AQA A-LEVEL FURTHER MATHEMATICS Paper 1 JUNE 2025 Combined
Question Paper and Mark Scheme
Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 1
Thursday 22 May 2025 Afternoon Time allowed: 2 hours
For Examiner’s Use
Materials
⚫ You must have the AQA Formulae and statistical tables booklet for
Question Mark
A‑level Mathematics and A‑level Further Mathematics. 1
⚫ You should have a graphical or scientific calculator that meets the 2
requirements of the specification.
3
Instructions 4
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
⚫ Fill in the boxes at the top of this page.
6
⚫ Answer all questions.
⚫ You must answer each question in the space provided for that question.
7
If you require extra space for your answer(s), use the lined pages at the end 8
of this book. Write the question number against your answer(s). 9
⚫ Do not write outside the box around each page or on blank pages.
10
⚫ Show all necessary working; otherwise marks for method may be lost.
⚫ Do all rough work in this book. Cross through any work that you do not want
11
to be marked. 12
13
Information 14
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100.
15
16
Advice 17
⚫ Unless stated otherwise, you may quote formulae, without proof,
18
from the booklet.
⚫ You do not necessarily need to use all the space provided. TOTAL
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The equation x2 + 4x + c = 0 has non‑real roots. Find
the range of possible values of c
Circle your answer.
[1 mark]
c4 c4 c4 c4
2 The point A on the Argand diagram represents the complex number z
The point B is the reflection in the imaginary axis of the point A
Im
O Re
A B
Which complex number does the point B represent?
Circle your answer.
[1 mark]
1
−z z −z
z
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, 3
Do not write
outside the
box
3 Which one of the following expressions cannot be evaluated by l’Hôpital’s rule?
Circle your answer.
[1 mark]
x x2 tanh x ex − 1
lim lim lim lim
x→0 cos x x→0 sin x x→0 2x x→0 ln (1+ x)
4 Which one of the following statements is always correct?
Tick (✓) one box.
[1 mark]
1
sinh2 x = (1 − cosh 2x )
2
sech2 x + tanh2 x = 1
cosech2 x + coth2 x = 1
1
cosh2 x = (cosh 2x −1)
2
Turn over for the next question
Turn over U
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G/Jun25/7367/1
, 4
Do not write
−1
1 outside the
The complex number z has argument tan
box
5
1
5
The complex number z2 = –2 – 4i
z1
Find arg
z2
Give your answer as a number in the range – π < α < π, to two decimal places.
[3 marks]
tyrionpapers.com
G/Jun25/7367/1
Question Paper and Mark Scheme
Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 1
Thursday 22 May 2025 Afternoon Time allowed: 2 hours
For Examiner’s Use
Materials
⚫ You must have the AQA Formulae and statistical tables booklet for
Question Mark
A‑level Mathematics and A‑level Further Mathematics. 1
⚫ You should have a graphical or scientific calculator that meets the 2
requirements of the specification.
3
Instructions 4
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
⚫ Fill in the boxes at the top of this page.
6
⚫ Answer all questions.
⚫ You must answer each question in the space provided for that question.
7
If you require extra space for your answer(s), use the lined pages at the end 8
of this book. Write the question number against your answer(s). 9
⚫ Do not write outside the box around each page or on blank pages.
10
⚫ Show all necessary working; otherwise marks for method may be lost.
⚫ Do all rough work in this book. Cross through any work that you do not want
11
to be marked. 12
13
Information 14
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100.
15
16
Advice 17
⚫ Unless stated otherwise, you may quote formulae, without proof,
18
from the booklet.
⚫ You do not necessarily need to use all the space provided. TOTAL
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The equation x2 + 4x + c = 0 has non‑real roots. Find
the range of possible values of c
Circle your answer.
[1 mark]
c4 c4 c4 c4
2 The point A on the Argand diagram represents the complex number z
The point B is the reflection in the imaginary axis of the point A
Im
O Re
A B
Which complex number does the point B represent?
Circle your answer.
[1 mark]
1
−z z −z
z
tyrionpapers.com
G/Jun25/7367/1
, 3
Do not write
outside the
box
3 Which one of the following expressions cannot be evaluated by l’Hôpital’s rule?
Circle your answer.
[1 mark]
x x2 tanh x ex − 1
lim lim lim lim
x→0 cos x x→0 sin x x→0 2x x→0 ln (1+ x)
4 Which one of the following statements is always correct?
Tick (✓) one box.
[1 mark]
1
sinh2 x = (1 − cosh 2x )
2
sech2 x + tanh2 x = 1
cosech2 x + coth2 x = 1
1
cosh2 x = (cosh 2x −1)
2
Turn over for the next question
Turn over U
tyrionpapers.com
G/Jun25/7367/1
, 4
Do not write
−1
1 outside the
The complex number z has argument tan
box
5
1
5
The complex number z2 = –2 – 4i
z1
Find arg
z2
Give your answer as a number in the range – π < α < π, to two decimal places.
[3 marks]
tyrionpapers.com
G/Jun25/7367/1
