AQA_2024: AS Further Mathematics - Paper 1
(Merged Question Paper and Marking Scheme)
(Monday 13 May 2024)
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
, AS Further Mathematics: Paper 1 (Monday 13 May 2024). Exam Preview
This paper typically covers core topics in Pure Mathematics, focusing on more advanced mathematical
concepts than in the standard AS Mathematics course. Key areas generally include:
1. Algebra and Functions:
Polynomials: Roots of polynomials, factorizing, and solving polynomial equations.
Rational Functions: Simplifying, analyzing, and graphing rational functions.
Exponential and Logarithmic Functions: Solving equations involving exponentials and logarithms,
properties of logarithms, and transformations of these functions.
2. Coordinate Geometry:
Straight Lines: Equations of lines, slopes, and intercepts, including finding the equation of a line through two
points or parallel/perpendicular lines.
Circles: Equation of a circle, understanding its center, radius, and various transformations.
Conic Sections: Parabolas, ellipses, and hyperbolas, understanding their equations and graphs.
3. Trigonometry:
Trigonometric Identities: Proving and applying identities such as Pythagorean identities, sum and difference
formulas, double-angle identities, and compound angle formulas.
Solving Trigonometric Equations: Finding general solutions to trigonometric equations.
Radian Measure: Converting between radians and degrees, and applying radian measure in various contexts.
4. Sequences and Series:
Arithmetic and Geometric Progressions: Understanding the nth term and sum of arithmetic and geometric
series, as well as applications.
Binomial Expansion: Expanding binomial expressions using the binomial theorem, including applications for
positive integer powers and approximations for fractional or negative powers.
5. Calculus:
Differentiation: Basic differentiation techniques, including rules for powers, product, quotient, and chain rule.
Applications such as finding tangents, velocity, and acceleration.
Integration: Indefinite and definite integrals, including techniques such as substitution and integration by
parts. Applications like finding areas under curves.
Applications of Differentiation: Using first and second derivatives to analyze graphs, determine turning
points, and apply optimization problems.
6. Vectors:
Vector Algebra: Understanding vector addition, scalar multiplication, and properties of vectors in 2D and 3D.
Dot Product and Cross Product:
7. Complex Numbers:
Basic Operations: Addition, subtraction, multiplication, and division of complex numbers.
Polar Form:.
Roots of Complex Numbers:.
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
, 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]
5 (b) Calculate |a| and |b|
[2 marks]
|a| = |b| =
5 (c) Calculate the acute angle between a and b
Give your answer to the nearest degree.
[2 marks]
G/Jun24/7366/1
, 5
Do not write
outside the
box
6 (a) On the axes below, sketch the graph of
y = cosh x
Indicate the value of any intercept of the curve with the axes.
[2 marks]
y
O x
6 (b) Solve the equation
cosh x = 2
Give your answers to three significant figures.
[2 marks]
Turn over U
G/Jun24/7366/1
, 6
Do not write
outside the
box
There are no questions printed on this page
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
G/Jun24/7366/1
(Merged Question Paper and Marking Scheme)
(Monday 13 May 2024)
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
, AS Further Mathematics: Paper 1 (Monday 13 May 2024). Exam Preview
This paper typically covers core topics in Pure Mathematics, focusing on more advanced mathematical
concepts than in the standard AS Mathematics course. Key areas generally include:
1. Algebra and Functions:
Polynomials: Roots of polynomials, factorizing, and solving polynomial equations.
Rational Functions: Simplifying, analyzing, and graphing rational functions.
Exponential and Logarithmic Functions: Solving equations involving exponentials and logarithms,
properties of logarithms, and transformations of these functions.
2. Coordinate Geometry:
Straight Lines: Equations of lines, slopes, and intercepts, including finding the equation of a line through two
points or parallel/perpendicular lines.
Circles: Equation of a circle, understanding its center, radius, and various transformations.
Conic Sections: Parabolas, ellipses, and hyperbolas, understanding their equations and graphs.
3. Trigonometry:
Trigonometric Identities: Proving and applying identities such as Pythagorean identities, sum and difference
formulas, double-angle identities, and compound angle formulas.
Solving Trigonometric Equations: Finding general solutions to trigonometric equations.
Radian Measure: Converting between radians and degrees, and applying radian measure in various contexts.
4. Sequences and Series:
Arithmetic and Geometric Progressions: Understanding the nth term and sum of arithmetic and geometric
series, as well as applications.
Binomial Expansion: Expanding binomial expressions using the binomial theorem, including applications for
positive integer powers and approximations for fractional or negative powers.
5. Calculus:
Differentiation: Basic differentiation techniques, including rules for powers, product, quotient, and chain rule.
Applications such as finding tangents, velocity, and acceleration.
Integration: Indefinite and definite integrals, including techniques such as substitution and integration by
parts. Applications like finding areas under curves.
Applications of Differentiation: Using first and second derivatives to analyze graphs, determine turning
points, and apply optimization problems.
6. Vectors:
Vector Algebra: Understanding vector addition, scalar multiplication, and properties of vectors in 2D and 3D.
Dot Product and Cross Product:
7. Complex Numbers:
Basic Operations: Addition, subtraction, multiplication, and division of complex numbers.
Polar Form:.
Roots of Complex Numbers:.
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
, 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]
5 (b) Calculate |a| and |b|
[2 marks]
|a| = |b| =
5 (c) Calculate the acute angle between a and b
Give your answer to the nearest degree.
[2 marks]
G/Jun24/7366/1
, 5
Do not write
outside the
box
6 (a) On the axes below, sketch the graph of
y = cosh x
Indicate the value of any intercept of the curve with the axes.
[2 marks]
y
O x
6 (b) Solve the equation
cosh x = 2
Give your answers to three significant figures.
[2 marks]
Turn over U
G/Jun24/7366/1
, 6
Do not write
outside the
box
There are no questions printed on this page
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
G/Jun24/7366/1
