Functions is based on the use of both algebraic and graphical conventions to describe, interpret and model relationships of and between changing quantities. Understanding functions will enable you to recognise and generalise connections between the same expressions while looking at the dependent and independent variables.
In functions, you will be able to find connections within patterns and to be able to precisely describe and solve real world problems and look at predicting future outcomes - maybe even your maths HSC mark!
Sin, cos and tan, cosec, sec, cot? Trigonometric Functions involves the study of geometric, algebraic, numerical and graphical representations. You may not think algebraic expressions solves real world problems but you will be wrong. Ever thrown a rock in the middle of a lake?
Trigonometric functions are mathematical models that describe the behaviours of many naturally occurring periodic phenomena, such as vibrations or waves as well as oscillatory behaviour found in pendulums, electric currents and radio signals.
Sounds daunting - but I swear, its not! Calculus is concerned with how quantities change and provides a framework of the changes and their consequences. Here, you will start with basic concepts and how they relate to gradient of a tangent and the instantaneous rate of change.
Once you become a master and understand the rules of calculus, problems will just fall out. Our recommendation to attack such a bit topic is to keep up and reach out for help when you need it (from your teacher). Calculus is new and an enjoyable ride - you will look back and realise how interesting it was one day - well maybe...
Exponential and Logarithmic Functions
If you were in the 5.3 course, you may have started to touch on logs and exponential functions. This topic will enable you to have an understanding of practical applications, such as exponential growth and decay, as well as applications within the Calculus topic. This topic will five into different real world situations including but not limited to rates of change in contexts such as population growth and compound interest.
And saving the best to last - Statistical Analysis. This topic involves the exploration, display, analysis and interpretation of data to identify and communicate key information. Be guaranteed that you WILL be asked a question about statistics within the HSC - this is a very popular questions with many marks awarded.
Basically you will need to describe and apply statistical techniques in order to analyse current situations or to predict future outcomes. Statistics are used in every day life - did you every watch any updates on COVID in the media? Businesses, scientific investigators and policy makers are always using statistics to make informed decisions so it is literally used in every day life.