2025 AQA A-LEVEL FURTHER MATHEMATICS Paper 3 Discrete
Question Paper & Mark Scheme (Merged) Friday 13 June 2025
[VERIFIED]
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.
G/LM/Jun25/G4007/V7 7367/3D
, 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 & Mark Scheme (Merged) Friday 13 June 2025
[VERIFIED]
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.
G/LM/Jun25/G4007/V7 7367/3D
, 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
