620-082 Preliminary Mathematics B

620-081 Preliminary Mathematics A (or equivalent)

This subject forms the second part of a two-semester sequence of subjects suitable for students who have taken standard mathematics in the final year of international secondary schools. On successful completion of 620-082, students will have acquired mathematical skills at least equivalent to those gained by the completion of VCE Mathematical Methods 3/4 and Specialist Mathematics 3/4.

Complex numbers topics include algebra of complex numbers, modulus, argument; Argand plane, polar form, de Moivre's theorem; solution of polynomial equations. Regions in the complex plane. Vectors topics include geometrical vectors; components, scalar product, resolutes, position vectors, differentiation of position vectors and kinematical applications. Calculus topics include derivatives of inverse functions including inverse trigonometric functions, chain rule applications, integration techniques using trigonometric and other substitutions and using partial fractions; areas of regions in the plane, volumes of solids of revolution; differential forms for velocity and acceleration, velocity-time graphs. Simple differential equations. Coordinate geometry topics include sketch graphs of rational functions; asymptotic behaviour and stationary points; and conic sections, including parametric forms.

Up to 24 pages of written assignmentsm (10%), a 3-hour end-of-semester written examination (75%) and class tests totalling not more than 1.5 hours (15%).