AQA A-LEVEL FURTHER MATHEMATICS Paper 3 Discrete 2025 Combined
Question Paper and Mark Scheme
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
⚫ You must have the AQA Formulae and statistical tables booklet for
A-level Mathematics and A-level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
⚫ 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
⚫ Use black ink or black ball-point pen. Pencil should only be used for drawing.
⚫ Fill in the boxes at the top of this page. 5
⚫ Answer all questions.
⚫ 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
⚫ Do not write outside the box around each page or on blank pages.
8
⚫ Show all necessary working; otherwise marks for method may be lost.
⚫ Do all rough work in this book. Cross through any work that you do not want
9
to be marked.
10
Information
⚫ The marks for questions are shown in brackets. TOTAL
⚫ The maximum mark for this paper is 50.
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the booklet.
⚫ You do not necessarily need to use all the space provided.
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
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
G/Jun25/7367/3D
, 3
Do not write
outside the
box
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
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
G/Jun25/7367/3D
, 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
G/Jun25/7367/3D
Question Paper and Mark Scheme
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
⚫ You must have the AQA Formulae and statistical tables booklet for
A-level Mathematics and A-level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
⚫ 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
⚫ Use black ink or black ball-point pen. Pencil should only be used for drawing.
⚫ Fill in the boxes at the top of this page. 5
⚫ Answer all questions.
⚫ 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
⚫ Do not write outside the box around each page or on blank pages.
8
⚫ Show all necessary working; otherwise marks for method may be lost.
⚫ Do all rough work in this book. Cross through any work that you do not want
9
to be marked.
10
Information
⚫ The marks for questions are shown in brackets. TOTAL
⚫ The maximum mark for this paper is 50.
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the booklet.
⚫ You do not necessarily need to use all the space provided.
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
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
G/Jun25/7367/3D
, 3
Do not write
outside the
box
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
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
G/Jun25/7367/3D
, 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
G/Jun25/7367/3D
