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
l You must have the AQA Formulae and statistical tables booklet for Question Mark
A‑level Mathematics and A‑level Further Mathematics. 1
l You should have a graphical or scientific calculator that meets the
2
requirements of the specification.
3
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
l Fill in the boxes at the top of this page.
6
l Answer all questions.
l 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
l Do not write outside the box around each page or on blank pages.
10
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want
11
to be marked. 12
13
Information
14
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100. 15
16
Advice 17
l Unless stated otherwise, you may quote formulae, without proof,
from the booklet. 18
l You do not necessarily need to use all the space provided. TOTAL
(JUN257367101) 7367/1
tyrionpapers.com
G/LM/Jun25/G4007/V8
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
2
1 The equation x + 4 x + c =0 has non-real roots.
Find the range of possible values of c
Circle your answer.
[1 mark]
c < 4 c ≤ 4 c ≥ 4 c > 4
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
3 Which one of the following expressions cannot be evaluated by l’Hôpital’s rule? box
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 2 x x→0 ln (1+ x )
4 Which one of the following statements is always correct?
Tick () one box.
[1 mark]
1
2
sinh= x
2
(1 − cosh 2 x )
sech2 x + tanh2 x =
1
cosech2 x + coth2 x =
1
1
cosh2 x
= (cosh 2 x − 1)
2
Turn over for the next question
Turn over U
(03) tyrionpapers.com
G/Jun25/7367/1
, 4
Do not write
outside the
box
1
5 The complex number z1 has argument tan −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]
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
(04) tyrionpapers.com
G/Jun25/7367/1
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
l You must have the AQA Formulae and statistical tables booklet for Question Mark
A‑level Mathematics and A‑level Further Mathematics. 1
l You should have a graphical or scientific calculator that meets the
2
requirements of the specification.
3
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
l Fill in the boxes at the top of this page.
6
l Answer all questions.
l 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
l Do not write outside the box around each page or on blank pages.
10
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want
11
to be marked. 12
13
Information
14
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100. 15
16
Advice 17
l Unless stated otherwise, you may quote formulae, without proof,
from the booklet. 18
l You do not necessarily need to use all the space provided. TOTAL
(JUN257367101) 7367/1
tyrionpapers.com
G/LM/Jun25/G4007/V8
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
2
1 The equation x + 4 x + c =0 has non-real roots.
Find the range of possible values of c
Circle your answer.
[1 mark]
c < 4 c ≤ 4 c ≥ 4 c > 4
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
(02) tyrionpapers.com
G/Jun25/7367/1
, 3
Do not write
outside the
3 Which one of the following expressions cannot be evaluated by l’Hôpital’s rule? box
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 2 x x→0 ln (1+ x )
4 Which one of the following statements is always correct?
Tick () one box.
[1 mark]
1
2
sinh= x
2
(1 − cosh 2 x )
sech2 x + tanh2 x =
1
cosech2 x + coth2 x =
1
1
cosh2 x
= (cosh 2 x − 1)
2
Turn over for the next question
Turn over U
(03) tyrionpapers.com
G/Jun25/7367/1
, 4
Do not write
outside the
box
1
5 The complex number z1 has argument tan −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]
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
(04) tyrionpapers.com
G/Jun25/7367/1
