Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 16 May 2025
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.
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.
• clearly
Answer all questions and ensure that your answers to parts of questions are
labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• Answers without working
You should show sufficient working to make your methods clear.
may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 5 questions.
• – usemarks
The for each question are shown in brackets
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
P74070A
©2025 Pearson Education Ltd.
Y:1/1/1/1/1/1/1/
*P74070A0120*
,1. In this question you must show all stages of your working.
Solutions based 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
The surface temperature of the water in a lake during a particular year is modelled by
the equation
15 27
S = 12 – cos x° – sin x° ( I )
2 10
where S is the temperature in degrees Celsius and x is the number of days after the start
of the year.
(a) Use the model to write down the surface temperature of the water in the lake at the
start of the year.
(1)
x
Using the substitution t = tan
2
(b) show that equation ( I ) can be rewritten as
At 2 Bt C
S=
10
1 t 2
where A, B and C are integers to be determined.
(3)
(c) Hence determine, according to the model, the number of days after the start of the
year when the surface temperature of the water in the lake is 10 °C for the second
time that year. Give your answer to the nearest day.
(5)
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2
*P74070A0220*
, Question 1 continued
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3
*P74070A0320* Turn over
, Question 1 continued
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4
*P74070A0420*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 16 May 2025
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.
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.
• clearly
Answer all questions and ensure that your answers to parts of questions are
labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• Answers without working
You should show sufficient working to make your methods clear.
may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 5 questions.
• – usemarks
The for each question are shown in brackets
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
P74070A
©2025 Pearson Education Ltd.
Y:1/1/1/1/1/1/1/
*P74070A0120*
,1. In this question you must show all stages of your working.
Solutions based 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
The surface temperature of the water in a lake during a particular year is modelled by
the equation
15 27
S = 12 – cos x° – sin x° ( I )
2 10
where S is the temperature in degrees Celsius and x is the number of days after the start
of the year.
(a) Use the model to write down the surface temperature of the water in the lake at the
start of the year.
(1)
x
Using the substitution t = tan
2
(b) show that equation ( I ) can be rewritten as
At 2 Bt C
S=
10
1 t 2
where A, B and C are integers to be determined.
(3)
(c) Hence determine, according to the model, the number of days after the start of the
year when the surface temperature of the water in the lake is 10 °C for the second
time that year. Give your answer to the nearest day.
(5)
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2
*P74070A0220*
, Question 1 continued
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3
*P74070A0320* Turn over
, Question 1 continued
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4
*P74070A0420*
