IGCSE Maths Paper 4: Extended Calculator Complete Guide

Quadratic and cubic equations, simultaneous equations, inequalities, sequences (including quadratic nth term), function notation, domain and range, composite and inverse functions, graphical transformations

Circle theorems with proofs, sine and cosine rules, 3D trigonometry, vectors in geometry, similarity and congruence, sector area and arc length, angle in alternate segment

Bounds calculations, compound interest and depreciation, reverse percentages, problems involving upper and lower bounds, standard form in context, proportion (direct and inverse)

Histograms with unequal class widths, cumulative frequency curves, combined probability, conditional probability, tree diagrams, expected frequency

Differentiation of polynomials, finding gradients of curves, stationary points, matrix operations, matrix transformations

Tackle Multi-Part Questions Strategically

Paper 4 questions typically have parts labelled a through e or beyond, with increasing difficulty. Always attempt every part, as earlier parts are often accessible even if you cannot complete later parts. Crucially, later parts sometimes use results from earlier parts. If you could not solve part a, use the answer given or implied and carry on, as you can still earn full marks for subsequent parts through follow-through marking. Never leave a multi-part question entirely blank because of one difficult section.

Master the Sine Rule and Cosine Rule

Trigonometry questions on Paper 4 go well beyond basic SOH CAH TOA. You must be confident with the sine rule for finding sides and angles in non-right-angled triangles, the cosine rule for situations where the sine rule cannot be applied, and the area formula involving sine. These appear in almost every Paper 4 sitting, often in real-world contexts like navigation, surveying, or architecture. Practise identifying which rule to apply based on the given information: two sides and an included angle suggests cosine rule, while two angles and a side suggests sine rule.

Develop Your Approach to Statistics Questions

Paper 4 statistics questions are more sophisticated than Core level. You need to draw and interpret histograms with unequal class widths, reading frequency density rather than frequency. Practise cumulative frequency diagrams and extracting the median, quartiles, and interquartile range. Box plot questions often ask you to compare two distributions, so prepare concise comparison statements that reference specific statistical measures.

Prepare for Vector Geometry Proofs

Vector questions on Paper 4 often require you to prove that points are collinear or that lines are parallel by expressing position vectors in terms of given vectors and showing relationships between them. These proofs follow a standard structure: express each relevant vector as a pathway through known points, simplify, and draw conclusions. Practise writing clear vector proof statements and understanding what it means for one vector to be a scalar multiple of another.

Reserve Time for Checking High-Value Questions

With 100 marks in 120 minutes, you have approximately 1.2 minutes per mark. However, not all marks are equally easy to earn. Budget your time so that you can check your working on questions worth 6 marks or more, as these carry the greatest potential for both earning and losing marks. A five-minute check at the end focusing on your largest questions can recover several marks.