AQA-A-level MATHEMATICS Paper 1 2020

AQA A LEVEL MATHEMATICS PAPER 1
2020


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Surname _________________________________________________________________________

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I declare this is my own work.



A-level
MATHEMATICS
Paper 1


Wednesday 3 June 2020 Afternoon 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
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
l Show all necessary working; otherwise marks for method may be lost. 7
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 8
9
Information
l The marks for questions are shown in brackets. 10
l The maximum mark for this paper is 100. 11
12
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the 13
booklet.
14
l You do not necessarily need to use all the space provided.
15
TOTAL




(JUN207357101)
PB/Jun20/E7 7357/1

, 2
Do not write
outside the
box
Answer all questions in the spaces provided.




1 The first three terms, in ascending powers of x, of the binomial expansion of
1
(9 þ 2 x) 2 are given by

1
x x2
(9 þ 2 x) 2  a þ 
3 54

where a is a constant.



1 (a) State the range of values of x for which this expansion is valid.

Circle your answer.
[1 mark]

2 2 9
jxj < jxj < jxj < 1 jxj <
9 3 2




1 (b) Find the value of a.

Circle your answer.
[1 mark]

1 2 3 9




(02)
Jun20/7357/1

, 3
Do not write
outside the
2 A student is searching for a solution to the equation f (x) ¼ 0 box


He correctly evaluates

f (1) ¼ 1 and f (1) ¼ 1

and concludes that there must be a root between 1 and 1 due to the change of sign.

Select the function f (x) for which the conclusion is incorrect.

Circle your answer.
[1 mark]

1 2x þ 1
f (x) ¼ f (x) ¼ x f (x) ¼ x 3 f (x) ¼
x xþ2



3 The diagram shows a sector OAB of a circle with centre O and radius 2


A B


2

θ
O

The angle AOB is y radians and the perimeter of the sector is 6

Find the value of y

Circle your answer.
[1 mark]
pffiffiffi
1 3 2 3




Turn over for the next question




Turn over
s




(03)
Jun20/7357/1

, 4
Do not write
outside the
4 (a) Sketch the graph of box


y ¼ 4  j2 x  6j

y




O x




[3 marks]

4 (b) Solve the inequality

4  j2 x  6j > 2
[2 marks]

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(04)
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