AQA_2024: A-level Further Mathematics - Paper 1
(Merged Question Paper and Marking Scheme)
(Wednesday 22 May 2024)
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 1
Wednesday 22 May 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.
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
8
of this book. Write the question number against your answer(s).
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 100.
15
Advice 16
Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet. 18
You do not necessarily need to use all the space provided.
TOTAL
, A-Level Further Mathematics: Paper 1 (Wednesday 22 May 2024)
Exam Preview Areas
1. Algebra:
o Polynomials: Solving equations, factorization, and roots.
o Rational Functions: Simplifying and analyzing expressions with ratios of polynomials.
o Exponential and Logarithmic Functions: Solving equations and graphing transformations.
o Partial Fractions: Breaking down complex rational expressions into simpler components.
2. Complex Numbers:
o Operations: Addition, subtraction, multiplication, and division of complex numbers.
o Polar Form: Converting between rectangular and polar form.
o De Moivre’s Theorem: Using it to find powers and roots of complex numbers.
3. Coordinate Geometry:
o Straight Lines and Circles: Working with equations, intersections, and tangents.
o Conic Sections: Parabolas, ellipses, hyperbolas—finding equations and analyzing shapes.
o Parametric Equations: Representing curves using parameters and converting between parametric and
Cartesian forms.
4. Calculus:
o Differentiation: Using chain, product, and quotient rules for rates of change, tangents, and
optimization.
o Integration: Techniques like substitution and integration by parts to find areas and solve problems.
o Differential Equations: Solving basic equations and applying them in real-world scenarios (e.g.,
population growth).
5. Vectors:
o Operations: Vector addition, scalar multiplication, and finding magnitudes.
o Dot Product: Analyzing angles between vectors.
o Cross Product: Finding areas of parallelograms and understanding 3D applications.
6. Sequences and Series:
o Arithmetic/Geometric Progressions: Finding terms and sums in sequences.
o Binomial Expansion: Expanding expressions of the form (a+b)n(a + b)^n(a+b)n and approximations
for fractional powers.
7. Mathematical Proof:
o Induction: Proving statements for all integers using the principle of mathematical induction.
o Logical Reasoning: Structuring clear and rigorous mathematical proofs, especially for functions and
sequences.
This paper assesses your ability to apply these concepts to complex problems and demonstrate clear reasoning,
focusing on both algebraic manipulation and geometric interpretation.
G/LM/Jun24/G4006/V8 7367/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The roots of the equation 20x3 – 16x2 – 4x + 7 = 0 are α, β and γ
Find the value of αβ + βγ + γα
Circle your answer.
[1 mark]
–4 –
1 1 4
5 5 5 5
iπ
2 The complex number z = e3
Which one of the following is a real number?
Circle your answer.
[1 mark]
z4 z5 z6 z7
G/Jun24/7367/1
, 3
Do not write
outside the
box
3 The function f is defined by
f (x) = x2 (x ℝ)
Find the mean value of f (x) between x = 0 and x = 2
Circle your answer.
[1 mark]
2 4 8 16
3 3 3 3
4 Which one of the following statements is correct?
Tick () one box.
[1 mark]
lim(x2 ln x) = 0
x 0
lim(x2 ln x) = 1
x 0
lim(x2 ln x) = 2
x 0
lim(x2 ln x) is not defined.
x 0
Turn over for the next question
Turn over U
G/Jun24/7367/1
, 4
Do not write
outside the
5 The points A, B and C have coordinates A(5, 3, 4), B(8, –1, 9) and C(12, 5, 10) box
The points A, B and C lie in the plane ∏
5 (a) Find a vector that is normal to the plane ∏
[3 marks]
G/Jun24/7367/1
, 5
Do not write
outside the
5 (b) Find a Cartesian equation of the plane ∏ box
[2 marks]
Turn over U
G/Jun24/7367/1
, 6
Do not write
outside the
box
6 The sequence u1, u2, u3, ... is defined by
u1 = 1
un+1 = un + 3n
Prove by induction that for all integers n ≥ 1
3 3
un = 2 n2 – 2 n + 1
[4 marks]
G/Jun24/7367/1
(Merged Question Paper and Marking Scheme)
(Wednesday 22 May 2024)
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 1
Wednesday 22 May 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.
