000001
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
S
Forename(s) _________________________________________________________________________
C
Candidate signature _________________________________________________________________________
I declare this is my own work.
TI
A-level
A
EM
FURTHER MATHEMATICS
Paper 3 Discrete
TH
Friday 7 June 2024 Afternoon Time allowed: 2 hours
A
Materials
l You must have the AQA Formulae and statistical tables booklet for For Examiner’s Use
M
A-level Mathematics and A-level Further Mathematics. Question Mark
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
ER
for which you are entered (either Mechanics or Statistics). You will have 2
2 hours to complete both papers.
3
Instructions 4
TH
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.
5
l Answer all questions.
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
R
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.
FU
l Show all necessary working; otherwise marks for method may be lost. 8
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 9
Information 10
l The marks for questions are shown in brackets.
TOTAL
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/V9 7367/3D
Page 1 of 24
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Which one of the following sets forms a group under the given binary operation?
Tick () one box.
[1 mark]
Set Binary Operation
S
{1, 2, 3} Addition modulo 4
C
{1, 2, 3} Multiplication modulo 4
TI
{0, 1, 2, 3} Addition modulo 4
A
{0, 1, 2, 3} Multiplication modulo 4
2
EM
A student is trying to find the solution to the travelling salesperson problem for
a network.
TH
They correctly find two lower bounds for the solution: 15 and 19
They also correctly find two upper bounds for the solution: 48 and 51
A
Based on the above information only, which of the following pairs give the best lower
M
bound and best upper bound for the solution of this problem?
Tick () one box.
ER
[1 mark]
Best Lower Bound Best Upper Bound
TH
15 48
R
15 51
FU
19 48
19 51
(02)
G/Jun24/7367/3D
Page 2 of 24
, 000003
3
Do not write
outside the
box
3 The simple-connected graph G has the adjacency matrix
A B C D
A 0 1 1 1
B 1 0 1 0
C 1 1 0 1
S
D 1 0 1 0
C
Which one of the following statements about G is true?
TI
Tick () one box.
[1 mark]
A
G is a tree
G is complete
EM
TH
G is Eulerian
A
G is planar
M
ER
Turn over for the next question
TH
R
FU
Turn over U
(03)
G/Jun24/7367/3D
Page 3 of 24
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
S
Forename(s) _________________________________________________________________________
C
Candidate signature _________________________________________________________________________
I declare this is my own work.
TI
A-level
A
EM
FURTHER MATHEMATICS
Paper 3 Discrete
TH
Friday 7 June 2024 Afternoon Time allowed: 2 hours
A
Materials
l You must have the AQA Formulae and statistical tables booklet for For Examiner’s Use
M
A-level Mathematics and A-level Further Mathematics. Question Mark
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
ER
for which you are entered (either Mechanics or Statistics). You will have 2
2 hours to complete both papers.
3
Instructions 4
TH
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.
5
l Answer all questions.
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
R
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.
FU
l Show all necessary working; otherwise marks for method may be lost. 8
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 9
Information 10
l The marks for questions are shown in brackets.
TOTAL
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/V9 7367/3D
Page 1 of 24
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Which one of the following sets forms a group under the given binary operation?
Tick () one box.
[1 mark]
Set Binary Operation
S
{1, 2, 3} Addition modulo 4
C
{1, 2, 3} Multiplication modulo 4
TI
{0, 1, 2, 3} Addition modulo 4
A
{0, 1, 2, 3} Multiplication modulo 4
2
EM
A student is trying to find the solution to the travelling salesperson problem for
a network.
TH
They correctly find two lower bounds for the solution: 15 and 19
They also correctly find two upper bounds for the solution: 48 and 51
A
Based on the above information only, which of the following pairs give the best lower
M
bound and best upper bound for the solution of this problem?
Tick () one box.
ER
[1 mark]
Best Lower Bound Best Upper Bound
TH
15 48
R
15 51
FU
19 48
19 51
(02)
G/Jun24/7367/3D
Page 2 of 24
, 000003
3
Do not write
outside the
box
3 The simple-connected graph G has the adjacency matrix
A B C D
A 0 1 1 1
B 1 0 1 0
C 1 1 0 1
S
D 1 0 1 0
C
Which one of the following statements about G is true?
TI
Tick () one box.
[1 mark]
A
G is a tree
G is complete
EM
TH
G is Eulerian
A
G is planar
M
ER
Turn over for the next question
TH
R
FU
Turn over U
(03)
G/Jun24/7367/3D
Page 3 of 24
