AS LEVEL FURTHER MATHEMATICS: Actual May 2025 PAST Further Pure Mathematics 1:
Further Pure Mathematics 1. All Assessment Questions & Mark Scheme [Edexcel 8FM0/21]
Exam Resource Summary
The May 2025 Edexcel AS Level Further Mathematics (8FM0) – Paper 21: Further Pure Mathematics 1 (Part of
Options A–D) – Merged Question Paper & Mark Scheme document integrates the full examination paper with
its complete mark scheme. This paper assesses students’ understanding of advanced pure mathematics topics,
including proof, complex numbers, matrices, advanced algebra and functions, further vectors and calculus. The
merged format presents each question immediately followed by its corresponding marking criteria, providing full
transparency of examiner expectations, mark allocation, and how successful responses are structured. This
resource is essential for targeted revision, self-assessment of problem-solving techniques, and the development
of analytical and mathematical reasoning skills required for success in the May 2025 AS Level Further
Mathematics Paper 21 examination.
Turn over
, 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
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)
Using the substitution t = tan
x
2
(b) show that equation ( I ) can be rewritten as
DO NOT WRITE IN THIS AREA
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)
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
3
Turn over
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
4
Further Pure Mathematics 1. All Assessment Questions & Mark Scheme [Edexcel 8FM0/21]
Exam Resource Summary
The May 2025 Edexcel AS Level Further Mathematics (8FM0) – Paper 21: Further Pure Mathematics 1 (Part of
Options A–D) – Merged Question Paper & Mark Scheme document integrates the full examination paper with
its complete mark scheme. This paper assesses students’ understanding of advanced pure mathematics topics,
including proof, complex numbers, matrices, advanced algebra and functions, further vectors and calculus. The
merged format presents each question immediately followed by its corresponding marking criteria, providing full
transparency of examiner expectations, mark allocation, and how successful responses are structured. This
resource is essential for targeted revision, self-assessment of problem-solving techniques, and the development
of analytical and mathematical reasoning skills required for success in the May 2025 AS Level Further
Mathematics Paper 21 examination.
Turn over
, 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
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)
Using the substitution t = tan
x
2
(b) show that equation ( I ) can be rewritten as
DO NOT WRITE IN THIS AREA
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)
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
3
Turn over
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
4
