2024_AQA-GCSE Mathematics – Higher Tier
Paper 2: Calculator
(Merged Question Paper and Marking Scheme)
Monday 3 June 2024
Please write clearly in block capitals.
Centre number
Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
GCSE
MATHEMATICS
Higher Tier Paper 2 Calculator
H
Monday 3 June 2024 Morning Time allowed: 1 hour 30 minutes
Materials
For this paper you must have: For Examiner’s Use
• a calculator Pages Mark
• mathematical instruments
• the Formulae Sheet (enclosed). 2–3
4–5
Instructions
6–7
• Use black ink or black ball-point pen. Draw diagrams in pencil.
8–9
• Fill in the boxes at the top of this page.
• Answer all questions. 10–11
• You must answer the questions in the spaces provided. Do not write 12–13
outside the box around each page or on blank pages. 14–15
• If you need extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 16–17
• Do all rough work in this book. Cross through any work you do not want to 18–19
be marked. 20–21
Information 22–23
• The marks for questions are shown in brackets. 24
• The maximum mark for this paper is 80. TOTAL
• You may ask for more answer paper, graph paper and tracing paper.
These must be tagged securely to this answer book.
Advice
In all calculations, show clearly how you work out your answer.
*JUN2483002H01*
IB/M/Jun24/G4007/E10 8300/2H
,GCSE Mathematics Higher Tier Paper 2: Calculator Summary
The GCSE Mathematics Higher Tier Paper 2: Calculator, scheduled for June 2025, will assess
students' mathematical skills with the use of a calculator. This paper will focus on more advanced
mathematical concepts, testing both the depth of knowledge and the ability to solve complex
problems efficiently using a calculator. The key areas covered include:
1. Number:
Arithmetic Operations: Performing calculations with integers, decimals, and fractions, including operations
such as addition, subtraction, multiplication, and division, as well as simplifying complex fractions.
Standard Form: Understanding and performing operations with numbers expressed in standard form (e.g.,
2.5×1042.5 \times 10^42.5×104), including multiplication and division of numbers in scientific notation.
Surds: Simplifying and calculating with surds, including operations such as multiplication, division, and
rationalizing denominators.
Powers and Roots: Using the calculator for calculating squares, square roots, cube roots, and working with
indices, including applying laws of indices for simplification and calculation.
2. Algebra:
Manipulating Expressions: Simplifying algebraic expressions by expanding brackets, factoring, and collecting
like terms.
Solving Equations: Solving linear equations, quadratic equations (by factorizing, completing the square, and
using the quadratic formula), and simultaneous equations using both algebraic and calculator methods.
Inequalities: Solving linear and quadratic inequalities and representing solutions on number lines or using
inequality notation.
Sequences: Identifying and continuing sequences, including arithmetic and geometric sequences, and deriving
nth terms from given sequences.
Graphs: Drawing and interpreting graphs of linear and quadratic functions, understanding the relationships
between variables, and using a calculator to determine the gradient and intercepts of linear functions.
Exponential Functions: Understanding and solving problems involving exponential growth or decay, including
the use of exponential functions in practical contexts.
3. Geometry and Measures:
Angles: Solving problems involving angles in polygons, parallel lines, and circles, using both geometric
reasoning and calculator-based methods.
Trigonometry: Using sine, cosine, and tangent to solve problems in right-angled triangles, including calculating
unknown sides or angles. Applying the sine and cosine rules for non-right-angled triangles.
Area and Volume: Calculating areas and volumes of various shapes (e.g., triangles, trapeziums, circles, and
composite shapes) and 3D objects such as cylinders, cones, and spheres, using appropriate formulae.
Pythagoras' Theorem: Applying Pythagoras’ Theorem to find missing sides in right-angled triangles, using both
manual methods and the calculator for precision.
Vectors: Understanding and performing basic vector operations, such as addition, subtraction, and scalar
multiplication, as well as solving geometric problems using vectors.
4. Statistics and Probability:
Averages and Measures of Spread: Calculating and interpreting the mean, median, mode, and range, as well
as understanding the standard deviation and its use in statistical analysis.
Probability: Calculating probabilities of single and multiple events, using the calculator for solving complex
probability problems, and understanding probability distributions.
Data Representation: Constructing and interpreting various types of graphs and charts, such as histograms,
box plots, and cumulative frequency graphs, and using the calculator to analyze and interpret statistical data.
Regression and Correlation: Understanding and using linear regression and correlation to analyze data, and
using the calculator to determine the line of best fit for a given data set.
5. Ratio, Proportion, and Rates of Change:
Ratios and Proportions: Solving problems involving direct and inverse proportionality, scaling, and comparing
ratios.
, Rates of Change: Using the concept of rates to solve problems involving speed, density, and currency
conversion, as well as interpreting gradients of graphs in real-life situations.
Direct and Inverse Proportionality: Solving problems that involve directly or inversely proportional quantities,
including setting up and solving equations.
6. Functional Mathematics:
Real-World Applications: Applying mathematical concepts to solve real-world problems, including financial
calculations (e.g., interest rates, loans, and investments) and interpreting results in context.
Estimation: Using the calculator to estimate solutions and check the reasonableness of answers to problems in
different contexts.
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 The diagram shows a circle, centre O, and three straight lines.
Use one word to describe each shaded region.
