AQA A-level MATHEMATICS Paper 1 QP 2021
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
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
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
(JUN217357101)
PB/Jun21/E5 7357/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 State the set of values of x which satisfies the inequality
(x 3)(2 x þ 7) > 0
Tick (3) one box.
[1 mark]
7
x: <x<3
2
7
x : x < 3 or x >
2
7
x : x < or x > 3
2
7
x : 3 < x <
2
2 Given that y ¼ ln (5 x)
dy
find
dx
Circle your answer.
[1 mark]
dy 1 dy 1 dy 5 dy
¼ ¼ ¼ ¼ ln 5
dx x d x 5x dx x dx
(02)
Jun21/7357/1
, 3
Do not write
outside the
3 A geometric sequence has a sum to infinity of 3 box
A second sequence is formed by multiplying each term of the original sequence by 2
What is the sum to infinity of the new sequence?
Circle your answer.
[1 mark]
The sum to
infinity does not 6 3 6
exist
4 Millie is attempting to use proof by contradiction to show that the result of multiplying
an irrational number by a non-zero rational number is always an irrational number.
Select the assumption she should make to start her proof.
Tick (3) one box.
[1 mark]
Every irrational multiplied by a non-zero rational
is irrational.
Every irrational multiplied by a non-zero rational
is rational.
There exists a non-zero rational and
an irrational whose product is irrational.
There exists a non-zero rational and
an irrational whose product is rational.
Turn over for the next question
Turn over
s
(03)
Jun21/7357/1
, 4
Do not write
outside the
5 The line L has equation box
3 y 4 x ¼ 21
The point P has coordinates (15, 2)
5 (a) Find the equation of the line perpendicular to L which passes through P.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5 (b) Hence, find the shortest distance from P to L.
[4 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun21/7357/1
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
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
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
(JUN217357101)
PB/Jun21/E5 7357/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 State the set of values of x which satisfies the inequality
(x 3)(2 x þ 7) > 0
Tick (3) one box.
[1 mark]
7
x: <x<3
2
7
x : x < 3 or x >
2
7
x : x < or x > 3
2
7
x : 3 < x <
2
2 Given that y ¼ ln (5 x)
dy
find
dx
Circle your answer.
[1 mark]
dy 1 dy 1 dy 5 dy
¼ ¼ ¼ ¼ ln 5
dx x d x 5x dx x dx
(02)
Jun21/7357/1
, 3
Do not write
outside the
3 A geometric sequence has a sum to infinity of 3 box
A second sequence is formed by multiplying each term of the original sequence by 2
What is the sum to infinity of the new sequence?
Circle your answer.
[1 mark]
The sum to
infinity does not 6 3 6
exist
4 Millie is attempting to use proof by contradiction to show that the result of multiplying
an irrational number by a non-zero rational number is always an irrational number.
Select the assumption she should make to start her proof.
Tick (3) one box.
[1 mark]
Every irrational multiplied by a non-zero rational
is irrational.
Every irrational multiplied by a non-zero rational
is rational.
There exists a non-zero rational and
an irrational whose product is irrational.
There exists a non-zero rational and
an irrational whose product is rational.
Turn over for the next question
Turn over
s
(03)
Jun21/7357/1
, 4
Do not write
outside the
5 The line L has equation box
3 y 4 x ¼ 21
The point P has coordinates (15, 2)
5 (a) Find the equation of the line perpendicular to L which passes through P.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5 (b) Hence, find the shortest distance from P to L.
[4 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun21/7357/1
