Cambridge Mathematics:
IGCSE Extended

Number in Cambridge IGCSE Extended Mathematics covers the full numerical syllabus at extended depth — including integers, decimals, fractions, percentages, and their interconversion, ordering and rounding including significant figures and decimal places, powers, roots, and standard form, prime factorisation, HCF and LCM, ratio and proportion, direct and inverse proportion, percentage change and reverse percentage, simple and compound interest, rates including speed and density, and estimation and limits of accuracy. Extended Number content is assessed across both IGCSE Extended papers and includes more demanding application questions than the Core tier, requiring students to choose appropriate methods in less familiar contexts.

Algebra in Cambridge IGCSE Extended Mathematics covers a significantly more demanding algebraic syllabus than the Core tier — including expression manipulation, expanding and factorising including the difference of two squares and quadratic trinomials, solving linear and simultaneous equations, solving quadratic equations by factorisation, completing the square, and the quadratic formula, algebraic fractions, rearranging complex formulae, inequalities and their representation on number lines, sequences including arithmetic and geometric progressions, direct and inverse variation, and an introduction to functions, composite functions, and inverse functions. Extended Algebra is one of the most heavily assessed areas of the IGCSE Extended examination.

Shape and Space in Cambridge IGCSE Extended Mathematics covers a broad and demanding geometric syllabus — including angle properties of lines, triangles, quadrilaterals, and polygons, circle theorems, congruence and similarity, Pythagoras’ theorem, trigonometric ratios in right-angled triangles, the sine and cosine rules for non-right-angled triangles, bearings and scale drawing, perimeter and area of 2D shapes including sectors, surface area and volume of 3D solids including spheres and cones, transformations including reflection, rotation, translation, and enlargement with matrix methods, and vectors in two dimensions. Shape and Space questions form a substantial proportion of both Extended examination papers.

Probability and Statistics in Cambridge IGCSE Extended Mathematics covers a more rigorous statistical and probability syllabus than the Core tier — including data collection and representation using bar charts, pie charts, histograms with unequal class widths, stem-and-leaf diagrams, scatter diagrams and lines of best fit, cumulative frequency curves, and box-and-whisker plots, calculating and interpreting mean, median, mode, range, quartiles, and interquartile range from raw data and frequency tables, probability including combined events using sample space diagrams and tree diagrams, and conditional probability. These statistical skills are assessed across both IGCSE Extended papers and require careful interpretation and accurate calculation.