AQA
A-level
FURTHER MATHEMATICS
Paper 2
Monday 5 June 2023 Time allowed: 2 hours
Materials
You must have the AQA Formulae and statistical tables booklet
for A-level Mathematics and A-level Further Mathematics.
You should have a graphical or scientific calculator that
meets the requirements of the specification.
Instructions
Use black ink or black ball-point pen. Pencil should only be used for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer each question in the space provided for that question.
If you require extra space for your answer(s), use the lined pages at
the end of this book. Write the question number against your
answer(s).
Do not write outside the box around each page or on blank pages.
Show all necessary working; otherwise marks for method may be lost.
Do all rough work in this book. Cross through any work that you do
not want to be marked.
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 100.
Advice
Unless stated otherwise, you may quote formulae, without
proof, from the booklet.
You do not necessarily need to use all the space provided.
7367/2
, 2
Do not write
outside the
box
Answer all questions in the spaces
provided.
1 Given that y ¼ sin x þ sinh x , d2y þ
find d x2
y
Circle your answer.
[1 mark]
2 sin x —2 sin x 2 sinh x —2 sinh
x
2 Which one of the expressions below is not equal to zero?
Circle your answer. [1 mark]
lim (2x e—x )(x5 lim ln x) ex lim (x3ex)
lim
x !1 x! 0 x !1 x!
0
x5
(02)
Jun23/7367/
2
, 3
Do not write
.1 1 1. outside the
box
3 The determinant A ¼ 2
. .
. 0
. 23
2
1
Which one of the determinants below has a value which is not equal to the
value of A?
Tick (3) one box.
[1 mark]
3 1 3
.2 0 2.
.3 2 1 .
.
.
.1 2 .
3
.1 0 2 .
.1 2 1 .
.2 2 .
2
.1 0 1.
.3 2 1.
.1 1 .
1
.3 2 1.
.2 0 2.
4 It is given that f (x) ¼ cosh—1 (x
— 3)
Which of the sets listed below is the greatest possible domain of the function f ?
Circle your answer.
[1 mark]
fx : x ≥ 4g fx : x ≥ 3g fx : x ≥ 1g fx : x ≥
0g
(03)
Jun23/7367/
2
, 4
Do not write
Turn over
s
(03)
Jun23/7367/
2
A-level
FURTHER MATHEMATICS
Paper 2
Monday 5 June 2023 Time allowed: 2 hours
Materials
You must have the AQA Formulae and statistical tables booklet
for A-level Mathematics and A-level Further Mathematics.
You should have a graphical or scientific calculator that
meets the requirements of the specification.
Instructions
Use black ink or black ball-point pen. Pencil should only be used for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer each question in the space provided for that question.
If you require extra space for your answer(s), use the lined pages at
the end of this book. Write the question number against your
answer(s).
Do not write outside the box around each page or on blank pages.
Show all necessary working; otherwise marks for method may be lost.
Do all rough work in this book. Cross through any work that you do
not want to be marked.
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 100.
Advice
Unless stated otherwise, you may quote formulae, without
proof, from the booklet.
You do not necessarily need to use all the space provided.
7367/2
, 2
Do not write
outside the
box
Answer all questions in the spaces
provided.
1 Given that y ¼ sin x þ sinh x , d2y þ
find d x2
y
Circle your answer.
[1 mark]
2 sin x —2 sin x 2 sinh x —2 sinh
x
2 Which one of the expressions below is not equal to zero?
Circle your answer. [1 mark]
lim (2x e—x )(x5 lim ln x) ex lim (x3ex)
lim
x !1 x! 0 x !1 x!
0
x5
(02)
Jun23/7367/
2
, 3
Do not write
.1 1 1. outside the
box
3 The determinant A ¼ 2
. .
. 0
. 23
2
1
Which one of the determinants below has a value which is not equal to the
value of A?
Tick (3) one box.
[1 mark]
3 1 3
.2 0 2.
.3 2 1 .
.
.
.1 2 .
3
.1 0 2 .
.1 2 1 .
.2 2 .
2
.1 0 1.
.3 2 1.
.1 1 .
1
.3 2 1.
.2 0 2.
4 It is given that f (x) ¼ cosh—1 (x
— 3)
Which of the sets listed below is the greatest possible domain of the function f ?
Circle your answer.
[1 mark]
fx : x ≥ 4g fx : x ≥ 3g fx : x ≥ 1g fx : x ≥
0g
(03)
Jun23/7367/
2
, 4
Do not write
Turn over
s
(03)
Jun23/7367/
2
