AQA QP 2023 A-level MATHEMATICS Paper 3 (7357/3)
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
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.
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). 7
l Do not write outside the box around each page or on blank pages.
8
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 9
to be marked. 10
11
Information
l The marks for questions are shown in brackets. 12
l The maximum mark for this paper is 100. 13
14
Advice 15
l Unless stated otherwise, you may quote formulae, without proof, from the
booklet. 16
l You do not necessarily need to use all the space provided. 17
TOTAL
PB/KL/Jun23/E7 7357/3
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 The graph of y ¼ f (x) is shown below.
y
O x
One of the four equations listed below is the equation of the graph y ¼ f (x)
Identify which one is the correct equation of the graph.
Tick (3) one box.
[1 mark]
y ¼ jx þ 2j þ 3
y ¼ jx þ 2j 3
y ¼ jx 2j þ 3
y ¼ jx 2j 3
(02)
Jun23/7357/3
, 3
Do not write
outside the
2 The trapezium rule is used to estimate the area of the shaded region in each of the box
graphs below.
Identify the graph for which the trapezium rule produces an overestimate.
Tick (3) one box.
[1 mark]
y
O x
y
O x
y
O x
y
O x
Turn over
s
(03)
Jun23/7357/3
, 4
Do not write
outside the
3 A curve with equation y ¼ f (x) passes through the point (3, 7) box
Given that f ’(3) ¼ 0 find the equation of the normal to the curve at (3, 7)
Circle your answer.
[1 mark]
7
y¼ x y¼0 x¼3 x¼7
3
4 Express
p
3
ffiffiffi
5 x
x2
in the form
5x p xq
where p and q are constants.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun23/7357/3
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
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.
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). 7
l Do not write outside the box around each page or on blank pages.
8
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 9
to be marked. 10
11
Information
l The marks for questions are shown in brackets. 12
l The maximum mark for this paper is 100. 13
14
Advice 15
l Unless stated otherwise, you may quote formulae, without proof, from the
booklet. 16
l You do not necessarily need to use all the space provided. 17
TOTAL
PB/KL/Jun23/E7 7357/3
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 The graph of y ¼ f (x) is shown below.
y
O x
One of the four equations listed below is the equation of the graph y ¼ f (x)
Identify which one is the correct equation of the graph.
Tick (3) one box.
[1 mark]
y ¼ jx þ 2j þ 3
y ¼ jx þ 2j 3
y ¼ jx 2j þ 3
y ¼ jx 2j 3
(02)
Jun23/7357/3
, 3
Do not write
outside the
2 The trapezium rule is used to estimate the area of the shaded region in each of the box
graphs below.
Identify the graph for which the trapezium rule produces an overestimate.
Tick (3) one box.
[1 mark]
y
O x
y
O x
y
O x
y
O x
Turn over
s
(03)
Jun23/7357/3
, 4
Do not write
outside the
3 A curve with equation y ¼ f (x) passes through the point (3, 7) box
Given that f ’(3) ¼ 0 find the equation of the normal to the curve at (3, 7)
Circle your answer.
[1 mark]
7
y¼ x y¼0 x¼3 x¼7
3
4 Express
p
3
ffiffiffi
5 x
x2
in the form
5x p xq
where p and q are constants.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun23/7357/3
