Number:
* Number and place value: Understanding place value, ordering numbers, rounding, significant figures, standard form.
* Calculations: Addition, subtraction, multiplication, and division of integers, decimals, and fractions. Order of operations (BODMAS/PEMDAS). Working with percentages, ratios, and proportions. Understanding prime numbers, factors, multiples, and LCM/HCF.
* Fractions, decimals, and percentages: Converting between these forms, calculations involving them.
* Indices and standard form: Laws of indices, calculations involving powers and roots, expressing numbers in standard form.
Algebra:
* Basic algebra: Simplifying expressions, expanding brackets, factorising expressions, solving linear equations and inequalities.
* Simultaneous equations: Solving linear simultaneous equations graphically and algebraically.
* Quadratics: Solving quadratic equations (factorising, quadratic formula, completing the square), sketching quadratic graphs.
* Sequences: Arithmetic and geometric sequences, finding nth terms.
* Graphs: Interpreting and drawing graphs, including linear, quadratic, and cubic graphs.
* Functions: Understanding function notation (f(x)), composite functions, inverse functions.
Ratio, Proportion, and Rates of Change:
* Ratio and proportion: Solving problems involving ratios and proportions, including direct and inverse proportion.
* Rates of change: Understanding speed, distance, time relationships.
* Percentage change: Calculating percentage increase and decrease.
Geometry and Measures:
* Shapes and space: Properties of 2D and 3D shapes, including angles, area, volume, and surface area. Congruence and similarity.
* Pythagoras' theorem and trigonometry: Using Pythagoras' theorem to find lengths in right-angled triangles. Using trigonometry (SOH CAH TOA) to find angles and lengths in right-angled triangles.
* Transformations: Translations, reflections, rotations, enlargements.
* Vectors: Understanding vectors, adding and subtracting vectors.
* Bearings: Measuring and using bearings.
* Units and conversions: Converting between different units of measurement.
Probability and Statistics:
* Data handling: Collecting, organising, and presenting data (tables, charts, graphs).
* Averages and range: Calculating mean, median, mode, and range.
* Probability: Understanding probability, calculating probabilities of simple events, and combined events (e.g., using tree diagrams).
* Scatter graphs: Interpreting scatter graphs and lines of best fit.
Important Considerations:
* Problem-solving: A significant portion of the GCSE Maths exam involves applying your knowledge to solve problems. Practice solving a wide variety of problems is crucial.
* Exam technique: Learn how to manage your time effectively during the exam, and understand the marking scheme.
* Past papers: Practicing with past papers is essential to familiarize yourself with the exam format and types of questions asked.
This is a comprehensive list, and the depth of knowledge required for each topic will vary. Your textbook and teacher will provide more specific details on the curriculum for your exam board. Make sure to consult your syllabus and resources provided by your school or exam board for the most accurate and up-to-date information.