OCR AS Level Further Mathematics B (MEI) Past Papers

OCR AS Level Further Mathematics B (MEI) (H635) is developed with Mathematics in Education and Industry and follows MEI's characteristic approach of contextualising abstract mathematics within real-world applications. The qualification consists of Core Pure (compulsory) plus one optional minor paper chosen from Mechanics A, Statistics A, Modelling with Algorithms, or Numerical Methods. Core Pure (H635/01, 1 hour 30 minutes, 75 marks) develops the foundations of further mathematics: complex numbers (arithmetic in Cartesian form, finding square roots of complex numbers, the fundamental theorem of algebra), matrices (addition, multiplication, determinants, inverse matrices, and geometric transformations of the plane), further algebra (rational functions, partial fractions, the method of differences for summing series), proof by mathematical induction (for divisibility, matrix powers, and summation formulae), and further calculus (integration using standard forms, reduction formulae, arc length). The optional components each occupy 1 hour 15 minutes. Mechanics A extends AS Mechanics to cover variable acceleration, projectile motion with air resistance, circular motion, and work-energy methods. Statistics A covers the Poisson distribution, continuous random variables (probability density functions, cumulative distribution functions), and hypothesis testing for the Poisson mean. Modelling with Algorithms covers graph theory, minimum spanning trees, shortest paths (Dijkstra's algorithm), and critical path analysis — with a strong emphasis on applying algorithms step-by-step and tracing execution. Numerical Methods covers iterative roots-finding techniques, numerical integration (trapezium rule, Simpson's rule), and numerical differentiation, with all methods contextualised in modelling scenarios. MEI's emphasis on mathematical communication means extended questions ask students to interpret results and comment on the validity of mathematical models alongside performing calculations.