AQA_2024: A-level 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
MATHEMATICS
Paper 2
Tuesday 11 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
1
requirements of the specification. 2
3
Instructions
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 8
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
15
The marks for questions are shown in brackets.
The maximum mark for this paper is 100.
16
17
Advice 18
Unless stated otherwise, you may quote formulae, without proof, from 19
the booklet. 20
You do not necessarily need to use all the space provided. 21
TOTAL
,For A-Level Mathematics - Paper 2, focus on the following key areas:
1. Algebra:
Polynomials: Understand the factor theorem and remainder theorem. Factorize cubic and quartic
polynomials and solve related equations.
Simultaneous Equations: Solve both linear and non-linear simultaneous equations using algebraic
and graphical methods.
Inequalities: Solve quadratic, linear, and rational inequalities. Represent solutions on a number line or
in interval notation.
2. Coordinate Geometry:
Equations of Lines: Solve problems involving the equation of a straight line in various forms (e.g., y =
mx + c, Ax + By = C). Understand the relationship between the gradient and the slope, and use the
point-slope form.
Circles: Solve problems related to circles, including finding the equation of a circle, the center, and
the radius. Work with tangents and the points of intersection between a line and a circle.
3. Trigonometry:
Trigonometric Ratios: Know and apply the basic trigonometric functions (sine, cosine, tangent) for
angles in both degrees and radians.
Trigonometric Identities: Use Pythagorean identities, sum and difference formulas, and double
angle formulas to simplify and solve equations.
4. Calculus:
Differentiation: Differentiate a variety of functions, including polynomial, exponential, logarithmic, and
trigonometric functions using basic rules (power rule, product rule, quotient rule, chain rule).
Stationary Points: Find and classify stationary points (minima, maxima, or inflection points) using the
first and second derivative tests.
5. Exponentials and Logarithms:
Exponential Functions: Solve problems involving exponential growth and decay, especially in real-
life applications such as population growth and radioactive decay.
Logarithmic Functions: Solve logarithmic equations and manipulate expressions using properties
such as log(ab) = log(a) + log(b) and log(a^n) = n * log(a).
6. Vectors:
Vector Operations: Add, subtract, and scale vectors. Use the dot product to calculate the angle
between vectors.
Position Vectors: Solve geometry problems using position vectors, such as finding the equation of a
line through two points and determining distances.
Applications: Use vectors in kinematics, for example, to solve problems involving velocity and
displacement.
7. Sequences and Series:
Arithmetic Sequences: Work with arithmetic sequences, including finding the n-th term and the
sum of the first n terms. & Geometric Sequences
G/LM/Jun24/G4005/E7 7357/2
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 One of the equations below is the equation of a circle.
Identify this equation.
[1 mark]
Tick (🗸) one box.
(x + 1)2 – (y + 2)2 = –36
(x + 1)2 – (y + 2)2 = 36
(x + 1)2 + (y + 2)2 = –36
(x + 1)2 + (y + 2)2 = 36
G/Jun24/7357/2
, 3
Do not write
outside the
2 The graph of y = f (x) intersects the x‑ axis at (–3, 0), (0, 0) and (2, 0) as shown in the box
diagram below.
y
A
–3 2 x
B
The shaded region A has an area of 189
The shaded region B has an area of 64
2
Find the value of
∫ –3
f (x) dx
Circle your answer.
[1 mark]
–253 –125 125 253
Turn over for the next question
Turn over U
G/Jun24/7357/2
(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
MATHEMATICS
Paper 2
Tuesday 11 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
1
requirements of the specification. 2
3
Instructions
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 8
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
15
The marks for questions are shown in brackets.
The maximum mark for this paper is 100.
16
17
Advice 18
Unless stated otherwise, you may quote formulae, without proof, from 19
the booklet. 20
You do not necessarily need to use all the space provided. 21
TOTAL
,For A-Level Mathematics - Paper 2, focus on the following key areas:
1. Algebra:
Polynomials: Understand the factor theorem and remainder theorem. Factorize cubic and quartic
polynomials and solve related equations.
Simultaneous Equations: Solve both linear and non-linear simultaneous equations using algebraic
and graphical methods.
Inequalities: Solve quadratic, linear, and rational inequalities. Represent solutions on a number line or
in interval notation.
2. Coordinate Geometry:
Equations of Lines: Solve problems involving the equation of a straight line in various forms (e.g., y =
mx + c, Ax + By = C). Understand the relationship between the gradient and the slope, and use the
point-slope form.
Circles: Solve problems related to circles, including finding the equation of a circle, the center, and
the radius. Work with tangents and the points of intersection between a line and a circle.
3. Trigonometry:
Trigonometric Ratios: Know and apply the basic trigonometric functions (sine, cosine, tangent) for
angles in both degrees and radians.
Trigonometric Identities: Use Pythagorean identities, sum and difference formulas, and double
angle formulas to simplify and solve equations.
4. Calculus:
Differentiation: Differentiate a variety of functions, including polynomial, exponential, logarithmic, and
trigonometric functions using basic rules (power rule, product rule, quotient rule, chain rule).
Stationary Points: Find and classify stationary points (minima, maxima, or inflection points) using the
first and second derivative tests.
5. Exponentials and Logarithms:
Exponential Functions: Solve problems involving exponential growth and decay, especially in real-
life applications such as population growth and radioactive decay.
Logarithmic Functions: Solve logarithmic equations and manipulate expressions using properties
such as log(ab) = log(a) + log(b) and log(a^n) = n * log(a).
6. Vectors:
Vector Operations: Add, subtract, and scale vectors. Use the dot product to calculate the angle
between vectors.
Position Vectors: Solve geometry problems using position vectors, such as finding the equation of a
line through two points and determining distances.
Applications: Use vectors in kinematics, for example, to solve problems involving velocity and
displacement.
7. Sequences and Series:
Arithmetic Sequences: Work with arithmetic sequences, including finding the n-th term and the
sum of the first n terms. & Geometric Sequences
G/LM/Jun24/G4005/E7 7357/2
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 One of the equations below is the equation of a circle.
Identify this equation.
[1 mark]
Tick (🗸) one box.
(x + 1)2 – (y + 2)2 = –36
(x + 1)2 – (y + 2)2 = 36
(x + 1)2 + (y + 2)2 = –36
(x + 1)2 + (y + 2)2 = 36
G/Jun24/7357/2
, 3
Do not write
outside the
2 The graph of y = f (x) intersects the x‑ axis at (–3, 0), (0, 0) and (2, 0) as shown in the box
diagram below.
y
A
–3 2 x
B
The shaded region A has an area of 189
The shaded region B has an area of 64
2
Find the value of
∫ –3
f (x) dx
Circle your answer.
[1 mark]
–253 –125 125 253
Turn over for the next question
Turn over U
G/Jun24/7357/2
