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11–12Mathematics Extension 1 11–12 Syllabus

Record of changes
Implementation from 2026
Expand for detailed implementation advice

Content

Year 12

Further applications of calculus
Multiplicity of zeroes of polynomial functions
Further rates of change
  • 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

Areas between curves and volumes of solids of revolution
  • Calculate areas of regions between curves determined by functions in both real-life and abstract contexts

Differential equations
  • 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

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