United Kingdom — Maths
DfE — National Curriculum, GCSE & A-Level subject content
The English maths curriculum runs from Year 1 to Year 13. Primary (KS1–KS2) and KS3 follow the National Curriculum programmes of study; Years 10–11 work towards GCSE (9–1) maths at Foundation or Higher tier; Years 12–13 study AS/A-Level maths (Pure, Statistics and Mechanics). Phrasing matches the major exam boards (AQA, Edexcel/Pearson, OCR), which all follow the same DfE subject content.
118 topics — click any topic for a full virtual lesson with worked examples.
Year 1 · Year 2
Key Stage 1 — Years 1 & 2
Early maths: counting and place value to 100, number bonds, the 2/5/10 times tables, halves and quarters, and lots of practical measuring, shape and money work.
Number & place value
Addition & subtraction
Multiplication & division
Measurement
Year 3 · Year 4 · Year 5 · Year 6
Key Stage 2 — Years 3 to 6
Builds fluency: numbers to 10,000,000, the full times tables, formal written methods for ×/÷, fractions, decimals and percentages, basic algebra, and geometry, statistics and ratio.
Number & place value
Calculation
- 📖→Column addition & subtractionUp to 4+ digits · Multi-step word problems
- 📖→Times tables to 12 × 12Rapid recall · Related division facts
- 📖→Long multiplication4-digit × 2-digit · Estimation to check
- 📖→Long & short divisionDividing by 1- and 2-digit numbers · Interpreting remainders
- 📖→Factors, multiples & primesCommon factors & multiples · Prime numbers · Square & cube numbers
- 📖→Order of operations (BODMAS)Brackets · Mixed operations
Fractions, decimals & percentages
Ratio, proportion & algebra
Measurement
Geometry
Year 7 · Year 8 · Year 9
Key Stage 3 — Years 7 to 9
Secondary foundations across the six GCSE content areas, building the algebra, ratio and geometry that GCSE develops further.
Number
- 📖→Integers, decimals & order of operationsFour operations · BIDMAS · Negative numbers
- 📖→Factors, multiples, primes, HCF & LCMPrime factorisation · HCF and LCM
- 📖→Powers & rootsIndex laws · Square & cube roots
- 📖→Standard formLarge & small numbers · Calculating in standard form
- 📖→Fractions & percentagesFour operations with fractions · Percentage of amounts · Percentage change
- 📖→Rounding & estimationDecimal places · Significant figures · Estimating calculations
Algebra
- 📖→Algebraic notation & simplifyingCollecting like terms · Multiplying & dividing terms
- 📖→Expanding & factorisingSingle brackets · Factorising into a bracket
- 📖→Linear equationsOne- and two-step · Unknowns on both sides · With brackets
- 📖→Linear inequalitiesSolving · Number-line representation
- 📖→Formulae & substitutionSubstitution · Writing & rearranging formulae
- 📖→SequencesTerm-to-term rules · nth term of linear sequences
- 📖→Coordinates & linear graphsPlotting y = mx + c · Gradient & intercept
Ratio, proportion & rates of change
Geometry & measures
- 📖→Angles & parallel linesAngle rules · Angles in polygons · Bearings
- 📖→Properties of shapesTriangles & quadrilaterals · Symmetry
- 📖→Area & perimeterTriangles, parallelograms, trapezia · Circles: area & circumference
- 📖→Volume & surface areaPrisms & cylinders · Surface area
- 📖→TransformationsReflection, rotation, translation, enlargement
- 📖→Pythagoras' theoremFinding the hypotenuse · Finding a shorter side
Probability
Year 10 · Year 11
GCSE Mathematics (9–1) — Years 10 & 11
The full GCSE (9–1) course, examined at Foundation tier (grades 1–5) or Higher tier (grades 4–9). Topics marked “Higher” appear only on the Higher paper.
