AQA A-level Further Mathematics
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
Thursday 25 May 2023 Afternoon Time allowed: 2 hours
, 2
Do not write
outside the
box
Materials ⚫ You must have the AQA Formulae and statistical tables booklet for For Examiner’s Use
A‑level Mathematics and A‑level Further Mathematics. ⚫ You should have a
graphical or scientific calculator that meets the requirements of the specification. Question Mark
Instructions ⚫ Use black ink or black ball‑point pen. Pencil should only be used 1
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 2
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 3
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 4
any work that you do not want to be marked.
5
Information ⚫ The marks for questions are shown in brackets. ⚫ The maximum
mark for this paper is 100.
6
Advice 7
⚫ Unless stated otherwise, you may quote formulae, without proof, from the
booklet. 8
⚫ You do not necessarily need to use all the space provided.
9
10
11
12
13
14
15
16
TOTAL
PB/KL/Jun23/E6
Answer all questions in the spaces provided.
Jun23/7367/1
, 3
Do not write
outside the
box
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]
Turn over
Jun23/7367/1
, 4
Do not write
outside the
box
jz 2 þ 3ij ¼ 2 jz þ 2 3ij ¼ 2 jz 2 þ 3ij ¼ 4 jz þ 2 3ij ¼ 4
(02)
3 1 2
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 equatio n is f (t)
Jun23/7367/1
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
Thursday 25 May 2023 Afternoon Time allowed: 2 hours
, 2
Do not write
outside the
box
Materials ⚫ You must have the AQA Formulae and statistical tables booklet for For Examiner’s Use
A‑level Mathematics and A‑level Further Mathematics. ⚫ You should have a
graphical or scientific calculator that meets the requirements of the specification. Question Mark
Instructions ⚫ Use black ink or black ball‑point pen. Pencil should only be used 1
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 2
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 3
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 4
any work that you do not want to be marked.
5
Information ⚫ The marks for questions are shown in brackets. ⚫ The maximum
mark for this paper is 100.
6
Advice 7
⚫ Unless stated otherwise, you may quote formulae, without proof, from the
booklet. 8
⚫ You do not necessarily need to use all the space provided.
9
10
11
12
13
14
15
16
TOTAL
PB/KL/Jun23/E6
Answer all questions in the spaces provided.
Jun23/7367/1
, 3
Do not write
outside the
box
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]
Turn over
Jun23/7367/1
, 4
Do not write
outside the
box
jz 2 þ 3ij ¼ 2 jz þ 2 3ij ¼ 2 jz 2 þ 3ij ¼ 4 jz þ 2 3ij ¼ 4
(02)
3 1 2
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 equatio n is f (t)
Jun23/7367/1
