AQA A LEVEL 30 REMOVED ACTUAL TEST PAPER WITH COMPLETE ANSWERS
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 1
Wednesday 4 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
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.
⚫ Answer all questions. 5
⚫ You must answer each question in the space provided for that question. 6
⚫ 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). 7
⚫ Do not write outside the box around each page or on blank pages. 8
⚫ Show all necessary working; otherwise marks for method may be lost. 9
⚫ Do all rough work in this book. Cross through any work that you do not want
to be marked. 10
11
Information
12
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100. 13
14
Advice
15
⚫ Unless stated otherwise, you may quote formulae, without proof, from
the booklet. 16
⚫ You do not necessarily need to use all the space provided. 17
TOTAL
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The equation of a curve is given by
y = 3ex
dy
Find an expression for
dx
Circle your answer.
[1 mark]
3e–x 3e1 3ex 3 xe x –1
2 A sequence is defined by
1
xn+1 = – xn with x1 = 32
4
The first four terms of the sequence are
32, –8, 2, –0.5
Which one of the following can be used to describe this sequence?
Circle your answer.
[1 mark]
Convergent Decreasing Increasing Periodic
G/Jun25/7357/1
, 3
Do not write
outside the
box
3 Express
log3 2x – log3 x
as a single logarithm.
Circle your answer.
[1 mark]
1
log log3 2 log3 x log3 2 x2
3 2
Turn over for the next question
Turn over U
G/Jun25/7357/1
, 4
Do not write
outside the
box
4 The first three terms, in ascending powers of x, of the binomial expansion
1
of (1 – 8x) 2 are
1 + nx – 8 x2
where n is a constant.
4 (a) State the range of values of x for which the expansion is valid.
Circle your answer.
[1 mark]
1 1
│x│ –8 │x│ – │x│ │x│ 8
8 8
4 (b) State the value of the constant n
Circle your answer.
[1 mark]
1
– 16 –4 4
2
G/Jun25/7357/1
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 1
Wednesday 4 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
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.
⚫ Answer all questions. 5
⚫ You must answer each question in the space provided for that question. 6
⚫ 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). 7
⚫ Do not write outside the box around each page or on blank pages. 8
⚫ Show all necessary working; otherwise marks for method may be lost. 9
⚫ Do all rough work in this book. Cross through any work that you do not want
to be marked. 10
11
Information
12
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100. 13
14
Advice
15
⚫ Unless stated otherwise, you may quote formulae, without proof, from
the booklet. 16
⚫ You do not necessarily need to use all the space provided. 17
TOTAL
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The equation of a curve is given by
y = 3ex
dy
Find an expression for
dx
Circle your answer.
[1 mark]
3e–x 3e1 3ex 3 xe x –1
2 A sequence is defined by
1
xn+1 = – xn with x1 = 32
4
The first four terms of the sequence are
32, –8, 2, –0.5
Which one of the following can be used to describe this sequence?
Circle your answer.
[1 mark]
Convergent Decreasing Increasing Periodic
G/Jun25/7357/1
, 3
Do not write
outside the
box
3 Express
log3 2x – log3 x
as a single logarithm.
Circle your answer.
[1 mark]
1
log log3 2 log3 x log3 2 x2
3 2
Turn over for the next question
Turn over U
G/Jun25/7357/1
, 4
Do not write
outside the
box
4 The first three terms, in ascending powers of x, of the binomial expansion
1
of (1 – 8x) 2 are
1 + nx – 8 x2
where n is a constant.
4 (a) State the range of values of x for which the expansion is valid.
Circle your answer.
[1 mark]
1 1
│x│ –8 │x│ – │x│ │x│ 8
8 8
4 (b) State the value of the constant n
Circle your answer.
[1 mark]
1
– 16 –4 4
2
G/Jun25/7357/1
