AQA_2024: A-level Further Mathematics - Paper 2
(Merged Question Paper and Marking Scheme)
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
,For A-Level Further Mathematics - Paper 2, focus on the following key areas:
1. Complex Numbers:
Arithmetic Operations: Perform addition, subtraction, multiplication, and division of complex numbers
in both rectangular and polar form.
Modulus and Argument: Find the modulus and argument of a complex number, and represent them
in polar form.
De Moivre’s Theorem: Use De Moivre's theorem to raise complex numbers to integer powers and
extract roots of complex numbers.
Roots of Unity: Understand and apply the concept of n-th roots of unity and their geometric
representation on the Argand diagram.
2. Matrices:
Matrix Operations: Addition, subtraction, multiplication, and inverse of matrices, including
determinants and rank of matrices.
Solving Systems of Equations: Solve systems of linear equations using matrices, including methods
like Gaussian elimination and Cramer's Rule.
Eigenvalues and Eigenvectors: Find eigenvalues and eigenvectors and apply them in
diagonalization and solving systems of linear equations.
3. Vectors:
Vector Algebra: Perform operations such as addition, scalar multiplication, and understand vector
projections.
Dot Product: Use the dot product to calculate the angle between two vectors and apply it in geometry
problems.
Cross Product: Understand the cross product of vectors in 3D, including its geometric interpretation
(finding areas of parallelograms, perpendicular vectors).
4. Differential Equations:
First-Order Differential Equations: Solve separable and linear first-order differential equations using
various techniques (e.g., separation of variables).
Higher-Order Differential Equations: Solve second-order linear differential equations (both
homogeneous and non-homogeneous), including methods such as undetermined coefficients and
variation of parameters.
5. Calculus:
Advanced Integration: Perform more advanced integration techniques, such as integration by parts,
substitution, and partial fractions.
Differentiation: Differentiate more complex functions, including using implicit differentiation,
logarithmic differentiation, and higher-order derivatives.
Applications of Calculus: Apply differentiation and integration to solve real-world problems involving
motion, growth models, and area under curves.
6. Sequences and Series:
Arithmetic and Geometric Sequences: Solve problems involving the sum of terms and the nth term
formula.
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
(Merged Question Paper and Marking Scheme)
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
,For A-Level Further Mathematics - Paper 2, focus on the following key areas:
1. Complex Numbers:
Arithmetic Operations: Perform addition, subtraction, multiplication, and division of complex numbers
in both rectangular and polar form.
Modulus and Argument: Find the modulus and argument of a complex number, and represent them
in polar form.
De Moivre’s Theorem: Use De Moivre's theorem to raise complex numbers to integer powers and
extract roots of complex numbers.
Roots of Unity: Understand and apply the concept of n-th roots of unity and their geometric
representation on the Argand diagram.
2. Matrices:
Matrix Operations: Addition, subtraction, multiplication, and inverse of matrices, including
determinants and rank of matrices.
Solving Systems of Equations: Solve systems of linear equations using matrices, including methods
like Gaussian elimination and Cramer's Rule.
Eigenvalues and Eigenvectors: Find eigenvalues and eigenvectors and apply them in
diagonalization and solving systems of linear equations.
3. Vectors:
Vector Algebra: Perform operations such as addition, scalar multiplication, and understand vector
projections.
Dot Product: Use the dot product to calculate the angle between two vectors and apply it in geometry
problems.
Cross Product: Understand the cross product of vectors in 3D, including its geometric interpretation
(finding areas of parallelograms, perpendicular vectors).
4. Differential Equations:
First-Order Differential Equations: Solve separable and linear first-order differential equations using
various techniques (e.g., separation of variables).
Higher-Order Differential Equations: Solve second-order linear differential equations (both
homogeneous and non-homogeneous), including methods such as undetermined coefficients and
variation of parameters.
5. Calculus:
Advanced Integration: Perform more advanced integration techniques, such as integration by parts,
substitution, and partial fractions.
Differentiation: Differentiate more complex functions, including using implicit differentiation,
logarithmic differentiation, and higher-order derivatives.
Applications of Calculus: Apply differentiation and integration to solve real-world problems involving
motion, growth models, and area under curves.
6. Sequences and Series:
Arithmetic and Geometric Sequences: Solve problems involving the sum of terms and the nth term
formula.
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