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
8
of this book. Write the question number against your answer(s).
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 100.
15
Advice 16
Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet. 18
You do not necessarily need to use all the space provided.
TOTAL
, A-Level Further Mathematics: Paper 1 (Wednesday 22 May 2024)
Exam Preview Areas
1. Algebra:
o Polynomials: Solving equations, factorization, and roots.
o Rational Functions: Simplifying and analyzing expressions with ratios of polynomials.
o Exponential and Logarithmic Functions: Solving equations and graphing transformations.
o Partial Fractions: Breaking down complex rational expressions into simpler components.
2. Complex Numbers:
o Operations: Addition, subtraction, multiplication, and division of complex numbers.
o Polar Form: Converting between rectangular and polar form.
o De Moivre’s Theorem: Using it to find powers and roots of complex numbers.
3. Coordinate Geometry:
o Straight Lines and Circles: Working with equations, intersections, and tangents.
o Conic Sections: Parabolas, ellipses, hyperbolas—finding equations and analyzing shapes.
o Parametric Equations: Representing curves using parameters and converting between parametric and
Cartesian forms.
4. Calculus:
o Differentiation: Using chain, product, and quotient rules for rates of change, tangents, and
optimization.
o Integration: Techniques like substitution and integration by parts to find areas and solve problems.
o Differential Equations: Solving basic equations and applying them in real-world scenarios (e.g.,
population growth).
5. Vectors:
o Operations: Vector addition, scalar multiplication, and finding magnitudes.
o Dot Product: Analyzing angles between vectors.
o Cross Product: Finding areas of parallelograms and understanding 3D applications.
6. Sequences and Series:
o Arithmetic/Geometric Progressions: Finding terms and sums in sequences.
o Binomial Expansion: Expanding expressions of the form (a+b)n(a + b)^n(a+b)n and approximations
for fractional powers.
7. Mathematical Proof:
o Induction: Proving statements for all integers using the principle of mathematical induction.
o Logical Reasoning: Structuring clear and rigorous mathematical proofs, especially for functions and
sequences.
This paper assesses your ability to apply these concepts to complex problems and demonstrate clear reasoning,
focusing on both algebraic manipulation and geometric interpretation.
G/LM/Jun24/G4006/V8 7367/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The roots of the equation 20x3 – 16x2 – 4x + 7 = 0 are α, β and γ
Find the value of αβ + βγ + γα
Circle your answer.
[1 mark]
–4 –
1 1 4
5 5 5 5
iπ
2 The complex number z = e3
Which one of the following is a real number?
Circle your answer.
[1 mark]
z4 z5 z6 z7
G/Jun24/7367/1
, 3
Do not write
outside the
box
3 The function f is defined by
f (x) = x2 (x ℝ)
Find the mean value of f (x) between x = 0 and x = 2
Circle your answer.
[1 mark]
2 4 8 16
3 3 3 3
4 Which one of the following statements is correct?
Tick () one box.
[1 mark]
lim(x2 ln x) = 0
x 0
lim(x2 ln x) = 1
x 0
lim(x2 ln x) = 2
x 0
lim(x2 ln x) is not defined.
x 0
Turn over for the next question
Turn over U
G/Jun24/7367/1
, 4
Do not write
outside the
5 The points A, B and C have coordinates A(5, 3, 4), B(8, –1, 9) and C(12, 5, 10) box
The points A, B and C lie in the plane ∏
5 (a) Find a vector that is normal to the plane ∏
[3 marks]
G/Jun24/7367/1
, 5
Do not write
outside the
5 (b) Find a Cartesian equation of the plane ∏ box
[2 marks]
Turn over U
G/Jun24/7367/1
, 6
Do not write
outside the
box
6 The sequence u1, u2, u3, ... is defined by
u1 = 1
un+1 = un + 3n
Prove by induction that for all integers n ≥ 1
3 3
un = 2 n2 – 2 n + 1
[4 marks]
G/Jun24/7367/1
