AQA QP 2023 A-level FURTHER MATHEMATICS Paper 3 (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
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 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 Mechanics or Statistics). You will have
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.
l Answer all questions. 6
l You must answer each question in the space provided for that question. 7
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). 8
l Do not write outside the box around each page or on blank pages.
9
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want TOTAL
to be marked.
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.
PB/KL/Jun23/E4 7367/3D
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The simple-connected graph G is shown below.
The graph G has n faces.
State the value of n
Circle your answer.
[1 mark]
2 3 4 5
2 Jonathan and Hoshi play a zero-sum game.
The game is represented by the following pay-off matrix for Jonathan.
Hoshi
Strategy H1 H2 H3
J1 2 3 2
J2 3 2 0
Jonathan
J3 4 1 3
J4 3 1 0
The game does not have a stable solution.
Which strategy should Jonathan never play?
Circle your answer.
[1 mark]
J1 J2 J3 J4
(02)
Jun23/7367/3D
, 3
Do not write
outside the
3 A student is solving a maximising linear programming problem. box
The graph below shows the constraints, feasible region and objective line for the
student’s linear programming problem.
y
250
225
200
175 B
150
C
125
100
75 Feasible region
50
25
A D
0
0 25 50 75 100 125 150 175 200 225 250 x
Objective line
Which vertex is the optimal vertex?
Circle your answer.
[1 mark]
A B C D
Turn over for the next question
Turn over
s
(03)
Jun23/7367/3D
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
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 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 Mechanics or Statistics). You will have
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.
l Answer all questions. 6
l You must answer each question in the space provided for that question. 7
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). 8
l Do not write outside the box around each page or on blank pages.
9
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want TOTAL
to be marked.
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.
PB/KL/Jun23/E4 7367/3D
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The simple-connected graph G is shown below.
The graph G has n faces.
State the value of n
Circle your answer.
[1 mark]
2 3 4 5
2 Jonathan and Hoshi play a zero-sum game.
The game is represented by the following pay-off matrix for Jonathan.
Hoshi
Strategy H1 H2 H3
J1 2 3 2
J2 3 2 0
Jonathan
J3 4 1 3
J4 3 1 0
The game does not have a stable solution.
Which strategy should Jonathan never play?
Circle your answer.
[1 mark]
J1 J2 J3 J4
(02)
Jun23/7367/3D
, 3
Do not write
outside the
3 A student is solving a maximising linear programming problem. box
The graph below shows the constraints, feasible region and objective line for the
student’s linear programming problem.
y
250
225
200
175 B
150
C
125
100
75 Feasible region
50
25
A D
0
0 25 50 75 100 125 150 175 200 225 250 x
Objective line
Which vertex is the optimal vertex?
Circle your answer.
[1 mark]
A B C D
Turn over for the next question
Turn over
s
(03)
Jun23/7367/3D
