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 2
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
2
Instructions
3
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. 4
l Answer all questions. 5
l You must answer each question in the space provided for that question. 6
l If you need extra space for your answer(s), use the lined pages at the end 7
of this book. Write the question number against your answer(s). 8
l Do not write outside the box around each page or on blank pages. 9
l Show all necessary working; otherwise marks for method may be lost. 10
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 11
12
Information 13
l The marks for questions are shown in brackets. 14
l The maximum mark for this paper is 100. 15
16
Advice 17
l Unless stated otherwise, you may quote formulae, without proof, from the 18
booklet.
19
l You do not necessarily need to use all the space provided.
20
TOTAL
PB/KL/Jun23/E6 7357/2
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 The graph of y ¼ ax 2 þ bx þ c has roots x ¼ 2 and x ¼ 5 , as shown in the
diagram below.
y
O 2 5 x
State the set of values of x which satisfy
ax 2 þ bx þ c > 0
Tick (3) one box.
[1 mark]
fx : x < 2g ¨ fx : x > 5g
fx : 0 < x < 2g ˙ fx : x > 5g
fx : 2 < x < 5g
fx : 2 > x > 5g
(02)
Jun23/7357/2
, 3
Do not write
outside the
2 It is given that box
ð6 ð6
f (x) d x ¼ 20 and f (x) d x ¼ 10
0 3
ð3
Find the value of f (x) d x
0
Circle your answer.
[1 mark]
30 10 10 30
3 A circle has equation
(x 5)2 þ ( y 13)2 ¼ 16
Find the radius of the circle.
Circle your answer.
[1 mark]
4 12 16 256
Turn over for the next question
Turn over
s
(03)
Jun23/7357/2
, 4
Do not write
outside the
4 A curve has equation box
x2 pffiffiffi
y¼ þ4 x
8
dy
4 (a) Find an expression for
dx
[3 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4 (b) The point P with coordinates (4, 10) lies on the curve.
Find an equation of the tangent to the curve at the point P
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun23/7357/2
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
A-level
MATHEMATICS
Paper 2
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
2
Instructions
3
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. 4
l Answer all questions. 5
l You must answer each question in the space provided for that question. 6
l If you need extra space for your answer(s), use the lined pages at the end 7
of this book. Write the question number against your answer(s). 8
l Do not write outside the box around each page or on blank pages. 9
l Show all necessary working; otherwise marks for method may be lost. 10
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 11
12
Information 13
l The marks for questions are shown in brackets. 14
l The maximum mark for this paper is 100. 15
16
Advice 17
l Unless stated otherwise, you may quote formulae, without proof, from the 18
booklet.
19
l You do not necessarily need to use all the space provided.
20
TOTAL
PB/KL/Jun23/E6 7357/2
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 The graph of y ¼ ax 2 þ bx þ c has roots x ¼ 2 and x ¼ 5 , as shown in the
diagram below.
y
O 2 5 x
State the set of values of x which satisfy
ax 2 þ bx þ c > 0
Tick (3) one box.
[1 mark]
fx : x < 2g ¨ fx : x > 5g
fx : 0 < x < 2g ˙ fx : x > 5g
fx : 2 < x < 5g
fx : 2 > x > 5g
(02)
Jun23/7357/2
, 3
Do not write
outside the
2 It is given that box
ð6 ð6
f (x) d x ¼ 20 and f (x) d x ¼ 10
0 3
ð3
Find the value of f (x) d x
0
Circle your answer.
[1 mark]
30 10 10 30
3 A circle has equation
(x 5)2 þ ( y 13)2 ¼ 16
Find the radius of the circle.
Circle your answer.
[1 mark]
4 12 16 256
Turn over for the next question
Turn over
s
(03)
Jun23/7357/2
, 4
Do not write
outside the
4 A curve has equation box
x2 pffiffiffi
y¼ þ4 x
8
dy
4 (a) Find an expression for
dx
[3 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4 (b) The point P with coordinates (4, 10) lies on the curve.
Find an equation of the tangent to the curve at the point P
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun23/7357/2
