A-level
FURTHER MATHEMATICS ACTUAL 2025
PAPER ERGED WITH MARK SCHEME
Paper 1
Please write clearly in block capitals.
Candid
Centre ate
number number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
For Examiner’s Use
A-level Question Mark
1
FURTHER MATHEMATICS 2
3
Paper 1
4
Thursday 22 May 2025 Afternoon 5
Time allowed: 2 hours
6
Materials
l You must have the AQA Formulae and statistical tables booklet for 7
A-level Mathematics and A-level Further Mathematics. l You should have a 8
graphical or scientific calculator that meets the requirements of the specification.
9
Instructions l Use black ink or black ball-point pen. Pencil should only be used 10
for drawing. l Fill in the boxes at the top of this page. l Answer all questions.
l You must answer each question in the space provided for that question. If 11
you require extra space for your answer(s), use the lined pages at the end of this 12
book. Write the question number against your answer(s). l Do not write outside
the box around each page or on blank pages. l Show all necessary working; 13
otherwise marks for method may be lost. l Do all rough work in this book. Cross 14
through any work that you do not want to be marked.
15
16
17
18
TOTAL
, 2
Do not write
outside the
box
Information l The marks for questions are shown in brackets. l The maximum mark for this paper is
100.
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l You do not
necessarily need to use all the space provided.
(JUN257367101) tyrionpapers.com 7367/1
G/LM/Jun25/G4007/V8
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]
c<4 c≤4 c≥4 c>4
tyrionpapers.com
G/Jun25/7367/1
, 3
Do not write
outside the
box
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)
Turn over U
tyrionpapers.com
G/Jun25/7367/1
, 4
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 tanhx ex−1
xlim→0 cosx xlim→0 sinx xlim→0 2x xlim→0ln (1+ x)
4 Which one of the following statements is always correct?
Tick () one box.
[1 mark]
sinh2x =(1− cosh2x)
sech2x + tanh2x =1
2 2 cosech x +coth x
=1
cosh2x =(cosh 2x −1)
Turn over for the next question
tyrionpapers.com
G/Jun25/7367/1
FURTHER MATHEMATICS ACTUAL 2025
PAPER ERGED WITH MARK SCHEME
Paper 1
Please write clearly in block capitals.
Candid
Centre ate
number number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
For Examiner’s Use
A-level Question Mark
1
FURTHER MATHEMATICS 2
3
Paper 1
4
Thursday 22 May 2025 Afternoon 5
Time allowed: 2 hours
6
Materials
l You must have the AQA Formulae and statistical tables booklet for 7
A-level Mathematics and A-level Further Mathematics. l You should have a 8
graphical or scientific calculator that meets the requirements of the specification.
9
Instructions l Use black ink or black ball-point pen. Pencil should only be used 10
for drawing. l Fill in the boxes at the top of this page. l Answer all questions.
l You must answer each question in the space provided for that question. If 11
you require extra space for your answer(s), use the lined pages at the end of this 12
book. Write the question number against your answer(s). l Do not write outside
the box around each page or on blank pages. l Show all necessary working; 13
otherwise marks for method may be lost. l Do all rough work in this book. Cross 14
through any work that you do not want to be marked.
15
16
17
18
TOTAL
, 2
Do not write
outside the
box
Information l The marks for questions are shown in brackets. l The maximum mark for this paper is
100.
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l You do not
necessarily need to use all the space provided.
(JUN257367101) tyrionpapers.com 7367/1
G/LM/Jun25/G4007/V8
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]
c<4 c≤4 c≥4 c>4
tyrionpapers.com
G/Jun25/7367/1
, 3
Do not write
outside the
box
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)
Turn over U
tyrionpapers.com
G/Jun25/7367/1
, 4
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 tanhx ex−1
xlim→0 cosx xlim→0 sinx xlim→0 2x xlim→0ln (1+ x)
4 Which one of the following statements is always correct?
Tick () one box.
[1 mark]
sinh2x =(1− cosh2x)
sech2x + tanh2x =1
2 2 cosech x +coth x
=1
cosh2x =(cosh 2x −1)
Turn over for the next question
tyrionpapers.com
G/Jun25/7367/1
