Maths

Fractions, decimals and percentages

• Fractions and percentages as operatorsFoundation+Higher
• Fractions in ratio problemsFoundation+Higher
• Terminating and recurring decimalsFoundation+Higher

Measures and accuracy

• Estimation and approximationFoundation+Higher
• Limits of accuracy and boundsFoundation+Higher
• Rounding and error intervalsFoundation+Higher
• Standard units of measure (mass, length, time, money)Foundation+Higher

Structure and calculation

• Calculating with roots and indicesHigher
• Exact calculation with fractions, surds and πFoundation+Higher
• Four operations and place valueFoundation+Higher
• Inverse operations and order of operationsFoundation+Higher
• Ordering integers, decimals and fractionsFoundation+Higher
• Powers and rootsHigher
• Prime numbers, factors and multiplesFoundation+Higher
• Standard formFoundation+Higher
• Systematic listing strategiesHigher

Graphs

• Coordinates in four quadrantsFoundation+Higher
• Equation of a circle and tangentHigher
• Gradients and areas under curvesHigher
• Gradients and intercepts of linear functionsFoundation+Higher
• Plotting non-standard and reciprocal graphs in real contextsHigher
• Roots, intercepts and turning points of quadraticsHigher
• Sketching and interpreting standard graphsHigher
• Straight-line graphs and y = mx + cHigher
• Translations and reflections of functionsHigher

Notation, vocabulary and manipulation

• Algebraic manipulation notationFoundation+Higher
• Equations vs identities and algebraic argumentHigher
• Functions, inverse and composite functionsFoundation+Higher
• Simplifying and manipulating algebraic expressionsHigher
• Standard formulae and rearrangingFoundation+Higher
• Substituting into formulaeFoundation+Higher
• Vocabulary of expressions, equations, formulae, identitiesFoundation+Higher

Sequences

• Generating sequencesFoundation+Higher
• nth term of sequencesFoundation+Higher
• Special sequencesHigher

Solving equations and inequalities

• Iterative methodsHigher
• Simultaneous equationsHigher
• Solving linear and quadratic inequalitiesFoundation+Higher
• Solving linear equationsFoundation+Higher
• Solving quadratic equationsFoundation+Higher
• Translating situations into algebraFoundation+Higher

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• Comparing lengths, areas and volumes by ratioFoundation+Higher
• Compound unitsFoundation+Higher
• Converting between standard and compound unitsFoundation+Higher
• Direct and inverse proportion problemsFoundation+Higher
• Dividing in a given ratioFoundation+Higher
• Gradient as rate of changeFoundation+Higher
• Growth and decay; compound interestHigher
• Instantaneous rate of changeHigher
• Inverse proportion equationsHigher
• Multiplicative relationships as ratio or fractionFoundation+Higher
• Percentages and percentage changeFoundation+Higher
• Proportion as equality of ratiosFoundation+Higher
• Quantity as a fraction of anotherFoundation+Higher
• Ratio notationFoundation+Higher
• Ratios linked to fractions and linear functionsFoundation+Higher
• Scale factors, scale diagrams and mapsFoundation+Higher

Mensuration and calculation

• Arc length and sector areaFoundation+Higher
• Area and volume formulae for triangles, parallelograms, trapezia, prismsFoundation+Higher
• Area of any triangle (½ab sin C)Higher
• Circumference, area of circle and 3D solidsFoundation+Higher
• Exact trig valuesFoundation+Higher
• Lengths, areas and volumes in similar figuresHigher
• Measuring lines, angles and bearingsFoundation+Higher
• Pythagoras' theorem and right-angled trigonometryHigher
• Sine rule and cosine ruleHigher
• Standard units of measureFoundation+Higher

Properties and constructions

• Angle properties and parallel linesFoundation+Higher
• Applying congruence and similarity to derive resultsFoundation+Higher
• Circle definitions and propertiesFoundation+Higher
• Circle theoremsHigher
• Combinations of transformationsHigher
• Congruence criteria for trianglesFoundation+Higher
• Constructing congruent and similar shapesFoundation+Higher
• Conventional geometric terms and notationFoundation+Higher
• Geometrical problems on coordinate axesFoundation+Higher
• Plans and elevations of 3D shapesFoundation+Higher
• Properties of 3D solidsFoundation+Higher
• Properties of quadrilaterals and trianglesFoundation+Higher
• Standard ruler-and-compass constructions and lociFoundation+Higher

Vectors

• Vector arithmeticHigher
• Vectors as 2D translationsFoundation+Higher

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• Conditional probabilityHigher
• Empirical samples and theoretical distributionsFoundation+Higher
• Enumerating sets and combinationsFoundation+Higher
• Exhaustive and mutually exclusive eventsFoundation+Higher
• Frequency of probability outcomesFoundation+Higher
• Independent and dependent combined eventsFoundation+Higher
• Randomness and expected outcomesFoundation+Higher
• Theoretical possibility spacesFoundation+Higher
• Theoretical probability and 0–1 scaleFoundation+Higher

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• Applying statistics to describe a populationFoundation+Higher
• Distributions: averages, spread, box plotsHigher
• Histograms and cumulative frequency graphsHigher
• Inferring properties from samplesFoundation+Higher
• Scatter graphs and bivariate dataFoundation+Higher
• Statistical tables, charts and diagramsFoundation+Higher