A-level
FURTHER MATHEMATICS ACTUAL 2025
PAPER MERGED WITH MARK SCHEME
Paper 3 Discrete
Please write clearly in block capitals.
Candid
Centre ate
number 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 TimeForallowed:
Examiner’s2Use
hours
Materials Question Mark
l You must have the AQA Formulae and statistical tables booklet for A-level 1
Mathematics and A-level Further Mathematics. l You should have a graphical or
scientific calculator that meets the requirements of the specification. 2
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 3
to complete both papers.
4
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. 5
l You must answer each question in the space provided for that question. If you
6
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 7
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 8
book. Cross through any work that you do not want to be marked.
9
10
TOTAL
, 2
Do not write
outside the
box
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.
(JUN2573673D01) G/LM/Jun25/G4007/V7 7367/3D
Answer all questions in the spaces provided.
G/Jun25/7367/3D
, 3
Do not write
outside the
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
Turn over U
G/Jun25/7367/3D
, 4
Do not write
outside the
box
(02)
2
The simplex algorithm is used to solve a linear programming problem, which results in the
following correct simplex tableau.
P x y r s value
1 0 0 25
0 0 1 7
–
0 1 0 5
Which one of the following gives the correct optimal values of P, x and y?
Tick () one box.
[1 mark]
P = 1, x = , y=0
P = 1, x = , y=1
G/Jun25/7367/3D
FURTHER MATHEMATICS ACTUAL 2025
PAPER MERGED WITH MARK SCHEME
Paper 3 Discrete
Please write clearly in block capitals.
Candid
Centre ate
number 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 TimeForallowed:
Examiner’s2Use
hours
Materials Question Mark
l You must have the AQA Formulae and statistical tables booklet for A-level 1
Mathematics and A-level Further Mathematics. l You should have a graphical or
scientific calculator that meets the requirements of the specification. 2
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 3
to complete both papers.
4
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. 5
l You must answer each question in the space provided for that question. If you
6
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 7
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 8
book. Cross through any work that you do not want to be marked.
9
10
TOTAL
, 2
Do not write
outside the
box
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.
(JUN2573673D01) G/LM/Jun25/G4007/V7 7367/3D
Answer all questions in the spaces provided.
G/Jun25/7367/3D
, 3
Do not write
outside the
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
Turn over U
G/Jun25/7367/3D
, 4
Do not write
outside the
box
(02)
2
The simplex algorithm is used to solve a linear programming problem, which results in the
following correct simplex tableau.
P x y r s value
1 0 0 25
0 0 1 7
–
0 1 0 5
Which one of the following gives the correct optimal values of P, x and y?
Tick () one box.
[1 mark]
P = 1, x = , y=0
P = 1, x = , y=1
G/Jun25/7367/3D