Choose from
arc chord sector segment tangent
[2 marks]
Region A
Region B
*02*
IB/M/Jun24/8300/2H
Paper 2: Calculator
(Merged Question Paper and Marking Scheme)
Monday 3 June 2024
Please write clearly in block capitals.
Centre number
Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
GCSE
MATHEMATICS
Higher Tier Paper 2 Calculator
H
Monday 3 June 2024 Morning Time allowed: 1 hour 30 minutes
Materials
For this paper you must have: For Examiner’s Use
• a calculator Pages Mark
• mathematical instruments
• the Formulae Sheet (enclosed). 2–3
4–5
Instructions
6–7
• Use black ink or black ball-point pen. Draw diagrams in pencil.
8–9
• Fill in the boxes at the top of this page.
• Answer all questions. 10–11
• You must answer the questions in the spaces provided. Do not write 12–13
outside the box around each page or on blank pages. 14–15
• If you need extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 16–17
• Do all rough work in this book. Cross through any work you do not want to 18–19
be marked. 20–21
Information 22–23
• The marks for questions are shown in brackets. 24
• The maximum mark for this paper is 80. TOTAL
• You may ask for more answer paper, graph paper and tracing paper.
These must be tagged securely to this answer book.
Advice
In all calculations, show clearly how you work out your answer.
*JUN2483002H01*
IB/M/Jun24/G4007/E10 8300/2H
,GCSE Mathematics Higher Tier Paper 2: Calculator Summary
The GCSE Mathematics Higher Tier Paper 2: Calculator, scheduled for June 2025, will assess
students' mathematical skills with the use of a calculator. This paper will focus on more advanced
mathematical concepts, testing both the depth of knowledge and the ability to solve complex
problems efficiently using a calculator. The key areas covered include:
1. Number:
Arithmetic Operations: Performing calculations with integers, decimals, and fractions, including operations
such as addition, subtraction, multiplication, and division, as well as simplifying complex fractions.
Standard Form: Understanding and performing operations with numbers expressed in standard form (e.g.,
2.5×1042.5 \times 10^42.5×104), including multiplication and division of numbers in scientific notation.
Surds: Simplifying and calculating with surds, including operations such as multiplication, division, and
rationalizing denominators.
Powers and Roots: Using the calculator for calculating squares, square roots, cube roots, and working with
indices, including applying laws of indices for simplification and calculation.
2. Algebra:
Manipulating Expressions: Simplifying algebraic expressions by expanding brackets, factoring, and collecting
like terms.
Solving Equations: Solving linear equations, quadratic equations (by factorizing, completing the square, and
using the quadratic formula), and simultaneous equations using both algebraic and calculator methods.
Inequalities: Solving linear and quadratic inequalities and representing solutions on number lines or using
inequality notation.
Sequences: Identifying and continuing sequences, including arithmetic and geometric sequences, and deriving
nth terms from given sequences.
Graphs: Drawing and interpreting graphs of linear and quadratic functions, understanding the relationships
between variables, and using a calculator to determine the gradient and intercepts of linear functions.
Exponential Functions: Understanding and solving problems involving exponential growth or decay, including
the use of exponential functions in practical contexts.
3. Geometry and Measures:
Angles: Solving problems involving angles in polygons, parallel lines, and circles, using both geometric
reasoning and calculator-based methods.
Trigonometry: Using sine, cosine, and tangent to solve problems in right-angled triangles, including calculating
unknown sides or angles. Applying the sine and cosine rules for non-right-angled triangles.
Area and Volume: Calculating areas and volumes of various shapes (e.g., triangles, trapeziums, circles, and
composite shapes) and 3D objects such as cylinders, cones, and spheres, using appropriate formulae.
Pythagoras' Theorem: Applying Pythagoras’ Theorem to find missing sides in right-angled triangles, using both
manual methods and the calculator for precision.
Vectors: Understanding and performing basic vector operations, such as addition, subtraction, and scalar
multiplication, as well as solving geometric problems using vectors.
4. Statistics and Probability:
Averages and Measures of Spread: Calculating and interpreting the mean, median, mode, and range, as well
as understanding the standard deviation and its use in statistical analysis.
Probability: Calculating probabilities of single and multiple events, using the calculator for solving complex
probability problems, and understanding probability distributions.
Data Representation: Constructing and interpreting various types of graphs and charts, such as histograms,
box plots, and cumulative frequency graphs, and using the calculator to analyze and interpret statistical data.
Regression and Correlation: Understanding and using linear regression and correlation to analyze data, and
using the calculator to determine the line of best fit for a given data set.
5. Ratio, Proportion, and Rates of Change:
Ratios and Proportions: Solving problems involving direct and inverse proportionality, scaling, and comparing
ratios.
, Rates of Change: Using the concept of rates to solve problems involving speed, density, and currency
conversion, as well as interpreting gradients of graphs in real-life situations.
Direct and Inverse Proportionality: Solving problems that involve directly or inversely proportional quantities,
including setting up and solving equations.
6. Functional Mathematics:
Real-World Applications: Applying mathematical concepts to solve real-world problems, including financial
calculations (e.g., interest rates, loans, and investments) and interpreting results in context.
Estimation: Using the calculator to estimate solutions and check the reasonableness of answers to problems in
different contexts.
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 The diagram shows a circle, centre O, and three straight lines.
Use one word to describe each shaded region.
Choose from
arc chord sector segment tangent
[2 marks]
Region A
Region B
*02*
IB/M/Jun24/8300/2H
