AQA_2024: AS 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.
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
,For AS Mathematics - Paper 1, focus on the following key areas:
1. Algebra:
Quadratic Equations: Solve quadratic equations by factorizing, completing the square, and using the
quadratic formula.
Simultaneous Equations: Solve linear and non-linear simultaneous equations, including linear-quadratic
systems.
Inequalities: Solve linear and quadratic inequalities and represent the solutions on number lines and
graphs.
Algebraic Manipulation: Simplify expressions involving surds, indices, and fractions.
Rational Expressions: Simplify and solve problems involving rational expressions, including adding,
subtracting, and multiplying.
2. Coordinate Geometry:
Equations of a Line: Understand the equation of a straight line, including slope-intercept form and point-
slope form. Solve problems involving midpoint, distance, and slope.
Circles: Understand the general equation of a circle and how to find the centre and radius.
Conic Sections: Study the properties of parabolas and ellipses in coordinate geometry.
3. Trigonometry:
Trigonometric Ratios: Know and apply the basic trigonometric ratios for angles in both degrees and
radians.
Sine and Cosine Rule: Solve problems involving triangles using the sine rule, cosine rule, and area of a
triangle.
Graphs of Trigonometric Functions: Understand the shapes and transformations of the sine, cosine, and
tangent functions.
Trig Equations: Solve trigonometric equations and use identities to simplify and solve.
4. Calculus:
Differentiation: Differentiate standard functions (e.g., polynomial, trigonometric, and exponential) using
basic rules (power rule, chain rule, product rule, quotient rule).
Stationary Points: Find the stationary points of a function and determine whether they are minima,
maxima, or points of inflection.
Integration: Integrate simple functions using basic integration rules and apply integration to find area under
curves.
5. Exponentials and Logarithms:
Exponential Functions: Understand the properties of exponential functions, especially y = e^x, and how to
solve problems involving growth and decay.
Logarithmic Functions: Solve logarithmic equations and use the properties of logarithms, including change
of base and solving exponential equations using logarithms.
6. Vectors:
7. Proof:
Mathematical Induction: Use inductive reasoning to prove statements about integers, particularly
sequences or sums.
Proof by Contradiction: Understand and apply proof by contradiction in solving problems.
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
(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 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
,For AS Mathematics - Paper 1, focus on the following key areas:
1. Algebra:
Quadratic Equations: Solve quadratic equations by factorizing, completing the square, and using the
quadratic formula.
Simultaneous Equations: Solve linear and non-linear simultaneous equations, including linear-quadratic
systems.
Inequalities: Solve linear and quadratic inequalities and represent the solutions on number lines and
graphs.
Algebraic Manipulation: Simplify expressions involving surds, indices, and fractions.
Rational Expressions: Simplify and solve problems involving rational expressions, including adding,
subtracting, and multiplying.
2. Coordinate Geometry:
Equations of a Line: Understand the equation of a straight line, including slope-intercept form and point-
slope form. Solve problems involving midpoint, distance, and slope.
Circles: Understand the general equation of a circle and how to find the centre and radius.
Conic Sections: Study the properties of parabolas and ellipses in coordinate geometry.
3. Trigonometry:
Trigonometric Ratios: Know and apply the basic trigonometric ratios for angles in both degrees and
radians.
Sine and Cosine Rule: Solve problems involving triangles using the sine rule, cosine rule, and area of a
triangle.
Graphs of Trigonometric Functions: Understand the shapes and transformations of the sine, cosine, and
tangent functions.
Trig Equations: Solve trigonometric equations and use identities to simplify and solve.
4. Calculus:
Differentiation: Differentiate standard functions (e.g., polynomial, trigonometric, and exponential) using
basic rules (power rule, chain rule, product rule, quotient rule).
Stationary Points: Find the stationary points of a function and determine whether they are minima,
maxima, or points of inflection.
Integration: Integrate simple functions using basic integration rules and apply integration to find area under
curves.
5. Exponentials and Logarithms:
Exponential Functions: Understand the properties of exponential functions, especially y = e^x, and how to
solve problems involving growth and decay.
Logarithmic Functions: Solve logarithmic equations and use the properties of logarithms, including change
of base and solving exponential equations using logarithms.
6. Vectors:
7. Proof:
Mathematical Induction: Use inductive reasoning to prove statements about integers, particularly
sequences or sums.
Proof by Contradiction: Understand and apply proof by contradiction in solving problems.
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
