AQA_2024: A-level Mathematics - Paper 3
(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
MATHEMATICS
Paper 3
Thursday 20 June 2024 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
You must have the AQA Formulae for A‑ level Mathematics booklet.
Question Mark
You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
2
Instructions 3
Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 4
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 need 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
13
Information
The marks for questions are shown in brackets.
14
The maximum mark for this paper is 100. 15
16
Advice 17
Unless stated otherwise, you may quote formulae, without proof, from 18
the booklet.
19
You do not necessarily need to use all the space provided.
TOTAL
,For A-Level Mathematics - Paper 3, focus on the following key areas:
1. Algebra:
Polynomials: Factorize higher-degree polynomials (cubic, quartic) and solve polynomial equations
using the factor theorem and remainder theorem.
2. Coordinate Geometry:
Equations of Lines: Work with straight lines in different forms (e.g., y = mx + c, Ax + By = C),
including parallel and perpendicular lines.
Circles: Solve problems involving the equation of a circle, its center, and radius. Find tangents and
intersections with other shapes.
Conic Sections: Solve and understand ellipses, parabolas, and hyperbolas, and their geometric
properties. Be able to identify and manipulate their general equations.
3. Trigonometry:
Trigonometric Ratios: Use and apply sine, cosine, tangent for angles in both radians and degrees.
Trigonometric Identities: Master key identities like Pythagorean identities, sum and difference
formulas, double angle formulas, and half-angle formulas.
4. Calculus:
Differentiation: Differentiate various functions (polynomials, exponentials, trigonometric, logarithmic)
using basic rules (product rule, quotient rule, chain rule).
Stationary Points: Find and classify stationary points (maxima, minima, inflection points) using first
and second derivative tests.
5. Exponentials and Logarithms:
Exponential Functions: Solve problems involving growth and decay, such as population growth or
radioactive decay.
Logarithmic Functions: Solve logarithmic equations and manipulate using properties like log(ab) =
log(a) + log(b) and log(a^n) = n * log(a).
6. Vectors:
Vector Operations: Perform vector addition, subtraction, and scalar multiplication. Use dot product to
calculate the angle between vectors.
Applications: Solve problems using vectors in geometry, such as finding the equation of a line through
two points or calculating distances in 2D or 3D space.
7. Sequences and Series:
Arithmetic Sequences: Solve problems involving arithmetic sequences, including the n-th term and
the sum of the first n terms.
Geometric Sequences: Solve problems involving geometric sequences, including finding the sum of
an infinite series where the common ratio is between -1 and 1.
G/LM/Jun24/G4005/E6 7357/3
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 Each of the series below shows the first four terms of a geometric series.
Identify the only one of these geometric series that is convergent.
[1 mark]
Tick (🗸) one box.
0.1 + 0.2 + 0.4 + 0.8 + …
1–1+1–1+…
128 – 64 + 32 – 16 + …
1+2+4+8+…
G/Jun24/7357/3
, 3
Do not write
outside the
box
2 The quadratic equation
4x2 + bx + 9 = 0
has one repeated real root.
Find b
Circle your answer.
[1 mark]
b=0 b = ±12 b = ±13 b = ±36
Turn over for the next question
Turn over U
G/Jun24/7357/3
(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
MATHEMATICS
Paper 3
Thursday 20 June 2024 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
You must have the AQA Formulae for A‑ level Mathematics booklet.
Question Mark
You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
2
Instructions 3
Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 4
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 need 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
13
Information
The marks for questions are shown in brackets.
14
The maximum mark for this paper is 100. 15
16
Advice 17
Unless stated otherwise, you may quote formulae, without proof, from 18
the booklet.
19
You do not necessarily need to use all the space provided.
TOTAL
,For A-Level Mathematics - Paper 3, focus on the following key areas:
1. Algebra:
Polynomials: Factorize higher-degree polynomials (cubic, quartic) and solve polynomial equations
using the factor theorem and remainder theorem.
2. Coordinate Geometry:
Equations of Lines: Work with straight lines in different forms (e.g., y = mx + c, Ax + By = C),
including parallel and perpendicular lines.
Circles: Solve problems involving the equation of a circle, its center, and radius. Find tangents and
intersections with other shapes.
Conic Sections: Solve and understand ellipses, parabolas, and hyperbolas, and their geometric
properties. Be able to identify and manipulate their general equations.
3. Trigonometry:
Trigonometric Ratios: Use and apply sine, cosine, tangent for angles in both radians and degrees.
Trigonometric Identities: Master key identities like Pythagorean identities, sum and difference
formulas, double angle formulas, and half-angle formulas.
4. Calculus:
Differentiation: Differentiate various functions (polynomials, exponentials, trigonometric, logarithmic)
using basic rules (product rule, quotient rule, chain rule).
Stationary Points: Find and classify stationary points (maxima, minima, inflection points) using first
and second derivative tests.
5. Exponentials and Logarithms:
Exponential Functions: Solve problems involving growth and decay, such as population growth or
radioactive decay.
Logarithmic Functions: Solve logarithmic equations and manipulate using properties like log(ab) =
log(a) + log(b) and log(a^n) = n * log(a).
6. Vectors:
Vector Operations: Perform vector addition, subtraction, and scalar multiplication. Use dot product to
calculate the angle between vectors.
Applications: Solve problems using vectors in geometry, such as finding the equation of a line through
two points or calculating distances in 2D or 3D space.
7. Sequences and Series:
Arithmetic Sequences: Solve problems involving arithmetic sequences, including the n-th term and
the sum of the first n terms.
Geometric Sequences: Solve problems involving geometric sequences, including finding the sum of
an infinite series where the common ratio is between -1 and 1.
G/LM/Jun24/G4005/E6 7357/3
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 Each of the series below shows the first four terms of a geometric series.
Identify the only one of these geometric series that is convergent.
[1 mark]
Tick (🗸) one box.
0.1 + 0.2 + 0.4 + 0.8 + …
1–1+1–1+…
128 – 64 + 32 – 16 + …
1+2+4+8+…
G/Jun24/7357/3
, 3
Do not write
outside the
box
2 The quadratic equation
4x2 + bx + 9 = 0
has one repeated real root.
Find b
Circle your answer.
[1 mark]
b=0 b = ±12 b = ±13 b = ±36
Turn over for the next question
Turn over U
G/Jun24/7357/3
