I regularly help students with A-Level Further Pure maths subjects (FP1, FP2 and FP3). This includes the following topics:
Complex numbers
Argand diagrams, modulus and argument, Euler's relation. De Moivre's theorem, roots, transformations on the Z-plane
Numerical solutions to equations
Coordinate systems
Ellipse, hyperbola
Matrix algebra
Linear transformations, rotations, reflections and enlargements, inverse, determinant, solving linear simultaneous equations, transpose, eigenvalues, eigenvectors, reducing a symmetrical matrix to diagonal form
Further series
Method of differences
Proof by mathematical induction
Further inequalities
First and second order differential equations
Integrating factor, Complementary Function (CF), Particular Integral (PI), boundary conditions, substitutions
Maclaurin and Taylor series
Polar coordinates
Hyperbolic functions
Differentiation and integration
Further integration
Reduction formulae, arc length, surface of revolution area
Further vectors
Vector (cross) product, triple scalar product