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2023 AQA A-level FURTHER MATHEMATICS 7367/3D Paper 3 Discrete Question Paper & Mark
scheme (Merged) June 2023 [VERIFIED]
A-level
FURTHER MATHEMATICS
Paper 3 Discrete
Wednesday 14 June 2023 afternoon Time allowed: 2 hours
Materials For Examiner’s Use
⚫ You must have the AQA Formulae and statistical tables booklet for 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 2
for which you are entered (either Mechanics or Statistics). You will have 2
hours to complete both papers. 3
Instructions 4
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
⚫ Fill in the boxes at the top of this page.
⚫ Answer all questions. 6
⚫ 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
⚫ Do not write outside the box around each page or on blank pages.
⚫ Show all necessary working; otherwise marks for method may be lost. 9
⚫ Do all rough work in this book. Cross through any work that you do not want TOTAL
to be marked.
Information
⚫ The marks for questions are shown in brackets.
⚫ 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.
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.
, 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
00 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
, 4
Do not write
outside the
4 The network below represents a system of water pipes in a geothermal power station. box
The numbers on each arc represent the lower and upper capacity for each pipe in
gallons per second.
D
0, 14 2, 21
B
H
6, 9 5, 18
5, 24 3, 9 7, 11
6, 12 E G
A J
1, 30 8, 17
4, 15
7, 23 2, 15
3, 10
7, 15 I
C
3, 28 8, 22
F
The water is taken from a nearby river at node A
The water is then pumped through the system of pipes and passes through one of
three treatment facilities at nodes H, I and J before returning to the river.
4 (a) The senior management at the power station want all of the water to undergo a final
quality control check at a new facility before it returns to the river.
Using the language of networks, explain how the network above could be modified to
include the new facility.
[2 marks]
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