AQA
A-LEVEL
FURTHER MATHEMATICS
Paper 1
7367/1
MAY 2023
CONTENT ON NEXT PAGE
[MERGED]
, Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 1
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics. Question Mark
l You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
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
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). 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.
9
l Do all rough work in this book. Cross through any work that you do not want
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
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.
TOTAL
PB/KL/Jun23/E6 7367/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find the number of solutions of the equation tanh x ¼ cosh x
Circle your answer.
[1 mark]
0 1 2 3
2 The diagram below shows a locus on an Argand diagram.
Im
O 2 Re
–3
Which of the equations below represents the locus shown above?
Circle your answer.
[1 mark]
jz 2 þ 3ij ¼ 2 jz þ 2 3ij ¼ 2 jz 2 þ 3ij ¼ 4 j z þ 2 3 ij ¼ 4
(02)
Jun23/7367/1
, 3
Do not write
outside the
1 2 box
3 The matrix A ¼ represents a transformation.
0 1
Which one of the points below is an invariant point under this transformation?
Circle your answer.
[1 mark]
(1, 1) (0, 2) (3, 0) (2, 1)
4 The solution of a second order differential equation is f ( t)
The differential equation models heavy damping.
Which one of the statements below could be true?
Tick (3) one box.
[1 mark]
f ( t) ¼ 2e t cos (3t) þ 5e t sin (3t)
f ( t) ¼ 3e t þ 4te t
f ( t) ¼ 7e t þ 2e 2t
f ( t) ¼ 8e t cos (3t 0:1)
Turn over for the next question
Turn over
s
(03)
Jun23/7367/1
A-LEVEL
FURTHER MATHEMATICS
Paper 1
7367/1
MAY 2023
CONTENT ON NEXT PAGE
[MERGED]
, Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 1
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics. Question Mark
l You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
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
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). 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.
9
l Do all rough work in this book. Cross through any work that you do not want
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
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.
TOTAL
PB/KL/Jun23/E6 7367/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find the number of solutions of the equation tanh x ¼ cosh x
Circle your answer.
[1 mark]
0 1 2 3
2 The diagram below shows a locus on an Argand diagram.
Im
O 2 Re
–3
Which of the equations below represents the locus shown above?
Circle your answer.
[1 mark]
jz 2 þ 3ij ¼ 2 jz þ 2 3ij ¼ 2 jz 2 þ 3ij ¼ 4 j z þ 2 3 ij ¼ 4
(02)
Jun23/7367/1
, 3
Do not write
outside the
1 2 box
3 The matrix A ¼ represents a transformation.
0 1
Which one of the points below is an invariant point under this transformation?
Circle your answer.
[1 mark]
(1, 1) (0, 2) (3, 0) (2, 1)
4 The solution of a second order differential equation is f ( t)
The differential equation models heavy damping.
Which one of the statements below could be true?
Tick (3) one box.
[1 mark]
f ( t) ¼ 2e t cos (3t) þ 5e t sin (3t)
f ( t) ¼ 3e t þ 4te t
f ( t) ¼ 7e t þ 2e 2t
f ( t) ¼ 8e t cos (3t 0:1)
Turn over for the next question
Turn over
s
(03)
Jun23/7367/1
