11–12Mathematics Extension 1 11–12 Syllabus
The new Mathematics Extension 1 11–12 Syllabus (2024) is to be implemented from 2026.
2025
- Plan and prepare to teach the new syllabus
2026, Term 1
- Start teaching new syllabus for Year 11
- Start implementing new Year 11 school-based assessment requirements
- Continue to teach the Mathematics Extension 1 Stage 6 Syllabus (2017) for Year 12
2026, Term 4
- Start teaching new syllabus for Year 12
- Start implementing new Year 12 school-based assessment requirements
2027
- First HSC examination for new syllabus
Content
Year 12
- MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
- ME1-12-05
applies calculus to solve problems involving polynomials, further rates of change, areas and volumes and differential equations
Develop models in contexts where a rate of change of a function can be expressed as a rate of change of a composition of two functions, so that the chain rule can be applied
Solve problems involving related rates of change using the chain rule, given the required formulas for problems relating to area, surface area or volume
Calculate areas of regions between curves determined by functions in both real-life and abstract contexts
Define a differential equation as an equation involving an unknown function and one or more of its derivatives
Define and identify the order of a differential equation as the order of the highest derivative contained within the equation
Recognise that a solution to a first order differential equations is a function, and that there may be infinitely many functions that are solutions to a given first order differential equation
Recognise the solutions to differential equations in the context of slope fields, and that slope fields are useful in determining the behaviour of solutions when the differential equation cannot be easily solved
Recognise that a unique solution of a differential equation can be determined when sufficient initial conditions are given, and refer to a problem involving a differential equation and initial conditions as an initial value problem (IVP)
Graph solutions to first order differential equations given a slope field and identify the unique solution curve that satisfies a set of initial conditions
Explore problems given a slope field representing a practical context and justify conclusions
Form a slope field for a first order differential equation using graphing applications
Recognise the features of a slope field corresponding to a first order differential equation and vice versa
Graph solutions of first order differential equations using graphing applications and examine the behaviour of solutions for different values of the constant of integration and initial conditions
Model and solve differential equations in practical scenarios including in chemistry, biology and economics