Read each question carefully before you start to answer it.
•• Try to answer every question.
Check your answers if you have time at the end.
2025 Pearson Edexcel As level further Mathematics Question Paper Option 1 June+
Mark scheme
,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)
3
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
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
■■■■
