Please write clearly in block capitals.
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
AS
FURTHER MATHEMATICS
AQA AS Further Mathematics Paper1(7366/1) Study Guide
2026
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
Question Mark
A‑level Mathematics and A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the 1
requirements of the specification. 2
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. 6
l You must answer each question in the space provided for that question.
7
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). 8
l Do not write outside the box around each page or on blank pages. 9
l Show all necessary working; otherwise marks for method may be lost.
10
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 11
12
Information 13
l The marks for questions are shown in brackets. 14
l The maximum mark for this paper is 80.
15
Advice 16
l Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet.
l You do not necessarily need to use all the space provided. TOTAL
(JUN247366101)
7366/1
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 Express cosh 2 x in terms of sinh x
Circle your answer.
[1 mark]
1 + sinh 2 x 1 – sinh 2 x sinh 2 x – 1 –1 – sinh 2 x
2 The function f is defined by
f (x) = 2 x + 3 0 ≤ x ≤ 5
The region R is enclosed by y = f (x), x = 5, the x-axis and the y-axis.
The region R is rotated through 2 π radians about the x-axis.
Give an expression for the volume of the solid formed.
Tick () one box.
[1 mark]
5
∫
π (2 x + 3) dx
0
5
∫
π (2 x + 3) 2 dx
0
5
2π
∫ (2x + 3) dx
0
5
∫ (2x + 3) dx
2π 2
0
(02)
, 3
Do not write
outside the
3 The matrix A is such that det(A) = 2 box
Determine the value of det(A–1)
Circle your answer.
[1 mark]
–2 – 1 1 2
2 2
4 The line L has vector equation
[] []
4 –9
r = –7 + λ 1
0 3
Give the equation of L in Cartesian form.
Tick () one box.
[1 mark]
x+4 y–7 z
= =
–9 1 3
x–4 y+7 z
= =
–9 1 3
x+9 y–1
= ,z=3
4 –7
x–9 y+1
= ,z=3
4 –7
Turn over U
(03)
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
AS
FURTHER MATHEMATICS
AQA AS Further Mathematics Paper1(7366/1) Study Guide
2026
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
Question Mark
A‑level Mathematics and A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the 1
requirements of the specification. 2
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. 6
l You must answer each question in the space provided for that question.
7
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). 8
l Do not write outside the box around each page or on blank pages. 9
l Show all necessary working; otherwise marks for method may be lost.
10
l Do all rough work in this book. Cross through any work that you do not want
to be marked. 11
12
Information 13
l The marks for questions are shown in brackets. 14
l The maximum mark for this paper is 80.
15
Advice 16
l Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet.
l You do not necessarily need to use all the space provided. TOTAL
(JUN247366101)
7366/1
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 Express cosh 2 x in terms of sinh x
Circle your answer.
[1 mark]
1 + sinh 2 x 1 – sinh 2 x sinh 2 x – 1 –1 – sinh 2 x
2 The function f is defined by
f (x) = 2 x + 3 0 ≤ x ≤ 5
The region R is enclosed by y = f (x), x = 5, the x-axis and the y-axis.
The region R is rotated through 2 π radians about the x-axis.
Give an expression for the volume of the solid formed.
Tick () one box.
[1 mark]
5
∫
π (2 x + 3) dx
0
5
∫
π (2 x + 3) 2 dx
0
5
2π
∫ (2x + 3) dx
0
5
∫ (2x + 3) dx
2π 2
0
(02)
, 3
Do not write
outside the
3 The matrix A is such that det(A) = 2 box
Determine the value of det(A–1)
Circle your answer.
[1 mark]
–2 – 1 1 2
2 2
4 The line L has vector equation
[] []
4 –9
r = –7 + λ 1
0 3
Give the equation of L in Cartesian form.
Tick () one box.
[1 mark]
x+4 y–7 z
= =
–9 1 3
x–4 y+7 z
= =
–9 1 3
x+9 y–1
= ,z=3
4 –7
x–9 y+1
= ,z=3
4 –7
Turn over U
(03)
