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 22 June 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/4A
Further Mathematics
Advanced
PAPER 4A: Further Pure Mathematics 2
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Green), calculator
Candidates may use any calculator permitted 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 boxes at the top of this page with your name,
••
centre 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.
•Information
Answers without working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 8 questions in this question paper. The total mark for this paper is 75.
The 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
P79399A
©2026 Pearson Education Ltd.
P:1/1/
*P79399A0128*
,1. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
The curve C has equation y = f ( x) where
3
1
f ( x) 3
x 2 1 x 4
3
Use algebraic integration to show that the length of C is
a 2 +b 5
where a and b are simplified rational constants to be determined.
(6)
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2
*P79399A0228*
, Question 1 continued
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(Total for Question 1 is 6 marks)
3
*P79399A0328* Turn over
, 2. The code on a combination lock consists of four single digits, XXXX, from the set
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
(a) Write down the total number of possible codes which consist of four distinct digits.
(1)
Given that the digits in the code may be repeated,
(b) write down the total number of possible codes,
(1)
(c) determine the total number of possible codes in which the sum of the four digits in
the code is
(i) equal to 33
(4)
(ii) less than 33
(4)
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4
*P79399A0428*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Monday 22 June 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/4A
Further Mathematics
Advanced
PAPER 4A: Further Pure Mathematics 2
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Green), calculator
Candidates may use any calculator permitted 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 boxes at the top of this page with your name,
••
centre 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.
•Information
Answers without working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 8 questions in this question paper. The total mark for this paper is 75.
The 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
P79399A
©2026 Pearson Education Ltd.
P:1/1/
*P79399A0128*
,1. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
The curve C has equation y = f ( x) where
3
1
f ( x) 3
x 2 1 x 4
3
Use algebraic integration to show that the length of C is
a 2 +b 5
where a and b are simplified rational constants to be determined.
(6)
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2
*P79399A0228*
, Question 1 continued
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(Total for Question 1 is 6 marks)
3
*P79399A0328* Turn over
, 2. The code on a combination lock consists of four single digits, XXXX, from the set
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
(a) Write down the total number of possible codes which consist of four distinct digits.
(1)
Given that the digits in the code may be repeated,
(b) write down the total number of possible codes,
(1)
(c) determine the total number of possible codes in which the sum of the four digits in
the code is
(i) equal to 33
(4)
(ii) less than 33
(4)
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4
*P79399A0428*
