VERIFIED 2025/2026 A-level FURTHER MATHEMATICS Paper 3 Discrete MERGED QUESTION PAPER + MARK SCHEME

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A-level
FURTHER MATHEMATICS
Paper 3 Discrete

Friday 13 June 2025 Afternoon 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
1
requirements of the specification.
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.
l Fill in the boxes at the top of this page. 5
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
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.
8
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
9
to be marked.
10
Information
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.




(JUN2573673D01)
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, 2
Do not write
outside the
Answer all questions in the spaces provided. box




1 The group A is of order 9

The group B is a proper, non-trivial subgroup of A

Find the order of B

Circle your answer.
[1 mark]

1        3        9        18




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outside the
2 The simplex algorithm is used to solve a linear programming problem, which results in box

the following correct simplex tableau.


P x y r s value

2 5
1 0 0 25
3 3


0
5
0 –1 1 7
3 3

1 1
0 1 0 5
3 3



Which one of the following gives the correct optimal values of P, x and y?

Tick () one box.
[1 mark]


2
P = 1, x = , y=0
3

5
P = 1, x = , y=1
3


P = 25, x = 0, y = 5


P = 25, x = 7, y = 5




Turn over for the next question




Turn over U


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, 4
Do not write
outside the
3 The group ( X, *) is an abelian group of order 4 box



The elements of X are
e, a, b and c

where e is the identity element of ( X, *)
The following is a partially completed Cayley table for ( X, *)

* e a b c

e e a b c

a a e c b

b b e a

c c e


Which one of the following fully completed Cayley tables for ( X, *) is correct?

Tick () one box.
[1 mark]


* e a b c * e a b c

e e a b c e e a b c

a a e c b a a e c b

b b a e a b b a e a

c c b c e c c c b e



* e a b c * e a b c

e e a b c e e a b c

a a e c b a a e c b

b b c e a b b c e a

c c a b e c c b a e




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