Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel GCE Advanced Subsidiary Level Further Mathematics (8FM0)
Pearson Edexcel Level 3 GCE
Paper 21 Further Pure Mathematics 1
Friday 17 May 2024
Afternoon Paper
reference 8FM0/21
Further Mathematics
� �
Advanced Subsidiary
Further Mathematics options
21: Further Pure Mathematics 1
(Part of options A, B, C and D)
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,
• Answer
centre number and candidate number.
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 should be given to three significant figures unless otherwise stated.
Answers without working may not gain full credit.
Information
••• The
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 5 questions.
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.
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
,1. 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
(a) Sketch the graph of the curve with equation
1
y
x2
(2)
(b) Solve, using algebra, the inequality
1
3 2x2 >
x2
(5)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
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, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
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Question 1 continued
(Total for Question 1 is 7 marks)
Turn over
3
, 2. An area of woodland contains a mixture of blue and yellow flowers.
A study found that the proportion, x, of blue flowers in the woodland area satisfies the
DO NOT WRITE IN THIS AREA
differential equation
dx xt(0.8 x)
t>0
dt x2 5t
where t is the number of years since the start of the study.
Given that exactly 3 years after the start of the study half of the flowers in the woodland
area were blue,
dy y yn
(a) use one application of the approximation formula n 1 to estimate
dx n h
the proportion of blue flowers in the woodland area half a year later.
(5)
(b) Deduce from the differential equation the proportion of flowers that will be blue in
the long term.
(1)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
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Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel GCE Advanced Subsidiary Level Further Mathematics (8FM0)
Pearson Edexcel Level 3 GCE
Paper 21 Further Pure Mathematics 1
Friday 17 May 2024
Afternoon Paper
reference 8FM0/21
Further Mathematics
� �
Advanced Subsidiary
Further Mathematics options
21: Further Pure Mathematics 1
(Part of options A, B, C and D)
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,
• Answer
centre number and candidate number.
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 should be given to three significant figures unless otherwise stated.
Answers without working may not gain full credit.
Information
••• The
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 5 questions.
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.
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
,1. 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
(a) Sketch the graph of the curve with equation
1
y
x2
(2)
(b) Solve, using algebra, the inequality
1
3 2x2 >
x2
(5)
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 7 marks)
Turn over
3
, 2. An area of woodland contains a mixture of blue and yellow flowers.
A study found that the proportion, x, of blue flowers in the woodland area satisfies the
DO NOT WRITE IN THIS AREA
differential equation
dx xt(0.8 x)
t>0
dt x2 5t
where t is the number of years since the start of the study.
Given that exactly 3 years after the start of the study half of the flowers in the woodland
area were blue,
dy y yn
(a) use one application of the approximation formula n 1 to estimate
dx n h
the proportion of blue flowers in the woodland area half a year later.
(5)
(b) Deduce from the differential equation the proportion of flowers that will be blue in
the long term.
(1)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
�
��
�
