Cambridge IGCSE & O Level Mathematics

Types of number, prime factors, HCF and LCM.

Set notation, Venn diagrams, complements, subsets and three-set problems.

Squares, square roots, cubes and cube roots.

Fractions, equivalent forms, recurring decimals and percentage conversion.

Ordering integers, decimals, fractions and percentages; inequalities.

Negative numbers, order of operations, decimals and fraction operations.

Index notation, multiplication/division laws, negative and fractional indices.

Writing and calculating with numbers in standard form.

Decimal places, significant figures, estimation and sensible accuracy.

Measurement bounds and bounds in calculations.

Ratio, sharing in a ratio and proportional reasoning.

Common rates, speed and other measures of rate.

Percentage change, reverse percentages, profit/loss and compound interest.

Efficient calculator use, standard form, checking accuracy, time and fractions.

24-hour time, time calculations, decimal hours and time zones.

Value for money and currency conversion.

Exponential growth and exponential decay.

Simplifying surds, manipulating surd expressions and rationalising denominators.

Using letters, substitution and evaluating algebraic expressions.

Simplifying, expanding, factorising algebraic expressions and completing the square.

Simplifying and combining algebraic fractions.

Index laws with numerical and algebraic expressions.

Linear, simultaneous and quadratic equations; rearranging formulae.

Solving inequalities and representing regions graphically.

Linear, quadratic, cubic and exponential sequences; nth-term rules.

Direct and other forms of proportion expressed algebraically.

Conversion graphs, travel graphs, rate of change and area under speed–time graphs.

Quadratic, cubic, reciprocal and exponential graphs; graphical solutions and gradients.

Recognising and sketching linear, quadratic, cubic, reciprocal and exponential families.

Function notation, domain/range, inverse and composite functions.

Gradient, line segments, distance, straight-line equations, parallel and perpendicular lines.

Angles, lines, bearings, polygons, solids, nets, congruence, similarity and circles.

Measuring and constructing angles/figures, including compass constructions and nets.

Scale drawings, maps and bearings.

Similar shapes and relationships between corresponding lengths, areas and volumes.

Line symmetry, rotational symmetry and symmetry of shapes/solids.

Straight-line, parallel-line, quadrilateral and polygon angle properties.

Circle symmetry, angle theorems and the alternate segment theorem.

Length, mass, capacity, area and volume units.

Perimeter, area, circumference, surface area and volume.

Pythagoras, trigonometric ratios, obtuse angles, non-right triangles and 3-D problems.

Reflection, rotation, translation, enlargement with integer, fractional and negative scale factors, describing and combining transformations.

Vectors and translations, vector notation, scalar multiplication, column vector operations, position vectors, magnitude and vector geometry.

Single events, complements, expected frequency, relative frequency, combined events, independent events and dependent-event trees.

Data collection, questionnaires, two-way tables, averages and grouped/continuous data.

Bar/pie charts, scatter diagrams, cumulative frequency, quartiles and histograms.