Maths

Graphs

• Coordinates in four quadrants
• Cubic and reciprocal graphsFoundation
• Deduce roots of quadratics algebraicallyFoundation
• Equation of a circle and tangent (Higher)Higher
• Equation of a line through two points or with given gradientFoundation
• Exponential and trigonometric graphs (Higher)Higher
• Exponential graphs in real contexts (Higher)Higher
• Gradients and area under graphs (Higher)Higher
• Gradients and intercepts of linear functions
• Perpendicular lines (Higher)Higher
• Plotting straight-line graphsFoundation
• Real-context graphs and kinematic problemsFoundation
• Reciprocal graphs in real contextsFoundation
• Recognise, sketch, interpret linear and quadratic graphsFoundation
• Roots, intercepts and turning points of quadratics — graphicallyFoundation
• Translations and reflections of functions (Higher)Higher
• Turning points by completing the square (Higher)Higher
• y = mx + c — parallel linesFoundation

Notation, vocabulary and manipulation

• Algebraic notation
• Algebraic proofs (Higher)Higher
• Equation vs identity; algebraic argumentFoundation
• Expanding products of two binomialsFoundation
• Expanding single bracketsFoundation
• Expanding two or more binomials (Higher)Higher
• Factorising — taking out common factorsFoundation
• Factorising quadratics ax^2+bx+c (Higher)Higher
• Factorising quadratics x^2+bx+cFoundation
• Functions — inputs and outputsFoundation
• Identities (Higher)Higher
• Inverse and composite functions (Higher)Higher
• Laws of indices in algebraic expressionsFoundation
• Manipulating algebraic fractions and surd expressions (Higher)Higher
• Simplifying — collecting like termsFoundation
• Standard mathematical formulae and rearranging
• Substitute into formulae and expressions
• Vocabulary of expressions, equations, formulae, inequalities, terms, factorsFoundation

Sequences

• Fibonacci, quadratic and geometric sequencesFoundation
• Generating sequences from term-to-term or position-to-term rules
• nth term of linear sequencesFoundation
• nth term of quadratic sequences (Higher)Higher
• Other sequences and surd ratios (Higher)Higher
• Triangular, square, cube number and arithmetic sequencesFoundation

Solving equations and inequalities

• Approximate solutions of equations from a graphFoundation
• Approximate solutions of quadratics from a graphFoundation
• Iterative methods for equations (Higher)Higher
• Linear equations with unknown on both sidesFoundation
• Quadratic equations with rearrangement, completing the square, quadratic formula (Higher)Higher
• Simultaneous equations (linear/linear)Foundation
• Simultaneous equations (linear/quadratic) (Higher)Higher
• Solving linear (one or two variables) and quadratic inequalities (Higher)Higher
• Solving linear equations in one unknownFoundation
• Solving linear inequalities in one variableFoundation
• Solving quadratics by factorisingFoundation
• Translating situations into algebraFoundation

Mensuration and calculation

• Arc lengths, angles and sector areasFoundation
• Area and volume formulae — triangles, parallelograms, trapezia, prisms, cylinders
• Area of a triangle Area = ½ab sin C (Higher)Higher
• Circumference and area of a circle; perimeters and composite shapesFoundation
• Congruence and similarity — lengths in similar figuresFoundation
• Exact values of sine, cosine and tangentFoundation
• Lengths, areas and volumes in similar figures (Higher)Higher
• Measure line segments and angles; bearings
• Pythagoras' theorem and trigonometric ratios SOHCAHTOAFoundation
• Sine rule and cosine rule (Higher)Higher
• Standard units of measure (geometry)
• Surface area and volume of spheres, pyramids, cones, composite solids and frustumsFoundation
• Trigonometry in 2D and 3D, general triangles (Higher)Higher