Number
- 📖→Structure & calculationFour operations · Factors, primes, HCF/LCM · Powers & roots · +1 more
- 📖→Fractions, decimals & percentagesConversions · Percentage change · Reverse percentages · +1 more
- 📖→Standard formWriting & ordering · Calculations
- 📖→Surds (Higher)Simplifying · Rationalising the denominator
- 📖→Bounds & accuracyRounding & significant figures · Upper & lower bounds · Error intervals
Algebra
- 📖→Notation, simplifying & expandingExpanding double/triple brackets · Factorising · Index laws
- 📖→Quadratic expressions & equationsFactorising · Quadratic formula · Completing the square (Higher)
- 📖→Linear equations & rearranging formulaeSolving · Changing the subject
- 📖→Simultaneous equationsTwo linear · Linear & quadratic (Higher)
- 📖→InequalitiesLinear inequalities · Graphical regions · Quadratic inequalities (Higher)
- 📖→Sequencesnth term (linear) · Quadratic sequences (Higher) · Geometric & Fibonacci
- 📖→GraphsStraight-line graphs · Quadratic, cubic & reciprocal · Exponential · +1 more
- 📖→Functions & equation of a circle (Higher)Function notation · Composite & inverse functions · x² + y² = r²
- 📖→Iteration (Higher)Iterative formulae · Solving equations numerically
Ratio, proportion & rates of change
Geometry & measures
- 📖→Angles & polygonsAngle rules · Interior/exterior angles · Bearings
- 📖→Congruence & similarityCongruent triangles · Similar shapes · Area & volume scale factors (Higher)
- 📖→Pythagoras & trigonometryPythagoras (2D & 3D) · SOHCAHTOA · Exact trig values
- 📖→Sine & cosine rules (Higher)Sine rule · Cosine rule · Area = ½ab sin C
- 📖→Circle theorems (Higher)The theorems · Proof & application
- 📖→Area, surface area & volumeCircles, sectors & arcs · Prisms, cylinders, cones & spheres
- 📖→Vectors (Higher)Vector notation · Vector arithmetic · Geometric proof
- 📖→Transformations & constructionsReflection, rotation, translation, enlargement · Constructions & loci
Probability
Statistics
- 📖→Sampling & data collectionPopulations & samples · Bias
- 📖→Charts & diagramsBar charts, pie charts · Stem-and-leaf · Time series
- 📖→Averages & spreadMean, median, mode, range · Grouped data & estimated mean
- 📖→Cumulative frequency & box plots (Higher)Median & quartiles · IQR · Comparing distributions
- 📖→Histograms (Higher)Frequency density · Unequal class widths
- 📖→Scatter graphs & correlationCorrelation · Line of best fit · Interpolation & extrapolation
Year 12 · Year 13
AS & A-Level Mathematics — Years 12 & 13
A-Level maths: compulsory Pure Mathematics plus applied Statistics and Mechanics. Overarching themes of mathematical argument, problem solving and modelling run throughout. AS covers roughly the Year 12 content.
Pure mathematics
- 📖→ProofDeduction & exhaustion · Disproof by counter-example · Proof by contradiction (A-Level)
- 📖→Algebra & functionsIndices & surds · Quadratics & discriminant · Polynomials & factor theorem · +2 more
- 📖→Coordinate geometryStraight lines · Circles · Parametric equations
- 📖→Sequences & seriesArithmetic & geometric series · Binomial expansion · Sigma notation · +1 more
- 📖→TrigonometryRadians, arcs & sectors · Trig identities & equations · Compound & double angle formulae · +1 more
- 📖→Exponentials & logarithmse^x and ln x · Laws of logarithms · Exponential models · +1 more
- 📖→DifferentiationFirst principles · Product, quotient & chain rules · Stationary points · +1 more
- 📖→IntegrationStandard integrals · Definite integrals & areas · By substitution & by parts · +1 more
- 📖→Numerical methodsLocating roots · Newton–Raphson · Iteration · +1 more
- 📖→Vectors2D & 3D vectors · Magnitude & direction · Position vectors & geometry
Statistics
- 📖→Statistical samplingPopulations & samples · Sampling methods
- 📖→Data presentation & interpretationMeasures of location & spread · Histograms & box plots · Outliers · +1 more
- 📖→ProbabilityVenn diagrams · Independent & mutually exclusive events · Conditional probability (A-Level)
- 📖→Statistical distributionsBinomial distribution · Normal distribution (A-Level) · Approximations
- 📖→Hypothesis testingBinomial tests · Normal mean tests (A-Level) · Correlation tests
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