A-Level Further Maths5 minComplex Numbers, Argand Diagrams & LociAdding, subtracting & multiplying complex numbers, complex equations, locust of points, modulus-argument & exponential form and de Moivre's.

A-Level Further Maths1 minProof by InductionProof by mathematical induction with sums, proving divisibility results and proof with matrices.

A-Level Further Maths2 minSeriesSums of natural numbers, squares & cubes, the method of differences, the Maclaurin series expansion and standard results.

A-Level Further Maths2 minRoots of PolynomialsWon't lie, this topic isn't particularly fun. It's just a whole lot of algebra and equations that you need to know and get right. At...

A-Level Further Maths3 minVectorsVector & Cartesian equations for lines & planes, scalar product, angles between lines & planes, points of intersection and perpendiculars.

A-Level Further Maths3 minFurther IntegrationImproper integrals, converging/diverging integrals, mean value of functions, inverse trigonometry, partial fractions & volumes of revolution

A-Level Further Maths2 minPolar CoordinatesConverting between polar and Cartesian systems, sketching polar curves, finding area enclosed by polar curves and finding tangents.

A-Level Further Maths1 minHyperbolic FunctionsHyperbolic functions as exponential functions, hyperbolic graphs, inverse hyperbolic functions, integrating & differentiating hyperbolics.

A-Level Further Maths3 minMatrices & Linear TransformationsMatrix addition & multiplication, determinants, inverse matrices, matrix systems & geometry, reflections, rotations, stretches & reverses.

A-Level Further Maths4 minDifferential EquationsIntegrating factor, second-order homogeneous and non-homogeneous differential equations, simple harmonic motion and coupled simultaneous.