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 1
Thursday 21 May 2026 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the Formulae and statistical tables booklet for
Question Mark
A‑level Mathematic A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
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.
l You must answer each question in the space provided for that question.
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).
l Do not write 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 book. Cross through any work that you do not want
to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100.
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. TOTAL
(JUN )
G/LM/Jun26/G4008/V6 7367/1
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 The vectors a and b are defined by
2 1–p
a = p b = 4
3 1
It is given that a • b = 0
Find the value of p
Circle your answer.
[1 mark]
– 5 – 5 5 5
2 3 3 2
2 The matrix A is defined by
– √3 1
2 2
A=
– 1 – √3
2 2
The matrix A represents an anticlockwise rotation through an angle θ radians.
Find the value of θ
Circle your answer.
[1 mark]
π 5π 7π 11π
6 6 6 6
(02)
G/Jun26/7367/1
, 3
Do not write
outside the
3 Find the integrating factor which could be used to solve the differential equation box
dy 3y
+ = x2 + 5
dx x
Circle your answer.
[1 mark]
3 3
3In x x 3 e x x
a + bi
4 Which one of the following expressions is equivalent to , where a and b are
2i
real numbers?
Circle your answer.
[1 mark]
– b – a i – b + a i b – a i b + a i
2 2 2 2 2 2 2 2
Turn over for the next question
Turn over U
(03)
G/Jun26/7367/1
, 4
Do not write
outside the
5 The complex number z satisfies both box
0 ≤ arg (z) ≤ tan–1 (2)
and
│ z│ ≤ 2
The region R is the locus of z
Sketch and shade the region R on the Argand diagram in Figure 1
[3 marks]
Figure 1
Im
3
2
1
–3 –2 –1 0 1 2 3 Re
–1
–2
–3
(04)
G/Jun26/7367/1
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 1
Thursday 21 May 2026 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the Formulae and statistical tables booklet for
Question Mark
A‑level Mathematic A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
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.
l You must answer each question in the space provided for that question.
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).
l Do not write 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 book. Cross through any work that you do not want
to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100.
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. TOTAL
(JUN )
G/LM/Jun26/G4008/V6 7367/1
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 The vectors a and b are defined by
2 1–p
a = p b = 4
3 1
It is given that a • b = 0
Find the value of p
Circle your answer.
[1 mark]
– 5 – 5 5 5
2 3 3 2
2 The matrix A is defined by
– √3 1
2 2
A=
– 1 – √3
2 2
The matrix A represents an anticlockwise rotation through an angle θ radians.
Find the value of θ
Circle your answer.
[1 mark]
π 5π 7π 11π
6 6 6 6
(02)
G/Jun26/7367/1
, 3
Do not write
outside the
3 Find the integrating factor which could be used to solve the differential equation box
dy 3y
+ = x2 + 5
dx x
Circle your answer.
[1 mark]
3 3
3In x x 3 e x x
a + bi
4 Which one of the following expressions is equivalent to , where a and b are
2i
real numbers?
Circle your answer.
[1 mark]
– b – a i – b + a i b – a i b + a i
2 2 2 2 2 2 2 2
Turn over for the next question
Turn over U
(03)
G/Jun26/7367/1
, 4
Do not write
outside the
5 The complex number z satisfies both box
0 ≤ arg (z) ≤ tan–1 (2)
and
│ z│ ≤ 2
The region R is the locus of z
Sketch and shade the region R on the Argand diagram in Figure 1
[3 marks]
Figure 1
Im
3
2
1
–3 –2 –1 0 1 2 3 Re
–1
–2
–3
(04)
G/Jun26/7367/1