Properties and constructions

• 3D shapes — properties of faces, surfaces, edges, vertices
• Alternate and corresponding angles on parallel linesFoundation
• Angle properties at a point and on a lineFoundation
• Angle sum in a triangle and polygonsFoundation
• Circle definitions and propertiesFoundation
• Circle theorems (Higher)Higher
• Combinations of transformations and invariance (Higher)Higher
• Congruence criteria for trianglesFoundation
• Conjecture and prove with congruence, similarity, PythagorasFoundation
• Fractional scale factors for enlargementFoundation
• Geometric terms and notation
• Geometrical problems on coordinate axes
• Negative scale factors for enlargement (Higher)Higher
• Plans and elevations of 3D shapesFoundation
• Properties of quadrilaterals, triangles and plane figures
• Standard ruler and compass constructions and lociFoundation
• Transformations — rotation, reflection, translation, enlargementFoundation

Vectors

• Translations as 2D vectors
• Vector addition, subtraction, scalar multiplication, column vectorsFoundation
• Vector geometric arguments and proofs (Higher)Higher

Fractions, decimals and percentages

• Fractions and percentages as operators
• Fractions in ratio problems
• Recurring decimals to fractions and vice versa (Higher)Higher
• Terminating decimals and corresponding fractionsFoundation

Measures and accuracy

• Error intervals (truncation and rounding)Foundation
• Estimation and checking calculations
• Limits of accuracy and bounds (Higher)Higher
• Rounding to decimal places and significant figuresFoundation
• Standard units of measure

Structure and calculation

• Calculate with roots and integer indicesFoundation
• Estimating powers and roots (Higher)Higher
• Exact calculation with fractionsFoundation
• Exact calculation with multiples of piFoundation
• Four operations on integers, decimals and fractions
• Fractional indices (Higher)Higher
• Household finance vocabulary
• Inverse operations and order of operations
• Ordering integers, decimals and fractions
• Positive integer powers and real rootsFoundation+Higher
• Prime numbers, factors and multiples
• Product rule for counting (Higher)Higher
• Standard form
• Surds — calculate, simplify, rationalise (Higher)Higher
• Systematic listing strategies (Foundation)Foundation

(top-level)

• Conditional probability (Higher)Higher
• Empirical samples and theoretical distributionsFoundation
• Enumerating sets — tables, grids, Venn diagramsFoundation
• Exhaustive sets and mutually exclusive events sum to 1
• Frequency of outcomes; tables and frequency trees
• Independent and dependent combined eventsFoundation
• Randomness, fairness and equally likely events
• Relative expected frequency and theoretical probability
• Theoretical possibility spaces
• Tree diagrams (Additional Foundation)Foundation

(top-level)

• Compare lengths, areas, volumes using ratioFoundation
• Compound units — density and pressureFoundation
• Compound units — density, pressureFoundation
• Compound units — speed, rates of pay, unit pricingFoundation
• Construct equations of direct/inverse proportion (Higher)Higher
• Converting between standard and compound unitsFoundation
• Direct and inverse proportion problems
• Express one quantity as a fraction of another
• General iterative processes (Higher)Higher
• Gradient as rate of change; proportion graphsFoundation
• Growth and decay problems including compound interestFoundation
• Instantaneous and average rate of change (Higher)Higher
• Inverse proportion equivalence and equationsFoundation
• Multiplicative relationship as ratio or fraction
• Percentage change problems and simple interestFoundation
• Percentages — definition, conversion, comparison
• Proportion as equality of ratios
• Ratio notation and simplest form
• Ratios linked to fractions and linear functions
• Scale factors, scale diagrams and maps
• Sharing a quantity in a given ratio
• Similarity and trigonometric ratios linksFoundation

(top-level)

• Box plots, quartiles, inter-quartile range (Higher)Higher
• Compare distributions — graphical and central tendency/spreadFoundation
• Histograms (equal and unequal class intervals) and cumulative frequency graphs (Higher)Higher
• Sampling and inference from a sample (Additional Foundation)Foundation
• Scatter graphs, correlation, line of best fit, interpolation/extrapolation
• Tables, charts and diagrams for categorical and discrete data
• Use statistics to describe a population