AQA_2024: AS Mathematics - Paper 1
(Merged Question Paper and Marking Scheme)
(Thursday 16 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
MATHEMATICS
Paper 1
Thursday 16 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
Instructions
3
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. 4
Answer all questions. 5
You must answer each question in the space provided for that question. 6
If you need extra space for your answer(s), use the lined pages at the end of 7
this book. Write the question number against your answer(s). 8
Do not write outside the box around each page or on blank pages.
Show all necessary working; otherwise marks for method may be lost. 9
Do all rough work in this book. Cross through any work that you do not want 10
to be marked. 11
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, from 17
the booklet. 18
You do not necessarily need to use all the space provided. 19
TOTAL
,AS Mathematics: Paper 1 (Thursday 16 May 2024)
Exam Preview Areas
This paper focuses on Pure Mathematics and typically covers fundamental topics in algebra, functions,
calculus, and trigonometry. Key areas include:
1. Algebra:
Quadratic Equations: Solving equations, factorizing, and using the quadratic formula.
Manipulating Algebraic Expressions: Simplifying, expanding, and factorizing expressions.
Polynomials: Understanding the roots, factorization, and solving polynomial equations.
Inequalities: Solving linear and quadratic inequalities.
2. Functions:
Types of Functions: Linear, quadratic, exponential, and reciprocal functions.
Graphing: Plotting and interpreting graphs of functions and transformations (e.g., translations,
reflections).
3. Trigonometry:
Basic Trigonometric Functions: Sine, cosine, and tangent, and their graphs.
Trigonometric Identities: Using identities such as sin2x+cos2x=1\sin^2 x + \cos^2 x =
1sin2x+cos2x=1, and solving trigonometric equations.
Solving Triangles: Using the sine and cosine rules to solve problems in non-right-angled triangles.
4. Calculus:
Differentiation: Basic differentiation rules (power rule, product rule, chain rule) and applying to
polynomial functions.
Applications of Differentiation: Finding tangents, stationary points (maximum, minimum), and solving
rate of change problems.
Integration: Basic integration techniques for polynomials and applications such as calculating areas
under curves.
5. Coordinate Geometry:
Straight Line Equations: The gradient-intercept form, finding the equation of a line, and calculating
distances between points.
Circles: Equation of a circle and finding the center and radius.
This paper tests your understanding of core mathematical concepts and your ability to apply them to solve
problems in algebra, functions, trigonometry, and calculus
G/LM/Jun24/G4004/E9 7356/1
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 It is given that tan θ° = k, where k is a constant.
Find tan (θ + 180)°
Circle your answer.
[1 mark]
–k –1 1
k
k k
1
2 Curve C has equation y =
(x – 1)2
State the equations of the asymptotes to curve C
Tick (🗸) one box.
[1 mark]
x = 0 and y = 0
x = 0 and y = 1
x = 1 and y = 0
x = 1 and y = 1
G/Jun24/7356/1
, 3
Do not write
outside the
√3 + 3√5 box
3 Express in the form a + √b , where a and b are integers.
√5 – √3
Fully justify your answer.
[4 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
, 4
Do not write
outside the
box
4 (a) (i) By using a suitable trigonometric identity, show that the equation
sin θ tan θ = 4 cos θ
can be written as
tan2 θ = 4
[1 mark]
4 (a) (ii) Hence solve the equation
sin θ tan θ = 4 cos θ
where 0° < θ < 360°
Give your answers to the nearest degree.
[3 marks]
G/Jun24/7356/1
, 5
Do not write
outside the
box
4 (b) Deduce all solutions of the equation
sin 3α tan 3α = 4 cos 3α
where 0° < α < 180°
Give your answers to the nearest degree.
[3 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
, 6
Do not write
outside the
box
5 A student is looking for factors of the polynomial f (x)
They suggest that (x – 2) is a factor of f (x)
The method they use to check this suggestion is to calculate f (–2)
They correctly calculate that f (–2) = 0
They conclude that their suggestion is correct.
5 (a) Make one comment about the student’s method.
[1 mark]
5 (b) Make two comments about the student’s conclusion.
[2 marks]
1
2
G/Jun24/7356/1
, 7
Do not write
outside the
box
6 Determine the set of values of x which satisfy the inequality
3x2 + 3x > x + 6
Give your answer in exact form using set notation.
[4 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
, 8
Do not write
outside the
box
7 A triangular field of grass, ABC, has boundaries with lengths as follows:
AB = 234 m BC = 225 m AC = 310 m
The field is shown in the diagram below.
B 225 m C
234 m 310 m
A
7 (a) Find angle A
[2 marks]
G/Jun24/7356/1
, 9
Do not write
outside the
box
7 (b) Farmers calculate the number of sheep they can keep in a field, by allowing one sheep
for every 1200 m2 of grass.
