AQA A-LEVEL MATHEMATICS Paper 3 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
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.
5
⚫ Fill in the boxes at the top of this page.
⚫ 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
19
20
G/LM/Jun25/G4006/E11 TOTAL 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
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
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.
5
⚫ Fill in the boxes at the top of this page.
⚫ 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
19
20
G/LM/Jun25/G4006/E11 TOTAL 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
