AQA A LEVEL MATHEMATICS PAPER3 JUNE
2020
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 3
Friday 12 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. 4
l Answer all questions. 5
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 6
of this book. Write the question number against your answer(s). 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 9
to be marked.
10
Information 11
l The marks for questions are shown in brackets. 12
l The maximum mark for this paper is 100. 13
14
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the 15
booklet. 16
l You do not necessarily need to use all the space provided. 17
18
TOTAL
(JUN207357301)
PB/Jun20/E6 7357/3
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 Given that
ð 10
f (x) dx ¼ 7
0
deduce the value of
ð 10
f (x) þ 1 dx
0
Circle your answer.
[1 mark]
3 7 8 17
2 Given that
6 cos y þ 8 sin y R cos (y þ a )
find the value of R.
Circle your answer.
[1 mark]
6 8 10 14
(02)
Jun20/7357/3
, 3
Do not write
outside the
3 Determine which one of these graphs does not represent y as a function of x. box
Tick (3) one box.
[1 mark]
y
x
y
x
y
x
y
x
Turn over
s
(03)
Jun20/7357/3
, 4
Do not write
outside the
4 p (x) ¼ 4x 3 15x 2 48x 36 box
4 (a) Use the factor theorem to prove that x 6 is a factor of p (x).
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4 (b) (i) Prove that the graph of y ¼ p (x) intersects the x-axis at exactly one point.
[4 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun20/7357/3
2020
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 3
Friday 12 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. 4
l Answer all questions. 5
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 6
of this book. Write the question number against your answer(s). 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 9
to be marked.
10
Information 11
l The marks for questions are shown in brackets. 12
l The maximum mark for this paper is 100. 13
14
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the 15
booklet. 16
l You do not necessarily need to use all the space provided. 17
18
TOTAL
(JUN207357301)
PB/Jun20/E6 7357/3
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 Given that
ð 10
f (x) dx ¼ 7
0
deduce the value of
ð 10
f (x) þ 1 dx
0
Circle your answer.
[1 mark]
3 7 8 17
2 Given that
6 cos y þ 8 sin y R cos (y þ a )
find the value of R.
Circle your answer.
[1 mark]
6 8 10 14
(02)
Jun20/7357/3
, 3
Do not write
outside the
3 Determine which one of these graphs does not represent y as a function of x. box
Tick (3) one box.
[1 mark]
y
x
y
x
y
x
y
x
Turn over
s
(03)
Jun20/7357/3
, 4
Do not write
outside the
4 p (x) ¼ 4x 3 15x 2 48x 36 box
4 (a) Use the factor theorem to prove that x 6 is a factor of p (x).
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4 (b) (i) Prove that the graph of y ¼ p (x) intersects the x-axis at exactly one point.
[4 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun20/7357/3
