Students perform operations with surds and fractional indices, use the definition of a logarithm to establish and apply the laws of logarithms and solve simple exponential equations. They investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations. Students apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation.