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
A-level
EM
FURTHER MATHEMATICS
Paper 2
TH
Monday 3 June 2024 Afternoon Time allowed: 2 hours
A
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
Question Mark
M
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
ER
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
l Fill in the boxes at the top of this page.
6
l Answer all questions.
7
TH
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 8
of this book. Write the question number against your answer(s). 9
l Do not write outside the box around each page or on blank pages. 10
l Show all necessary working; otherwise marks for method may be lost. 11
R
l Do all rough work in this book. Cross through any work that you do not want 12
to be marked. 13
FU
14
Information
l The marks for questions are shown in brackets. 15
l The maximum mark for this paper is 100. 16
17
Advice 18
l Unless stated otherwise, you may quote formulae, without proof, 19
from the booklet.
l You do not necessarily need to use all the space provided.
20
TOTAL
G/LM/Jun24/G4006/V7 7367/2
Page 1 of 36
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 It is given that
2 5
1 λ =0
3 –6
where λ is a constant.
S
Find the value of λ
C
Circle your answer.
TI
[1 mark]
A
–28 –8 8 28
2
EM
The movement of a particle is described by the simple harmonic equation
TH
..
x = – 25 x
..
where x metres is the displacement of the particle at time t seconds, and x m s–2 is
A
the acceleration of the particle.
M
The maximum displacement of the particle is 9 metres.
Find the maximum speed of the particle.
ER
Circle your answer.
[1 mark]
15 m s–1 45 m s–1 75 m s–1 135 m s–1
TH
R
FU
(02)
G/Jun24/7367/2
Page 2 of 36
,000003
3
Do not write
outside the
box
3 The function g is defined by
g(x) = sech x (x ∈ ℝ)
Which one of the following is the range of g ?
Tick () one box.
[1 mark]
– ∞ < g(x) ≤ –1
S
C
– 1 ≤ g(x) < 0
TI
0 < g(x) ≤ 1
A
1 ≤ g(x) ≤ ∞
EM
TH
4 The function f is a quartic function with real coefficients.
A
The complex number 5i is a root of the equation f (x) = 0
M
Which one of the following must be a factor of f (x)?
ER
Circle your answer.
[1 mark]
(x 2 – 25) (x 2 – 5) (x 2 + 5) (x 2 + 25)
TH
R
FU
Turn over U
(03)
G/Jun24/7367/2
Page 3 of 36
, 000004
4
Do not write
outside the
box
5 The first four terms of the series S can be written as
S = (1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + ...
5 (a) Write an expression, using ∑ notation, for the sum of the first n terms of S [1 mark]
_____________________________________________________________________________________
S
_____________________________________________________________________________________
C
_____________________________________________________________________________________
TI
5 (b) Show that the sum of the first n terms of S is equal to
A
1
n (n + 1)(n + 2)
3
[2 marks]
EM
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
A
_____________________________________________________________________________________
M
_____________________________________________________________________________________
_____________________________________________________________________________________
ER
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
R
_____________________________________________________________________________________
FU
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
G/Jun24/7367/2
Page 4 of 36
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
A-level
EM
FURTHER MATHEMATICS
Paper 2
TH
Monday 3 June 2024 Afternoon Time allowed: 2 hours
A
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
Question Mark
M
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
ER
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
l Fill in the boxes at the top of this page.
6
l Answer all questions.
7
TH
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 8
of this book. Write the question number against your answer(s). 9
l Do not write outside the box around each page or on blank pages. 10
l Show all necessary working; otherwise marks for method may be lost. 11
R
l Do all rough work in this book. Cross through any work that you do not want 12
to be marked. 13
FU
14
Information
l The marks for questions are shown in brackets. 15
l The maximum mark for this paper is 100. 16
17
Advice 18
l Unless stated otherwise, you may quote formulae, without proof, 19
from the booklet.
l You do not necessarily need to use all the space provided.
20
TOTAL
G/LM/Jun24/G4006/V7 7367/2
Page 1 of 36
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 It is given that
2 5
1 λ =0
3 –6
where λ is a constant.
S
Find the value of λ
C
Circle your answer.
TI
[1 mark]
A
–28 –8 8 28
2
EM
The movement of a particle is described by the simple harmonic equation
TH
..
x = – 25 x
..
where x metres is the displacement of the particle at time t seconds, and x m s–2 is
A
the acceleration of the particle.
M
The maximum displacement of the particle is 9 metres.
Find the maximum speed of the particle.
ER
Circle your answer.
[1 mark]
15 m s–1 45 m s–1 75 m s–1 135 m s–1
TH
R
FU
(02)
G/Jun24/7367/2
Page 2 of 36
,000003
3
Do not write
outside the
box
3 The function g is defined by
g(x) = sech x (x ∈ ℝ)
Which one of the following is the range of g ?
Tick () one box.
[1 mark]
– ∞ < g(x) ≤ –1
S
C
– 1 ≤ g(x) < 0
TI
0 < g(x) ≤ 1
A
1 ≤ g(x) ≤ ∞
EM
TH
4 The function f is a quartic function with real coefficients.
A
The complex number 5i is a root of the equation f (x) = 0
M
Which one of the following must be a factor of f (x)?
ER
Circle your answer.
[1 mark]
(x 2 – 25) (x 2 – 5) (x 2 + 5) (x 2 + 25)
TH
R
FU
Turn over U
(03)
G/Jun24/7367/2
Page 3 of 36
, 000004
4
Do not write
outside the
box
5 The first four terms of the series S can be written as
S = (1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + ...
5 (a) Write an expression, using ∑ notation, for the sum of the first n terms of S [1 mark]
_____________________________________________________________________________________
S
_____________________________________________________________________________________
C
_____________________________________________________________________________________
TI
5 (b) Show that the sum of the first n terms of S is equal to
A
1
n (n + 1)(n + 2)
3
[2 marks]
EM
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
A
_____________________________________________________________________________________
M
_____________________________________________________________________________________
_____________________________________________________________________________________
ER
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
R
_____________________________________________________________________________________
FU
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
G/Jun24/7367/2
Page 4 of 36
