AQA A-LEVEL FURTHER MATHEMATICS Paper 2 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 2
Friday 6 June 2025 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
⚫ You must have the AQA Formulae and statistical tables booklet for
A‑level Mathematics and A‑level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the 1
requirements of the specification. 2
Instructions 3
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 4
⚫ Fill in the boxes at the top of this page. 5
⚫ Answer all questions.
6
⚫ 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 7
of this book. Write the question number against your answer(s). 8
⚫ Do not write outside the box around each page or on blank pages. 9
⚫ Show all necessary working; otherwise marks for method may be lost.
10
⚫ Do all rough work in this book. Cross through any work that you do not want
to be marked. 11
12
Information 13
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100.
14
15
Advice 16
⚫ Unless stated otherwise, you may quote formulae, without proof,
17
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.
a c
1 The vectors and are perpendicular.
b 1
Which one of the following statements must be true?
Tick (✓) one box.
[1 mark]
a = bc
b = ac
a = – bc
b = – ac
2 The quadrilateral Q1 has an area of 5 cm2
4 −1
The matrix represents the transformation T
2 1
The transformation T acts on Q1 to give the quadrilateral Q2
Find the area of Q2
Circle your answer.
[1 mark]
5 cm2 10 cm2 30 cm2 180 cm2
G/Jun25/7367/2
, 3
Do not write
outside the
d
( sin )
−1 box
3 Find x − 2cos−1 x
dx
Circle your answer.
[1 mark]
−3 −1 1 3
1− x2 1− x2 1− x2 1− x2
4 The function f is defined by f (x) = 16 − x2 ( x ℝ)
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
Turn over U
G/Jun25/7367/2
, 4
Do not write
outside the
The complex number z = (3 + 4 i )( 5 + ci) , where c is an integer.
box
5
It is given that Re (z) = 7
Find the value of c
[2 marks]
G/Jun25/7367/2
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 2
Friday 6 June 2025 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
⚫ You must have the AQA Formulae and statistical tables booklet for
A‑level Mathematics and A‑level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the 1
requirements of the specification. 2
Instructions 3
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 4
⚫ Fill in the boxes at the top of this page. 5
⚫ Answer all questions.
6
⚫ 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 7
of this book. Write the question number against your answer(s). 8
⚫ Do not write outside the box around each page or on blank pages. 9
⚫ Show all necessary working; otherwise marks for method may be lost.
10
⚫ Do all rough work in this book. Cross through any work that you do not want
to be marked. 11
12
Information 13
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100.
14
15
Advice 16
⚫ Unless stated otherwise, you may quote formulae, without proof,
17
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.
a c
1 The vectors and are perpendicular.
b 1
Which one of the following statements must be true?
Tick (✓) one box.
[1 mark]
a = bc
b = ac
a = – bc
b = – ac
2 The quadrilateral Q1 has an area of 5 cm2
4 −1
The matrix represents the transformation T
2 1
The transformation T acts on Q1 to give the quadrilateral Q2
Find the area of Q2
Circle your answer.
[1 mark]
5 cm2 10 cm2 30 cm2 180 cm2
G/Jun25/7367/2
, 3
Do not write
outside the
d
( sin )
−1 box
3 Find x − 2cos−1 x
dx
Circle your answer.
[1 mark]
−3 −1 1 3
1− x2 1− x2 1− x2 1− x2
4 The function f is defined by f (x) = 16 − x2 ( x ℝ)
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
Turn over U
G/Jun25/7367/2
, 4
Do not write
outside the
The complex number z = (3 + 4 i )( 5 + ci) , where c is an integer.
box
5
It is given that Re (z) = 7
Find the value of c
[2 marks]
G/Jun25/7367/2
