Curriculum+Level+8+Mathematics+and+statistics

Curriculum levels

=Level Eight Mathematics and Statistics= 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:

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 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.

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.