AQA_2024: AS Further Mathematics - Paper 1
(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.
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
,Key areas:
1. Algebra:
Polynomials: Understand how to factorize polynomials, use the remainder theorem, and perform
long division.
Equations and Inequalities: Solve quadratic, cubic, and quartic equations, as well as
simultaneous equations and inequalities.
Sequences and Series: Familiarize yourself with arithmetic sequences, geometric sequences, and
their sum formulas. Understand binomial expansions and their applications.
2. Calculus:
Differentiation: Be able to differentiate various functions, including product rule, quotient rule, and
chain rule.
Integration: Know basic integration rules (e.g., power rule), and understand definite and indefinite
integrals. Focus on using integration for areas under curves.
Applications: Understand real-life applications of differentiation and integration, including maxima
and minima, kinematics, and area under curves.
3. Matrices:
Operations: Learn how to add, subtract, and multiply matrices, and apply inverse matrices.
Determinants: Understand the concept of determinants, especially for 2x2 and 3x3 matrices, and their
use in solving linear equations.
Eigenvalues and Eigenvectors: Know how to compute eigenvalues and eigenvectors and understand
their applications in solving systems of linear equations.
4. Complex Numbers:
Arithmetic Operations: Learn how to add, subtract, multiply, and divide complex numbers.
Polar Form: Be familiar with converting complex numbers to polar form and performing operations in
polar form.
Argand Diagrams: Know how to represent complex numbers on the Argand diagram.
5. Vectors:
Vector Algebra: Understand vector addition, subtraction, and scalar multiplication.
Dot and Cross Products: Learn how to calculate and apply the dot product and cross product in 2D
and 3D geometry.
Applications: Be able to solve problems related to displacement, velocity, and force using vectors.
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
(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.
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
,Key areas:
1. Algebra:
Polynomials: Understand how to factorize polynomials, use the remainder theorem, and perform
long division.
Equations and Inequalities: Solve quadratic, cubic, and quartic equations, as well as
simultaneous equations and inequalities.
Sequences and Series: Familiarize yourself with arithmetic sequences, geometric sequences, and
their sum formulas. Understand binomial expansions and their applications.
2. Calculus:
Differentiation: Be able to differentiate various functions, including product rule, quotient rule, and
chain rule.
Integration: Know basic integration rules (e.g., power rule), and understand definite and indefinite
integrals. Focus on using integration for areas under curves.
Applications: Understand real-life applications of differentiation and integration, including maxima
and minima, kinematics, and area under curves.
3. Matrices:
Operations: Learn how to add, subtract, and multiply matrices, and apply inverse matrices.
Determinants: Understand the concept of determinants, especially for 2x2 and 3x3 matrices, and their
use in solving linear equations.
Eigenvalues and Eigenvectors: Know how to compute eigenvalues and eigenvectors and understand
their applications in solving systems of linear equations.
4. Complex Numbers:
Arithmetic Operations: Learn how to add, subtract, multiply, and divide complex numbers.
Polar Form: Be familiar with converting complex numbers to polar form and performing operations in
polar form.
Argand Diagrams: Know how to represent complex numbers on the Argand diagram.
5. Vectors:
Vector Algebra: Understand vector addition, subtraction, and scalar multiplication.
Dot and Cross Products: Learn how to calculate and apply the dot product and cross product in 2D
and 3D geometry.
Applications: Be able to solve problems related to displacement, velocity, and force using vectors.
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
