Please write clearly in block capitals.
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
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)
G/LM/Jun25/G4007/V7 7367/3D
, 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
(02)
G/Jun25/7367/3D
, 3
Do not write
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
(03)
G/Jun25/7367/3D
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
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)
G/LM/Jun25/G4007/V7 7367/3D
, 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
(02)
G/Jun25/7367/3D
, 3
Do not write
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
(03)
G/Jun25/7367/3D
