AQA_2024: AS 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.
AS
MATHEMATICS
Paper 2
Thursday 23 May 2024 Afternoon Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
You must have the AQA Formulae for A‑ level Mathematics booklet.
You should have a graphical or scientific calculator that meets the Question Mark
requirements of the specification. 1
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).
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
14
The marks for questions are shown in brackets.
The maximum mark for this paper is 80. 15
16
Advice 17
Unless stated otherwise, you may quote formulae, without proof, from
the booklet. TOTAL
You do not necessarily need to use all the space provided.
,For AS Mathematics - Paper 2, focus on the following key areas:
1. Algebra:
Polynomials: Factor and solve polynomial equations. Apply the factor theorem and remainder
theorem to simplify and solve.
Equations of Curves: Solve problems involving quadratic, cubic, and quartic equations. Understand
their properties and graphs.
Inequalities: Solve linear, quadratic, and rational inequalities, and express the solution on a number
line or interval notation.
Partial Fractions: Decompose rational expressions into partial fractions for integration or
simplification.
2. Coordinate Geometry:
Equations of Lines and Circles: Solve problems involving straight lines and circles, such as finding
the equation of a line given two points or a line's gradient.
Conic Sections: Study and analyze ellipses, hyperbolas, and parabolas, understanding their
equations and properties.
Distance and Midpoint: Use the distance formula and midpoint formula to solve geometry problems
involving points in 2D space.
3. Trigonometry:
Basic Trigonometric Identities: Learn and apply Pythagorean identities, sum and difference
identities, and double angle identities.
Trigonometric Equations: Solve basic trigonometric equations involving sin, cos, and tan,
including equations with multiple angles.
Radian Measure: Convert between degrees and radians, and solve problems involving angular
displacement and velocity.
4. Calculus:
Differentiation: Differentiate functions such as polynomials, exponentials, and trigonometric functions.
Use the chain rule, product rule, and quotient rule.
5. Exponential and Logarithmic Functions:
Exponential Functions: Solve problems involving growth and decay using exponential functions.
Logarithmic Functions: Solve equations involving logarithms and use logarithmic properties for
simplification and solving.
6. Vectors:
Vector Operations: Perform vector addition, subtraction, and scalar multiplication. Understand how to
calculate the dot product and use it to find angles between vectors.
Applications: Use vectors in geometry, including finding the equation of a line given two points and
solving problems involving position vectors.
7. Sequences and Series:
Arithmetic Sequences: Work with sequences where the difference between consecutive terms is
constant. Solve for the n-th term and the sum of the first n terms.
G/LM/Jun24/G4004/E8 7356/2
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 Line L has equation
5y = 4x + 6
Find the gradient of a line parallel to line L
Circle your answer.
[1 mark]
–5 –4 4 5
4 5 5 4
2 One of the equations below is true for all values of x
Identify the correct equation.
Tick () one box.
[1 mark]
cos2 x = –1 – sin2 x
cos2 x = –1 + sin2 x
cos2 x = 1 – sin2 x
cos2 x = 1 + sin2 x
G/Jun24/7356/2
, 3
Do not write
outside the
box
3 It is given that
3 loga x = loga 72 – 2 loga 3
Solve the equation to find the value of x
Fully justify your answer.
[4 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/2
(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.
AS
MATHEMATICS
Paper 2
Thursday 23 May 2024 Afternoon Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
You must have the AQA Formulae for A‑ level Mathematics booklet.
You should have a graphical or scientific calculator that meets the Question Mark
requirements of the specification. 1
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).
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
14
The marks for questions are shown in brackets.
The maximum mark for this paper is 80. 15
16
Advice 17
Unless stated otherwise, you may quote formulae, without proof, from
the booklet. TOTAL
You do not necessarily need to use all the space provided.
,For AS Mathematics - Paper 2, focus on the following key areas:
1. Algebra:
Polynomials: Factor and solve polynomial equations. Apply the factor theorem and remainder
theorem to simplify and solve.
Equations of Curves: Solve problems involving quadratic, cubic, and quartic equations. Understand
their properties and graphs.
Inequalities: Solve linear, quadratic, and rational inequalities, and express the solution on a number
line or interval notation.
Partial Fractions: Decompose rational expressions into partial fractions for integration or
simplification.
2. Coordinate Geometry:
Equations of Lines and Circles: Solve problems involving straight lines and circles, such as finding
the equation of a line given two points or a line's gradient.
Conic Sections: Study and analyze ellipses, hyperbolas, and parabolas, understanding their
equations and properties.
Distance and Midpoint: Use the distance formula and midpoint formula to solve geometry problems
involving points in 2D space.
3. Trigonometry:
Basic Trigonometric Identities: Learn and apply Pythagorean identities, sum and difference
identities, and double angle identities.
Trigonometric Equations: Solve basic trigonometric equations involving sin, cos, and tan,
including equations with multiple angles.
Radian Measure: Convert between degrees and radians, and solve problems involving angular
displacement and velocity.
4. Calculus:
Differentiation: Differentiate functions such as polynomials, exponentials, and trigonometric functions.
Use the chain rule, product rule, and quotient rule.
5. Exponential and Logarithmic Functions:
Exponential Functions: Solve problems involving growth and decay using exponential functions.
Logarithmic Functions: Solve equations involving logarithms and use logarithmic properties for
simplification and solving.
6. Vectors:
Vector Operations: Perform vector addition, subtraction, and scalar multiplication. Understand how to
calculate the dot product and use it to find angles between vectors.
Applications: Use vectors in geometry, including finding the equation of a line given two points and
solving problems involving position vectors.
7. Sequences and Series:
Arithmetic Sequences: Work with sequences where the difference between consecutive terms is
constant. Solve for the n-th term and the sum of the first n terms.
G/LM/Jun24/G4004/E8 7356/2
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 Line L has equation
5y = 4x + 6
Find the gradient of a line parallel to line L
Circle your answer.
[1 mark]
–5 –4 4 5
4 5 5 4
2 One of the equations below is true for all values of x
Identify the correct equation.
Tick () one box.
[1 mark]
cos2 x = –1 – sin2 x
cos2 x = –1 + sin2 x
cos2 x = 1 – sin2 x
cos2 x = 1 + sin2 x
G/Jun24/7356/2
, 3
Do not write
outside the
box
3 It is given that
3 loga x = loga 72 – 2 loga 3
Solve the equation to find the value of x
Fully justify your answer.
[4 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/2
