000001
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
S
Surname _________________________________________________________________________
C
Forename(s) _________________________________________________________________________
TI
Candidate signature _________________________________________________________________________
I declare this is my own work.
A
A-level
EM
FURTHER MATHEMATICS
Paper 3 Mechanics
TH
Friday 7 June 2024 Afternoon Time allowed: 2 hours
Materials
A
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
M
l You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
l You must ensure you have the other optional Question Paper/Answer Book
2
for which you are entered (either Discrete or Statistics). You will have
ER
2 hours to complete both papers. 3
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing.
5
l Fill in the boxes at the top of this page.
TH
l Answer all questions. 6
l 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 7
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.
R
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. TOTAL
FU
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 50.
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.
G/LM/Jun24/G4006/V7 7367/3M
Page 1 of 16
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 A particle moves in a circular path so that at time t seconds its position vector, r metres,
is given by
r = 4 sin(2t)i + 4 cos(2 t )j
S
Find the velocity of the particle, in m s –1, when t = 0
C
Circle your answer.
[1 mark]
TI
8i –8j 8j 8i – 8j
A
EM
2 As a particle moves along a straight horizontal line, it is subjected to a force
F newtons that acts in the direction of motion of the particle.
TH
t
At time t seconds, F =
5
Calculate the magnitude of the impulse on the particle between t = 0 and t = 3
A
Circle your answer.
[1 mark]
M
0.3 N s 0.6 N s 0.9 N s 1.8 N s
ER
TH
R
FU
(02)
G/Jun24/7367/3M
Page 2 of 16
, 000003
3
Do not write
outside the
box
3 A conical pendulum consists of a light string and a particle of mass m kg
The conical pendulum completes horizontal circles with radius r metres and
angular speed ω radians per second. The string makes an angle θ with the
downward vertical.
The tension in the string is T newtons.
S
The conical pendulum and the forces acting on the particle are shown in the diagram.
C
θ
TI
A
T
EM
mg
TH
Which one of the following statements is correct?
Tick () one box.
A
[1 mark]
T cos θ = mrω 2
M
T sin θ = mrω 2
ER
mω2
T cos θ = r
TH
mω2
T sin θ = r
R
FU
Turn over U
(03)
G/Jun24/7367/3M
Page 3 of 16
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
S
Surname _________________________________________________________________________
C
Forename(s) _________________________________________________________________________
TI
Candidate signature _________________________________________________________________________
I declare this is my own work.
A
A-level
EM
FURTHER MATHEMATICS
Paper 3 Mechanics
TH
Friday 7 June 2024 Afternoon Time allowed: 2 hours
Materials
A
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
M
l You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
l You must ensure you have the other optional Question Paper/Answer Book
2
for which you are entered (either Discrete or Statistics). You will have
ER
2 hours to complete both papers. 3
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing.
5
l Fill in the boxes at the top of this page.
TH
l Answer all questions. 6
l 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 7
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.
R
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. TOTAL
FU
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 50.
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.
G/LM/Jun24/G4006/V7 7367/3M
Page 1 of 16
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 A particle moves in a circular path so that at time t seconds its position vector, r metres,
is given by
r = 4 sin(2t)i + 4 cos(2 t )j
S
Find the velocity of the particle, in m s –1, when t = 0
C
Circle your answer.
[1 mark]
TI
8i –8j 8j 8i – 8j
A
EM
2 As a particle moves along a straight horizontal line, it is subjected to a force
F newtons that acts in the direction of motion of the particle.
TH
t
At time t seconds, F =
5
Calculate the magnitude of the impulse on the particle between t = 0 and t = 3
A
Circle your answer.
[1 mark]
M
0.3 N s 0.6 N s 0.9 N s 1.8 N s
ER
TH
R
FU
(02)
G/Jun24/7367/3M
Page 2 of 16
, 000003
3
Do not write
outside the
box
3 A conical pendulum consists of a light string and a particle of mass m kg
The conical pendulum completes horizontal circles with radius r metres and
angular speed ω radians per second. The string makes an angle θ with the
downward vertical.
The tension in the string is T newtons.
S
The conical pendulum and the forces acting on the particle are shown in the diagram.
C
θ
TI
A
T
EM
mg
TH
Which one of the following statements is correct?
Tick () one box.
A
[1 mark]
T cos θ = mrω 2
M
T sin θ = mrω 2
ER
mω2
T cos θ = r
TH
mω2
T sin θ = r
R
FU
Turn over U
(03)
G/Jun24/7367/3M
Page 3 of 16
