AQA A-LEVEL FURTHER MATHEMATICS 7367/1 PAPER 1
FINAL EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED).
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 scientific calculator that meets the
requirements of the specification. 1
2
Instructions
l Use black ink or black ball-point pen. Pencil should only be used for 3
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 7
at the end 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.
l Show all necessary working; otherwise marks for method may be 9
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
l The marks for questions are shown in brackets. TOTAL
l The maximum mark for this paper is 100.
Advice
l Unless stated otherwise, you may quote formulae, without
proof, from the booklet.
l You do not necessarily need to use all the space provided.
(JUN227367101) 7367/1
PB/Jun22/E9
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The displacement of a particle from its equilibrium position is x metres at time
t seconds.
The motion of the particle obeys the differential equation
2
d x ¼ 9x
2
dt
Calculate the period of its motion in seconds.
Circle your answer.
[1 mark]
p 2p p 2p
9 9 3 3
(02)
Jun22/7367/1
, 3
Do not write
outside the
2 Simplify box
6p 6p
cos 13 þ i sin 13
2p 2p
cos 13 i sin 13
Tick (3) one box.
[1 mark]
8p 8p
cos 13 þ i sin13
8p 8p
cos 13 i sin13
4p 4p
cos 13 þ i sin13
4p 4p
cos 13 i sin13
Turn over for the next question
Turn over
s
(03)
Jun22/7367/1
, 4
Do not write
outside the
dy box
3 Given that y ¼ sech x , find d
x
Tick (3) one box.
[1 mark]
sech x tanh x
sech x tanh x
cosech x coth x
cosech x coth x
4 The vector v is an eigenvector of the matrix N with corresponding eigenvalue 4
The vector v is also an eigenvector of the matrix M with corresponding eigenvalue 3
Given that
2
NM v ¼ lv
find the value of l
Circle your answer.
[1 mark]
10 24 36 144
(04)
Jun22/7367/1
FINAL EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED).
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 scientific calculator that meets the
requirements of the specification. 1
2
Instructions
l Use black ink or black ball-point pen. Pencil should only be used for 3
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 7
at the end 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.
l Show all necessary working; otherwise marks for method may be 9
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
l The marks for questions are shown in brackets. TOTAL
l The maximum mark for this paper is 100.
Advice
l Unless stated otherwise, you may quote formulae, without
proof, from the booklet.
l You do not necessarily need to use all the space provided.
(JUN227367101) 7367/1
PB/Jun22/E9
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The displacement of a particle from its equilibrium position is x metres at time
t seconds.
The motion of the particle obeys the differential equation
2
d x ¼ 9x
2
dt
Calculate the period of its motion in seconds.
Circle your answer.
[1 mark]
p 2p p 2p
9 9 3 3
(02)
Jun22/7367/1
, 3
Do not write
outside the
2 Simplify box
6p 6p
cos 13 þ i sin 13
2p 2p
cos 13 i sin 13
Tick (3) one box.
[1 mark]
8p 8p
cos 13 þ i sin13
8p 8p
cos 13 i sin13
4p 4p
cos 13 þ i sin13
4p 4p
cos 13 i sin13
Turn over for the next question
Turn over
s
(03)
Jun22/7367/1
, 4
Do not write
outside the
dy box
3 Given that y ¼ sech x , find d
x
Tick (3) one box.
[1 mark]
sech x tanh x
sech x tanh x
cosech x coth x
cosech x coth x
4 The vector v is an eigenvector of the matrix N with corresponding eigenvalue 4
The vector v is also an eigenvector of the matrix M with corresponding eigenvalue 3
Given that
2
NM v ¼ lv
find the value of l
Circle your answer.
[1 mark]
10 24 36 144
(04)
Jun22/7367/1
