*In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:*

### Mathematics

**Patterns and relationships**

- Apply the geometry of conic sections.
- Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions.
- Use permutations and combinations.
- Use curve fitting, log modelling, and linear programming techniques.
- Develop network diagrams to find optimal solutions, including critical paths.

**Equations and expressions**

- Manipulate trigonometric expressions.
- Form and use trigonometric, polynomial, and other non-linear equations.
- Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context.
- Manipulate complex numbers and present them graphically.

**Calculus**

- Identify discontinuities and limits of functions.
- Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods.
- Form differential equations and interpret the solutions.

### Statistics

**Statistical investigation**

Carry out investigations of phenomena, using the statistical enquiry cycle:

- conducting experiments using experimental design principles, conducting surveys, and using existing data sets
- finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions
- using informed contextual knowledge, exploratory data analysis, and statistical inference
- communicating findings and evaluating all stages of the cycle.

Make inferences from surveys and experiments:

- determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
- using methods such as resampling or randomisation to assess the strength of evidence.

**Statistical literacy**

Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:

- critiquing causal-relationship claims
- interpreting margins of error.

**Probability**

Investigate situations that involve elements of chance:

- calculating probabilities of independent, combined, and conditional events
- calculating and interpreting expected values and standard deviations of discrete random variables
- applying distributions such as the Poisson, binomial, and normal.