AQA A-Level Further Mathematics Past Papers & Mark Schemes

AQA A-Level Further Mathematics (specification code 7367) extends far beyond A-Level Mathematics into territory that underpins university-level mathematics, physics, and engineering. The qualification assumes fluency in all core A-Level Mathematics content — the further content builds directly on top of it. Papers 1 and 2 both examine the compulsory Further Pure Mathematics content. This is the theoretical core of the qualification and includes: proof by induction; complex numbers including polar form, de Moivre's theorem, roots of unity, and loci in the Argand plane; matrices including transformations, determinants, eigenvalues, and eigenvectors; further algebra covering roots of polynomials (Newton's identities, sums of powers) and series; further calculus including reduction formulae, arc length, and surface area of revolution; further vectors covering the equations of lines and planes in three dimensions and the angle between them; polar coordinates; hyperbolic functions and their identities; first and second-order differential equations including the method of undetermined coefficients and variation of parameters. Paper 3 is optional content — your school will have chosen one of three routes. Discrete Mathematics covers algorithms (bubble sort, quick sort, Dijkstra's), graph theory (spanning trees, Eulerian and Hamiltonian paths), linear programming (graphical and simplex methods), critical path analysis, and network flows. Mechanics covers circular motion, centre of mass and moments for composite bodies, work and energy with variable forces, elastic strings and springs, simple harmonic motion, and damped/forced oscillations. Statistics covers the Poisson distribution, continuous probability distributions, chi-squared contingency table tests, the product moment correlation coefficient, and non-parametric tests. Further Mathematics is taken concurrently with A-Level Mathematics and typically sits alongside physics or computer science for students intending to study quantitative subjects at university. The two qualifications share no examination papers — A-Level Maths is examined entirely separately.