AQA
A-level
FURTHER MATHEMATICS
7367/3D
Paper 3 Discrete
Version: 1.0 Final
PB/KL/Jun23/E4 7367/3D
A-level
FURTHER MATHEMATICS
Paper 3
... [Show More] Discrete
Time allowed: 2 hours
Materials
l You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
l 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 hours to complete both papers.
Instructions
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.
l Answer all questions.
l 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
of this book. Write the question number against your answer(s).
l Do not write outside the box around each page or on blank pages.
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
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.
Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
For Examiner’s Use
Question Mark
1
2
3
4
5
6
7
8
9
TOTAL
I declare this is my own work.
2
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 34 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
Jonathan
J1 23 2
J2 320
J3 4 1 3
J4 310
The game does not have a stable solution.
Which strategy should Jonathan never play?
Circle your answer.
[1 mark]
J1 J2 J3 J4
Jun23/7367/3D
Do not write
outside the
box
(02)
3
3 A student is solving a maximising linear programming problem.
The graph below shows the constraints, feasible region and objective line for the
student’s linear programming problem.
0 100 150 200
0
50
100
150
200
250
y
25
75
125
175
225
50
Objective line
25 75 125 175 225 250 x
A D
C
Feasible region
B
Which vertex is the optimal vertex?
Circle your answer.
[1 mark]
A BCD
Turn over for the next question
Do not write
outside the
box
Jun23/7367/3D
Turn over s
(03)
4
4 The network below represents a system of water pipes in a geothermal power station.
The numbers on each arc represent the lower and upper capacity for each pipe in
gallons per second.
B
D
C
F
I
7, 23
3, 28
3, 10 7, 15
2, 15
8, 22
4, 15
A J
H
E G
1, 30 8, 17
5, 18
7, 11
2, 21
6, 12
3, 9
0, 14
6, 9
5, 24
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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4 (b) Find the value of the cut {A, B, C, D, E} {F, G, H, I, J }
[1 mark]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
Do not write
outside the
box
Jun23/7367/3D
(04)
5
4 (c) Tim, a trainee engineer at the power station, correctly calculates the value of the
cut {A, B, C, D, E, F } {G, H, I, J } to be 106 gallons per second.
Tim then claims that the maximum flow through the network of pipes is 106 gallons
per second.
Comment on the validity of Tim’s claim.
[2 marks]
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
Turn over for the next question
Do not write
outside the
box
Jun23/7367/3D
Turn over s
(05)
6
5 A student is solving the following linear programming problem.
Minimise Q ¼ 4x 3y
subject to x þ y 520
2x 3y 570
and x 0, y 0
5 (a) The student wants to use the simplex algorithm to solve the linear
programming problem.
They modify the linear programming problem by int [Show Less]