OCR A-Level Further Mathematics A Past Papers & Mark Schemes

OCR A-Level Further Mathematics A (H245) is built around a compulsory pure core examined across two papers, supplemented by two optional papers chosen from four applied strands. This structure gives students genuine flexibility to play to their strengths — a rarity in A-Level mathematics. Pure Core 1 (Y541, 1 hour 30 minutes, 75 marks) covers complex numbers including Argand diagrams and de Moivre's theorem, matrices and their applications to transformations, proof by induction, roots of polynomials, and series including the method of differences. Pure Core 2 (Y542, 1 hour 30 minutes, 75 marks) extends into hyperbolic functions, polar coordinates and curves, further calculus techniques (integration by parts, reduction formulae, arc length and surface area of revolution), differential equations (first and second order), and vectors including the vector product and equations of lines and planes in three dimensions. The four optional papers (each Y543–Y546, 1 hour 15 minutes, 60 marks) are: Statistics — hypothesis testing, continuous random variables, combinations of random variables, and estimation; Mechanics — dimensional analysis, work-energy-power, impulse and momentum, circular motion, and centres of mass; Discrete Mathematics — network algorithms (Dijkstra's, Kruskal's, Prim's), linear programming, critical path analysis, and game theory; and Additional Pure Mathematics — number theory, groups, further vectors, and surfaces. Students sit all four papers in the same examination series. The two pure core papers contribute 75 marks each (approximately 28% each) while the two optional papers contribute 60 marks each (approximately 22% each), giving a total of 270 marks. Unlike Mathematics A where calculator use is restricted in one paper, all four Further Mathematics A papers permit a scientific or graphical calculator.