Mathematics

Types of number, HCF and LCM

Primes, factors, multiples, and finding HCF and LCM by prime factorisation.

Fractions, decimals and percentages

Converting between them and calculating with fractions.

Indices and standard form

The laws of indices and writing very large or small numbers.

Ratio, proportion and percentage

Sharing in a ratio, direct and inverse proportion, and percentage change.

Estimation, bounds and limits of accuracy

Rounding, estimating, and the upper and lower bounds of a measurement.

Surds

Simplifying exact roots and rationalising denominators.

Expanding and factorising

Brackets, common factors, quadratics and the difference of two squares.

Linear equations and rearranging formulae

Solving equations and changing the subject of a formula.

Simultaneous equations

Solving pairs of equations by elimination and substitution.

Inequalities

Solving and representing inequalities on a number line and in regions.

Solving quadratic equations

Solving by factorising and by the quadratic formula.

Sequences

Term-to-term and position-to-term rules, including the nth term.

Graphs of functions

Recognising and sketching quadratic, cubic, reciprocal and exponential graphs.

Functions

Function notation, composite and inverse functions.

Straight line graphs

Gradient, intercept, y = mx + c, and parallel and perpendicular lines.

Angles and polygons

Angle rules, parallel lines, and the angles in polygons.

Circle theorems

The angle rules in circles, and how to justify them.

Similarity and congruence

Similar shapes, scale factors for area and volume, and congruence conditions.

Constructions, loci, bearings and symmetry

Ruler-and-compass constructions, describing positions, and symmetry.

Area, volume and surface area

The standard formulae, and choosing the right one.

Arcs and sectors

Working with parts of a circle.

Pythagoras and right-angled trigonometry

Finding sides and angles in right-angled triangles.

Sine rule, cosine rule and area of a triangle

Trigonometry in triangles without a right angle.

Transformations

Reflection, rotation, translation and enlargement — and describing them fully.

Vectors

Column vectors, magnitude, and vector geometry.

Probability of single and combined events

Calculating probabilities and using tree diagrams.

Relative frequency and expected frequency

Estimating probability from data, and predicting outcomes.

Averages and representing data

Mean, median, mode, range, and choosing the right average.

Cumulative frequency and box plots

Medians, quartiles and interquartile range from a curve.

Histograms and scatter diagrams

Frequency density, and correlation between two variables.