Year 11 Mathematics Advanced

TERM 3, 2025

Trigonometric Functions and Identities

Students will define the reciprocal trigonometric functions, sketch the graphs of reciprocal trigonometric functions in both radians and degrees, prove and apply the Pythagorean identities, prove trigonometric identities and evaluate trigonometric expressions using angles of any magnitude and complementary angle results. They will also simplify trigonometric expressions and solve trigonometric equations, including those that reduce to quadratic equations, as well as learn to solve transcendental equations; that is equations that cannot be solved easily, however, an approximation can be found after carefully graphing the functions on the same plane.

Calculus

Students will find the derivative of a polynomial, including the sum or difference of two functions. They will understand and use the product, quotient and chain rules to differentiate functions and calculate derivatives of power functions to solve problems. Students will use the derivative in a variety of contexts, including but not limited to finding the equation of a tangent or normal to a graph of a power function at a given point, determining the velocity of a particle given its displacement from a point as a function of time and determining the acceleration of a particle given its velocity at a point as a function of time.

Logs and Exponentials

Students will define logarithms and indices, recognise and use the inverse relationship between logarithms and exponentials, derive the logarithmic laws from the index laws and use the algebraic properties of logarithms to simplify and evaluate logarithmic expressions, use the change of base law, interpret and use logarithmic scales and solve algebraic, graphical and numerical problems involving logarithms in a variety of practical and abstract contexts.