AQA
A-level
MATHEMATICS
7357/1
Paper 1 Question Paper + Mark scheme (Merged)
June 2021
Version: 1.0 Final
7357/1 PB/Jun21/E5 (JUN217357101)
A-level
MATHEMATICS
Paper 1
Time allowed: 2 hours
Materials
l You m
...
AQA
A-level
MATHEMATICS
7357/1
Paper 1 Question Paper + Mark scheme (Merged)
June 2021
Version: 1.0 Final
7357/1 PB/Jun21/E5 (JUN217357101)
A-level
MATHEMATICS
Paper 1
Time allowed: 2 hours
Materials
l 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.
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 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
TOTAL
I declare this is my own work.
2
Answer all questions inthespacesprovided.
1 State thesetofvaluesof x which satisfiestheinequality
(x 3)(2x þ 7) > 0
Tick (3) one box.
[1 mark]
x :
7
2
< x < 3
x : x < 3 or x >
7
2
x : x <
7
2
or x > 3
x : 3 < x <
7
2
2 Given that y ¼ ln (5x)
find
dy
dx
Circle youranswer.
[1 mark]
dy
dx
¼
1
x
dy
dx
¼
1
5x
dy
dx
¼
5
x
dy
dx
¼ ln 5
Jun21/7357/1
Do notwrite
outside the
box
(02)
3
3 A geometricsequencehasasumtoinfinityof 3
A secondsequenceisformedbymultiplyingeachtermoftheoriginalsequenceby 2
What isthesumtoinfinityofthenewsequence?
Circle youranswer.
[1 mark]
The sumto
infinity doesnot 6 3 6
exist
4 Millie isattemptingtouseproofbycontradictiontoshowthattheresultofmultiplying
an irrationalnumberbyanon-zerorationalnumberisalwaysanirrationalnumber.
Select theassumptionsheshouldmaketostartherproof.
Tick (3) one box.
[1 mark]
Every irrationalmultipliedbyanon-zerorational
is irrational.
Every irrationalmultipliedbyanon-zerorational
is rational.
There existsanon-zerorationaland
an irrationalwhoseproductisirrational.
There existsanon-zerorationaland
an irrationalwhoseproductisrational.
Turn overforthenextquestion
Do notwrite
outside the
box
Jun21/7357/1
Turn over
s
(03)
4
5 The line L has equation
3y 4x ¼ 21
The point P has coordinates(15,2)
5 (a) Find theequationofthelineperpendicularto L which passesthrough P.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5 (b) Hence, findtheshortestdistancefrom P to L.
[4 marks]
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