2025 AQA A-LEVEL FURTHER MATHEMATICS Paper 1
Question Paper & Mark Scheme (Merged) Thursday 22 May
2025 [VERIFIED]
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
G/LM/Jun25/G4007/V8 7 3 6 7/1
tyrionp ape rs. com
, 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
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
x0 cos x x0 sin x x0 2x x0 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
box
5 The complex number z 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]
tyrionpapers.com
G/Jun25/7367/1
Question Paper & Mark Scheme (Merged) Thursday 22 May
2025 [VERIFIED]
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
G/LM/Jun25/G4007/V8 7 3 6 7/1
tyrionp ape rs. com
, 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
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
x0 cos x x0 sin x x0 2x x0 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
box
5 The complex number z 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]
tyrionpapers.com
G/Jun25/7367/1
