Calculus

Area of Study- Calculus (Unit 1- done just prior to Unit 2, in semester 2)

In this area of study students cover constant and average rates of change and an introduction to instantaneous rate of change of a function in familiar contexts, including graphical and numerical approaches to estimating and approximating these rates of change.

Area of Study- Calculus (Unit 2)

In this area of study students cover first principles approach to differentiation, differentiation and anti-differentiation of polynomial functions and power functions by rule, and related applications including the analysis of graphs.

Key Skills and knowledge (Outlined from Units 1 and 2 of the 2016-2021 Mathematical Methods Study Design)

• average and instantaneous rates of change and their interpretation with respect to the graphs of functions
• use graphical, numerical and algebraic approaches to find an approximate value or the exact value (as appropriate) for the gradient of a secant or tangent to a curve at a given point
• the rules for finding derivatives and anti-derivatives of simple power functions and polynomial functions
• use Newton’s method to find a numerical approximation to a root of a cubic polynomial function
• evaluate limiting values of a function
• use a variety of approaches (numerical, graphical, first principles and by rule) to find the value of the derivative of a function at a given point
• use first principles to find by hand the derivative of simple polynomial functions up to degree 3
• find by hand the derivative function and an anti-derivative function for a simple power function, or a polynomial function of low degree
• find a family of anti-derivative functions for a given power or polynomial function, and determine a specific anti-derivative given a boundary condition

Assessment Overview

Topic tests will assess:

• key knowledge and skills,
• ability to problem-solve and use the mathematics in context,
• use of the CAS, to assist problem-solving