AQA
A-level
MATHEMATICS
Paper 1
Wednesday 3 June 2025 Afternoon Time allowed: 2 hours
Materials You must have the AQA Formulae for A‑ level Mathematics booklet. For Examiner’s Use
You should have a graphical or scientific calculator that meets the requirements
of the specification. Question Mark
Instructions Use black ink or black ball‑ point pen. Pencil should only be used 1
for drawing. Fill in the boxes at the top of this page. Answer all questions.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TOTAL
, 2
Do not write
outside the
box
Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
I declare this is my own work.
You must answer each question in the space provided for that question. If you need extra space for
your answer(s), use the lined pages at the end of this book. Write the question number against your
answer(s).
Show all necessary working; otherwise marks for method may be lost. Do all rough work in this
book. Cross through any work that you do not want to be marked.
Information The marks for questions are shown in brackets. The maximum mark for this paper is
100.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet. You do not
necessarily need to use all the space provided.
(JUN207357101) PB/Jun20/E7 7357/1
Answer all questions in the spaces provided.
1
The first three terms, in ascending powers of x, of the binomial expansion of (9 þ
2x) are given by
x
x2 (9 þ 2x) a þ
3 54
where a is a constant.
Jun20/7357/1
, 3
Do not write
outside the
box
1 (a) for which this expa nsion is valid.
State the range of values of x
Circle your answer.
[1 mark]
jx j < 1
jx j < jx j < jx j <
1 (b)
Find the value of a.
Circle your answer. [1 mark]
1 2 3 9
(02)
Turn over
Jun20/7357/1
, 4
Do not write
outside the
box
2
A student is searching for a solution to the equation f (x) ¼ 0 He
correctly evaluates
f (1) ¼ 1 and f (1) ¼ 1
and concludes that there must be a root between 1 and 1 due to the change of sign.
Select the function f (x) for which the conclusion is incorrect.
Circle your answer.
[1 mark]
1 f (x) ¼ x3 2x þ 1
f (x ) ¼ f (x ) ¼ x f (x ) ¼
x x þ2
3
The diagram shows a sector OAB of a circle with centre O and radius 2
A B
2
θ
O
The angle AOB is y radians and the perimeter of the sector is 6
Find the value of y
Circle your answer. [1 mark]
Jun20/7357/1
A-level
MATHEMATICS
Paper 1
Wednesday 3 June 2025 Afternoon Time allowed: 2 hours
Materials You must have the AQA Formulae for A‑ level Mathematics booklet. For Examiner’s Use
You should have a graphical or scientific calculator that meets the requirements
of the specification. Question Mark
Instructions Use black ink or black ball‑ point pen. Pencil should only be used 1
for drawing. Fill in the boxes at the top of this page. Answer all questions.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TOTAL
, 2
Do not write
outside the
box
Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
I declare this is my own work.
You must answer each question in the space provided for that question. If you need extra space for
your answer(s), use the lined pages at the end of this book. Write the question number against your
answer(s).
Show all necessary working; otherwise marks for method may be lost. Do all rough work in this
book. Cross through any work that you do not want to be marked.
Information The marks for questions are shown in brackets. The maximum mark for this paper is
100.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet. You do not
necessarily need to use all the space provided.
(JUN207357101) PB/Jun20/E7 7357/1
Answer all questions in the spaces provided.
1
The first three terms, in ascending powers of x, of the binomial expansion of (9 þ
2x) are given by
x
x2 (9 þ 2x) a þ
3 54
where a is a constant.
Jun20/7357/1
, 3
Do not write
outside the
box
1 (a) for which this expa nsion is valid.
State the range of values of x
Circle your answer.
[1 mark]
jx j < 1
jx j < jx j < jx j <
1 (b)
Find the value of a.
Circle your answer. [1 mark]
1 2 3 9
(02)
Turn over
Jun20/7357/1
, 4
Do not write
outside the
box
2
A student is searching for a solution to the equation f (x) ¼ 0 He
correctly evaluates
f (1) ¼ 1 and f (1) ¼ 1
and concludes that there must be a root between 1 and 1 due to the change of sign.
Select the function f (x) for which the conclusion is incorrect.
Circle your answer.
[1 mark]
1 f (x) ¼ x3 2x þ 1
f (x ) ¼ f (x ) ¼ x f (x ) ¼
x x þ2
3
The diagram shows a sector OAB of a circle with centre O and radius 2
A B
2
θ
O
The angle AOB is y radians and the perimeter of the sector is 6
Find the value of y
Circle your answer. [1 mark]
Jun20/7357/1