Find the maximum number of sheep which can be kept in the field ABC
[3 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
(Merged Question Paper and Marking Scheme)
(Thursday 16 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
MATHEMATICS
Paper 1
Thursday 16 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
Instructions
3
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. 4
Answer all questions. 5
You must answer each question in the space provided for that question. 6
If you need extra space for your answer(s), use the lined pages at the end of 7
this book. Write the question number against your answer(s). 8
Do not write outside the box around each page or on blank pages.
Show all necessary working; otherwise marks for method may be lost. 9
Do all rough work in this book. Cross through any work that you do not want 10
to be marked. 11
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, from 17
the booklet. 18
You do not necessarily need to use all the space provided. 19
TOTAL
,AS Mathematics: Paper 1 (Thursday 16 May 2024)
Exam Preview Areas
This paper focuses on Pure Mathematics and typically covers fundamental topics in algebra, functions,
calculus, and trigonometry. Key areas include:
1. Algebra:
Quadratic Equations: Solving equations, factorizing, and using the quadratic formula.
Manipulating Algebraic Expressions: Simplifying, expanding, and factorizing expressions.
Polynomials: Understanding the roots, factorization, and solving polynomial equations.
Inequalities: Solving linear and quadratic inequalities.
2. Functions:
Types of Functions: Linear, quadratic, exponential, and reciprocal functions.
Graphing: Plotting and interpreting graphs of functions and transformations (e.g., translations,
reflections).
3. Trigonometry:
Basic Trigonometric Functions: Sine, cosine, and tangent, and their graphs.
Trigonometric Identities: Using identities such as sin2x+cos2x=1\sin^2 x + \cos^2 x =
1sin2x+cos2x=1, and solving trigonometric equations.
Solving Triangles: Using the sine and cosine rules to solve problems in non-right-angled triangles.
4. Calculus:
Differentiation: Basic differentiation rules (power rule, product rule, chain rule) and applying to
polynomial functions.
Applications of Differentiation: Finding tangents, stationary points (maximum, minimum), and solving
rate of change problems.
Integration: Basic integration techniques for polynomials and applications such as calculating areas
under curves.
5. Coordinate Geometry:
Straight Line Equations: The gradient-intercept form, finding the equation of a line, and calculating
distances between points.
Circles: Equation of a circle and finding the center and radius.
This paper tests your understanding of core mathematical concepts and your ability to apply them to solve
problems in algebra, functions, trigonometry, and calculus
G/LM/Jun24/G4004/E9 7356/1
, 2
Do not write
outside the
box
Section A
Answer all questions in the spaces provided.
1 It is given that tan θ° = k, where k is a constant.
Find tan (θ + 180)°
Circle your answer.
[1 mark]
–k –1 1
k
k k
1
2 Curve C has equation y =
(x – 1)2
State the equations of the asymptotes to curve C
Tick (🗸) one box.
[1 mark]
x = 0 and y = 0
x = 0 and y = 1
x = 1 and y = 0
x = 1 and y = 1
G/Jun24/7356/1
, 3
Do not write
outside the
√3 + 3√5 box
3 Express in the form a + √b , where a and b are integers.
√5 – √3
Fully justify your answer.
[4 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
, 4
Do not write
outside the
box
4 (a) (i) By using a suitable trigonometric identity, show that the equation
sin θ tan θ = 4 cos θ
can be written as
tan2 θ = 4
[1 mark]
4 (a) (ii) Hence solve the equation
sin θ tan θ = 4 cos θ
where 0° < θ < 360°
Give your answers to the nearest degree.
[3 marks]
G/Jun24/7356/1
, 5
Do not write
outside the
box
4 (b) Deduce all solutions of the equation
sin 3α tan 3α = 4 cos 3α
where 0° < α < 180°
Give your answers to the nearest degree.
[3 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
, 6
Do not write
outside the
box
5 A student is looking for factors of the polynomial f (x)
They suggest that (x – 2) is a factor of f (x)
The method they use to check this suggestion is to calculate f (–2)
They correctly calculate that f (–2) = 0
They conclude that their suggestion is correct.
5 (a) Make one comment about the student’s method.
[1 mark]
5 (b) Make two comments about the student’s conclusion.
[2 marks]
1
2
G/Jun24/7356/1
, 7
Do not write
outside the
box
6 Determine the set of values of x which satisfy the inequality
3x2 + 3x > x + 6
Give your answer in exact form using set notation.
[4 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
, 8
Do not write
outside the
box
7 A triangular field of grass, ABC, has boundaries with lengths as follows:
AB = 234 m BC = 225 m AC = 310 m
The field is shown in the diagram below.
B 225 m C
234 m 310 m
A
7 (a) Find angle A
[2 marks]
G/Jun24/7356/1
, 9
Do not write
outside the
box
7 (b) Farmers calculate the number of sheep they can keep in a field, by allowing one sheep
for every 1200 m2 of grass.
Find the maximum number of sheep which can be kept in the field ABC
[3 marks]
Turn over for the next question
Turn over U
G/Jun24/7356/1
