000001
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
S
Forename(s) _________________________________________________________________________
C
Candidate signature _________________________________________________________________________
TI
I declare this is my own work.
A
AS
EM
FURTHER MATHEMATICS
Paper 1
TH
Monday 13 May 2024 Afternoon Time allowed: 1 hour 30 minutes
A
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
M
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
ER
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
TH
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
R
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
FU
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
G/LM/Jun24/G4001/V5 7366/1
Page 1 of 32
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
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
S
C
TI
2 The function f is defined by
A
f (x) = 2 x + 3 0≤x≤5
EM
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.
TH
Give an expression for the volume of the solid formed.
Tick () one box.
[1 mark]
A
5
∫
π (2 x + 3) dx
M
0
5
∫
π (2 x + 3) 2 dx
ER
0
5
2π
∫ (2x + 3) dx
TH
0
5
2π
∫ (2x + 3) dx
2
R
0
FU
(02)
G/Jun24/7366/1
Page 2 of 32
,000003
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
S
C
TI
4 The line L has vector equation
[] []
4 –9
A
r = –7 + λ 1
0 3
EM
Give the equation of L in Cartesian form.
Tick () one box.
TH
[1 mark]
x+4 y–7 z
= =
–9 1 3
A
x–4 y+7 z
M
= =
–9 1 3
ER
x+9 y–1
= ,z=3
4 –7
x–9 y+1
TH
= ,z=3
4 –7
R
FU
Turn over U
(03)
G/Jun24/7366/1
Page 3 of 32
, 000004
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]
______________________________________________________________________________________
S
______________________________________________________________________________________
C
______________________________________________________________________________________
TI
5 (b) Calculate |a| and |b|
[2 marks]
A
______________________________________________________________________________________
EM
______________________________________________________________________________________
______________________________________________________________________________________
TH
______________________________________________________________________________________
______________________________________________________________________________________
A
|a| = ____________________________ |b| = ____________________________
M
5 (c) Calculate the acute angle between a and b
ER
Give your answer to the nearest degree.
[2 marks]
______________________________________________________________________________________
TH
______________________________________________________________________________________
______________________________________________________________________________________
R
______________________________________________________________________________________
FU
______________________________________________________________________________________
______________________________________________________________________________________
(04)
G/Jun24/7366/1
Page 4 of 32
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
S
Forename(s) _________________________________________________________________________
C
Candidate signature _________________________________________________________________________
TI
I declare this is my own work.
A
AS
EM
FURTHER MATHEMATICS
Paper 1
TH
Monday 13 May 2024 Afternoon Time allowed: 1 hour 30 minutes
A
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
M
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
ER
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
TH
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
R
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
FU
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
G/LM/Jun24/G4001/V5 7366/1
Page 1 of 32
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
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
S
C
TI
2 The function f is defined by
A
f (x) = 2 x + 3 0≤x≤5
EM
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.
TH
Give an expression for the volume of the solid formed.
Tick () one box.
[1 mark]
A
5
∫
π (2 x + 3) dx
M
0
5
∫
π (2 x + 3) 2 dx
ER
0
5
2π
∫ (2x + 3) dx
TH
0
5
2π
∫ (2x + 3) dx
2
R
0
FU
(02)
G/Jun24/7366/1
Page 2 of 32
,000003
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
S
C
TI
4 The line L has vector equation
[] []
4 –9
A
r = –7 + λ 1
0 3
EM
Give the equation of L in Cartesian form.
Tick () one box.
TH
[1 mark]
x+4 y–7 z
= =
–9 1 3
A
x–4 y+7 z
M
= =
–9 1 3
ER
x+9 y–1
= ,z=3
4 –7
x–9 y+1
TH
= ,z=3
4 –7
R
FU
Turn over U
(03)
G/Jun24/7366/1
Page 3 of 32
, 000004
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]
______________________________________________________________________________________
S
______________________________________________________________________________________
C
______________________________________________________________________________________
TI
5 (b) Calculate |a| and |b|
[2 marks]
A
______________________________________________________________________________________
EM
______________________________________________________________________________________
______________________________________________________________________________________
TH
______________________________________________________________________________________
______________________________________________________________________________________
A
|a| = ____________________________ |b| = ____________________________
M
5 (c) Calculate the acute angle between a and b
ER
Give your answer to the nearest degree.
[2 marks]
______________________________________________________________________________________
TH
______________________________________________________________________________________
______________________________________________________________________________________
R
______________________________________________________________________________________
FU
______________________________________________________________________________________
______________________________________________________________________________________
(04)
G/Jun24/7366/1
Page 4 of 32
