Circular Functions
The Reciprocal Circular Functions
Vectors
Introduction to vectors
Resolution of a vector into rectangular components
Scalar product of vectors
Vector projections
Differentiation and rational functions
Differentiation (Specialist Maths)
Derivatives of x = f(y)
Derivatives of inverse circular functions
Second derivatives
Implicit differentiation
Techniques of integration
Antidifferentiation (Year 12 Spesh)
Antiderivatives involving inverse circular functions
Integration using substitution
Definite integrals by substitution
Use of trigonometric identities for integration
Partial fractions
Integration by parts
Kinematics
Position, velocity and acceleration
Constant acceleration
Complex Numbers
Starting to build the complex numbers
Modulus, conjugate and division of complex numbers
Polar form of a complex number
Basic operations on complex numbers in polar form
Solving quadratic equations over the complex plane
Using DeMoivre’s theorem to solve equations
Applications of Integration
Area of a region between two curves
Volumes of solids of revolution
Lengths of curves in the plane
Differential Equations
An introduction to differential equations
Differential equations involving a function of the independent variable
Differential equations involving a function of the dependent variable
Separation of variables