AQA A-level FURTHER MATHEMATICS 7367/1 Paper 1 Version: 1.0 Final 7367/1 PB/KL /Jun23/E6A-level
FURTHER MATHEMATICS
Paper 1
Thursday 25 May 2023 Afternoon Time allowed: 2 hours
Materials
lYou must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics.
lYou should have a graphical or scientific calculator that meets the requirements of the specification.
Instructions
lUse black ink or black ball‑point pen. Pencil should only be used for drawing.
lFill in the boxes at the top of this page.
lAnswer all questions.
lYou 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).
lDo not write outside the box around each page or on blank pages.
lShow all necessary working; otherwise marks for method may be lost.
lDo all rough work in this book. Cross through any work that you do not wantto be marked.
Information
lThe marks for questions are shown in brackets.
lThe maximum mark for this paper is 100.
Advice
lUnless stated otherwise, you may quote formulae, without proof, from thebooklet.
lYou do not necessarily need to use all the space provided.Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
For Examiner’s Use
Question Mark
1
23456789
101112131415
16
TOTALI declare this is my own work. 2
Answer allquestions in the spaces provided.
1 Find the number of solutions of the equation tanh x¼cosh x
Circle your answer.
[1 mark]
01 23
2 The diagram below shows a locus on an Argand diagram.
2 ReIm
– 3O
Which of the equations below represents the locus shown above?
Circle your answer.
[1 mark]
jz/C02þ3ij¼2 jzþ2/C03ij¼2 jz/C02þ3ij¼4 jzþ2/C03ij¼4
Jun23/7367/1Do not write
outside the
box
(02) 3
3 The matrix A¼12
01/C20/C21
represents a transformation.
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)¼2e/C0tcos (3 t)þ5e/C0tsin (3 t)
f(t)¼3e/C0tþ4te/C0t
f(t)¼7e/C0tþ2e/C02t
f(t)¼8e/C0tcos (3 t/C00:1)
Turn over for the next questionDo not write
outside the
box
Jun23/7367/1Turn overs
(03)
FURTHER MATHEMATICS
Paper 1
Thursday 25 May 2023 Afternoon Time allowed: 2 hours
Materials
lYou must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics.
lYou should have a graphical or scientific calculator that meets the requirements of the specification.
Instructions
lUse black ink or black ball‑point pen. Pencil should only be used for drawing.
lFill in the boxes at the top of this page.
lAnswer all questions.
lYou 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).
lDo not write outside the box around each page or on blank pages.
lShow all necessary working; otherwise marks for method may be lost.
lDo all rough work in this book. Cross through any work that you do not wantto be marked.
Information
lThe marks for questions are shown in brackets.
lThe maximum mark for this paper is 100.
Advice
lUnless stated otherwise, you may quote formulae, without proof, from thebooklet.
lYou do not necessarily need to use all the space provided.Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
For Examiner’s Use
Question Mark
1
23456789
101112131415
16
TOTALI declare this is my own work. 2
Answer allquestions in the spaces provided.
1 Find the number of solutions of the equation tanh x¼cosh x
Circle your answer.
[1 mark]
01 23
2 The diagram below shows a locus on an Argand diagram.
2 ReIm
– 3O
Which of the equations below represents the locus shown above?
Circle your answer.
[1 mark]
jz/C02þ3ij¼2 jzþ2/C03ij¼2 jz/C02þ3ij¼4 jzþ2/C03ij¼4
Jun23/7367/1Do not write
outside the
box
(02) 3
3 The matrix A¼12
01/C20/C21
represents a transformation.
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)¼2e/C0tcos (3 t)þ5e/C0tsin (3 t)
f(t)¼3e/C0tþ4te/C0t
f(t)¼7e/C0tþ2e/C02t
f(t)¼8e/C0tcos (3 t/C00:1)
Turn over for the next questionDo not write
outside the
box
Jun23/7367/1Turn overs
(03)
