Please write clearly in block capitals.
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
A-level
MATHEMATICS
Paper 3
Thursday 19 June 2025 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae for A‑level Mathematics booklet.
Question Mark
l You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
3
Instructions
4
l Use black ink or black ball-point pen. Pencil should only be used for drawing.
l Fill in the boxes at the top of this page.
5
l Answer all questions. 6
l You must answer each question in the space provided for that question. 7
l If you need 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. 11
l Do all rough work in this book. Cross through any work that you do not 12
want to be marked 13
14
Information
15
l The marks for questions are shown in brackets.
16
l The maximum mark for this paper is 100.
17
Advice 18
l Unless stated otherwise, you may quote formulae, without proof, from 19
the booklet. 20
l You do not necessarily need to use all the space provided. TOTAL
(JUN257357301) 7357/3
G/LM/Jun25/G4006/E11
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 A student states that the product of two irrational numbers is always irrational.
One of the options is a counter example that shows the student’s statement
is incorrect.
Identify the counter example.
Circle your answer.
[1 mark]
1 1
e × 0 = 0 π × π = 1 × √ 6 = √ 3 2 × √ 3 = √ 6
√2
(02)
G/Jun25/7357/3
, 3
Do not write
outside the
2 The diagram shows the graph of y = arctan x box
y
a
O x
–a
The graph has horizontal asymptotes at y = –a and y = a
State the value of a
Circle your answer.
[1 mark]
π 1 π π
4 2
Turn over for the next question
Turn over U
(03)
G/Jun25/7357/3
, 4
Do not write
outside the
3 The function f is defined by box
f (x) = e x for x ∈ ℝ
Identify which one of the following statements describes the function f
Tick () one box.
[1 mark]
Decreasing and concave
Decreasing and convex
Increasing and concave
Increasing and convex
(04)
G/Jun25/7357/3
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
A-level
MATHEMATICS
Paper 3
Thursday 19 June 2025 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae for A‑level Mathematics booklet.
Question Mark
l You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
3
Instructions
4
l Use black ink or black ball-point pen. Pencil should only be used for drawing.
l Fill in the boxes at the top of this page.
5
l Answer all questions. 6
l You must answer each question in the space provided for that question. 7
l If you need 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. 11
l Do all rough work in this book. Cross through any work that you do not 12
want to be marked 13
14
Information
15
l The marks for questions are shown in brackets.
16
l The maximum mark for this paper is 100.
17
Advice 18
l Unless stated otherwise, you may quote formulae, without proof, from 19
the booklet. 20
l You do not necessarily need to use all the space provided. TOTAL
(JUN257357301) 7357/3
G/LM/Jun25/G4006/E11
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 A student states that the product of two irrational numbers is always irrational.
One of the options is a counter example that shows the student’s statement
is incorrect.
Identify the counter example.
Circle your answer.
[1 mark]
1 1
e × 0 = 0 π × π = 1 × √ 6 = √ 3 2 × √ 3 = √ 6
√2
(02)
G/Jun25/7357/3
, 3
Do not write
outside the
2 The diagram shows the graph of y = arctan x box
y
a
O x
–a
The graph has horizontal asymptotes at y = –a and y = a
State the value of a
Circle your answer.
[1 mark]
π 1 π π
4 2
Turn over for the next question
Turn over U
(03)
G/Jun25/7357/3
, 4
Do not write
outside the
3 The function f is defined by box
f (x) = e x for x ∈ ℝ
Identify which one of the following statements describes the function f
Tick () one box.
[1 mark]
Decreasing and concave
Decreasing and convex
Increasing and concave
Increasing and convex
(04)
G/Jun25/7357/3
