AQA A level Mathematics Past Paper 1 and Mark Scheme 7357/1

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A-level
MATHEMATICS
Paper 1


Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae for A‑level Mathematics booklet.
l You should have a graphical or scientific calculator that meets the Question Mark
requirements of the specification.
1
Instructions 2
l Use black ink or black ball-point pen. Pencil should only be used for drawing. 3
l Fill in the boxes at the top of this page.
l Answer all questions. 4
l You must answer each question in the space provided for that question. 5
l If you need extra space for your answer(s), use the lined pages at the end 6
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. 7
l Show all necessary working; otherwise marks for method may be lost. 8
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 9
10
Information 11
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100. 12
13
Advice 14
l Unless stated otherwise, you may quote formulae, without proof, from the
booklet. 15
l 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.




1 Find the coefficient of x 7 in the expansion of (2 x  3)7

Circle your answer.
[1 mark]

2187 128 2 128




dy
2 Given that y ¼ 2 x 3 find
dx
Circle your answer.
[1 mark]

dy dy dy x 4 dy
¼ 5x2 ¼ 6x2 ¼ ¼ 6x3
dx dx dx 2 dx




(02)
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, 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 ln x y ¼ 2 ln x y ¼ ln y ¼ ln 2 x
2 2




4 Given that y is a small angle, find an approximation for cos 2 y

Circle your answer.
[1 mark]

y2
1 2  2y2 1  2y2 1  y2
2




Turn over for the next question




Turn over
s




(03)
Jun23/7357/1

, 4
Do not write
outside the
5 box
5 The graph of y ¼ is shown in the diagram below.
ex 1

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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(04)
Jun23/7357/1