AQA-7367-3D-FURTHER MATHEMATICS QUESTION PAPER 3D;Discrete-A LEVEL-7Jun24-PM

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A-level



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FURTHER MATHEMATICS
Paper 3 Discrete
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Friday 7 June 2024 Afternoon Time allowed: 2 hours
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Materials
l You must have the AQA Formulae and statistical tables booklet for For Examiner’s Use
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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
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for which you are entered (either Mechanics or Statistics). You will have 2
2 hours to complete both papers.
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Instructions 4
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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.
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l Answer all questions.
l 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
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of this book. Write the question number against your answer(s). 7
l Do not write outside the box around each page or on blank pages.
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l Show all necessary working; otherwise marks for method may be lost. 8
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 9

Information 10
l The marks for questions are shown in brackets.
TOTAL
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.




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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




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{1, 2, 3} Addition modulo 4




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{1, 2, 3} Multiplication modulo 4




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{0, 1, 2, 3} Addition modulo 4




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{0, 1, 2, 3} Multiplication modulo 4



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A student is trying to find the solution to the travelling salesperson problem for
a network.
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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
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Based on the above information only, which of the following pairs give the best lower
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bound and best upper bound for the solution of this problem?
Tick () one box.
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[1 mark]


Best Lower Bound Best Upper Bound
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15 48
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15 51
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19 48

19 51




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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




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D 1 0 1 0




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Which one of the following statements about G is true?




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Tick () one box.
[1 mark]




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G is a tree


G is complete
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G is Eulerian
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G is planar
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Turn over for the next question
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Turn over U


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