Curriculum+Level+7+Mathematics+and+statistics

Curriculum levels

=Level Seven 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 co-ordinate geometry techniques to points and lines. • Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs. • Use arithmetic and geometric sequences and series. • Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions. • Choose appropriate networks to fi nd optimal solutions.

Equations and expressions
• Manipulate rational, exponential, and logarithmic algebraic expressions. • Form and use linear, quadratic, and simple trigonometric equations. • Form and use pairs of simultaneous equations, one of which may be non-linear.

Calculus
• Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs. • Apply differentiation and anti-differentiation techniques to polynomials.

Statistical investigation
• Carry out investigations of phenomena, using the statistical enquiry cycle: – conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets; – evaluating the choice of measures for variables and the sampling and data collection methods used; – using relevant contextual knowledge, exploratory data analysis, and statistical inference. • Make inferences from surveys and experiments: – making informal predictions, interpolations, and extrapolations; – using sample statistics to make point estimates of population parameters; – recognising the effect of sample size on the variability of an estimate.

Statistical literacy
• Evaluate statistically based reports: – interpreting risk and relative risk; – identifying sampling and possible non-sampling errors in surveys, including polls.

Probability
• Investigate situations that involve elements of chance: – comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions; – calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.