Math Games

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 timeseries data), seeking explanations, and making predictions;
– using informed contextual knowledge, exploratory data analysis, and statistical inference;
– communicating fi ndings and evaluating all stages of the cycle.
• Make inferences from surveys and experiments:
– determining estimates and confi dence 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.

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 fi tting, log modelling, and linear programming techniques.
• Develop network diagrams to fi nd 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 antidifferentiation techniques to functions and relations, using both analytical and numerical methods.
• Form differential equations and interpret the solutions.