Complex Numbers
- Solving any quadratic; Four rules; Polynomial equations – roots in conjugate pairs; Argand diagrams; Modulus-argument form and conversion; x and in mod-arg form, including use of radians and compund angle formulae; Simple loci
- De Moivre; eiθ; Complex roots; Geometrical problems
- +, -, x; Linear transformations in 2D and some 3D (3D vectors assumed); Successive transformations in 2D; Invariant points and lines; Determinants and inverses of 2x2 matrices
- Inverses of 3 x 3 matrices; 3 linear simultaneous equations and geometrical interpretations
- of polynomial equations up to quartics
- series, divisibility tests, matrices
- Method of differences including partial fractions
- including awareness of validity
- Equation of line in 3D and plane in vector and Cartesian forms; Scalar product and applications; Intersection of line and plane; Perpendicular distance between 2 lines, point to line, point to plane
- Integration where integrand extends to infinity; Volumes of revolution; Mean value of a function; Integration using partial fractions with quadratic factors; Integration inverse trig functions; Integration using trigonometric substitutions
- including area enclosed by polar curve
- Definitions; Graphs; Differentiation and Integration; Inverse hyperbolic functions including logarithm forms; Integration with hyperbolic substitutions
- Integrating factor; General and particular solutions; Modelling; Second order equations (auxiliary equation for homogeneous equations; non-homogeneous equations using complementary function and particular integral); Simple harmonic motion equation; Model damped oscillations; Model situations with 1 indpt and 2 dpt variables as a pair of coupled 1st order simultaneous equations eg predator/prey