The GCSE (General Certificate of Secondary Education) exams in the UK typically cover a range of mathematics topics.

The specific topics may vary slightly depending on the exam board, but here is a comprehensive list of the main topics covered in GCSE mathematics:

Number and Algebra:

- Number properties and calculations
- Fractions, decimals, and percentages
- Ratio and proportion
- Algebraic expressions and equations
- Indices and standard form
- Inequalities

Geometry and Measures:

- Properties of angles, lines, and polygons
- Perimeter, area, and volume
- Pythagoras’ theorem and trigonometry
- Transformations (translations, rotations, reflections)
- Symmetry and congruence
- Construction and loci

Statistics and Probability:

- Data collection and presentation
- Measures of central tendency (mean, median, mode)
- Probability and tree diagrams
- Statistical diagrams and charts
- Averages and range

Ratio, Proportion, and Rates of Change:

- Direct and inverse proportion
- Rates of change and gradient
- Percentage change
- Compound interest

Handling Data:

- Probability and Venn diagrams
- Sampling techniques and bias
- Statistical analysis and interpretation
- Scatter graphs and correlation

It’s worth noting that the GCSE mathematics curriculum may also include problem-solving, mathematical reasoning, and functional skills such as financial mathematics or applications of mathematics in real-world contexts.

Remember to consult the specific exam board’s syllabus for the most accurate and up-to-date information on the topics covered in GCSE mathematics.

### Edexel Exam Board

The following is a list of topics typically covered in the Edexcel GCSE Mathematics specification:

Number:

- Fractions, decimals, and percentages
- Indices and standard form
- Ratio, proportion, and rates of change
- Rational and irrational numbers
- Surds

Algebra:

- Algebraic manipulation and simplification
- Solving equations and inequalities
- Sequences (including arithmetic and geometric progressions)
- Graphs of linear and quadratic functions
- Simultaneous equations and inequalities
- Algebraic proofs

Geometry and Measures:

- Properties of shapes (angles, triangles, quadrilaterals, polygons, circles)
- Perimeter, area, and volume calculations
- Pythagoras’ theorem and trigonometry
- Transformations (translations, reflections, rotations, enlargements)
- Constructions and loci
- Similarity and congruence

Statistics and Probability:

- Data collection, presentation, and interpretation
- Averages and measures of spread
- Probability and Venn diagrams
- Statistical diagrams and representations
- Sampling and estimation

Ratio, Proportion, and Rates of Change:

- Direct and inverse proportion
- Percentage change
- Compound interest
- Growth and decay

Calculus (Higher Tier Only):

- Differentiation and integration concepts (rates of change, gradients, areas under curves)

It’s important to note that the specific content and depth of each topic may vary slightly depending on the tier (Foundation or Higher) and the particular specification being followed. It’s advisable to consult the official Edexcel GCSE Mathematics specification for the most accurate and up-to-date information.