11–12Mathematics Advanced 11–12 Syllabus

Use index laws to simplify expressions and solve problems involving positive, negative, zero or fractional indices

Expand, factorise and simplify algebraic expressions

Simplify expressions involving algebraic fractions

Expand and simplify expressions involving surds

Describe a relation between two sets as an association between the elements of one set and the elements of the other set

Substitute numeric and algebraic expressions into the formulas of functions

Apply the vertical line test on the graph of a relation to determine whether it represents a function

Refer to a value in the domain of a function at which the function is 0 as a zero of the function

Choose and apply appropriate techniques to graph a straight line given its equation

Find the equation of a line that is parallel or perpendicular to a given line

Solve linear inequalities and graph the solution on a number line

Identify the axis of symmetry and vertex of a parabola by completing the square on its quadratic function

Find the equation of a parabola given sufficient graphical features

Solve problems by finding the solution to simultaneous equations involving a linear and a quadratic function, or two quadratic functions, both algebraically and graphically

Solve quadratic inequalities

Construct and use linear functions to model and solve problems in real-world situations, identifying the independent and dependent variables and any restrictions on these variables, and justify conclusions in the context of the problem

Use linear inequalities to model and solve problems in real-world situations, and justify conclusions in the context of the problem

Solve practical problems involving a pair of simultaneous linear equations both algebraically and graphically, with and without graphing applications, and justify conclusions in the context of the problem

Construct and use simultaneous equations to model and solve a problem where cost and revenue are represented by linear equations, identify and analyse the break-even point, and justify conclusions in the context of the problem

Model and solve practical problems involving quadratic functions and justify conclusions in the context of the problem

Analyse and solve problems involving direct and inverse variation

Extend the definitions of domain and range to relations

Recognise domains and ranges of functions and relations given in interval notation, as inequalities and as worded descriptions

Determine and describe the domain and range of functions and relations, using interval notation, inequalities or worded descriptions

Solve problems involving even and odd functions

Determine the equations of composite functions

Interpret piecewise-defined functions, where the function is defined differently in different parts of the domain

Graph piecewise-defined functions involving functions covered in the scope of the Mathematics Advanced course, test if they are even or odd, and determine the domain and range

Define informally that a function is continuous at a point if the curve can be drawn through the point without lifting the pen off the paper

Identify points where piecewise-defined functions and other functions are not continuous

Define a discontinuity of a function informally as a point where the function is not continuous