2025 AQA A-LEVEL MATHEMATICS Paper 3 Question Paper &
Mark Scheme (Merged) Thursday 19 June 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
MATHEMATICS
Paper 3
Thursday 19 June 2025 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
You must have the AQA Formulae for A‑ level Mathematics booklet. Question Mark
You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
3
Instructions
4
Use black ink or black ball‑ point pen. Pencil should only be used for drawing.
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. 7
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
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. 11
Do all rough work in this book. Cross through any work that you do not 12
want to be marked 13
14
Information
15
The marks for questions are shown in brackets.
16
The maximum mark for this paper is 100.
17
Advice 18
Unless stated otherwise, you may quote formulae, without proof, from 19
the booklet. 20
You do not necessarily need to use all the space provided. TOTAL
G/LM/Jun25/G4006/E11 7357/3
, 2
Do not write
outside the
box
Section A
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=1 × √6 = √3 2 × √3 = √6
π √2
G/Jun25/7357/3
, 3
Do not write
outside the
box
2 The diagram shows the graph of y = arctan x
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
G/Jun25/7357/3
, 4
Do not write
outside the
box
3 The function f is defined by
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
G/Jun25/7357/3
Mark Scheme (Merged) Thursday 19 June 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
MATHEMATICS
Paper 3
Thursday 19 June 2025 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
You must have the AQA Formulae for A‑ level Mathematics booklet. Question Mark
You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
3
Instructions
4
Use black ink or black ball‑ point pen. Pencil should only be used for drawing.
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. 7
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
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. 11
Do all rough work in this book. Cross through any work that you do not 12
want to be marked 13
14
Information
15
The marks for questions are shown in brackets.
16
The maximum mark for this paper is 100.
17
Advice 18
Unless stated otherwise, you may quote formulae, without proof, from 19
the booklet. 20
You do not necessarily need to use all the space provided. TOTAL
G/LM/Jun25/G4006/E11 7357/3
, 2
Do not write
outside the
box
Section A
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=1 × √6 = √3 2 × √3 = √6
π √2
G/Jun25/7357/3
, 3
Do not write
outside the
box
2 The diagram shows the graph of y = arctan x
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
G/Jun25/7357/3
, 4
Do not write
outside the
box
3 The function f is defined by
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
G/Jun25/7357/3
