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NSW Curriculum
NSW Education Standards Authority

11–12Mathematics Standard 11–12 Syllabus

Record of changes
Implementation from 2026
Expand for detailed implementation advice

Content

Year 12 – Standard 2

Ratios and rates
Ratios
  • Recognise ratios and explain their relationship with fractions

  • Express a ratio in simplest form

  • Determine the ratio of two quantities

  • Divide a quantity in a given ratio

  • Solve practical problems involving ratios

  • Solve practical ratio problems involving the capture-recapture technique

  • Explain the relationship between ratios and map scales and apply this relationship to solve problems in a variety of practical contexts

  • Construct scale drawings, with and without using digital tools

  • Estimate and compare quantities, materials and costs using measurements taken from scale drawings and building plans with commonly used symbols

  • Calculate the perimeter, or area of a section of land using the Trapezoidal rule where appropriate, from a site plan, an aerial photograph, a radial survey or a map that includes a scale

Rates
  • Explain the difference between ratios and rates

  • Represent given information as a unit rate

  • Convert between rates

  • Make comparisons between rates in a variety of practical contexts

  • Compare unit prices to determine best buys

  • Use rates to solve problems in a variety of practical contexts

  • Interpret and analyse distance–time graphs to solve problems related to speed, distance and time

  • Examine fuel consumption rates to compare the efficiency of vehicles

  • Apply units of energy to calculate kilowatt hours and solve problems involving the consumption of energy

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