Further Calculus Skills

Further Calculus Skills focuses on the advanced differentiation and integration techniques required for the Mathematics Extension 1 syllabus, extending beyond the foundational rules of Mathematics Advanced. This topic emphasizes the application of the chain, product, and quotient rules to complex composite functions, specifically those involving inverse trigonometric and logarithmic forms. Students master the method of integration by substitution and the use of trigonometric identities to simplify and evaluate non-standard integrals. The curriculum prioritises algebraic fluency in manipulating derivatives and integrals to solve problems involving rates of change, growth and decay models, and the properties of inverse functions.