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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 Question Mark
requirements of the specification. 1
Instructions 2
⚫ Use black ink or black ball-point pen. Pencil should only be used for drawing. 3
⚫ Fill in the boxes at the top of this page.
⚫ Answer all questions. 4
⚫ You must answer each question in the space provided for that question. 5
⚫ 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). 6
⚫ Do not write outside the box around each page or on blank pages. 7
⚫ Show all necessary working; otherwise marks for method may be lost. 8
⚫ Do all rough work in this book. Cross through any work that you do not want
9
to be marked.
10
Information 11
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100. 12
13
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the 14
booklet. 15
⚫ You do not necessarily need to use all the space provided. 16
TOTAL
PB/KL/Jun23/E7 7357/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
7 7
1 Find the coefficient of x in the expansion of (2x 3)
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 dx ¼ 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
1 y 2 2y 2 1 2y 2 1 y2
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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