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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.
You should have a graphical or scientific calculator that meets the
requirements of the specification. Question Mark
You must ensure you have the other optional Question Paper/Answer 1
Book for which you are entered (either Mechanics or Statistics). You will
have 2 hours to complete both papers. 2
Instructions 3
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.
Answer all questions. 4
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 5
end of this book. Write the question number against your answer(s). 6
Do not write outside the box around each page or on blank pages.
Show all necessary working; otherwise marks for method may be lost. 7
Do all rough work in this book. Cross through any work that you do not want 8
to be marked.
9
TOTAL
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
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
, 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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