ACTUAL JUNE 2024 AQA A-LEVEL FURTHER MATHEMATICS PAPER 2 7367/2 QUESTION PAPER
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 2
Monday 3 June 2024 Afternoon Time allowed: 2 hours
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.
1
⚫ You should have a graphical or scientific calculator that meets the
requirements of the specification. 2
3
Instructions 4
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
⚫ Fill in the boxes at the top of this page.
6
⚫ Answer all questions.
7
⚫ 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
⚫ Do not write outside the box around each page or on blank pages. 10
⚫ Show all necessary working; otherwise marks for method may be lost. 11
⚫ Do all rough work in this book. Cross through any work that you do not want 12
to be marked. 13
14
Information
⚫ The marks for questions are shown in brackets.
15
⚫ The maximum mark for this paper is 100. 16
17
Advice 18
⚫ Unless stated otherwise, you may quote formulae, without proof, 19
from the booklet. 20
⚫ You do not necessarily need to use all the space provided.
TOTAL
G/LM/Jun24/G4006/V7 7367/2
, 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.
Find the value of λ
Circle your answer.
[1 mark]
–28 –8 8 28
2 The movement of a particle is described by the simple harmonic equation
..
x = –25x
..
where x metres is the displacement of the particle at time t seconds, and x m s–2 is
the acceleration of the particle.
The maximum displacement of the particle is 9 metres.
Find the maximum speed of the particle.
Circle your answer.
[1 mark]
15 m s–1 45 m s–1 75 m s–1 135 m s–1
G/Jun24/7367/2
, 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
– 1 ≤ g(x) < 0
0 < g(x) ≤ 1
1 ≤ g(x) ≤
4 The function f is a quartic function with real coefficients.
The complex number 5i is a root of the equation f (x) = 0
Which one of the following must be a factor of f (x)?
Circle your answer.
[1 mark]
(x2 – 25) (x2 – 5) (x2 + 5) (x2 + 25)
Turn over U
G/Jun24/7367/2
, 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]
5 (b) Show that the sum of the first n terms of S is equal to
1
n(n + 1)(n + 2)
3
[2 marks]
G/Jun24/7367/2
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 2
Monday 3 June 2024 Afternoon Time allowed: 2 hours
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.
1
⚫ You should have a graphical or scientific calculator that meets the
requirements of the specification. 2
3
Instructions 4
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
⚫ Fill in the boxes at the top of this page.
6
⚫ Answer all questions.
7
⚫ 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
⚫ Do not write outside the box around each page or on blank pages. 10
⚫ Show all necessary working; otherwise marks for method may be lost. 11
⚫ Do all rough work in this book. Cross through any work that you do not want 12
to be marked. 13
14
Information
⚫ The marks for questions are shown in brackets.
15
⚫ The maximum mark for this paper is 100. 16
17
Advice 18
⚫ Unless stated otherwise, you may quote formulae, without proof, 19
from the booklet. 20
⚫ You do not necessarily need to use all the space provided.
TOTAL
G/LM/Jun24/G4006/V7 7367/2
, 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.
Find the value of λ
Circle your answer.
[1 mark]
–28 –8 8 28
2 The movement of a particle is described by the simple harmonic equation
..
x = –25x
..
where x metres is the displacement of the particle at time t seconds, and x m s–2 is
the acceleration of the particle.
The maximum displacement of the particle is 9 metres.
Find the maximum speed of the particle.
Circle your answer.
[1 mark]
15 m s–1 45 m s–1 75 m s–1 135 m s–1
G/Jun24/7367/2
, 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
– 1 ≤ g(x) < 0
0 < g(x) ≤ 1
1 ≤ g(x) ≤
4 The function f is a quartic function with real coefficients.
The complex number 5i is a root of the equation f (x) = 0
Which one of the following must be a factor of f (x)?
Circle your answer.
[1 mark]
(x2 – 25) (x2 – 5) (x2 + 5) (x2 + 25)
Turn over U
G/Jun24/7367/2
, 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]
5 (b) Show that the sum of the first n terms of S is equal to
1
n(n + 1)(n + 2)
3
[2 marks]
G/Jun24/7367/2
