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NSW Curriculum
NSW Education Standards Authority

11–12Mathematics Advanced 11–12 Syllabus

Record of changes
Implementation from 2026
Expand for detailed implementation advice

Content

Year 12

Random variables
Discrete random variables
  • Define a discrete random variable to be uniformly distributed if it has finitely many values, all with the same probability, and use it to model random phenomena with equally likely outcomes

  • Generate a probability distribution for a given discrete random variable and represent the probability distribution in graphical and tabular form

  • Solve problems involving probabilities, expectation and variance of discrete random variables

Continuous random variables
  • Estimate the probability that a continuous random variable falls in some interval using relative frequencies and histograms obtained from data

  • Apply the properties of a probability density function to solve problems and justify conclusions

  • Find the mode from a given probability density function

  • Use a cumulative distribution function to calculate the median and quartiles for a continuous random variable

  • Find the probability density function from a given cumulative distribution function

The normal distribution
  • Identify the normal distribution as a continuous probability distribution that is used to model many naturally occurring phenomena

  • Identify the graph of the probability density function of a normal distribution, the normal curve, as an ‘ideal’ bell-shaped curve, symmetrical about its mean which is equal to its mode and median, and as having most values concentrated about the mean

  • Identify contexts that can be approximately modelled by a normal random variable

  • Apply the empirical rule to make judgements and solve problems involving probabilities of normally distributed data: that for normal distributions, approximately 68% of data lie within one standard deviation of the mean, approximately 95% within two standard deviations of the mean and approximately 99.7% within three standard deviations of the mean

  • Recognise features of the normal curve, and identify the global maximum and points of inflection

  • Solve problems involving finding the mean or standard deviation of a normal random variable given the probability of an event less or more extreme than a given outcome

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