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2023 AQA A-level MATHEMATICS 7357/1 Paper 1 Question Paper & Mark scheme (Merged) June
2023 [VERIFIED]
A-level
MATHEMATICS
Paper 1
Tuesday 6 June 2023 afternoon Time allowed: 2 hours
Materials For Examiner’s Use
You must have the AQA Formulae for A‑level Mathematics booklet. You should have a graphical or scientific calculator that meets the
requirements of the specification.
Question Mark
Instructions 1
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. 2
Answer all questions. 3
You must answer each question in the space provided for that question. 4
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). 5
Do not write outside the box around each page or on blank pages. 6
Show all necessary working; otherwise marks for method may be lost.
7
Do all rough work in this book. Cross through any work that you do not want
to be marked. 8
9
Information
The marks for questions are shown in brackets. 10
The maximum mark for this paper is 100. 11
12
Advice
Unless stated otherwise, you may quote formulae, without proof, from 13
the booklet. 14
You do not necessarily need to use all the space provided.
15
16
TOTAL
PB/KL/Jun23/E7 7357/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 7 7
Find the coefficient of x in the expansion of 3)
(2x Circle your answer.
[1 mark]
2187 128 2 128
3 dy
2 Given that y ¼ 2x find d
x
Circle your answer.
[1 mark]
4
dy dy dy x dy
2 2 3
d x ¼ 5x d x ¼ 6x dx¼ 2 d x ¼ 6x
(02)
Jun23/7357/1
, 3
Do not write
outside the
3 The curve with equation y ¼ ln x is transformed by a stretch parallel to the x-axis with box
scale factor 2
Find the equation of the transformed
curve. Circle your answer.
[1 mark]
1 x
y ¼ 2 ln x y ¼ 2 ln x y ¼ ln 2 y ¼ ln 2x
4 Given that y is a small angle, find an approximation for cos 2y
Circle your answer.
[1 mark]
2 2 2 2
1 y 2 2y 1 2y 1 y
2
Turn over for the next question
Turn over
s
(03)
Jun23/7357/1
, 4
Do not write
outside the
5 box
x
5 The graph of y ¼ e 1 is shown in the diagram below.
y
O 1 4 x
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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