AQA_2024: A-level Mathematics - Paper 1
(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 1
Tuesday 4 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.
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. 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
16
Advice
Unless stated otherwise, you may quote formulae, without proof, from the 17
booklet. 18
You do not necessarily need to use all the space provided. 19
20
TOTAL
,For A-Level Mathematics - Paper 1, focus on the following key areas:
1. Algebra:
Quadratic Equations: Solve quadratic equations using factorization, the quadratic formula, and
completing the square. Understand the discriminant and its implications for real roots.
Simultaneous Equations: Solve linear and non-linear simultaneous equations algebraically and
graphically.
Polynomials: Work with polynomials, including factor theorem and remainder theorem. Solve
higher-degree polynomials and factorize them.
Inequalities: Solve linear, quadratic, and rational inequalities. Represent solutions on a number line.
Rational Expressions: Simplify, add, subtract, multiply, and divide rational expressions.
2. Coordinate Geometry:
Equations of a Line: Understand and manipulate equations of straight lines in different forms (e.g., y
= mx + c, Ax + By = C). Solve problems involving distance, midpoint, and gradient.
Circles: Know the equation of a circle and how to find its center and radius. Solve problems involving
tangents and intersections with other shapes.
Conic Sections: Understand and solve problems involving parabolas, ellipses, and hyperbolas.
Know their general equations and properties.
3. Trigonometry:
Trigonometric Ratios: Understand sine, cosine, and tangent functions. Work with angles in radians
and degrees.
Trigonometric Identities: Know and apply Pythagorean identities, sum and difference formulas,
double angle formulas, and half-angle formulas.
Trigonometric Equations: Solve equations involving trigonometric functions, including equations with
multiple angles.
Graphs of Trigonometric Functions: Understand the transformation of sine, cosine, and tangent
graphs, including amplitude, period, and phase shift.
4. Calculus:
Differentiation: Differentiate polynomials, exponentials, logarithmic functions, and trigonometric
functions. Use the power rule, product rule, quotient rule, and chain rule.
Stationary Points: Find and classify stationary points (maxima, minima, or inflection points) using the
first and second derivative tests.
Applications of Differentiation: Solve problems involving rates of change, tangents, and normal
lines.
Integration: Integrate simple functions, including polynomials and trigonometric functions. Use
integration to find areas under curves and solve problems in motion.
5. Exponentials and Logarithms:
Exponential Functions: Solve problems involving exponential growth and decay. Understand and use
the function y = e^x.
Logarithmic Functions: Solve logarithmic equations and use properties such as log(ab) = log(a) +
log(b) and log(a^n) = n * log(a).
6. Vectors:
G/LM/Jun24/G4005/E6 7357/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find the coefficient of x in the expansion of
(4x3 – 5 x 2 + 3x – 2)(x5 + 4x + 1)
Circle your answer.
[1 mark]
–5 –2 7 11
G/Jun24/7357/1
, 3
Do not write
outside the
2 The function f is defined by f (x) = e x + 1 for x ℝ box
Find an expression for f –1(x)
Tick (🗸) one box.
[1 mark]
f –1(x) = ln (x – 1)
f –1(x) = ln (x) – 1
1
f –1(x) =
ex + 1
x–1
f –1(x) = e
Turn over for the next question
Turn over U
G/Jun24/7357/1
(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 1
Tuesday 4 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.
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. 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
16
Advice
Unless stated otherwise, you may quote formulae, without proof, from the 17
booklet. 18
You do not necessarily need to use all the space provided. 19
20
TOTAL
,For A-Level Mathematics - Paper 1, focus on the following key areas:
1. Algebra:
Quadratic Equations: Solve quadratic equations using factorization, the quadratic formula, and
completing the square. Understand the discriminant and its implications for real roots.
Simultaneous Equations: Solve linear and non-linear simultaneous equations algebraically and
graphically.
Polynomials: Work with polynomials, including factor theorem and remainder theorem. Solve
higher-degree polynomials and factorize them.
Inequalities: Solve linear, quadratic, and rational inequalities. Represent solutions on a number line.
Rational Expressions: Simplify, add, subtract, multiply, and divide rational expressions.
2. Coordinate Geometry:
Equations of a Line: Understand and manipulate equations of straight lines in different forms (e.g., y
= mx + c, Ax + By = C). Solve problems involving distance, midpoint, and gradient.
Circles: Know the equation of a circle and how to find its center and radius. Solve problems involving
tangents and intersections with other shapes.
Conic Sections: Understand and solve problems involving parabolas, ellipses, and hyperbolas.
Know their general equations and properties.
3. Trigonometry:
Trigonometric Ratios: Understand sine, cosine, and tangent functions. Work with angles in radians
and degrees.
Trigonometric Identities: Know and apply Pythagorean identities, sum and difference formulas,
double angle formulas, and half-angle formulas.
Trigonometric Equations: Solve equations involving trigonometric functions, including equations with
multiple angles.
Graphs of Trigonometric Functions: Understand the transformation of sine, cosine, and tangent
graphs, including amplitude, period, and phase shift.
4. Calculus:
Differentiation: Differentiate polynomials, exponentials, logarithmic functions, and trigonometric
functions. Use the power rule, product rule, quotient rule, and chain rule.
Stationary Points: Find and classify stationary points (maxima, minima, or inflection points) using the
first and second derivative tests.
Applications of Differentiation: Solve problems involving rates of change, tangents, and normal
lines.
Integration: Integrate simple functions, including polynomials and trigonometric functions. Use
integration to find areas under curves and solve problems in motion.
5. Exponentials and Logarithms:
Exponential Functions: Solve problems involving exponential growth and decay. Understand and use
the function y = e^x.
Logarithmic Functions: Solve logarithmic equations and use properties such as log(ab) = log(a) +
log(b) and log(a^n) = n * log(a).
6. Vectors:
G/LM/Jun24/G4005/E6 7357/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find the coefficient of x in the expansion of
(4x3 – 5 x 2 + 3x – 2)(x5 + 4x + 1)
Circle your answer.
[1 mark]
–5 –2 7 11
G/Jun24/7357/1
, 3
Do not write
outside the
2 The function f is defined by f (x) = e x + 1 for x ℝ box
Find an expression for f –1(x)
Tick (🗸) one box.
[1 mark]
f –1(x) = ln (x – 1)
f –1(x) = ln (x) – 1
1
f –1(x) =
ex + 1
x–1
f –1(x) = e
Turn over for the next question
Turn over U
G/Jun24/7357/1
