GCSE Revision Notes

GCSE Mathematics notes

Topic-by-topic GCSE Mathematics notes with worked examples, common mistakes and practice questions with Gradion feedback.

Algebra

Algebra is the language of GCSE Maths — manipulating expressions, solving equations and working with graphs. Master it and the rest of the paper gets easier.

Linear Equations Quadratic Equations Simultaneous Equations Sequences Expanding & Factorising Straight-Line Graphs (y = mx + c)Inequalities Rearranging Formulae Algebraic Fractions

Number

Number underpins the whole GCSE Maths paper. Confidence with fractions, percentages, indices and rounding earns quick, reliable marks throughout.

Fractions, Decimals & Percentages Indices & Surds Standard Form Rounding & Estimation HCF, LCM & Prime Factorisation

Ratio & Proportion

Ratio and proportion compare quantities and scale them up or down. They appear across recipes, maps, best-buy and mixture questions in every GCSE paper.

Percentage Change Direct & Inverse Proportion Compound Measures (Speed, Density, Pressure)

Geometry & Measures

Geometry and measures cover angles, shape, area, volume and the theorems that connect them. Clear diagrams and known angle facts win steady marks.

Pythagoras' Theorem Trigonometry (SOH CAH TOA)Circle Theorems Area & Perimeter Volume & Surface Area Transformations Angles & Polygons Vectors Similar Shapes & Congruence Bearings

Probability

Probability measures how likely an event is, from 0 (impossible) to 1 (certain). Careful counting of outcomes is the key to reliable marks.

Tree Diagrams Venn Diagrams & Set Notation

Statistics

Statistics is about collecting, representing and interpreting data. Averages and spread summarise data, while charts reveal patterns and comparisons.

Scatter Graphs & Correlation Cumulative Frequency & Box Plots Histograms & Frequency Density

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