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Further Pure 2

The second pure option paper: group theory, eigenvectors, number theory and the recurrence relations that close the algebra of sequences.

Further Maths · 12 topics.

• Groups and their axioms
• Subgroups, Lagrange's theorem and isomorphism
• Reduction formulae
• Arc length and surface area
• Eigenvalues and eigenvectors
• Diagonalisation and the Cayley-Hamilton theorem
• Further loci and regions in the Argand diagram
• Transformations of the complex plane
• The Euclidean algorithm and Bezout's identity
• Modular arithmetic and Fermat's little theorem
• Combinatorics
• Recurrence relations