AQA AS Further Mathematics Past Papers & Mark Schemes

Complex numbers are the signature topic of Further Mathematics, and AS-level questions typically combine arithmetic with geometric interpretation on the Argand diagram. Master the basics first: addition, multiplication, division (multiply by the conjugate), modulus and argument. Then practise loci problems — the locus of |z − a| = r is a circle centred at a with radius r, and |z − a| = |z − b| is the perpendicular bisector of the line segment from a to b. Sketch loci on Argand diagrams accurately, marking key points with their complex number labels. Matrix questions at AS level focus on 2×2 and 3×3 operations. For 2×2 matrices, you should be able to find the determinant and inverse by inspection. For 3×3 matrices, practise the cofactor method systematically — errors in signs (the alternating +/− pattern in the cofactor matrix) are the most common source of lost marks. When solving simultaneous equations using matrices, remember that a zero determinant indicates either no solution or infinitely many solutions — the question will usually ask you to interpret this geometrically. For the optional papers, preparation strategy differs by route. Discrete Mathematics requires you to follow algorithms precisely — the mark scheme checks each step of a sorting or graph algorithm, not just the final answer. Practise each algorithm by hand with small datasets, writing out every iteration. Mechanics questions at this level reward clear vector notation and consistent use of positive direction conventions. Statistics questions often require careful setup of the null and alternative hypotheses before any calculation — state these explicitly in every hypothesis test. Further Mathematics papers tend to have a steeper difficulty gradient than standard Mathematics papers. The first few questions on each paper are accessible, but the final questions demand genuine mathematical insight. Allocate time accordingly — secure the marks on questions 1–6 before spending extensive time on the challenging final questions.