Number: Integers, decimals, fractions, and percentages | Powers, roots, and standard form | Prime numbers, factors, multiples, LCM, HCF | Ratio and proportion
Algebra: Simplifying, expanding, and factorising | Solving linear and quadratic equations | Rearranging formulas | Graphs of linear and quadratic functions | Sequences
Geometry and Measures: Angles, polygons, perimeter, area, and volume | Pythagoras' theorem and basic trigonometry | Transformations and constructions
Statistics and Probability: Averages and range | Probability (basic and combined events) | Data representation (graphs, charts, scatter diagrams)
Ratio and Proportion: Direct and inverse proportion | Speed, distance, time, and compound measures (e.g., density)
Higher Tier Extras: Advanced trigonometry (sine/cosine rules) | Quadratics (completing the square, quadratic formula) | Vectors and functions | Circle theorems
Number: Fractions, decimals, and percentages | Rounding, estimation, and significant figures | Standard form and basic powers | Ratio and proportion
Algebra: Simplifying and expanding expressions | Solving linear equations and inequalities | Substituting into formulas and rearranging | Graphs of linear functions | Sequences (arithmetic)
Geometry and Measures: Properties of angles, triangles, and polygons | Perimeter, area, and volume (including compound shapes) | Pythagoras' theorem (right-angled triangles) | Basic trigonometry (sine, cosine, tangent) | Transformations (translations, rotations, reflections, enlargements)
Statistics and Probability: Mean, median, mode, and range | Probability basics (including probability trees) | Data handling (charts, tables, bar graphs)
Ratio and Proportion: Direct proportion problems | Speed, distance, time calculations | Scale drawings and maps
Number: Advanced fractions, decimals, percentages | Standard form and surds | Bounds and error intervals | Ratio and proportion (including inverse proportion)
Algebra: Solving quadratic and simultaneous equations | Completing the square and the quadratic formula | Algebraic fractions and rearranging complex formulas | Graphs of quadratic, cubic, and reciprocal functions | Sequences (arithmetic, geometric)
Geometry and Measures: Pythagoras’ theorem and advanced trigonometry (sine/cosine rules, area of triangles) | Circle theorems and tangents | Vectors (magnitude and direction) | Transformations, including enlargements and rotations | Volume and surface area of 3D shapes
Statistics and Probability: Conditional probability and Venn diagrams | Histograms and cumulative frequency | Box plots and quartiles | Probability trees and combined events
Ratio and Proportion: Direct and inverse proportion in algebraic and geometric contexts | Compound measures (density, pressure, speed) | Rates of change (gradient and real-world applications)