AQA
A-level
MATHEMATICS
7357/1
Paper 1
Version: 1.0 Final
PB/KL/Jun23/E7 7357/1
A-level
MATHEMATICS
Paper 1
Time allowed: 2 hours
Materials
l
... [Show More] You must have the AQA Formulae for A‑level Mathematics booklet.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
Instructions
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.
l Answer all questions.
l You must answer each question in the space provided for that question.
l 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).
l Do not write outside the box around each page or on blank pages.
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want
to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100.
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the
booklet.
l You do not necessarily need to use all the space provided.
Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
For Examiner’s Use
Question Mark
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
TOTAL
I declare this is my own work.
2
Answer all questions in the spaces provided.
1 Find the coefficient of x7 in the expansion of (2x 3)7
Circle your answer.
[1 mark]
2187 128 2 128
2 Given that y ¼ 2x3 find dy
dx
Circle your answer.
[1 mark]
dy
dx
¼ 5x2 dy
dx
¼ 6x2 dy
dx
¼ x4
2
dy
dx
¼ 6x3
Jun23/7357/1
Do not write
outside the
box
(02)
3
3 The curve with equation y ¼ ln x is transformed by a stretch parallel to the x-axis with
scale factor 2
Find the equation of the transformed curve.
Circle your answer.
[1 mark]
y ¼ 1
2 ln x y ¼ 2 ln x y ¼ ln x
2 y ¼ ln 2x
4 Given that y is a small angle, find an approximation for cos 2y
Circle your answer.
[1 mark]
1 y2
2 2 2y2 1 2y2 1 y2
Turn over for the next question
Do not write
outside the
box
Jun23/7357/1
Turn over s
(03)
4
5 The graph of y ¼ 5
ex 1 is shown in the diagram below.
O 1 4 x
y
The trapezium rule with 6 ordinates (5 strips) is to be used to find an approximation
for the shaded area.
The values required to obtain this approximation are shown in the table below.
x 1 1.6 2.2 2.8 3.4 4
y 2.90988 1.26485 0.62305 0.32374 0.17263 0.09329
5 (a) Use the trapezium rule with 6 ordinates (5 strips) to find an approximate value for the
shaded area.
Give your answer to four decimal places.
[3 marks]
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