ACTUAL JUNE 2024 AQA A-LEVEL FURTHER MATHEMATICS PAPER 3 7367/3D QUESTION PAPER
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 3 Discrete
Friday 7 June 2024 Afternoon Time allowed: 2 hours
Materials
⚫ You must have the AQA Formulae and statistical tables booklet for For Examiner’s Use
A-level Mathematics and A-level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
⚫ You must ensure you have the other optional Question Paper/Answer Book
for which you are entered (either Mechanics or Statistics). You will have 2
2 hours to complete both papers.
3
Instructions 4
⚫ Use black ink or black ball-point pen. Pencil should only be used for drawing.
⚫ Fill in the boxes at the top of this page.
5
⚫ Answer all questions.
⚫ 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
of this book. Write the question number against your answer(s). 7
⚫ Do not write outside the box around each page or on blank pages.
⚫ Show all necessary working; otherwise marks for method may be lost. 8
⚫ Do all rough work in this book. Cross through any work that you do not want
to be marked. 9
Information 10
⚫ The marks for questions are shown in brackets.
TOTAL
⚫ The maximum mark for this paper is 50.
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the booklet.
⚫ You do not necessarily need to use all the space provided.
G/LM/Jun24/G4006/V9 7367/3D
, 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
{1, 2, 3} Addition modulo 4
{1, 2, 3} Multiplication modulo 4
{0, 1, 2, 3} Addition modulo 4
{0, 1, 2, 3} Multiplication modulo 4
2 A student is trying to find the solution to the travelling salesperson problem for
a network.
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
Based on the above information only, which of the following pairs give the best lower
bound and best upper bound for the solution of this problem?
Tick (✓) one box.
[1 mark]
Best Lower Bound Best Upper Bound
15 48
15 51
19 48
19 51
G/Jun24/7367/3D
, 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
D 1 0 1 0
Which one of the following statements about G is true?
Tick (✓) one box.
[1 mark]
G is a tree
G is complete
G is Eulerian
G is planar
Turn over for the next question
Turn over U
G/Jun24/7367/3D
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 3 Discrete
Friday 7 June 2024 Afternoon Time allowed: 2 hours
Materials
⚫ You must have the AQA Formulae and statistical tables booklet for For Examiner’s Use
A-level Mathematics and A-level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
⚫ You must ensure you have the other optional Question Paper/Answer Book
for which you are entered (either Mechanics or Statistics). You will have 2
2 hours to complete both papers.
3
Instructions 4
⚫ Use black ink or black ball-point pen. Pencil should only be used for drawing.
⚫ Fill in the boxes at the top of this page.
5
⚫ Answer all questions.
⚫ 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
of this book. Write the question number against your answer(s). 7
⚫ Do not write outside the box around each page or on blank pages.
⚫ Show all necessary working; otherwise marks for method may be lost. 8
⚫ Do all rough work in this book. Cross through any work that you do not want
to be marked. 9
Information 10
⚫ The marks for questions are shown in brackets.
TOTAL
⚫ The maximum mark for this paper is 50.
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the booklet.
⚫ You do not necessarily need to use all the space provided.
G/LM/Jun24/G4006/V9 7367/3D
, 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
{1, 2, 3} Addition modulo 4
{1, 2, 3} Multiplication modulo 4
{0, 1, 2, 3} Addition modulo 4
{0, 1, 2, 3} Multiplication modulo 4
2 A student is trying to find the solution to the travelling salesperson problem for
a network.
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
Based on the above information only, which of the following pairs give the best lower
bound and best upper bound for the solution of this problem?
Tick (✓) one box.
[1 mark]
Best Lower Bound Best Upper Bound
15 48
15 51
19 48
19 51
G/Jun24/7367/3D
, 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
D 1 0 1 0
Which one of the following statements about G is true?
Tick (✓) one box.
[1 mark]
G is a tree
G is complete
G is Eulerian
G is planar
Turn over for the next question
Turn over U
G/Jun24/7367/3D
