WJEC A Level Further Pure Mathematics A — Unit Papers & Mark Schemes

Proof by induction questions follow a predictable structure but demand precision. State the base case, assume the result for k, prove it for k+1, and write a clear concluding statement. Common targets include series summation formulae, divisibility results, and matrix power expressions. Practise writing induction proofs until the logical framework is automatic. Complex numbers pervade this unit. Ensure you can convert fluently between Cartesian (a + bi) and polar (r(cosθ + i sinθ)) forms, apply de Moivre’s theorem for powers and roots, and locate roots of unity on the Argand diagram. Many questions combine complex number algebra with geometric interpretation — visualising the Argand diagram strengthens both understanding and speed. Matrix questions frequently test eigenvalue and eigenvector calculations. Practise finding eigenvalues by solving the characteristic equation det(A – λI) = 0, then computing the corresponding eigenvectors. Understanding the geometric meaning (stretching along eigenvector directions) helps you verify answers intuitively.