A-level
FURTHER MATHEMATICS ACTUAL 2025
PAPER MERGED WITH MARK SCHEME
Paper 2
Please write clearly in block capitals.
Candid
Centre ate
number number
Surname _________________________________________________________________________
For Examiner’s Use
Question Mark
Forename(s) _________________________________________________________________________
1
Candidate signature _________________________________________________________________________
2
I declare this is my own work. 3
A-level 4
FURTHER MATHEMATICS 5
6
Paper 2
7
Friday 6 June 2025 Afternoon Time allowed:
8 2 hours
Materials 9
l You must have the AQA Formulae and statistical tables booklet for
A-level Mathematics and A-level Further Mathematics. l You should have a 10
graphical or scientific calculator that meets the requirements of the specification.
11
Instructions l Use black ink or black ball-point pen. P encil should only be used
for drawing. l Fill in the boxes at the top of this page. l Answer all questions. 12
l You must answer each question in the space provided for that question. If
you require extra space for your answer(s), use the lined pages at the end of this 13
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; 14
otherwise marks for method may be lost. l Do all rough work in this book. Cross
through any work that you do not want to be marked. 15
16
17
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.
(JUN257367201) G/LM/Jun25/G4007/V5 7367/2
Answer all questions in the spaces provided.
1 a c
The vectors and are perpendicular.
1
b
Which one of the following statements must be true?
Tick () one box.
[1 mark]
a = bc
b = ac
a = –bc
b = –ac
G/Jun25/7367/2
, 3
Do not write
outside the
box
2 The quadrilateral Q has an area of 5 cm2
1
4 −1
The matrix represents the transformation T 2 1
The transformation T acts on Q to give the quadrilateral Q2
1
Find the area of Q
2
Circle your answer.
[1 mark]
5 cm2 10 cm2 30 cm2 180 cm2
(02)
3 d
Find (sin−1x −2cos−1x )
dx
Circle your answer.
[1 mark]
−3 −1 1 3
1−x2 1−x2 1−x2 1−x2
Turn over U
G/Jun25/7367/2
, 4
Do not write
outside the
box
4 The function f is defined by f ( )x = −16 x2 (x∈)
On which of the following intervals is the mean value of f the greatest?
Tick () one box.
[1 mark]
0≤x≤1
0≤x≤2
0≤x≤3
0≤x≤4
Turn over for the next question
(03)
G/Jun25/7367/2
FURTHER MATHEMATICS ACTUAL 2025
PAPER MERGED WITH MARK SCHEME
Paper 2
Please write clearly in block capitals.
Candid
Centre ate
number number
Surname _________________________________________________________________________
For Examiner’s Use
Question Mark
Forename(s) _________________________________________________________________________
1
Candidate signature _________________________________________________________________________
2
I declare this is my own work. 3
A-level 4
FURTHER MATHEMATICS 5
6
Paper 2
7
Friday 6 June 2025 Afternoon Time allowed:
8 2 hours
Materials 9
l You must have the AQA Formulae and statistical tables booklet for
A-level Mathematics and A-level Further Mathematics. l You should have a 10
graphical or scientific calculator that meets the requirements of the specification.
11
Instructions l Use black ink or black ball-point pen. P encil should only be used
for drawing. l Fill in the boxes at the top of this page. l Answer all questions. 12
l You must answer each question in the space provided for that question. If
you require extra space for your answer(s), use the lined pages at the end of this 13
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; 14
otherwise marks for method may be lost. l Do all rough work in this book. Cross
through any work that you do not want to be marked. 15
16
17
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.
(JUN257367201) G/LM/Jun25/G4007/V5 7367/2
Answer all questions in the spaces provided.
1 a c
The vectors and are perpendicular.
1
b
Which one of the following statements must be true?
Tick () one box.
[1 mark]
a = bc
b = ac
a = –bc
b = –ac
G/Jun25/7367/2
, 3
Do not write
outside the
box
2 The quadrilateral Q has an area of 5 cm2
1
4 −1
The matrix represents the transformation T 2 1
The transformation T acts on Q to give the quadrilateral Q2
1
Find the area of Q
2
Circle your answer.
[1 mark]
5 cm2 10 cm2 30 cm2 180 cm2
(02)
3 d
Find (sin−1x −2cos−1x )
dx
Circle your answer.
[1 mark]
−3 −1 1 3
1−x2 1−x2 1−x2 1−x2
Turn over U
G/Jun25/7367/2
, 4
Do not write
outside the
box
4 The function f is defined by f ( )x = −16 x2 (x∈)
On which of the following intervals is the mean value of f the greatest?
Tick () one box.
[1 mark]
0≤x≤1
0≤x≤2
0≤x≤3
0≤x≤4
Turn over for the next question
(03)
G/Jun25/7367/2
