ACTUAL MAY 2024 AQA AS FURTHER MATHEMATICS PAPER 1 7366/1 QUESTION PAPER
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
Paper 1
Monday 13 May 2024 Afternoon Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
⚫ You must have the AQA Formulae and statistical tables booklet for
Question Mark
A‑level Mathematics and A‑level Further Mathematics.
⚫ You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
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. 6
⚫ 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
⚫ Do not write outside the box around each page or on blank pages. 9
⚫ Show all necessary working; otherwise marks for method may be lost. 10
⚫ Do all rough work in this book. Cross through any work that you do not want
11
to be marked.
12
Information 13
⚫ The marks for questions are shown in brackets.
14
⚫ The maximum mark for this paper is 80.
15
Advice 16
⚫ Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet.
⚫ You do not necessarily need to use all the space provided. TOTAL
G/LM/Jun24/G4001/V5 7366/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Express cosh2 x in terms of sinh x
Circle your answer.
[1 mark]
1 + sinh2 x 1 – sinh2 x sinh2 x – 1 –1 – sinh2 x
2 The function f is defined by
f (x) = 2x + 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 2π radians about the x‑axis.
Give an expression for the volume of the solid formed.
Tick (✓) one box.
[1 mark]
5
π (2x + 3) dx
0
5
π (2x + 3)2 dx
0
5
2π
(2x + 3) dx
0
5
2π
(2x + 3) dx
0
2
G/Jun24/7366/1
, 3
Do not write
outside the
box
3 The matrix A is such that det(A) = 2
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
–9
[] [ ]
4
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
G/Jun24/7366/1
, 4
Do not write
outside the
box
5 The vectors a and b are given by
a = 3i + 4j – 2k and b = 2i – j – 5k
5 (a) Calculate a.b
[1 mark]
5 (b) Calculate |a| and |b|
[2 marks]
|a| = |b| =
5 (c) Calculate the acute angle between a and b
Give your answer to the nearest degree.
[2 marks]
G/Jun24/7366/1
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
Paper 1
Monday 13 May 2024 Afternoon Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
⚫ You must have the AQA Formulae and statistical tables booklet for
Question Mark
A‑level Mathematics and A‑level Further Mathematics.
⚫ You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
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. 6
⚫ 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
⚫ Do not write outside the box around each page or on blank pages. 9
⚫ Show all necessary working; otherwise marks for method may be lost. 10
⚫ Do all rough work in this book. Cross through any work that you do not want
11
to be marked.
12
Information 13
⚫ The marks for questions are shown in brackets.
14
⚫ The maximum mark for this paper is 80.
15
Advice 16
⚫ Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet.
⚫ You do not necessarily need to use all the space provided. TOTAL
G/LM/Jun24/G4001/V5 7366/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Express cosh2 x in terms of sinh x
Circle your answer.
[1 mark]
1 + sinh2 x 1 – sinh2 x sinh2 x – 1 –1 – sinh2 x
2 The function f is defined by
f (x) = 2x + 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 2π radians about the x‑axis.
Give an expression for the volume of the solid formed.
Tick (✓) one box.
[1 mark]
5
π (2x + 3) dx
0
5
π (2x + 3)2 dx
0
5
2π
(2x + 3) dx
0
5
2π
(2x + 3) dx
0
2
G/Jun24/7366/1
, 3
Do not write
outside the
box
3 The matrix A is such that det(A) = 2
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
–9
[] [ ]
4
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
G/Jun24/7366/1
, 4
Do not write
outside the
box
5 The vectors a and b are given by
a = 3i + 4j – 2k and b = 2i – j – 5k
5 (a) Calculate a.b
[1 mark]
5 (b) Calculate |a| and |b|
[2 marks]
|a| = |b| =
5 (c) Calculate the acute angle between a and b
Give your answer to the nearest degree.
[2 marks]
G/Jun24/7366/1
